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More About
This Textbook
Overview
For anyone who needs to learn calculus, the best place to start is by gaining a solid foundation in precalculus concepts. This new book provides that foundation. It includes only the topics that they'll need to succeed in calculus. Axler explores the necessary topics in greater detail. Readers will benefit from the straightforward definitions and examples of complex concepts. Step-by-step solutions for odd-numbered exercises are also included so they can model their own applications of what they've learned. In addition, chapter openers and end-of-chapter summaries highlight the material to be learned. Any reader who needs to learn precalculus will benefit from this book.
6 Applications of Trigonometry 457
6.1 Using Trigonometry to Compute Area 458
The Area of a Triangle via Trigonometry 458
Ambiguous Angles 459
The Area of a Parallelogram via Trigonometry 461
The Area of a Polygon 462
Exercises, Problems, and Worked-out Solutions 463
6.2 The Law of Sines and the Law of Cosines 469
The Law of Sines 469
Using the Law of Sines 470
The Law of Cosines 472
Using the Law of Cosines 473
When to Use Which Law 475
Exercises, Problems, and Worked-out Solutions 476
6.3 Double-Angle and Half-Angle Formulas 483
The Cosine of 2θ 483
The Sine of 2θ 484
The Tangent of 2θ 485
The Cosine and Sine of θ2 485
The Tangent of θ2 488
Exercises, Problems, and Worked-out Solutions 489
6.4 Addition and Subtraction Formulas 497
The Cosine of a Sum and Difference 497
The Sine of a Sum and Difference 499
The Tangent of a Sum and Difference 500
Exercises, Problems, and Worked-out Solutions 501
6.5 Transformations of Trigonometric Functions 507
Amplitude 507
Period 509
Phase Shift 512
Exercises, Problems, and Worked-out Solutions 514
6.6 Polar Coordinates∗ 523
Defining Polar Coordinates 523
Converting from Polar to Rectangular Coordinates 524
Converting from Rectangular to Polar Coordinates 525
Graphs of Polar Equations 529
Exercises, Problems, and Worked-out Solutions 531
6.7 Vectors and the Complex Plane∗ 534
An Algebraic and Geometric Introduction to Vectors 534
The Dot Product 540
The Complex Plane 542
De Moivre's Theorem 546
Exercises, Problems, and Worked-out Solutions 547
Chapter Summary and Chapter Review Questions 551
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About this course
This distance learning course provides the information you will need to prepare for the AQA A-Level in Maths with Statistics. In this home study course, you will focus on four core topics of algebra, geometry, trigonometry and calculus, which make up two-thirds of the A-Level qualification. The remaining third is focused on the study of statistics, including estimation, probability and distributions. The course is optimized for students studying at home and includes full tutor support via email.
A-Level Maths with Statistics is a valuable complement to other A-Level courses with a statistical element, such as biology, sociology or psychology, and for those wishing to study these subjects at a higher level. A-Level Maths with Statistics is also applicable to many jobs and careers and is a well-respected qualification that can be used for career progression and further training whilst in employment.
Entry requirements
English reading and writing skills, and maths to at least GCSE grade C or equivalent are required. You will need to have general skills and knowledge base associated with a GCSE course or equivalent standard.
This specification is designed to:
develop the student's understanding of mathematics and mathematical processes in a way that promotes confidence and fosters enjoyment
develop abilities to reason logically and to recognise incorrect reasoning, to generalise and to construct mathematical proofs
extend their range of mathematical skills and techniques and use them in more difficult unstructured problems
use mathematics as an effective means of communication
acquire the skills needed to use technology such as calculators and computers effectively, to recognise when such use may be inappropriate and to be aware of limitations
develop an awareness of the relevance of mathematics to other fields of study, to the world of work and to society in general
On this course you will study six units:
AS Level
Unit 1 MPC1 Core 1
Unit 2 MPC2 Core 2
Unit 3 MS1B Statistics 1B
A2 Level
Unit 4 MPC3 Core 3
Unit 5 MPC4 Core 4
Unit 6 MS2B Statistics 2
Each unit has 1 written paper of 1 hour 30 minutes.
Course Content
AS Level
Unit 1 MPC1 Core 1
Co-ordinate Geometry
Quadratic functions
Differentiation
Integration
Unit 2 MPC2 Core 2
Algebra and Functions
Sequences and Series
Trigonometry
Exponentials and logarithms
Differentiation
Integration
Unit 3 MS1B Statistics 1B
Statistical Measures
Probability
Discrete Random Variables
Normal Distribution
Estimation
A2 Level
Unit 4 MPC3 Core 3
Algebra and Functions
Trigonometry
Exponentials and Logarithms
Differentiation
Integration
Numerical Methods
Unit 5 MPC4 Core 4
Algebra and Functions
Coordinate Geometry in the (x, y) plane
Sequences and Series
Trigonometry
Exponentials and Logarithms
Differentiation and Integration
Vectors
Unit 6 MS2B Statistics 2
Poisson distribution
Continuous random variables
The t-distribution
Hypothesis Testing
Chi-squared tests
AS +A2 = A Level in Maths with Statistics. Both AS and A2 level courses and examinations must be successfully completed to gain a full A Level.
AQA Specification 6360
The course comes to you as a paper-based packExams are taken at an AQA centre and we can provide an extensive list of centres for you. Please read our FAQs for further information
Our A Levels come with tutor support for 24 months.
You will have access to a tutor, via email, who will mark your work and guide you through the course to help you be ready for your examinations. In addition you will be supplied with a comprehensive Study Guide which will help you through the study and assessment process.
This online distance learning course in A-Level Pure Mathematics is designed to support students through their study of the AQA Pure Mathematics A-Level. The course offers a comprehensive guide to the study of pure mathematics, encouraging a sound understanding of algebra, trigonometry, calculus, logarithms, differentiation, mathematical reasoning and proofs.Including tutor support via email, this online home study course provides the information you will need to study this challenging, rigorous and rewarding discipline. Pure mathematics is a well-respected A-Level and is relevant to both employment and to higher level study in many subjects, including science, computing and engineering. Its combination of numeracy, logic and reasoning provide a solid basis of transferable skills that can aid progression in the workplac
Psychology is an engaging and challenging subject that offers fascinating insights into the workings of the human mind. With this distance learning online course in A-Level Psychology, you can study at home with UK Distance Learning & Publishing, confident that our experienced tutors are always on hand to offer you guidance and support.In this online home study A-Level Psychology course, you will study a broad range of topics. These include important contemporary issues such as memory, attachment, stress, sleep and celebrity. Students will also study psychopathology, specialising in schizophrenia.Through studying psychology, we can learn more about how we think, whilst simultaneously developing our own powers of critical and evaluative thought. This well-respected A-Level subject is ideal for those who aspire to study psychology at university or to work in a related field. It is also suitable for those who simply want to further their own knowledge of this demanding discipline
This online distance learning course in A-Level Religious Studies approaches the subject of religion as an academic discipline, allowing students to develop their own views and values through a critical, reflective and evaluative approach. The course is optimized for study at home and tpotally online, according to the AQA A-Level specification. The units studied include: Introduction to Religious Studies; Studies in Religion; and Religion and Human Experience. Particular attention is given to the topics of World Religions: Buddhism and to the Christian New Testament. This distance learning course is suitable for those who want to learn more about religious studies for their own interest or for those who wish to study for an A-Level qualification as preparation for study at a higher level. A-Level Religious Studies is a particularly good complement for Philosophy or History A-Levels and is suitable for those who intend to study Religious Studies or Theology at university level. The course is suitable for students or all religions or none and no prior knowledge of religious studies is required.
In this online distance learning course A-Level Accounting, you will study the fundamental aspects of both financial and management accounting to gain an understanding of the purpose of accounting and major accounting methods. Study online to learn valuable transferable skills, such as problem-solving, data skills, planning, presenting arguments and making recommendations. No prior knowledge of accounting is necessary. This course can be taken at anytime and anywhere using our online learning platform.Successful completion of the A-Level accounting exam (as administered by AQA) will provide you with the AQA A-Level Accounting qualification: a valuable addition to any CV.
This distance learning A-Level Citizenship course explores and debates the issues relevant to local and global citizenship, helping students to take an informed and effective role in society.
In this course, you will study online and at home to learn more about such concepts as identity, democracy, power and justice and you will be encouraged to approach different viewpoints and opinions critically, in order to gain a deeper understanding of contemporary debates surrounding modern citizenship. Closely based on the AQA A-Level Citizenship specification, the course encourages an active and participatory approach to citizenship, including the opportunity to conduct individual research in an area of personal interest.
So whether you seek a deeper knowledge of citizenship to prepare you for study at university level, or whether you simply want to become a more informed member of society, this home study course will give you a valuable overview of contemporary citizenship issues, allowing you to become an active and engaged global citizen.
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Mathematical Excursions - 3rd edition
Summary: MATHEMATICAL EXCURSIONS, Third Edition, teaches students that mathematics is a system of knowing and understanding our surroundings. For example, sending information across the Internet is better understood when one understands prime numbers; the perils of radioactive waste take on new meaning when one understands exponential functions; and the efficiency of the flow of traffic through an intersection is more interesting after seeing the system of traffic lights represented in a math...show moreematical form. Students will learn those facets of mathematics that strengthen their quantitative understanding and expand the way they know, perceive, and comprehend their world. We hope you enjoy the journey578494 -used book - book appears to be recovered - has some used book stickers - free tracking number with every order. book may have some writing or highlighting, or used book stickers on front ...show moreor back ...show less
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teacher edition with book tape/ stickers on cover New inside no writing or marks includes all Students content and all answers. text only no access code or other supplements. ship immediately - Exped...show moreited shipping available ...show less40.87 +$3.99 s/h
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Easy Precalculus Step-by-StepTake it step-by-step for pre-calculus success! The quickest route to learning a subject is through a solid grounding in the basics. So what you won't find in Easy Pre-calculus Step-by-Stepis a lot of endless drills. Instead, you get a clear explanation that breaks down complex concepts into easy-to-understand steps, followed by highly focused exercises that are linked to core skills--enabling learners to grasp when and how to apply those techniques. This book features: Large step-by-step charts breaking down each step within a process and showing clear connections between topics and annotations to clarify difficulties Stay-in-step panels show how to cope with variations to the core steps Step-it-up exercises link practice to the core steps already presented Missteps and stumbles highlight common errors to avoid You can master pre-calculus as long as you take it Step-by-Step!
Carolyn Wheater teaches middle and upper school mathematics at the Nightingale-Bamford School in New York City. She has taught math and computer technology for 30 years to students from preschool through college. She is a member of the National Council of Teachers of Mathematics (NCTM) and the Association of Teachers in Independent Schools.
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...
More About
This Book
you the knowledge you need to gain math confidence.
Includes:
One, five and ten-minute introductions to key principles to get you started.
Lots of instant help with common problems and quick tips for success, based on the author's many years of experience.
Meet the Author
Trevor Johnson and Hugh Neill are both very well established authors, A Level examiners and maths consultants. Trevor is the Chief Examiner for Edexcel's International GCSE and was joint editor and author of the recently published Edexcel GCSE Mathematics 2013
With the exception of the chapter index (which goes according to
With the exception of the chapter index (which goes according to a mixed approach rather than a structural one), and also the paperback binding (which allows for an unravelling of the composition with prolonged use)--this is a very helpful and informative book. Great for reviewing forgotten concepts and also learning some more advanced subject matter. Works just fine for anybody needing to touch up basic math skills, but just as well for one who needs to study more advanced topics for college or career purposes. I wouldn't necessarily recommend this for one who needs extensive study in arithmetic(basic math), nor for one who needs to advance in a particular topic. However, it is great for exposing oneself to beginner and intermediate levels of all the essentials.
2 out of 2 people found this review helpful.
Was this review helpful? YesNoThank you for your feedback.Report this reviewThank you, this review has been flagged.
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Geometric Algebra: An Algebraic System for Computer Games and Animation
This book uses 3D colour drawings and tabulations of algebraic expansions to provide new insights into geometric algebra and its application to computer games and animation. It is filled with many worked examples and full-colour illustrations and tables.
Geometric algebra is still treated as an obscure branch of algebra and most books have been written by competent mathematicians in a very abstract style. This restricts the readership of such books especially by programmers working in computer graphics, who simply want guidance on algorithm design.
Geometric algebra provides a unified algebraic system for solving a wide variety of geometric problems. John Vince reveals the beauty of this algebraic framework and communicates to the reader new and unusual mathematical concepts using colour illustrations, tabulations, and easy-to-follow algebraic proofs.
The book includes many worked examples to show how the algebra works in practice and is essential reading for anyone involved in designing 3D geometric algorithms.
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Mathematics - Calculus (464 results)
Mathematical HandbookContaining the Chief Formulas of Algebra, Trigonometry, Circular and Hyperbolic Functions, Differential and Integral Calculus, and Analytical Geometry, Together With Mathematical Tables
by Edwin P. Seaver
The uses which this book may serve hardly need to be pointed out. Some years ago the writer composed the part relating to Trigonometry and used it as a syllabus for instruction in his college classes. It served its purpose and soon went out of print. But a stray copy of it found its way to the table of a well-known civil engineer, to whom it proved constantly useful, and by whom it was often referred to as "his memory." This engineer has suggested a revision and republication of the original book with important enlargements. Accordingly there have been added Sections on Algebra, the Differential and Integral Calculus, and Analytic Geometry. The subject of Hyperbolic Functions, which now receives much more attention than formerly, has been more fully treated. Tables have been added, which include not only those universally used, but also some - like those of the Hyperbolic Functions, of the Natural Logarithms of Numbers, and that of the Velocity of Falling Bodies (v= 2 gh) - that have been hitherto not readily accessible.<br><br>Of course no efforts have been spared to secure correctness in the printing of the formulas and the tables; but persons experienced in such work need not be reminded of the improbability that the first edition of a book of this kind should be absolutely free from error. The writer and the publishers can only add, that notice of any errors that may be detected will be thankfully received, and the necessary corrections will be promptly made and published. Also, suggestions of desirable additions to the book and of other improvements are invited with a view to their use in possible future editions.
Florian Cajori's A History of Mathematics is a seminal work in American mathematics. The book is a summary of the study of mathematics from antiquity through World War I, exploring the evolution of advanced mathematics. As the first history of mathematics published in the United States, it has an important place in the libraries of scholars and universities. A History of Mathematics is a history of mathematics, mathematicians, equations and theories; it is not a textbook, and the early chapters do not demand a thorough understanding of mathematical concepts. The book starts with the use of mathematics in antiquity, including contributions by the Babylonians, Egyptians, Greeks and Romans. The sections on the Greek schools of thought are very readable for anyone who wants to know more about Greek arithmetic and geometry. Cajori explains the advances by Indians and Arabs during the Middle Ages, explaining how those regions were the custodians of mathematics while Europe was in the intellectual dark ages. Many interesting mathematicians and their discoveries and theories are discussed, with the text becoming more technical as it moves through Modern Europe, which encompasses discussion of the Renaissance, Descartes, Newton, Euler, LaGrange and Laplace. The final section of the book covers developments in the late 19th and early 20th Centuries. Cajori describes the state of synthetic geometry, analytic geometry, algebra, analytics and applied mathematics. Readers who are not mathematicians can learn much from this book, but the advanced chapters may be easier to understand if one has background in the subject matter. Readers will want to have A History of Mathematics on their bookshelves.
One of the purposes of the elementary working courses in mathematics of the freshman and sophomore years is to exhibit the bond that unites the experimental sciences. "The bond of union among the physical sciences is the mathematical spirit and the mathematical method which pervade them." For this reason, the applications of mathematics, not to artificial problems, but to the more elementary of the classical problems of natural science, find a place in every working course in mathematics. This presents probably the most difficult task of the text-book writer,- namely, to make clear to the student that mathematics has to do with the laws of actual phenomena, without at the same time undertaking to teach technology, or attempting to build upon ideas which the student does not possess. It is easy enough to give examples of the application of the processes of mathematics to scientific problems; it is more difficult to exhibit by these problems, how, in mathematics, the very language and methods of thought fit naturally into the expression and derivation of scientific laws and of natural concepts.<br><br>It is in this spirit that the authors have endeavored to develop the fundamental processes of the calculus which play so important a part in the physical sciences; namely, to place the emphasis upon the mode of thought in the hope that, even though the student may forget the details of the subject, he will continue to apply these fundamental modes of thinking in his later scientific or technical career. It is with this purpose in mind that problems in geometry, physics, and mechanics have been freely used. The problems chosen will be readily comprehended by students ordinarily taking the first course in the calculus.<br><br>A second purpose in an elementary working course in mathematics is to secure facility in using the rules of operation which must be applied in calculations.
The present volume is intended to form a sound introduction to a study of the Integral Calculus, suitable for a student beginning the subject. Like its companion, the Differential Calculus for Beginners, it does not therefore aim at completeness, but rather at the omission of all portions of the subject which are usually regarded as best left for a later reading.<br><br>It will be found, however, that the ordinary processes of integration are fully treated, as also the principal methods of Rectification and Quadrature, and the calculation of the volumes and surfaces of solids of revolution. Some indication is also afforded to the student of other useful applications of the Integral Calculus, such as the general method to be employed in obtaining the position of a Centroid, or the value of a Moment of Inertia.
The present small volume is intended to form a sound introduction to a study of the Differential Calculus suitable for the beginner. It does not therefore aim at completeness, but rather at the omission of all portions which are usually considered best left for a later reading. At the same time it has been constructed to include those parts of the subject prescribed in Schedule I. of the Regulations for the Mathematical Tripos Examination for the reading of students for Mathematical Honours in the University of Cambridge.<br><br>Particular attention has been given to the examples which are freely interspersed throughout the text. For the most part they are of the simplest kind, requiring but little analytical skill. Yet it is hoped they will prove sufficient to give practice in the processes they are intended to illustrate.
The Elements of the Differential Calculus: Founded on the Method of Rates was written by John Minot Rice William Woolsey Johnson in 1874. This is a 75 page book, containing 15992 words and 7 pictures. Search Inside is enabled for this title.
eBook
Vector AnalysisA Text-Book for the Use of Students of Mathematics and Physics
by Edwin Bidwell Wilson
When I undertook to adapt the lectures of Professor Gibbs on Vector Analysis for publication in the Yale Bicentennial Series, Professor Gibbs himself was already so fully engaged upon his work to appear in the same series, Elementary Principles in Statistical Mechanics, that it was understood no material assistance in the composition of this book could be expected from him. For this reason he wished me to feel entirely free to use my own discretion alike in the selection of the topics to be treated and in the mode of treatment. It has been my endeavor to use the freedom thus granted only in so far as was necessary for presenting his method in text-book form.<br><br>By far the greater part of the material used in the following pages has been taken from the course of lectures on Vector Analysis delivered annually at the University by Professor Gibbs. Some use, however, has been made of the chapters on Vector Analysis in Mr. Oliver Heaviside's Electromagnetic Theory (Electrician Series, 1893) and in Professor Föppl's lectures on Die Maxwell'sche Theorie der Electricitāt (Teubner, 1894). My previous study of Quaternions has also been of great assistance.<br><br>The material thus obtained has been arranged in the way which seems best suited to easy mastery of the subject. Those Arts, which it seemed best to incorporate in the text but which for various reasons may well be omitted at the first reading have been marked with an asterisk (*). Numerous illustrative examples have been drawn from geometry, mechanics, and physics. Indeed, a large part of the text has to do with applications of the method.
The importance of the natural sciences is so generally recognized as to need no emphatic statement. Noris it necessary to point out the dependence of the sciences upon the study and knowledge of mathematics. This dependence is closer and more direct in the case of calculus than in the case of any other branch of mathematics, unless, perhaps, we except elementary algebra and trigonometry. It is primarily for the purpose of making the elements of the calculus directly and familiarly available to students of physics, chemistry and other sciences that the present book is written. At the same time it is hoped that the book will be found well adapted to the use of those who wish an elementary knowledge of calculus for its cultural value. No knowledge of Analytic Geometry is assumed on the part of students using the present text. On the other hand the idea of coordinate axes and their use in the graphical representation and study of simple algebraic and transcendental functions is introduced in the first chapter and used continually throughout the work. The student becomes familiar with the fundamental ideas of analytic geometr -, learns to use both algebraic and geometric methods in the study of functions, and becomes acquainted with the forms and equations of simple curves without definition of those curves or detailed study of their properties. The student thus acquires all the knowledge of analytic geometry necessary to an understanding of the elements of calculus; and assuming on his part a knowledge of elementary algebra and trigonometry, the calculus is made available for a first college course.
The authors have to express their thanks to Professors Irving P. Church, G. A. Goodenough, and William A. Granville, who have kindly given permission for the use of special material, tables, and constants from their works, and to whom proper credit is given where such material appears. Thanks are also due to John D. Ball, of the Consulting Engineering Department of the General Electric Company, for coefficients of hysteresis loss in iron.<br><br>The authors are especially indebted to Professors Ernst J. Berg and John N. Vedder of Union College, and to Professor William D. Ennis of the Brooklyn Polytechnic Institute, for a critical reading of the manuscript and for valuable suggestions; also to Professors Charles F. F. Garis and Walter L. Upson of Union College for advice in connection with certain sections.
The first five show distinctly that the independent variable is ac, whereas the last three do not explicitly indicate the variable and should not be used unless there is no chance of a misunderstanding.2. The fundamental formulas of differential calculus are derived directly from the application of the dehnition (2)or (3)and from a few fundamental propositions in limits. First may be mentioned(5) D(u 31; 11) -- Du j;Dv, +vDu. (6) (7)It may be recalled that(4), which is the rule for differentiating a function of a function, follows from the application of the theorem that the limit of a product is the product of the limits to the fractional identity- -- ;whence Aa: Ay Aa: lim 55: limA 2 lim 534: limi lim 934, which is equivalent to(4). Similarly, if y= f(.1:)and if rc, as the inverse function of y, be written re :f-1(y) from analogy withy =-sins: and :c=- sin 1 y, the relation(5) follows from the fact that AxAy and AyAa: are reciprocals. The next three result from the immediate application of the theorems concerning limits of sums, products, and quotients( 21).The rule for differentiating a power is derived in case nis integral by the application of the binomial theorem. and the limit when A.r=0is clearly n:1: 1.The result may be extended to rational values of the index nby writing n= B, y :xii, 1 I ::xl and by differentiating both sides of the equation and reducing. To prove that(7) still holds when nis irrational, it would be necessary to have a workable definition of irrational numbers and to develop the properties of such numbers in greater detail than seems wise at this point. The formula is therefore assumed in accordance with the principle of permanence of form( 178), just as formulas like ama =a +of the theory of exponents, which may readily be proved for rational bases and exponents, are assumed without proof to hold also for irrational bases and exponents. See, however, 18-25 and the exercises thereunder. It is frequently better to regard the quotient as the product u- v-1and apply(6). TFor when Arn = 0, then Ay= 0 or AyAn: could not approach a limit.
In course of an attempt to apply direct vector methods to certain problems of Electricity and Hydrodynamics, it was felt that, at least as a matter of consistency, the foundations of Vector Analysis ought to be placed on a basis independent of any reference to cartesian coordinates and the main theorems of that Analysis established directly from first principles. The result of my work in this connection is embodied in the present paper and an attempt is made here to develop the Differential and Integral Calculus of Vectors from a point of view which is believed to be new.<br><br>In order to realise the special features of my presentation of the subject, it will be convenient to recall briefly the usual method of treatment. In any vector problem we are given certain relations among a number of vectors and we have to deduce some other relations which these same vectors satisfy. Now what we do in the usual method is to resolve each vector into three arbitrary components and thus rob it first entirely of its vectorial character. The various characteristic vector operators like the gradient and curl are also subjected to the same process of dissection. We then work the whole problem out with our familiar scalar calculus, and when the necessary analysis has been completed, we collect our components and read the result in vector language.
Felix Klein on one occasion termed the executive element in mathematics. All the methods discussed in the present volume are developed with the principal object of providing means whereby the desired results may be expressed ultimately in numerical form. In mathematical analysis the question as to what is implied by the solution of a particular problem is one to which no clear answer has been given. When dealing with a differential equation, for example, we frequently regard the problem suggested as having been solved when a proof of the existence of a solution is forthcoming. Even in certain sections of theoretical mechanics we are on occasion satisfied merely with the construction of the differential equations governing the processes under consideration, and a proof that these equations do actually determine the solution. However important the proof of an existence theorem may be, the determination of the solution itself must be regarded as of no less consequence. By this is implied not simply a qualitative discussion of the functions contained in the integral, but a quantitative numerical expression for the solution either in the form of a table providing the values of the dependent variables for all values of the independent variables that come into question, or as a curve representing the required function in graphical form relative to some convenient system of co-ordinate axes.
This text on Integral Calculus completes the course in mathematics begun in the Analytic Geometry and continued in the Differential Calculus. Throughout this course I have endeavored to encourage individual work and to this end have presented the detailed methods and formulas rather as suggestions than as rules necessarily to be followed. The book contains more exercises than are ordinarily needed. As material for review, however, a supplementary list of exercises is placed at the end of the text. The appendix contains a short table of integrals which includes most of the forms occurring in the exercises. Through the courtesy of Prof. R.G. Hudson I have taken a two-page table of natural logarithms from his Engineers Manual. I am indebted to Professors H.W. Tyler, C.L. E.Moore, and Joseph Lipka for suggestions and assistance in preparing the manuscript. H.B. Phillips. Cambridge, Mass. June, 1917.
In issuing a second edition of the present volume it has been found desirable to enlarge it considerably beyond its original limits. The necessity for this has arisen partly Irom the increased requirements of the class of students for whom the book was originally written, and partly from the expressed opinion of many teachers that its sphere of usefulness might be thereby extended. Chapters have been added on Maxima and Minima of Several Independent Variables, on Elimination, on Lagranges and Laplace sTheorems, on Changing the Independent Variable, and one giving a short account of the principal properties of the best-known curves, which may be convenient for reference. A number of isolated theorems and processes, which do not find a convenient place elsewhere, have been put into a separate chapter entitled Miscellaneous Theorema Considerable additions have been made to some of the original articles, and others have been rewritten. Many additional sets of easy examples, specially illustrative of the theorems and methods proved or explained in the immediately preceding bookwork, have been inserted, in the hope that a selection from these will firmly fix in the mind of the student the leading principles and processes to be adopted in their solution before attacking the generally more difficult problems at the ends of the chapters. In a text-book of this character there will not be found much that is new or original, the object being to present to the student as succinct an account as possible of the most important results and methods which are up to the present time known, and to afford sufficient scope for practice in their use.
The aim of this work is to give a brief exposition of some of the devices employed in solving differential equations. The book presupposes only a knowledge of the fundamental formulæ of integration, and may be described as a chapter supplementary to the elementary works on the integral calculus.<br><br>The needs of two classes of students, with whom the author has been brought into contact in the course of his experience as a teacher, have determined the character of the work. For the sake of students of physics and engineering who wish to use the subject as a tool, and have little time to devote to general theory, the theoretical explanations have been made as brief as is consistent with clearness and sound reasoning, and examples have been worked in full detail in almost every case. Practical applications have also been constantly kept in mind, and two special chapters dealing with geometrical and physical problems have been introduced.<br><br>The other class for which the book is intended is that of students in the general courses in Arts and Science, who have more time to gratify any interest they may feel in this subject, and some of whom may be intending to proceed to the study of the higher mathematics.
Ix this book we have sought to give an account of a department of mathematics which is now generally regarded as fundamental. j Alist of the men to whom the successive advances of the subject I are due, includes, with few exceptions, the names of the greatest, fFrench and German mathematicians of the century, from Cauchy and Gauss onward. And in line with these advances lie the chief fields of mathematical activity at the present day. The most legitimate extensions of elementary analysis lead so fdirectly into the Theory of Functions, that recent writers on Algebra, Trigonometry, the Calculus, etc., give theories which are indispenj sable parts of our subject. But since these theories are not found I in many current text-books, it appears most convenient for the generality of readers to make the earlier chapters complete in themselves. Thus an account is given inch. i. of the geometric representation of elementary operations; and inch. iii., before the 1 introduction of Weierstrasss theory of the analytic function, the theory of convergence is discussed at some length. We have aimed at a full presentation of the standard parts of lithe subject, with certain exceptions. Of these exceptions, three must be stated. Inch. ii., the theory of real functions of a real variable is given only so far as seems necessary as a basis for what follows. In the account of Abelian integrals (ch. x.), our object.is to induct the reader as simply and rapidly as possible. into what is itself a suitable theme for more than one large volume. And we nave entirely passed over the automorphic functions, since it was tot possible to give even an introductory sketch within the space at ur disposal. However, an account of some of Kroneckers work, vhich is necessary for the study of Kleins recent developments of the theory of Abelian functions, is included inch. vi.; and ch. viii.
This book presents a first course in the calculus substantially as the author has taught it at the University of Michigan for a number of years. The following points may be mentioned as more or less prominent features of the book.<br><br>In the treatment of each topic, the text is intended to contain a precise statement of the fundamental principle involved, and to insure the student's clear understanding of this principle, without distracting his attention by the discussion of a multitude of details. The accompanying exercises are intended to present the problem in hand in a great variety of forms and guises, and to train the student in adapting the general methods of the text to fit these various forms. The constant aim is to prevent the work from degenerating into mere mechanical routine, as it so often tends to do. Wherever possible, except in the purely formal parts of the course, the summarizing of the theory into rules or formulas which can be applied blindly has been avoided. For instance, in the chapter on geometric applications of the definite integral, stress is laid on the fact that the basic formulas are those of elementary geometry, and special formulas involving a coordinate system are omitted.<br><br>Where the passage from theory to practice would be too difficult for the average student, worked examples are inserted.
This volume embodies the lectures given on the subject to graduate students over a period of four repetitions. The point of view is the result of many years of consideration of the whole field. The author has examined the various methods that go under the name of Vector, and finds that for all purposes of the physicist and for most of those of the geometer, the use of quaternions is by far the simplest in theory and in practice. The various points of view are mentioned in the introduction, and it is hoped that the essential differences are brought out. The tables of comparative notation scattered through the text will assist in following the other methods.<br><br>The place of vector work according to the author is in the general field of associative algebra, and every method so far proposed can be easily shown to be an imperfect form of associative algebra. From this standpoint the various discussions as to the fundamental principles may be understood. As far as the mere notations go, there is not much difference save in the actual characters employed. These have assumed a somewhat national character. It is unfortunate that so many exist.<br><br>The attempt in this book has been to give a text to the mathematical student on the one hand, in which every physical term beyond mere elementary terms is carefully defined. On the other hand for the physical student there will be found a large collection of examples and exercises which will show him the utility of the mathematical methods.
eBook
Applied CalculusPrinciples and Applications, Essentials for Students and Engineers
by Robert Gibbes Thomas
This book as a first course in the Calculus is not designed to be a complete exposition of the Calculus in either its principles or its applications. It is an effort to make clear the basic principles and to show that fundamental ideas are involved in familiar problems. While formulas and algebraic methods are necessary aids to concise and formal presentation, they are not essential to the expression of the principles and underlying ideas of the Calculus. These can be expressed in plain language without the use of symbols - one writer challenging the citing of a single instance where it cannot be done.<br><br>The practice is common, at least with "thoughtless thinkers," of blindly using formulas without any true conception of the ideas for which they are but the symbolic expression. The formulas of the Calculus are an invaluable aid in economy of thought, but their effective use is dependent upon an adequate knowledge of their derivation. The object of this book is to set forth the methods of the Calculus in such a way as to lead to a working and fruitful knowledge of its elements, to exhibit something of its power, and to induce its use as an efficient tool. No claim is made for absolute rigor in all the deductions, but confidence is invited in the soundness of the reasoning employed and in the logical conclusions obtained.<br><br>There are students, and engineers also, who when constrained to use the Calculus look upon it as a necessary evil.
The theory of functions of a real variable, as developed during the last few decades, is a body of doctrine resting, first upon a definite conception of the arithmetic continuum which forms the field of the variable, and which includes a precise arithmetic theory of the nature of a limit, and secondly, upon a definite conception of the nature of the functional relation. The procedure of the theory consists largely in the development, based upon precise definitions, of a classification of functions, according as they possess, or do not possess, certain peculiarities, such as continuity, different ability, &c., throughout the domain of the variable, or at points forming a selected set contained in that domain. The detailed consequences of the presence, or of the absence, of such peculiarities are then traced out, and are applied for the purpose of obtaining conditions for the validity of the processes of Mathematical Analysis. These processes, which have been long employed in the so-called Infinitesimal Calculus, consist essentially in the ascertainment of the existence, and in the evaluation, of limits, and are subject, in every case, to restrictive assumptions which are necessary conditions of their validity. The object to be attained by the theory of functions of a real variable consists then largely in the precise formulation of necessary and sufficient conditions for the validity of the limiting processes of Analysis. A necessary requisite in such formulation is a language descriptive of particular aggregates of values of the variable, in relation to which functions possess definite peculiarities. This language is provided by the Theory of Sets of Points, also known, in its more general aspect, as the Theory of Aggregates, which contains an analysis of the peculiarities of structure and of distribution in the field of the variable which such sets of points may possess. This theory, which had its origin in the exigencies of a critical theory of functions, and has since received wide applications, not only in Pure Analysis, but also in Geometry, must be regarded as an integral part of the subject. A most important part of the theory of functions is the theory of the representation of functions in a prescribed manner, especially by means of series or sequences of functions of prescribed types.
The clearer view of the science thus afforded the teacher, the inspiration to improve his methods of presenting it, the increased interest in the class-work, the tendency of the subject to combat stagnation of curricula, these are a few of the reasons for approving the present renaissance of the study. This phase of scientific history which Montucla brought into such repute it must be confessed rather by his literary style than by his exactness and which writers like De Morgan in England, Chasles in France, Quetelet in Belgium, Hankel and Baltzer in Germany, and Boncompagni in Italy encouraged as the century wore on, is seeing a great revival in our day. This new movement is headed by such scholars as GUnther, EnestrOm, Loria, Paul Tannery, and 2 uthen, but especially by Moritz Cantor, whose Vorlesungen Hber GeschUhte der Mathematik must long remain the worlds standard. In any movement of this kind compendia are always necessary for those who lack either the time or the linguistic power to read the leading treatises. Several such works have recently appeared in various languages. But the most systematic attempt in this direction is the work here translated. The writers of most hand books of this kind feel called upon to collect a store of anecdotes, to incorporate tales of no historic value, and to minimize the real history of the science. Fink, on the other hand, omits biography entirely, referring the reader to a brief table in the appendix or to the encyclopedias.
Under the traditional plan of studying trigonometry, college algebra, analytic geometry, and calculus separately, a student can form no conception of the character and possibilities of modern mathematics, nor of the relations of its several branches as parts of a unified whole, until he has taken several successive courses. Nor can he, early enough, get the elementary working knowledge of mathematical analysis, including integral calculus, which is rapidly becoming indispensable for students of the natural and social sciences. Moreover, he must deal with complicated technique in each introductory course; and must study many topics apart from their uses in other subjects, thus missing their full significance and gaining little facility in drawing upon one subject for help in another.<br><br>To avoid these disadvantages of the separate-subject plan the unified course presented here has been evolved. This enables even those students who can take only one semesters work to get some idea of differential and integral calculus, trigonometry, and logarithms. And specialist students, as experience has shown; acquire an excellent command of mathematical tools by first getting a birds-eye view of the field, and then proceeding to perfect their technique.<br><br>A regular course in calculus, following this, can proceed more rapidly than usual, include more advanced topics, and give a fine grasp: the principles and processes have become an old story. And the regular course in analytic geometry can be devoted to a genuine study of the geometrical properties of loci, since most of the type equations, basic formulas, and calculus methods are already familiar.
In an introductory course on the Differential and Integral Calculus the subject of Infinite Series forms an important topic. The presentation of this subject should have in view first to make the beginner acquainted with the nature and use of infinite series and secondly to introduce him to the theory of these series in such a way that he sees at each step precisely what the question at issue is and never enters on the proof of a theorem till he feels that the theorem actually requires proof. Aids to the attainment of these ends are: (a) a variety of illustrations, taken from the cases that actually arise in practice, of the application of series to computation both in pure and applied mathematics; (b) a full and careful exposition of the meaning and scope of the more difficult theorems; (c) the use of diagrams and graphical illustrations in the proofs.<br><br>The pamphlet that follows is designed to give a presentation of the kind here indicated. The references are to Byerly's Differential Calculus, Integral Calculus, and Problems in Differential Calculus, and to B. O. Peirce's Short Table of Integrals; all published by Ginn & Co., Boston.
This work is a development of the infinitesimal calculus as far as the first differentials of algebraic functions of one windependent variable and their corresponding integrals. That is to say, it is restricted to the absolute rudiments of the science. Within these narrow limits how Aever, the treatment is tolerably full, and Qsuffices to show how far-reaching a mathematical instrument the Calculus is, even in its elementary steps. This seems to the author to be the best way of communicating a working knowledge of the science; namely, to teach a few elementary rules and then put them into immediate use, as far as they will go. The student then recognizes the necessity of the more advanced steps. Very little is said at the start about the logical basis of the science. The few remarks which it seemed necessary to make upon this topic are reserved for the final chapter.
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General Visualization Quick Start
Brett Champion
This course explores Mathematica's built-in tools for creating visualizations from functions or data. You'll learn how to customize plots with styles, labels, and other features that are common across the visualization functions.
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Learn how to incorporate engaging digital content into physics classrooms with Mathematica, Wolfram|Alpha, and other Wolfram technologies. This Wolfram Technology for STEM Education: Virtual Conference for Education ...
Wolfram technologies are the tools for providing interactive and engaging materials for STEM education. In this video, Conrad Wolfram shares examples and explains why Wolfram is uniquely positioned to be ...
This video explains the principles of volume rendering and the art of constructing the right transfer functions. Markus van Almsick explores the drawbacks and extravagant possibilities of this new visualization ...
Wolfram SystemModeler can be used to model safety-critical systems. This Wolfram Virtual Conference Spring 2013 talk takes a closer look at an aircraft flap system, showing how component faults can be modeled and how their effects on system behavior ...
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This outstanding text by two well-known authors treats numerical analysis with mathematical rigor, but presents a minimum of theorems and proofs. Oriented toward computer solutions of problems, it stresses error analysis and computational efficiency, and compares different solutions to the same problem. Following an introductory chapter on sources of error and computer arithmetic, the text covers such topics as approximation and algorithms; interpolation; numerical differentiation and numerical quadrature; the numerical solution of ordinary differential equations; functional approximation by least squares and by minimum-maximum error techniques; the solution of nonlinear equations and of simultaneous linear equations; and the calculation of eigenvalues and eigenvectors of matrices. This second edition also includes discussions of spline interpolation, adaptive integration, the fast Fourier transform, the simplex method of linear programming, and simple and double QR algorithms. Problems some strictly mathematical, others requiring a computer appear at the end of each chapter.
Useful to programmers and stimulating for theoreticians, this text covers the major methods of numerical integration. It offers a balanced presentation: certain sections derive from or allude to deep results of analysis, but most of the final results are expressed in a form accessible to anyone with a background in calculus. An extensive introduction outlines the uses and advantages of numerical integration and includes formulas and guides to orthogonal polynomials and specific integrals. Subsequent chapters explore approximate integration over finite and infinite intervals, error analysis, approximate integration in two or more dimensions, and automatic integration. Five helpful appendixes conclude the text.
More editions of Methods of Numerical Integration: Second Edition (Dover Books on Mathematics):
Last paragraph to First Edition Preface
This book presents what we think are the major methods of numerical integration. We have tried to produce a balanced work that is both useful to the programmer and stimulating to the theoretician. There are portions of the book where deep results of analysis are derived or are alluded to;yet, it has been our hope that most of the final results have been expressed in a way that is accessible to those with a background only in calculus.
More editions of Methods of Numerical Integration (Computer Science and Applied Mathematics):
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Essentials of Discrete Mathematics112.37
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About the Book
The Second Edition of David Hunter's Essentials of Discrete Mathematics is the ideal text for a one-term discrete mathematics course to serve computer science majors, as well as students from a wide range of other disciplines. The material is organized around five types of mathematical thinking: logical, relational, recursive, quantitative, and analytical. This presentation results in a coherent outline that steadily builds upon mathematical sophistication. Graphs are introduced early and are referred to throughout the text, providing a richer context for examples and applications. Students will encounter algorithms near the end of the text, after they have acquired enough skills and experience to analyze them properly. The final chapter contains in-depth case studies from a variety of fields, including biology, sociology, linquistics, economics, and music.
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history traces the development of mathematical ideas and the careers of the mathematicians responsible for them. Originally published in 1972, it is now available as a three volume paperback edition. Volume 1 looks at the discipline's origins in Babylon and Egypt, the creation of geometry and trigonometry by the Greeks, and the role of mathematics in the medieval and early modern periods. Volume 2 focuses on calculus, the rise of analysis in the nineteenth century, and the number theories of Dedekind and Dirichlet. The concluding volume covers the revival of projective geometry, the emergence of abstract algebra, the beginnings of topology, and the influence of Godel on recent mathematical study.
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"Outstanding scholarship and readability. One of only a couple of books available in English for in-depth historical studies at the fourth year/graduate level."--Charles V. Jones, Ball State University
"The consistently high quality of presentation, the accuracy, the readable style, and the stress on the conceptual development of mathematics make [these volumes] a most desirable reference."--Choice
"Without a doubt a book which should be in the library of every institution where mathematics is either taught or played."--The Economist
"What must be the definitive history of mathematical thought....Probably the most comprehensive account of mathematical history we have yet had."--Saturday Review
About the Author
Morris Kline is Professor of Mathematics, Emeritus, at the Courant Institute of Mathematical Sciences, New York University, where he directed the Division of Electromagnetic Research for twenty years.
Most Helpful Customer Reviews
As one might expect from a 3-volume history, _Mathematical Thought_ is comprehensive; Kline covers basically all the important mathematical developments from ancient times (e.g. the Babylonians) until about 1930. Note that (as Klein himself mentions) the coverage of ancient mathematics, while taking up a good half of the first volume, is necessarily modest, and if that is the reader's primary interest, s/he would do best to seek out specific histories on the Greeks, Chinese, etc. [Kline gives several useful references, as always]. The reader interested in the 18th and 19th centuries will find plenty of food for thought. For example, the story of non-Euclidean geometry is covered well, and Kline does a good job of putting the discoveries in the light of the times. One notable thing I learned is that Lobachevsky and Bolyai were not the discoverers of non-Euclidean geometry, nor were they the first to publish material on that subject. Others before had expressed the opinion that non-Euclidean gometry was consistent and as viable a geometry as Euclidean (e.g. Kluegel, Lambert...even Gauss!) It remained for Beltrami to later show that if Euclidean geometry were consistent, so is non-Euclidean. Of course, important events like the invention of Galois theory are also mentioned. Really, if it's a major mathematical development before 1930, Kline will have it somewhere in these 3-volumes. Incidentally, Kline advances the interesting theory that Lobachevsky and Bolyai somehow learned of Gauss' work on non-Euclidean geometry (which he kept secret and was not learned of until after his death) through close friends of Gauss: Bartel (mentor to Lobachevsky) and Bolyai's father, Farkas.Read more ›
The only reader I think Kline's book would be right for is one who wants a single source for the history of mathematics and who is not willing to use more specialized books. I have had Kline's history for years and I sometimes look something up in it, am disappointed by his presentation, and then look for the topic in another book.
For a reader who wants an accessible and reliable general history of mathematics I recommend Victor Katz's "A History of Mathematics". Kline covers European mathematics in more detail than Katz does, but Katz is a better one volume work, and I suggest that anyone who wants more detail than what Katz gives should use one of the following references instead of turning to Kline.
The two volume "Abrégé d'histoire des mathématiques" edited and partially written by Dieudonne, Moritz Cantor's "Vorlesungen über Geschichte der Mathematik", and the two volume "Companion Encyclopedia" edited by Ivor Grattan-Guinness are all reliable and cover in detail much material. Dieudonne's Histoire is not comprehensive, but it is excellent for the material it does cover, mostly in function theory and the theory of numbers.
For a mathematically knowledgeable reader who wants a structural history of certain parts of mathematics, I recommend Bourbaki's "Elements of the History of Mathematics". That book however is not meant to be a comprehensive history of mathematics, and really should be thought of as a history of the parts of mathematics that interested Bourbaki, written from their point of view. It is however reliable and specific in its details.
For the history of Greek mathematics one cannot do better than to read Heath's books and translations.Read more ›
if flawed. Not only do you have to wade through the gentleman amateur flavour of the first couple of hundred pages or so, but Kline manages to describe William Hamilton as 'the greatest English theoretical physicist after Newton'; even an Irishman would concede that the greatest English theoretical physicist after Newton was Maxwell - Hamilton was third. However with the first impact tremors announcing the approach of Leonard Euler, when the technical issues start to thicken, things improve enormously. Kline is clearly in awe of Euler, and does a good job of communicating why awe is appropriate.
It is nevertheless fortunate that the history of mathematics, unlike that of science, is a discipline essentially invulnerable to whiggish prejudice.
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This is a short eBook that describes how to get free high school Algebra 1 help online without having to spend any money, buy anything, join any free trials, or anything like that. Free High School Algebra 1 Help Online | Algebra 1 Help.org.
A short ebook explaining a simple way to subtract integers for people who have trouble subtracting integers. This uses a method based on simply changing a subtraction problem to an addition problem based on helping people with algebra. How to Subtract Integers Without Getting Confused | Algebra 1 Help.org
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978013148101533
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Starting at $51.51Analysis with an Introduction to Proof
Analysis with an Introduction to Proof
Summary
By introducing logic and by emphasizing the structure and nature of the arguments used, this book helps readers transition from computationally oriented mathematics to abstract mathematics with its emphasis on proofs.Uses clear expositions and examples, helpful practice problems, numerous drawings, and selected hints/answers. Offers a new boxed review of key terms after each section. Rewrites many exercises. Features more than 250 true/false questions. Includes more than 100 practice problems. Provides exceptionally high-quality drawings to illustrate key ideas. Provides numerous examples and more than 1,000 exercises.A thorough reference for readers who need to increase or brush up on their advanced mathematics skills.
Table of Contents
Preface
ix
Logic and Proof
1
(35)
Logical Connectives
1
(10)
Quantifiers
11
(6)
Techniques of Proof: I
17
(9)
Techniques of Proof: II
26
(10)
Sets and Functions
36
(63)
Basic Set Operations
36
(14)
Relations
50
(10)
Functions
60
(17)
Cardinality
77
(13)
Axioms for Set Theory
90
(9)
The Real Numbers
99
(57)
Natural Numbers and Induction
99
(9)
Ordered Fields
108
(9)
The Completeness Axiom
117
(12)
Topology of the Reals
129
(9)
Compact Sets
138
(8)
Metric Spaces
146
(10)
Sequences
156
(34)
Convergence
156
(9)
Limit Theorems
165
(9)
Monotone Sequences and Cauchy Sequences
174
(7)
Subsequences
181
(9)
Limits and Continuity
190
(41)
Limits of Functions
190
(9)
Continuous Functions
199
(10)
Properties of Continuous Functions
209
(7)
Uniform Continuity
216
(7)
Continuity in Metric Spaces
223
(8)
Differentiation
231
(37)
The Derivative
231
(10)
The Mean Value Theorem
241
(10)
L'Hospital's Rule
251
(8)
Taylor's Theorem
259
(9)
Integration
268
(26)
The Riemann Integral
268
(9)
Properties of the Riemann Integral
277
(9)
The Fundamental Theorem of Calculus
286
(8)
Infinite Series
294
(25)
Convergence of Infinite Series
294
(8)
Convergence Tests
302
(10)
Power Series
312
(7)
Sequences and Series of Functions
319
(28)
Pointwise and Uniform Convergence
319
(10)
Applications of Uniform Convergence
329
(9)
Uniform Convergence of Power Series
338
(9)
Glossary of Terms
347
(14)
References
361
(1)
Hints for Selected Exercises
362
(18)
Index
380
Excerpts
A student's first encounter with analysis has been widely regarded as the most difficult course in the undergraduate mathematics curriculum. This is due not so much to the complexity of the topics as to what the student is asked to do with them. After years of emphasizing computation (with only a brief diversion in high school geometry), the student is now expected to be able to read, understand, and actually construct mathematical proofs. Unfortunately, often very little groundwork has been laid to explain the nature and techniques of proof.This text seeks to aid students in their transition to abstract mathematics in two ways: by providing an introductory discussion of logic, and by giving attention throughout the text to the structure and nature of the arguments being used. The first three editions have been praised for their readability and their student-oriented approach. This revision builds on those strengths. Small changes have been made in many sections to clarify the exposition, more than 150 new exercises have been added, and each section now ends with a review of key terms. This emphasizes the important role of definitions and helps students organize their studying. In the back of the book there is now a Glossary of Key Terms that gives the meaning of each term and lists the page on which the term is first introduced.A unique feature of the text is the inclusion of more than 250 true/false questions that relate directly to the reading. These questions have been carefully worded to anticipate common student errors. They encourage the students to read the text carefully and think critically about what they have read. Often the justification for an answer of "false" will be an example that the students can add to their growing collection of counterexamples. The ordering of these true/false questions has been updated in this edition to follow more closely the flow of each section.As in earlier editions, the text also includes more than a hundred practice problems. Generally, these problems are not very difficult, and it is intended that students should stop to work them as they read. The answers are given at the end of each section just prior to the exercises. The students should also be encouraged to read (if not attempt) most of the exercises. They are viewed as an integral part of the text and vary in difficulty from the routine to the challenging. Those exercises that are used in A later section are marked with an asterisk. Exercises marked by a star * have hints in the back of the book. These hints should be used only after a serious attempt to solve an exercise has proved futile.The overall organization of the book remains the same as in the earlier editions. The first chapter takes a careful (albeit nontechnical) look at the laws of logic and then examines how these laws are used in the structuring of mathematical arguments. The second chapter discusses the two main foundations of analysis: sets and functions. This provides an elementary setting in which to practice the techniques encountered in the previous chapter.Chapter 3 develops the properties of the real numbersRas a complete ordered field and introduces the topological concepts of neighborhoods, open sets, closed sets, and compact sets. The remaining chapters cover the topics usually included in an analysis of functions of a real variable: sequences, continuity, differentiation, integration, and series.The text has been written in a way designed to provide flexibility in the pacing of topics. If only one term is available, the first chapter can be assigned as outside reading. Chapter 2 and the first half of Chapter 3 can be covered quickly, again with much of the reading being left to the student. By so doing, the remainder of the book can be covered adequately in a single semester. Alternatively, depending on the students' background and interests, one can concentrate on developing the first five chapt
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MATH 205A:
First Half of Elementary Algebra
This course is the first half of the Elementary Algebra course. It will cover signed numbers, evaluation of expressions, ratios and proportions, solving linear equations, and applications. Graphing of lines, the slope of a line, graphing linear equations, solving systems of equations, basic rules of exponents, and operations on polynomials will be covered.
MATH 205B:
Second Half of Elementary Algebra
Prerequisite: Math 205A with a grade of 'C' or better.
Advisory: Concurrent enrollment in Guidance 563B is advised.
Transferable: GAV-GE: B4
This course contains the material covered in the second half of the Elementary Algebra Course. It will cover factoring, polynomials, solving quadratic equations by factoring, rational expressions and equations, complex fractions, radicals and radical equations, solving quadratic equations by completing the square and the quadratic formula. Application problems are integrated throughout the topics.
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Math Center Level 2 1.0.1.6
Math software for students studying precalculus and calculus. Math Center Level 2 consists of a Scientific Calculator, a Graphing Calculator 2D Numeric, a Graphing Calculator 2D Parametric, a Graphing Calculator 2D Polar, an Integer Calculator, and a Rational Calculator. The Scientific Calculator works in scientific mode. There are options to save and print calculation history, to change font, and standard editing options. Graphing Calculator 2D Numeric is a further development of Graphing Calculator2D from Math Center Level 1. It has extended functionality: hyperbolic functions are added. There are also added new capabilities which allow calculating series, product series, Permutations, Combinations, Newton Binomial Coefficients, and Gauss Binomial Coefficients . Graphing Calculator 2D Numeric has capability to build graphs for first and second derivatives, definite integral (area under curve) and length integral (length of curve). Since these calculations are done numerically, not symbolically, the calculator is called Numeric. Graphing Calculator 2D Parametric is a generalization of Graphing Calculator 2D Numeric. Now x and y are functions on parameter tau. Since all calculations are done twice, for x and y, there was some sacrificing of precision in order to keep speed of calculations. So, although it is possible to build the same graph of y=f(x) in parametric calculator using x=1, y=f(x), the Graphing Calculator 2D Numeric will build it with greater precision. Graphing Calculator 2D Polar is a specialization of Graphing Calculator 2D Numeric.
Probability Analysis Software for Windows that provides an easy-to-use tool for using Discrete and Continuous Distributions, handling all the Probability Combinations for you with Graphing and info. Designed for Windows - optimised for Windows XPPrice: $35.00 Size: 2.4 MB
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| 677.169 | 1 |
Mathematical Discovery 1
Gives students a firm grounding in the main ideas of algebra and calculus. In algebra, students learn concepts and symbolic manipulation used when calculating with large numbers of variables. In calculus, they learn concepts used when working with continuously changing variables. Both ways of thinking are essential in Mathematics and when creating and using mathematical models in Science, Engineering and Commerce.
All students whose degree requires first-year mathematics may take MATH1210 in preference to MATH1110. There is substantial overlap between MATH1110 and MATH1210; students' performance on this common material is compared and used to scale the marks to ensure that comparable students achieve comparable grades.
Not for credit with MATH1110.
Available in 2015
Callaghan Campus
Semester 1
Previously offered in 2014
Objectives
1. To develop a firm foundation for later studies in algebra and analysis, the two main branches of mathematics.
2. To develop an understanding of high school mathematics by developing a more rigorous approach.
3. To develop students' capacity for effective reasoning, and their ability to use their mathematical skills elsewhere.
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SEVENTH GRADE
The Seventh Grade mathematics curriculum features an in-depth, integrated
preparation for algebra and geometry. Concepts include basic operations with fractions,
decimals, number theory, measurement, data interpretation, geometry, integers,
algebraic concepts, and percents. A variety of problem-solving techniques, real-world
applications, and technology will be used when applying these concepts. This course is
designed to prepare students for eighth grade mathematics or Pre-Algebra1 the basic operations with decimals, fractions,
and mixed numbers. (P, M, N)
a. Compare, order, round, and estimate decimals.
b. Add, subtract, multiply, and divide decimals in real-life situations with and without
calculators.
c. Use powers of ten to multiply and divide decimals.
d. Convert among decimals, fractions, and mixed numbers.
e. Express ratios as fractions.
f. Add, subtract, multiply, and divide fractions and mixed numbers.
g. Use estimation to add, subtract, multiply, and divide fractions.
2. Apply and use basic principles of number sense. (P, M, N)
a. Use patterns to develop the concept of exponents.
b. Write numbers in standard and exponential form.
c. Convert between standard form and scientific notation.
d. Find and use prime factorization with exponents to obtain the greatest common
factor (GCF) and least common multiple (LCM).
e. Describe and extend patterns in sequences.
f. Identify and use the commutative, associative, distributive, and identity
properties.
g. Use patterns to develop the concepts of roots of perfect squares with and without
calculators.
3. Use units of measurement with standard systems. (P, D, M, G, N)
a. Convert within a standard measurement system (English and metric).
b. Convert temperature using the Fahrenheit and Celsius formulas.
c. Use standard units of measurement to solve application problems.
2 Collect, organize, and summarize data and use simple probability. (P, D, M, G, N)
a. Organize data in a frequency table.
b. Interpret and construct histograms, line, and bar graphs.
c. Interpret and construct circle graphs when given degrees.
d. Interpret and construct stem and leaf plots and line plots from data.
e. Estimate and compare data including mean, median, mode, and range of a set of
data.
f. Predict and recognize data from statistical graphs.
g. Determine probability of a single event.
h. Use simple permutations and combinations.
5. Use concepts of geometry in angles and polygons and extend the concepts
of perimeter and area. (P, G, M, N)
a. Identify polygons to twelve sides.
b. Classify and compare the properties of quadrilaterals.
c. Classify and measure angles of all types.
d. Classify triangles by sides and angles.
e. Find the perimeter of polygons.
f. Find the area of triangles and quadrilaterals.
g. Find the circumference and area of a circle.
h. Identify congruent segments, angles, and polygons.
i. Develop relationships of faces, vertices, and edges of three-dimensional figures.
j. Perform transformations (rotations, reflections, translations) on plane figures
using physical models and graph paper.
k. Investigate symmetry of polygons.
l. Develop and apply the Pythagorean Theorem to find missing sides of right
triangles.
3 Develop and apply the basic operations of integers. (P, D, M, G, N)
a. Recognize and write integers including opposites and absolute value.
b. Compare and order integers.
c. Graph ordered pairs on a coordinate plane.
d. Add, subtract, multiply, and divide integers with and without calculators.
7. Create and apply algebraic expressions and equations. (P, G, N)
a. Translate between simple algebraic expressions and verbal phrases.
b. Use the order of operations to simplify and/or evaluate numerical and algebraic
expressions with and without calculators.
c. Solve linear equations using the addition, subtraction, multiplication, and division
properties of equality with integer solutions.
d. Write and solve equations that represent problem-solving situations.
e. Write a real-world situation from a given equation.
8. Survey and apply concepts of ratio, proportion, and percent. (P, D, M, G, N)
a. Explore equivalent ratios and express them in simplest form.
b. Solve problems involving proportions.
c. Determine unit rates.
d. Use models to illustrate the meaning of percent.
e. Convert among decimals, fractions, mixed numbers, and percents.
f. Determine the percent of a number.
g. Estimate decimals, fractions, and percents.
h. Use proportions and equations to solve problems with rate, base, and part with
and without calculators.
i. Find the percent of increase and decrease.
j. Solve problems involving sales tax, discount, and simple interest with and without
calculators.
4
Course: 7
Unit Theme: Concepts and Basic Operations
Suggested Suggested
Comp. Obj. Teaching Strategies Assessment
1 a, b Using grocery store and discount store ads, discuss Discussion;
8 c, j the cost of advertised items. Estimate and compare Student work sample
total costs of items when given a certain amount of
money to spend. Identify unit prices of several items
and compare prices in order to find best buys.
1 a, b Using baseball batting averages from the newspaper, Student work sample
4 e round the averages to the nearest hundredth. Using
calculators, estimate and calculate team averages.
1 a, b Using a menu from a local restaurant, calculate the Student work sample
8 j total cost of a meal, including tax and tip.
1 d, e, f, g Using recipes, double, triple and quadruple the Presentation;
3 c ingredients. Calculate ingredients needed to serve the Teacher observation
8 b class. Using several recipes, work in groups to plan a
menu to serve at a party. Use addition, subtraction,
multiplication, and division of fractions and mixed
numbers, as well as whole numbers. Estimate these
using calculators.
5
Course: 7
Unit Theme: Number Sense
Suggested Suggested
Comp. Obj. Teaching Strategies Assessment
2 a Use a table to visualize the patterns in the concept of ● Teacher observation
exponents.
1 b, c Research distances from each planet to the sun. ● Presentation;
2 Make a poster. Use findings to write standard form Student work sample
and scientific notation. Use the calculator to develop
this concept.
2 b, d Use a Venn diagram to find the GCF and LCM . ● Student work sample;
In groups, find the prime numbers using the Sieve Teacher observation;
of Eratosthenes. Written response;
Divide the greater number by the lesser number to Presentation
find GCF (Euclidean Algorithm).
Research mathematicians—Eratosthenes and
Euclid.
Use this method of division of prime numbers to
find LCM.
2 60, 12
2 30, 6
3 15, 3
5 5, 1
1, 1
2 2 3 5 60
Work in pairs to form fractions from statistics in a ● Student work sample
1 d, e
2 d school football game such as number of passes
8 a completed out of number thrown. Determine in
simplest form.
2 e Discover the Fibonacci sequence in a pine cone or ● Presentation
pineapple spiral. Make a bulletin board from facts
about this sequence in nature.
2 e Derive a sequence of pay which would give the most ● Teacher observation
money at the end of the month for each student such
as the same amount paid each day or a small amount
doubled everyday.
2 f Give everyday examples (putting on socks and shoes) ● Presentation
using the properties—commutative, associative,
distributive, and identity.
2 a, g Using graph paper, draw squares. Discuss the sides ● Presentation;
and note representation of square root. These Teacher observation
squares represent ―perfect squares.‖
6
Course: 7
Unit Theme: Measurement
Suggested Suggested
Comp. Obj. Teaching Strategies Assessment
3 a, b, c Collect data on high and low temperatures for one ● Student work sample;
week. Calculate the Celsius temperature from a given Presentation;
Fahrenheit temperature. Teacher-made test
1 c Convert metric units by multiplying and dividing by ● Student work sample;
3 a, c powers of 10. Teacher-made test
3 a, c Bring in grocery items and collect labels and note ● Student work sample
weight, capacity, etc. Convert among units of standard
and metric measurement.
7
Course: 7
Unit Theme: Data and Probability
Suggested Suggested
Comp. Obj. Teaching Strategies Assessment
4 a, b, c, d, Collect and chart data on the height of students and ● Rubric
e, f length of arms. Organize in a frequency table. (Note
the mean, median, mode, and range using a line plot.)
Organize data on a double bar graph. When given
degrees, construct a circle graph of heights and
lengths and compare data.
4 g In groups, flip coins and write expected outcomes. ● Student response;
Rubric
4 g Use a spinner with letters. Find the probability that the ● Student response;
pointer will stop on a certain letter. Rubric
4 h Introduce permutations and combinations using a ● Student response
calculator (factorial key).
4 h Imagine a certain number of students eating at a ● Rubric
restaurant. Calculate the different ways the group can
be seated at a chosen number of tables. Choose
three ingredients from a list of five at the salad bar
(name the five ingredients). Ask ―In how many ways
can three ingredients be chosen from the five?‖
8
Course: 7
Unit Theme: Geometry
Suggested Suggested
Comp. Obj. Teaching Strategies Assessment
5 a, b, c, d Use a Venn diagram to classify polygons. ● Teacher observation
5 a, b, c, d, Use quilt pattern books, measure angles of triangles ● Project;
e, f, h and classify by sides and angles. Find the polygons Presentation
and classify. Measure sides of polygons and find
perimeter and area. Note congruence of angles and
polygons.
1 b Verify the formula for circumference by measuring ● Demonstration;
5 g, f various sizes of cans or circular objects with string. Written response
5 i Recognize and identify faces and edges of objects ● Discussion;
found in the classroom and on the campus. Written response
5 j Research M. C. Escher and model rotations, ● Student work sample;
reflections, and translations using graph paper. Draw Presentation
tessellations.
5 k Determine symmetry of capital letters of the alphabet. ● Presentation
Draw the lines of symmetry and create a poster.
5 l Have the students draw a diagram of their room at ● Presentation;
home. Place a chosen object in the corner of the Student work sample
room. Determine the placement of other furniture,
stereo system and speakers, etc. The meaning and
application of the Pythagorean Theorem will be
developed.
9
Course: 7
Unit Theme: Integers
Suggested Suggested
Comp. Obj. Teaching Strategies Assessment
3 b, c Research the high and low temperatures for five cities ● Presentation;
6 a, b, d in different regions of the United States for a week. Project;
Find the difference in temperature among these cities. Student work sample
Perform this activity in the winter and in the spring and
order/compare. (Note: Below 0) Use calculators.
6 a, b Use number lines to compare and order integers and ● Student work sample;
graph the integers. Teacher-made test
6 c Name coordinates and create patterns or figures (e.g., ● Teacher observation
butterfly, umbrella, sailboat) by plotting points.
6 c Using a United States map, plot locations of chosen ● Student work samples
cities, national parks, and other points of interests.
Find latitude and longitude.
10
Course: 7
Unit Theme: Expressions and Equations
Suggested Suggested
Comp. Obj. Teaching Strategies Assessment
7 a, b, c, d, e Read a sentence such as 2 x 10 as, 2 times what ● Student work sample;
number is 10. A correct response will be 5. Write the Teacher made test
related numerical expression and equation. Repeat
this activity several times, and use the same procedure
to write related multiplication and division sentences
along with addition and subtraction.
7 a, b, c, d, e Use similarities and differences in appearance and ● Written response;
dress of students. Write and solve equations about Teacher observation
these criteria. Algebraic expressions may be written
from phrases stated about appearance and dress.
7 c, d Use algebra tiles to model and solve equations. ● Teacher observation;
Student work samples
11
Course: 7
Unit Theme: Ratio, Proportion, and Percent
Suggested Suggested
Comp. Obj. Teaching Strategies Assessment
8 a Play ―Concentration‖ to find matching pairs of ● Discussion;
equivalent fractions. Teacher observation
8 b, f, h Compare the number of boys and girls in various ● Student work samples
classrooms and convert boy/girl ratios to percent. Use
proportions to convert percent and predict the number
of boys or girls in other classes.
8 c Provide a price list from local grocery stores. Identify ● Presentation;
unit prices of several items and compare prices in Student work samples
order to find best buys.
1 a, b Show percent of change (increase or decrease) on ● Teacher observation;
8 d, i graph paper. Recognize and explain percent of Rubric
change as shown on graph paper.
8 e, g Using a spinner, play a game by naming percents for ● Teacher observation;
fractions, fractions for percents, percents for decimals, Student work samples
and decimals for percents as the pointer lands on
these sections. (Extension: Write estimations of the
percent, decimal, fraction.)
8 h Assign each group a part, rate, or base problem. Write ● Teacher observation;
problems from an ad in the newspaper of the type Student work samples
problem using proportions and equations. Exchange
among groups the assigned problems.
1 a, b Have students look at advertisements for discount ● Student work
8 j sales. Select one item and write the specific size, samples;
brand, and other characteristics. From several stores Teacher-made test
find the actual price of the same item. Compare
prices to see if the sale is actually as good as the ad
indicates. Calculate the discount and sale price to find
the best store and best savings. Calculate the sales
tax on the items.
12
EIGHTH GRADE
The Eighth Grade mathematics curriculum will incorporate concepts which provide
a smooth transition from concrete to abstract relationships in preparation for high school
mathematics courses. Concepts include real numbers, algebraic concepts, geometric
principles, ratio, proportion, percents, number theory, measurements, data analysis, and
the coordinate system. A variety of problem-solving techniques and technology will be
used when applying these concepts, which will enable students to solve real life
problems. This course is designed to prepare students for Pre-Algebra.
The competencies are printed in bold face type and are required to be taught. The
competencies combine the content strands13 basic operations using real numbers.
(P, D, G, N)
a. Classify and give examples of real numbers such as natural, whole, integers,
rational, and irrational.
b. Identify, compare, and order fractions and decimals.
c. Round and estimate fractions and decimals.
d. Solve real-life problems involving addition, subtraction, multiplication, and
division of fractions, decimals, and mixed numbers.
e. Determine the absolute value and additive inverse of real numbers.
f. Classify, compare, and order integers and rational numbers.
g. Add, subtract, multiply, and divide integers and rational numbers with and without
calculators.
2. Use basic concepts of number sense and perform operations involving order
of operations, exponents, scientific notation. (P, M, N)
a. Simplify expressions using order of operations.
b. Use the rules of exponents when multiplying or dividing like bases, and when
raising a power to a power.
c. Multiply and divide numbers by powers of ten.
d. Convert between standard form and scientific notation.
e. Multiply and divide numbers written in scientific notation.
f. Evaluate and estimate powers, squares, and square roots with and without
calculators.
14 Use properties to create and simplify algebraic expressions and solve linear
equations and inequalities. (P, G, N)
a. Identify and apply the commutative, associative, and distributive properties.
b. Distinguish between numerical and algebraic expressions, equations, and
inequalities.
c. Convert between word phrases or sentences and algebraic expressions,
equations, or inequalities.
d. Simplify and evaluate numerical and algebraic expressions.
e. Solve and check one and two-step linear equations and inequalities.
f. Solve and check multi-step linear equations using the distributive property.
g. Graph solutions to inequalities on a number line.
h. Write a corresponding real-life situation from an algebraic expression.
4. Apply the concepts of ratio, proportion, and percent to solve real-life
problems. (P, D, M, G, N)
a. Write ratios comparing given data.
b. Convert among ratios, decimals, and percents.
c. Solve proportions.
d. Solve for part, rate, or base.
e. Find commissions and rates of commission, discounts, sale prices, sales tax, and
simple interest.
f. Find percent of increase and decrease.
g. Write and solve real-life word problems using percents with and without
calculators.
1. Convert and use standard units (English and metric) of measurement.
(P, D, M, G, N)
a. Convert, perform basic operations, and solve word problems using standard
measurements.
b. Measure line segments and find dimensions of given figures using standard
measurements.
c. Write and solve real-life problems involving standard measurements.
d. Select appropriate units of measurement for real-life problems.
15 Apply geometric principles to polygons, angles, and two and three-
dimensional figures. (P, M, G, N)
a. Identify parallel, perpendicular, intersecting, and skew lines.
b. Identify and describe characteristics of polygons.
c. Find the perimeter and area of polygons and circumference and area of circles.
d. Classify, draw, and measure acute, obtuse, right, and straight angles.
e. Identify and find the missing angle measure for adjacent, vertical,
complementary, and supplementary angles.
f. Locate and identify angles formed by parallel lines cut by a transversal (e.g.,
corresponding, alternate interior, and alternate exterior).
g. Classify triangles by sides and angles and find the missing angle measure.
h. Identify three-dimensional figures and describe their faces, vertices, and edges.
i. Use the Pythagorean Theorem to solve problems, with and without a calculator.
7. Interpret, organize, and make predictions about a variety of data using
concepts of probability and statistics. (P, D, M, G, N)
a. Interpret and construct frequency tables and charts.
b. Find mean, median, mode, and range of a given set of data.
c. Interpret and construct bar, line, circle graphs, and pictographs from given data.
d. Interpret and construct stem-and-leaf, box-and-whisker, and scatterplots from
given data.
e. Predict patterns or trends based on given data.
f. Use combinations and permutations in application problems.
g. Calculate and apply basic probability.
1. Apply the principles of graphing in the coordinate system. (P, D, M, G, N)
a. Identify the x- and y-axis, the origin, and the quadrants of a coordinate plane.
b. Plot ordered pairs.
c. Label the x and y coordinates for a given point.
d. Using tables, graph simple linear equations.
16
Course: 8
Unit Theme: Concepts and Basic Operations
Suggested Suggested
Comp. Obj. Teaching Strategies Assessment
1 a Use yarn to create a Venn diagram of natural, whole, Student work sample;
integers, rational, and irrational numbers. Choose an Observation
index card with a number on it and place in the correct
place.
1 b, e, f Use a number line to locate and compare numbers, Student work sample;
including absolute values and additive inverses. Teacher-made test
1 f, g Using a weather map, compare temperatures around Discussion;
5 c the country. Find differences and average weekly Student presentation
temperatures.
1 c, d, g Use maps, bus and plane schedules and fares, hotel Project;
rates, etc., to plan a vacation. Estimate total Rubric;
expenses. Teacher observation
17
Course: 8
Unit Theme: Number Sense
Suggested Suggested
Comp. Obj. Teaching Strategies Assessment
2 a Divide the class into two groups. A student from each Student work sample;
group goes to the board to work an order of operations Observation
problem. The first correct answer wins and marks the
tic-tac-toe board. Continue until one group wins.
2 b, c Distribute problems involving multiplying and dividing Constructed response;
like bases or powers of ten. Work in groups looking for Discussion;
a shortcut (a rule) for solving the problems. Discuss Teacher observation
how rules can make solving problems easier.
2 d, e Use magazines and newspaper articles to find Discussion;
examples of very large and very small numbers. Using Constructed response;
the examples, write the numbers in scientific notation, Teacher-made test
convert between standard form and scientific notation.
Using different combinations, multiply and divide the
numbers in scientific notation. Discuss the advantage
of writing these numbers in scientific notation.
2 f Play Jeopardy with powers, squares, and square roots. Teacher observation;
From an overhead transparency, select a category and Discussion;
point value. Allow calculators on some categories and Performance-based
point values.
2 Using grid paper, cut out squares presenting Rubric;
f Teacher observation
1 6
2 through 2 powers. Discuss characteristics of the
amount of squares and shapes that can be made from
them. Each time the exponent is reduced by 1, the
number of squares will be half. Emphasize 2° = 1.
18
Course: 8
Unit Theme: Expressions, Equations, and Inequalities
Suggested Suggested
Comp. Obj. Teaching Strategies Assessment
3 a Divide the class into two teams. On an overhead, Teacher observation;
write problems that can be solved easier by using Discussion
properties. For example: 25 6 4 25 4 6 .
One person from each team races to get the correct
answer. (Explain the use of properties with each
`
problem.) The team with the most number of correct
answers wins.
a, b, c, d, Play Algebraic Jeopardy. From an overhead Student work sample;
3 Teacher observation
e, f, h transparency, choose a category and point value (e.g.,
expressions for 40). Categories include expressions,
word phrases/sentences, properties, equations,
inequalities, or algebraic phrases/sentences. Points
range from 10 to 50 based on level of difficulty.
Answers must be in the form of a question. Team with
the most points when board is completed wins.
3 g Distribute a set of index cards containing inequalities. Teacher observation;
The set should contain pairs of inequalities that have Discussion
the same solution. Students solve and graph their
inequalities on a number line, then search for the
classmate with the same solution. Prizes or bonus
points could be given for the first few pairs to match.
19
Course: 8
Unit Theme: Ratio, Proportion, and Percent
Suggested Suggested
Comp. Obj. Teaching Strategies Assessment
4 a, b Count and record the number of boys and girls in the Student work sample;
class. Write ratio of boys to girls, girls to boys, girls to Discussion ;
total, etc. Convert the ratios to decimals and percents. Teacher-made test
4 a, b Play Percent Bingo. Make cards containing a column Discussion;
for ratios, decimals (two columns), and percents (two Teacher observation
columns). Draw a game piece and call it out. Players
cover all spaces (except the one called out) that have
3
the same meaning (e.g., 75% = .75 = 4 ). First player
to cover spaces vertically, horizontally, or diagonally
wins. Discuss winner's answers.
4 c, d Investigate the connections among test grades, total Presentation;
problems, and number correct. Use proportions to find Discussion;
how many problems would have to be correct on a 25 Observation;
problem test to make an A, B, C, D, F. Find how many Student work sample;
items were on the test if they made a grade of 80 and Rubric
got 12 correct. Find the grade when given the number
of problems on the test and the number correct.
4 e, f, g In groups, research local newspapers or businesses Student work sample;
about percent topics (commissions, sales, percent Teacher-made test
increase/decrease, interest) involving ways percent is
used in business. Allow a specified amount of time,
then have groups report findings to the class. Use
calculators to convert among fractions, decimals, and
percents involved in the groups findings.
(Extend: Invite a guest speaker to discuss this topic.)
20
Course: 8
Unit Theme: Measurement
Suggested Suggested
Comp. Obj. Teaching Strategies Assessment
5 a, c, d Design a deck to be added to a patio. Use basic ● Project;
6 c operations to find the perimeter and area and to find Rubric
the amount of materials needed for the job. Select
appropriate units of measurement.
5 b Given objects found in any classroom (e.g., books, ● Performance-based
paper clips, desktops), measure and find the assessment
dimensions of these objects.
21
Course: 8
Unit Theme: Geometry
Suggested Suggested
Comp. Obj. Teaching Strategies Assessment
6 a, b, c, d, Use manipulatives (e. g., D-Stix, plastic straws, flat Performance-based;
g, h spaghetti, or connectors) to construct angles, Student work sample
polygons, lines, triangles, and three-dimensional
figures. Discuss the characteristics of each.
6 c Use geoboards or cm grid paper to make or draw Performance-based;
shapes and find the perimeter and area (except Project;
circles). Trace or draw a circle on the grid paper and Student work sample;
use the above information to estimate the area and Observation
circumference of the circle. Introduce formulas and
have students calculate the area, perimeter, and
circumference using formulas.
6 d Use a protractor to draw and measure angles. Classify Performance-based;
each angle. Teacher-made test
6 e, f, g From given pictures, find the angle measure of Student work sample;
adjacent, vertical, complementary, and supplementary Discussion;
angles. Locate and identify corresponding and Presentation;
alternate interior and exterior angles. Classify Rubric
triangles and find missing angle measures. Draw one
line on each of two transparencies. Arrange them so
that they are parallel, then draw a transversal. Discuss
the angles formed. Move transparencies to prove
relationships among angles.
6 b, d, i Have students sketch right triangles on grid paper. Performance-based;
Use the Pythagorean theorem to find the measure of Teacher observation;
the hypotenuse. Verify the measure with a ruler or by Student work sample,
counting the squares on the grid paper. Teacher-made test
22
Course: 8
Unit Theme: Probability and Statistics
Suggested Suggested
Comp. Obj. Teaching Strategies Assessment
7 a, c Interview classmates to determine their favorite foods. Project;
Construct a frequency table and bar graph from the Student work sample
data.
5 a, d For each family member record age, height in inches, Performance-based;
7 b, d, e and birth month. Find mean, median, mode, and Project;
range of heights. Construct various plots from data Student work sample;
(e.g., scatter plot from height and age, and from height Discussion;
and month born, to determine if there is a correlation). Observation
Predict from height/age plots. Use the graphing
calculator to find the mean, median, and mode and to
construct histograms, scatter plots, and box and
whisker.
7 c Given a salary, plan a monthly budget, then construct Rubric;
a circle graph. Student work sample
7 f, g Use coins, number cubes, menu items, and group Performance-based;
memberships to calculate basic probability, Discussion;
combinations, and permutations. Student work sample
23
Course: 8
Unit Theme: Coordinate System
Suggested Suggested
Comp. Obj. Teaching Strategies Assessment
8 a, b, c, d Write a linear equation on the overhead. Give each Teacher observation;
row of the class different values to use in solving the Student work sample;
equation. Let one row choose their own values. When Teacher-made test
all have finished, have each row plot their points on a
wall coordinate grid. Discuss the reasons that all
points fall on the same line. If any points are not on
the line, look for mistakes in calculations or have the
class determine why the points are not on the line.
Discuss the x-axis, the y-axis, the quadrants, and their
characteristics.
8 a, b, c In pairs, listen to a selection of 20 song excerpts. ● Teacher observation;
Each student rates the song on a scale from –5 to 5 Rubric
based on whether or not they like the song. Using the
ratings, the partners form an ordered pair. Plot the
ordered pairs and discuss if partners are musically
compatible and use quadrants in discussion.
8 b, c, d Graph linear equations on graph paper and check for ● Student work sample;
accuracy using the graphing calculator. Teacher-made test
24
PRE-ALGEBRA
The Pre-Algebra course is to serve as a bridge between elementary mathematics
and Algebra. This course will build a foundation of algebraic concepts through the use
of manipulatives and cooperative learning. Concepts include algebraic expressions,
linear equations, polynomials, factoring, inequalities, geometry, statistics, and graphing.
Students will learn to utilize the graphing calculator in appropriate situations. Problem
solving, reasoning, estimation, and connections between math and everyday
applications will be emphasized throughout Pre-Algebra. This course is designed to
prepare students for Algebra I. This is a one credit course, if taken at the high school
level25 Explain, classify, and perform basic operations on the set of real numbers.
(P, D, M, G, N)
a. Classify numbers as natural, whole, integer, rational, irrational, and real.
b. Identify and apply the properties of real numbers (include the use of mental
mathematics and estimation methods).
c. Model absolute value of real numbers as a measure of distance.
d. Compare and order the real numbers and perform operations with rational
numbers.
e. Evaluate numerical and algebraic expressions using order of operations.
f. Convert between repeating decimals and fractions.
g. Recognize and evaluate perfect squares and approximate square roots.
2. Solve, check, and graph linear equations and inequalities in one variable.
(P, G, N)
a. Relate the language of mathematics to indicate mathematical operations.
b. Translate between verbal expressions and algebraic expressions.
c. Given an algebraic expression, write a corresponding real-life situation.
d. Simplify algebraic expressions by combining like terms and using the
distributive property.
e. Solve, check, and graph one-step and two-step linear equations and
inequalities.
f. Solve and check multi-step linear equations and inequalities with variables on
both sides involving the distributive property.
26 Recognize and perform basic operations on polynomials. (P, G, N)
a. Classify types of polynomials.
b. Determine the degree of polynomials.
c. Simplify polynomials by combining like terms.
d. Arrange polynomials in ascending or descending order of a variable.
e. Use the rules of exponents to multiply and divide monomials.
f. Use the rules of exponents to multiply monomials by polynomials.
g. Model and use the distributive property and rules of exponents to multiply
binomials by binomials.
h. Multiply and divide numbers involving scientific notation.
i. Use manipulative models to demonstrate operations of monomials and
polynomials.
4. Use ratios, proportions, and percents to solve problems. (P, M, G, N)
a. Represent, convert, and explain relationships among fractions, ratios, decimals,
and percents in problem solving.
b. Use proportions and equations to find part, rate, or base in real-world
situations.
c. Explain solutions and processes orally and in writing.
5. Use concepts of probability and statistics to interpret information. (P, D, G, N)
a. Model the Fundamental Counting Principle to determine possible outcomes of
an event.
b. Use combinations and permutations in application problems.
c. Calculate and apply basic probability.
d. Collect, display, analyze, and draw appropriate conclusions from data.
e. Interpret and construct stem-and-leaf, box-and-whisker, and scatter plots from
data.
27 Solve, check, and graph solutions of equations and inequalities in two
variables using the coordinate system. (P, D, M, G, N)
a. Given a set of ordered pairs, draw a coordinate system using an appropriate
scale.
b. Create a table to graph equations and inequalities that are presented in slope
intercept form.
c. Use calculators/computers to check accuracy of tables and graphs as
needed.
d. Identify slope as positive, negative, zero, or undefined from a graph.
e. Calculate slope from two points graphically and algebraically.
f. Identify x- and y- intercepts from a graph.
g. Identify the solution of a system of equations from a graph.
7. Use and apply properties and formulas to solve geometric problems. (P, D, M,
G, N)
a. Calculate perimeter, area, circumference, and volume using appropriate
formulas.
b. Recognize the irrational number pi (π) as the ratio of circumference to
diameter of any given circle.
c. Solve problems involving the use of the Pythagorean Theorem.
d. Classify triangles by sides and angles.
e. Use properties of similar triangles to solve problems.
f. Recognize and determine degree measure of angles formed by parallel lines
cut by a transversal.
g. Develop, extend, and model the relationships of faces, vertices, and edges of
three-dimensional figures.
h. Perform transformations on plane figures.
28
Course: Pre-Algebra
Unit Theme: Concepts and Basic Operations
Suggested Suggested
Comp. Obj. Teaching Strategies Assessment
1 a Make a Venn diagram of the real number system. ● Rubric;
Student work sample
1 b Given cards with variables, addition sign, multiplication ● Student response;
sign, parentheses, and equal sign written on them, Teacher observation
teams will arrange cards to create examples of
properties.
1 c Create a number line on the floor. Model │3│ by ● Teacher observation
walking from 0 to 3. Model │–3│ by walking from 0 to
-3. Same number of steps were taken, but in opposite
directions. Have students model other examples of
absolute value.
1 d Choose four students as Olympic Athletes. Choose ● Teacher observation;
seven students as judges. Students (athletes) Performance
compete in categories such as high jump, toe-touch, assessment
handstand, etc. Rank events according to difficulty
and assign degree of difficulty to each. Judges score
each athletes performance. Determine winners of
gold, silver, and bronze by removing low and high
score, total remaining five scores and multiply by
degree of difficulty.
1 d, e, f, g To each group distribute the recipe for Butterfinger pie ● Performance
in which the quantity of each ingredient is a numerical assessment
or algebraic expression to be evaluated. Expressions
should include decimals, fractions, perfect squares,
and square roots. Once the group has determined the
correct measurements make the recipe.
Recipe:
● 12 oz. cream cheese
● 12 oz. Cool Whip
● 6 crushed Butterfingers
Mix together in graham cracker pie crust.
29
ourse: Pre-Algebra
Unit Theme: Equations and Inequalities
Suggested Suggested
Comp. Obj. Teaching Strategies Assessment
2 a, b, c Brainstorm list of words that indicate math operations ● Student work sample;
including real-life words such as deduction, raise, in Rubric
addition. Encourage use of a thesaurus. Using the list
of words, write an algebraic expression that
corresponds to each word or combination of words.
Emphasize that some words may change meaning
depending upon context.
2 a, b, d Use algebra tiles to develop definitions of like terms. ● Discussion;
2
Explain that y and y are related because same color, Student work sample
but the exponent creates a square with each side
having a length of Y.
.
1 y
y y
2 e, f Progress from working problems using manipulatives ● Student work sample;
to abstract. Teacher-made test
2 e, f Use graphing calculators to solve equations ● Student response
graphically. Such as 2x 3 5x 4 .
2 e, f Play inequality BINGO Blackout. (see Glossary) Teacher observation
Distribute to students a Bingo Card that contains
fractions and decimals in each space. Give an
inequality for the students to solve. The students with
the correct answer on their card will cover the space.
The first person to cover spaces vertically, horizontally,
or diagonally will be declared the winner.
30
Course: Pre-Algebra
Unit Theme: Polynomials
Suggested Suggested
Comp. Obj. Teaching Strategies Assessment
3 a, d, i Give students a card with part of an algebraic ● Student response;
expression written on it. Have students line up to Discussion
create the given expression. Students will hold up the
cards and explain what they are and what they do.
3 b Make a set of 24 cards. The set should contain 12 ● Teacher observation
cards with polynomials written on them, all with
different degrees. The other 12 cards should have the
numerical degrees written on them. Turn all cards face
down and play ―Concentration‖ to form pairs that
match a polynomial to its corresponding degree.
3 c Use algebra tiles to illustrate combining like terms. ● Teacher observation;
Performance
assessment
3 e, f, g Use algebra tiles to model multiplication of monomials ● Performance
and polynomials. Each factor represents either the assessment
length or width of a rectangle. The area of the
rectangle formed is the answer.
.
1 d Use a graphing calculator to explore results of Rubric;
3 d,h multiplying and dividing numbers involving scientific Performance
notation. Students should discover the result of raising assessment
10 to a positive or negative power.
31
Course: Pre-Algebra
Unit Theme: Ratio, Proportion, and Percent
Suggested Suggested
Comp. Obj. Teaching Strategies Assessment
4 a, b, c Use a real estate guide to choose a house to ● Student work sample;
purchase. Given options such as 10% down payment, Rubric
1
20 year mortgage at a fixed rate of 7 2 , calculate down
payment, principal, interest, principal plus interest, and
monthly payment.
4 a, c Find examples of decimals, fractions, and percents in ● Rubric
the newspaper. Convert each example. Discuss pros
and cons for using each number form in its given
context.
4 a Explore the ―golden ratio‖ and its influence on artists, ● Project;
architects, and mathematicians throughout the years. Rubric
Students work in cooperative groups to construct
objects that use the ―golden ratio‖ in its design.
4 b, c Given a recipe that serves no more than six people, ● Rubric
convert it to serve the entire class. Explain each step.
32
Course: Pre-Algebra
Unit Theme: Probability and Statistics
Suggested Suggested
Comp. Obj. Teaching Strategies Assessment
5 a Given a packet of cut-out doll clothes such as pants ● Presentation;
and shirts in different colors, arrange clothes and Student work sample;
determine possible number of outfits. Develop the Teacher observation;
Fundamental Counting Principle. Discussion
5 b Have small groups determine the number of possible ● Presentation;
order arrangements for their group and compare with Discussion;
factorial. Extend to arrangement of students in a line Teacher observation
for permutations and combinations. Use calculators as
needed.
5 c, d Assign a number to each letter of the alphabet (some ● Discussion;
6 a positive, some negative, one zero). Write student Student work sample;
initials on different colored sticky dots and create Teacher observation
ordered pairs using the value given to the initials.
Place dots on graph board and calculate probability of
dots in each quadrant, colors in each quadrant, etc.
5 e Organize height of each student into stem- and leaf- ● Teacher observation
plot. Extension: Use graphing calculators to analyze
information by creating a box and whisker.
33
Course: Pre-Algebra
Unit Theme: Coordinate System
Suggested Suggested
Comp. Obj. Teaching Strategies Assessment
6 a, c Create an Etch-A-Sketch style figure on graph paper. Rubric
List the ordered pairs in the order necessary to
connect each ordered pair if they were vertices of the
figure. Enter the ordered pairs in the graphing
calculator and view the figure. Adjust the window and
scale appropriately to show entire figure.
6 b, c, f Using a graphing calculator, enter a linear equation. ● Teacher observation
Use table function (if available) or build a table to view
ordered pairs and determine intercepts.
6 d Indicate type of slope of the segments used in forming ● Discussion
capital letters.
6 e Use a meter stick and level to determine slope of ● Student work sample;
handicap ramp, stairs, and other structure examples Teacher observation
found on campus.
6 g Use a graphing calculator to determine solution to ● Teacher observation
system of equations.
34
Course: Pre-Algebra
Unit Theme: Geometry
Suggested Suggested
Comp. Obj. Teaching Strategies Assessment
1 a Calculate surface area of desk and textbook. Measure ● Project
7 d and cut contact paper to cover.
1 a Make a poster showing ratio of circumference to ● Student work sample
7 b diameter for circles of varying size.
1 c Measure distance at the baseball field from home plate ● Teacher observation
7 g to first base and first base to second base. Use the
Pythagorean Theorem to calculate distance from
second base to home plate. Measure actual distance
from second base to home plate and compare results
to calculation.
7 d Go on a scavenger hunt around campus to find ● Presentation
examples of different types of angles and triangles.
Identify examples according to classification.
4 e Have students measure their height and the length of ● Teacher observation;
7 b their shadow. Measure the shadow of an object such Discussion;
as a tree or flagpole. Use similar triangles to Student work sample
approximate height of object.
7 f Use masking tape on the floor to create parallel lines ● Teacher observation
cut by a transversal. Number the interior and exterior
angles 1 to 8. Play ―twister‖ by placing hands and feet
on indicated pairs of angles.
7 g Use tagboard and three-dimensional patterns to create ● Discussion;
polyhedra. Use as classroom, library, or office Student work sample
decorations.
7 h Use Miras to demonstrate symmetry, translations, ● Presentation;
rotations, and reflections of figures. After using Miras Student work sample;
to discover transformations, use centimeter grid paper Discussion;
to complete transformations from given figures. Teacher observation
(Extension: M. C. Escher video)
35
TRANSITION TO ALGEBRA
Transition to Algebra is an elective course intended to be a bridge between the
concrete concepts of Pre-Algebra and the abstract concepts of Algebra I and Geometry.
This course will be activity-based, allowing students to explore and investigate algebraic
and geometric concepts to build a stronger foundation of basic skills. Such explorations
should emphasize physical models, data, graphs, and other mathematical
representations in appropriate situations that facilitate the learning process. This course
is designed for those students who have completed Pre-Algebra and desire an
alternative before taking Algebra I instruction36 model real numbers and their properties. (P, M, G, N)
a. Identify the subsets of real numbers.
b. Compare, order, and locate real numbers on a number line.
c. Evaluate expressions with real numbers using order of operations emphasizing
integers, rational numbers, and absolute value.
d. Identify and demonstrate the properties of real numbers.
e. Model real-life situations using real numbers.
f. Evaluate powers, squares, square roots, and simplify non-perfect squares.
g. Multiply and divide numbers involving scientific notation.
2. Demonstrate the connections between algebra and geometry. (P, D, M, G, N)
a. Use formulas (e.g., perimeter, circumference, area, Pythagorean Theorem,
distance, midpoint, slope) to solve problems.
b. Reinforce formulas experimentally to verify solutions.
c. Given a formula, solve for a specified variable of degree one.
d. Apply ratios and proportions to solve problems.
e. Using an appropriate scale, plot a set of ordered pairs and identify the domain
and range.
f. Calculate and apply concepts of probability.
g. Explain and illustrate how changes in one variable may result in a change in
another variable.
3. Explain and communicate the language of algebra. (P, D, M, N)
a. Translate between verbal expressions and algebraic expressions.
b. Use convincing arguments to justify solutions.
c. Recognize and demonstrate the difference in ―evaluate,‖ ―simplify,‖ and ―solve.‖
37 Solve and graph equations and inequalities in one or two variables. (P, D, G, N)
a. Solve and check multi-step equations and inequalities, including distributive
property, variables on both sides, and rational coefficients.
b. Graph solutions to inequalities in one variable.
c. Graph linear equations, and investigate the concepts of slope and y-intercept.
d. Explore slope as a rate of change.
e. Discuss the differences between the solutions of linear equations and
inequalities.
f. Use appropriate technology to explore and identify families of graphs (e.g., x is a
line, x2 is a u shape, |x| is a v shape).
5. Model and simplify polynomials. (P, M, G, N)
a. Use manipulatives to model operations of polynomials.
b. Model polynomial operations to problems involving perimeter and area.
c. Use exponent rules to multiply and divide monomials.
d. Determine greatest common factor (GCF) and least common multiple (LCM) of
polynomials.
e. Arrange polynomials in descending or ascending order and determine the
degree.
38
Course: Transition to Algebra
Unit Theme: Real Numbers
Suggested Suggested
Comp. Obj. Teaching Strategies Assessment
1 a Show relationships using visual organizers among the Observation;
subsets of the set of real numbers. Rubric
1 b Distribute cards containing a rational or irrational Observation
number, arrange in order and justify placement. After
ordering, place cards on a number line.
1 c Have teams comprised of four students form numerical Self-assessment using
expressions to represent the numbers 1 to 26. Teams graphing calculator
will use grouping symbols, the digits 1,2,3, and 5 only
once, and the four basic operations to create the
expression.
1 d From a list of equations, identify the property illustrated Teacher-made test
by each.
1 e Prepare a poster illustrating the use of real numbers Rubric;
from examples found in newspapers, magazines, and Checklist
other resources. Write an explanation for each
example.
1 f Create a table with three columns. Self-assessment using
a calculator
Numbers Square Square number
1 1 1 = 1
2 4 4 = 2
15 225 225 = 15
Use the table to estimate the square root of non-perfect
squares.
1 g Use the graphing calculator in scientific model to Self-assessment using
discover rules for multiplying and dividing numbers in graphing calculator
scientific notation.
39
Course: Transition to Algebra
Unit Theme: Connections
Suggested Suggested
Comp. Obj. Teaching Strategies Assessment
2 a Given a formula, explain orally and in writing, Observation;
representations of the variable and the process for Rubric
applying the formula.
2 a, b Relate the midpoint formula to the average of two Observation
grades by graphing the two grades and the average on
a number line and emphasizing the location of the
average.
2 a, b, g Using a compass, construct a circle with a given radius. Observation
Use the formula to calculate area, and verify by
estimating the area using the grid. Explain the
increase to area if the radius is doubled or tripled.
2 a, b, e Plot two points on a coordinate plane. Use the ● Observation
Pythagorean Theorem to find distance. Show how the
distance formula is derived from the Pythagorean
Theorem.
2 c Working in pairs, one student runs a specified distance Rubric
while another uses a stopwatch to measure the time.
Replace the distance run, and time in the formula to
determine speed.
2 d Use scale drawings to determine actual Teacher test;
measurements. Rubric
2 f Using a deck of cards, calculate the probability of Observation
drawing a specific card from the deck.
40
Course: Transition to Algebra
Unit Theme: Communication
Suggested Suggested
Comp. Obj. Teaching Strategies Assessment
3 a Make charts of words that indicate various operations. Rubric
Note difference among ―more than,‖ ―less than,‖ ―is
more than,‖ and ―is less than.‖
3 b Given a solved equation with mistakes, verify and Observation;
4 a explain why process is incorrect. Rubric
3 c Given several expressions and equations, sort and Observation
classify according to the term ―evaluate,‖ ―simplify,‖ and
―solve.‖
41
Course: Transition to Algebra
Unit Theme: Graphing
Suggested Suggested
Comp. Obj. Teaching Strategies Assessment
4 a Use manipulatives (e.g., algebra tiles or blocks) to Observation
model processes used to solve equations.
4 a, b List ten solutions to an inequality and graph on a Observation
number line. Show other possible solutions by
shading.
4 c Graph linear equations on a graphing calculator to Self-assessment on
explore slope and y-intercept. graphing calculator
4 d Using a graphing calculator, enter Observation;
y x, y 2 x, y 1
x , and y 1
x , one at a time. Student response
2 4
Explore what happens with the steepness of each line.
4 c, e Graph an equation such as y 3 2 . Have Observation
students choose solutions from a set of given ordered
pairs (sticky notes on board work well) and place them
in the correct place on the graph. Next, change the
equation to an inequality and repeat procedure.
Compare and contrast the equation and inequality.
4 f Explore graphs of simple linear, quadratic, and ● Observation
absolute value equations on graphing calculators.
Students will model the graphs represented on the
calculator, using their arms.
42
Course: Transition to Algebra
Unit Theme: Polynomials
Suggested Suggested
Comp. Obj. Teaching Strategies Assessment
5 a Use algebra tiles to show differences among Observation
" x x" and " x x", " x y" and " x y", "( y 1) x"
and "( y 1) x"
2 a Given a rectangle of specific length and width, extend Observation;
5 b length and width by a variable and calculate new Constructed response
perimeter and area in terms of the variable.
5 c Use expanded notation to multiply or divide monomials. Teacher test
For example:
x6 x x x x x x
x x x x x4
x 2
x x
5 d Use factor trees and charts to determine GCF and Teacher test
LCM.
5 e On index cards, write terms of a two or three variable Observation
polynomial. Order terms in descending or ascending
order and determine degree.
43
ALGEBRA I
The Algebra I course will provide opportunities for students to develop and
communicate an understanding of algebraic representation as a prerequisite to all
higher mathematics courses. Concepts covered in this course include real numbers
and their properties, functions, algebraic expressions, linear equations and inequalities,
systems of equations and inequalities, graphing polynomials, formulas, slope, data
analysis and probability. The use of graphing calculators will be an integral part of this
course. This course is designed to prepare students for Geometry and/or Algebra II.
This44 use real numbers and their properties. (P, M, N)
a. Describe the real number system using a diagram to show the relationships of
component sets of numbers that compose the set of real numbers.
b. Model properties and equivalence relationships of real numbers.
c. Demonstrate and apply properties of real numbers to algebraic expressions.
d. Perform basic operations on square roots excluding rationalizing denominators.
2. Recognize, create, extend, and apply patterns, relations, and functions and
their applications. (P, D, G, N)
a. Analyze relationships between two variables, identify domain and range, and
determine whether a relation is a function.
b. Explain and illustrate how change in one variable may result in a change in
another variable.
c. Determine the rule that describes a pattern and determine the pattern given
the rule.
d. Apply patterns to graphs and use appropriate technology.
3. Simplify algebraic expressions, solve and graph equations, inequalities and
systems in one and two variables. (P, D, G, N)
a. Solve, check, and graph linear equations and inequalities in one variable,
including rational coefficients.
b. Graph and check linear equations and inequalities in two variables.
c. Solve and graph absolute value equations and inequalities in one variable.
d. Use algebraic and graphical methods to solve systems of linear equations and
inequalities.
e. Translate problem-solving situations into algebraic sentences and determine
solutions.
45 Explore and communicate the characteristics and operations of polynomials.
(P, M, G, N)
a. Classify polynomials and determine the degree.
b. Add, subtract, multiply, and divide polynomial expressions.
c. Factor polynomials using algebraic methods and geometric models.
d. Investigate and apply real-number solutions to quadratic equations algebraically
and graphically.
e. Use convincing arguments to justify unfactorable polynomials.
f. Apply polynomial operations to problems involving perimeter and area.
5. Utilize various formulas in problem-solving situations. (P, D, M, G, N)
a. Evaluate and apply formulas (e.g., circumference, perimeter, area, volume,
Pythagorean Theorem, interest, distance, rate, and time).
b. Reinforce formulas experimentally to verify solutions.
c. Given a literal equation, solve for any variable of degree one.
d. Using the appropriate formula, determine the length, midpoint, and slope of a
segment in a coordinate plane.
e. Use formulas (e.g., point-slope and slope-intercept) to write equations of lines.
6. Communicate using the language of algebra. (P, D, M, G, N)
a. Recognize and demonstrate the appropriate use of terms, symbols, and
notations.
b. Distinguish between linear and non-linear equations.
c. Translate between verbal expressions and algebraic expressions.
d. Apply the operations of addition, subtraction, and scalar multiplication to
matrices.
e. Use scientific notation to solve problems.
f. Use appropriate algebraic language to justify solutions and processes used in
solving problems.
467. Interpret and apply slope as a rate of change. (P, D, M, G, N)
a. Define slope as a rate of change using algebraic and geometric
representations.
b. Interpret and apply slope as a rate of change in problem-solving situations.
c. Use ratio and proportion to solve problems including direct variation b kxg
y .
d. Apply the concept of slope to parallel and perpendicular lines.
8. Analyze data and apply concepts of probability. (P, D, M, G, N)
a. Collect, organize, graph, and interpret data sets, draw conclusions, and make
predictions from the analysis of data.
b. Define event and sample spaces and apply to simple probability problems.
c. Use counting techniques, permutations, and combinations to solve probability
problems.
47
Course: Algebra I
Unit Theme: Real Numbers
Suggested Suggested
Comp. Obj. Teaching Strategies Assessment
1 a Write a journal, paragraph, or story to explain how the Rubric
set of real numbers is like a family tree.
1 b Write each of the following on small individual paper Teacher observation
squares: A, A, B, B, C, C, -, +, x, , IF, and THEN, =,
( ), and 0. Use these to model properties and
equivalence relationships.
1 c Create foursomes such as: Teacher test;
6 f Constructed response
3 x 4 3x 12 3x 2 x 5x
Distributive Property 5x 3 3 5x
Which one does not belong? Explain.
1 d Find the perimeter and area of a rectangle with radical Teacher test
terms as dimensions.
1 b, c, d Use and identify appropriate properties to explain a ● Teacher test;
6 f computational procedure. Extension: Given a real Constructed response
world or mathematical problem identify the operational
strategies involved and justify.
48
Course: Algebra I
Unit Theme: Patterns
Suggested Suggested
Comp. Obj. Teaching Strategies Assessment
2 a, b, d Using equations involving rational numbers, such as Rubric
7 a y .05x to represent the value of x nickels, explore
how changes in x affect y. Identify domain as nickels
and range as value. Use a T-chart to graph the relation
and verify with graphing calculator.
2 c Use algebraic expressions to represent consecutive Rubric
even or odd even integers that have a particular sum.
Given a set of consecutive even or odd integers, write
a verbal expression to represent the set.
49
Course: Algebra I
Unit Theme: Graphing
Suggested Suggested
Comp. Obj. Teaching Strategies Assessment
3 a Use manipulatives (e.g., algebra tiles or algeblocks) to Teacher test
model the process of solving linear equations. Check
solutions using the graphing calculator or substitution.
3 b Group students in pairs. Give each pair a set of linear Observation
equations directing one student to graph using a
graphing calculator and the other not using a
calculator. Compare results and switch roles.
3 c Create a ―zero finder‖ as pictured to illustrate the Teacher test
absolute value as a distance from the origin. For
example:
x2 5
5 4 3 2 1 0 1 2 3 4 5
3 2 1 0 1 2 3 4 5 6 7
Position with zero on the zero finder above the two on
the number line because two makes the expression
inside the absolute value zero. The solutions to the
equation are five units from two on the number line.
3 d Use colored pencils to sketch and shade systems of Teacher test
linear inequalities.
3 d Use Algebra Tiles and the graphing calculator to solve Rubric
systems of equations.
3 d Compare solutions of systems of equations versus Observation
inequalities. Use the graphing calculator to explore the
different outcomes.
3 e Create constructed response items that involve Teacher test;
translating problem-solving situations into algebraic Rubric
sentences. Have students solve and exchange papers.
-
50
Course: Algebra I
Unit Theme: Polynomials
Suggested Suggested
Comp. Obj. Teaching Strategies Assessment
4 a On each wall of the classsroom, put the classifications Observation
6 a of polynomials. Write assigned polynomials on index
cards and place on the correct wall. In groups of four,
assign a degree to each group and have them create a
polynomial of that degree and present to large group.
4 b, c, f Given a rectangle of given length and width, extend the Teacher test
length and width by a variable and find the perimeter
and area. Given the area of a rectangle in one
variable, find the length and width.
4 b Use the algebra tiles to model operations with Teacher test
polynomial expressions.
4 c, d Use the quadratic formula to solve trinomial Teacher test
equations, and use solutions to write binomial factors.
4 d Graph quadratic equations on a graphing calculator to Teacher test
relate the x-intercepts to solutions.
4 e Use a graphing calculator to graph a quadratic Teacher test
6 f equation with no x-intercepts. Relate to the
connections among x-intercepts, real solutions, and
factors.
4 b, c, f Use algebra tiles to determine factors of a polynomial ● Observation
expression.
4 b, c, f Use algebra tiles to create a rectangle of any area. ● Constructed response
5 a Determine the dimensions and perimeter of the
sketched rectangle.
51
Course: Algebra I
Unit Theme: Formulas
Suggested Suggested
Comp. Obj. Teaching Strategies Assessment
5 a, b Given a cardboard box, measure the length, width and Rubric;
height to determine perimeter of a side, area of a side, Teacher test
and volume of the box. Find the diagonal of a side of
the box. Extension: Determine the relationship
between the dimensions of the box and the volume of
the box.
5 a, b Determine and justify comparable pricing for different Presentation;
6 f size pizzas. Rubric
5 a, d Plot two points in a coordinate plane and use formulas Teacher test
to calculate length, midpoint, and slope. Make
comparisons among the formulas used for calculations.
5 c, e On index cards, write variables, symbols, operations, Observation
and the equal sign, one per card. As formulas are
given verbally, demonstrate by holding up appropriate
index cards. EXTENSION: In pairs, demonstrate the
―Golden Rule of Algebra‖ to solve for lengths using the
perimeter formula.
5 e Draw a line segment with endpoints in different ● Teacher test
quadrants. Choose the appropriate formula to write the
equation of the line formed using the line segment.
Explain and show how standard form, point-slope
formula, and slope-intercept formula are related.
52
Course: Algebra I
Unit Theme: Communication
Suggested Suggested
Comp. Obj. Teaching Strategies Assessment
6 a, b Given several equations, classify as linear or non-linear Observation;
and verify with a graphing calculator. Teacher test
6 c From two lists, match the algebraic expressions to their Rubric;
corresponding verbal expressions. Extension: Create a Teacher test
real-world problem using the corresponding matched
algebraic and verbal expressions.
6 d Using two different brands of regular and diet soft Teacher test
drinks arrange the price of each in matrix form and
show the price doubling by using scalar multiplication.
6 a, e Using states that are rectangular in shape, estimate Presentation
their actual area in square feet. Express the estimated
area in scientific notation.
6 e, f Explore problems involving scientific notation using the ● Rubric
graphing calculator. Explain the difference between
multiplying by a positive power of ten and by a negative
power of ten.
6 a, e, f Give examples of large numbers or small numbers ● Rubric
containing more than three non-zero digits correctly
represented in scientific notation. Explain and justify
each example.
53
Course: Algebra I
Unit Theme: Slope
Suggested Suggested
Comp. Obj. Teaching Strategies Assessment
7 a, b Relate income to the number of hours worked in Teacher test
equations such as:
y $5.25x and y $15.85x
Use the graphing calculator to compare the change of
income (y) as it relates to the change in hourly wage
(slope).
7 a, b Place a yardstick across the incline of a set of steps. Rubric
Measure the vertical change versus the horizontal
change, then explore how changing these distances
affect the steepness of the steps.
7 c Using a bicycle, demonstrate how the revolutions of the Teacher test
pedal and the rear wheel illustrate the concept of direct
variation. For example, y 3x . (In a particular gear
perhaps the ratio is 3 to 1)
x = number of revolutions of pedal
y = number of revolutions of rear wheel
Using a graphing calculator, graph a series of Observation
7 d
equations to discover the relationship of slope to
parallel and perpendicular lines.
54
Course: Algebra I
Unit Theme: Probability
Suggested Suggested
Comp. Obj. Teaching Strategies Assessment
8 a In groups, assign each a topic from which to design Rubric
and conduct a survey. Compile, graph, and interpret
results and present to class. Extension: Use computer
graphing software to organize collected data.
6 a Define ―events‖ and ―sample space‖ for experiments Observation
8 b involving number cubes, spinners, coin flipping, and
cards.
6 f Determine how many handshakes there would be ● Rubric
8 c between five people if everyone had to shake hands
with each person exactly once. Explain or sketch how
the answer was determined.
55
GEOMETRY
The Geometry course is the study of two and three-dimensional figures. This
course will provide the opportunity for students to develop spatial sense and reasoning
skills. Students will use the language of geometry to communicate an understanding of
the properties and characteristics that encompass geometry. Students will also
investigate patterns and relationships among geometric shapes. This course is
designed for students who have successfully completed Algebra I. This is a one-credit write their own objectives to meet the
needs of students in their school district.
56 Communicate using the language of geometry. (P, M, G, N)
a. Define and recognize terms and symbols of geometry and use them to
communicate mathematical ideas.
b. Differentiate between inductive and deductive reasoning.
c. Use properties, theorems, postulates, and definitions to justify relationships
involved with segment and angle congruence.
d. Develop and evaluate mathematical arguments and proofs.
2. Identify, explore, discuss, and apply properties, theorems, postulates, and
definitions related to angles, lines, and circles. (P, M, G, N)
a. Identify and classify angles.
b. Identify, explore, and apply angle relationships formed by parallel lines cut by a
transversal.
c. Explore, discuss, and apply the relationships among parts of a circle and
between arcs and angles.
d. Use angle and segment relationships to find unknown measures related to
circles.
3. Identify, explore, discuss, and apply properties, theorems, postulates, and
definitions related to polygons. (P, M, G, N)
a. Identify and name different types of polygons and their subsets.
b. Classify triangles and apply postulates and theorems to test for triangle
congruence and triangle inequality.
c. Identify altitude, median, angle bisectors, and perpendicular bisectors in a
triangle.
d. Apply definitions, postulates, and theorems to find angle measurements in
polygons.
57 Explore and demonstrate the connections between algebra and geometry. (P,
M, G, N)
a. Apply ratios and proportions to solve for unknown measures in similar polygons.
b. Solve for missing measurements in right triangles using the Pythagorean
Theorem, special right triangle relationships, geometric mean, and trigonometric
functions.
c. Relate algebraic formulas to geometric properties to solve problems in the
coordinate plane.
d. Explore how change in perimeter results in a change in area.
5. Investigate, classify, compare, and contrast two and three-dimensional
geometric figures. (P, M, G, N)
a. Find the areas of triangles, quadrilaterals, and regular polygons.
b. Find the area and circumference of a circle.
c. Find the volumes of rectangular prisms, cylinders, pyramids, cones, and spheres.
d. Use protractors, compasses, rulers, and/or technology to construct geometric
figures and drawings.
e. Compare, contrast, and classify two-dimensional figures and investigate their
characteristics.
f. Compare, contrast, and classify three-dimensional figures and investigate their
characteristics.
g. Use measurement to design and build a three-dimensional object.
6. Explore applications of patterns and transformational geometry. (P, D, M, G,
N)
a. Identify symmetry in common objects as examples of point, line, and rotational
symmetry.
b. Create designs using symmetry.
c. Recognize and describe images of figures obtained by applying reflections,
translations, rotations, and dilations.
d. Create tessellations using translations and rotations.
e. Determine the effect of scale factors on dilations.
f. Use geometric probability to predict results.
58
Course: Geometry
Unit Theme: Communication
Suggested Suggested
Comp. Obj. Teaching Strategies Assessment
1 a As an on-going project, create a book consisting of Project;
illustrations, real-life examples, and applications Rubric
illustrating terms and symbols of geometry.
1 b Given situations that require logical thinking, classify Teacher test
as inductive or deductive reasoning.
1 c, d On index cards, write statements and reasons to a two Rubric
column proof (one per card). Shuffle, distribute, then
have students put in logical order.
59
Course: Geometry
Unit Theme: Segment and Angle Relationships
Suggested Suggested
Comp. Obj. Teaching Strategies Assessment
1 a Use a protractor to measure angles and classify Observation;
2 a according to definitions. Teacher test
5 d
1 a, c Construct a moveable model of parallel lines cut by a Observation
2 b transversal from three strips of tagboard fastened
5 d together with brads. Measure the various angles and
show the relationship among the angles.
1 a Create a display illustrating parts of a circle, their Rubric
2 a, c definitions and properties.
5 d
1 a, c, d Construct a circle of any radius. Use a straight-edge Observation;
2 c, d to draw various angles formed by segments. Use a Teacher test
5 d protractor to measure and draw conclusions about
formulas used to find these unknown measures. (Can
be enhanced with appropriate technology.)
60
Course: Geometry
Unit Theme: Polygons
Suggested Suggested
Comp. Obj. Teaching Strategies Assessment
1 a Design mobiles that illustrate the shape and Rubric
3 a characteristics of quadrilaterals.
5 e
1 a, c, d Given labeled sets of triangles, match to the Teacher test
3 b appropriate congruence postulate or theorem.
1 c, d Given three straws of different lengths, explore the Observation
3 b question: ―Is it always possible to form a triangle?‖
3 c Fold different types of triangles to illustrate medians, Observation
altitudes, and bisectors.
1 a, c Draw a polygon. Connect a vertex to the non-adjacent Teacher test
3 a, b, d vertices and form triangles. Discover the polygon
interior angle theorem by counting the triangles and
finding the sum of angles.
61
Course: Geometry
Unit Theme: Connections
Suggested Suggested
Comp. Obj. Teaching Strategies Assessment
1 a, d Given two similar polygons, use highlighters to color Teacher test
4 a code corresponding parts; set up ratios and
proportions to find unknown measures.
4 a Use actual measures of a room in the school or home Rubric
5 d, g to make a scale drawing. Build a scale model of the
room.
1 a, c Plot four vertices of a quadrilateral in a coordinate Rubric;
3 a plane. Use algebraic formulas to classify the Checklist
4 c quadrilateral and justify the conclusion.
5 e
1 a Form a square with string. Measure a side and Observation;
4 d calculate perimeter and area. Cut the string in half and Rubric
5 a repeat procedure. Record results and determine
relationship between change in perimeter and resulting
area.
62
Course: Geometry
Unit Theme: Two and Three-Dimensional Figures
Suggested Suggested
Comp. Obj. Teaching Strategies Assessment
5 a, e Given a variety of regular polygons, compare and ● Student work
justify the relationship between the number of sides samples;
and the number of diagonals. Rubric
1 a, c Construct a circle and inscribe a regular polygon of n Teacher test
5 a, b, d sides. Estimate area then calculate actual area by
using the Area of Regular Polygon Theorem.
1 a Construct a single square with straightedge and Presentation;
5 a, d, e compass using least number of steps as possible. Project;
Write instructions for the created construction. Rubric
5 b, c Measure and calculate the volume of cans of various Teacher test
sizes in metric units. Test calculations by filling with
water. (1cc = 1ml)
1 c, d Design and construct models of geometric solids and Project; Rubric
5 d, f create a table illustrating the relationship among faces,
edges, and vertices of the solids.
63
Course: Geometry
Unit Theme: Patterns or Transformations
Suggested Suggested
Comp. Obj. Teaching Strategies Assessment
1 a Collect logos from newspapers and magazines and Rubric
6 a identify types of symmetry.
1 a Given an example of optical art: discuss symmetry Teacher test;
6 a, b involved to include features of the work and its relation Presentation;
to symmetry groups. Extension: In groups, create a Rubric
similar revision of an optical art.
6 b Draw half of a symmetrical design, exchange designs Observation
and complete the drawing using vertical line symmetry.
1 a Design an original border on graph paper that Rubric
6 c incorporates reflections, translations, and rotations.
1 a Sketch a figure in the coordinate plane. Place the Observation
6 c, e vertices in a matrix . Apply scalar multiplication to
obtain vertices of the dilated figure.
1 a Use pattern blocks to create tessellations. Investigate Project;
6 d works of M. C. Escher and use them as a model to Rubric
create original tessellations.
6 f Divide a poster board into several rectangular regions. Observation
Calculate the probability of a tossed penny landing in a
particular region.
64
SURVEY OF MATHEMATICAL TOPICS
Survey of Mathematical Topics is designed to provide students with the skills
necessary in making wise financial decisions. The basic concepts of algebra will be
reviewed and extended as students solve real-life problems which affect them and their
families. This course will provide skills in probability and statistics, logic, linear
programming, and regression analysis. Students are encouraged to use a variety of
techniques and appropriate technology (calculators and/or computers) to solve
problems. This course is designed for students who have successfully completed
Algebra I, Geometry, and/or65 the skills necessary to manage personal finance. (P, D, M, N)
a. Develop a household budget.
b. Maintain and balance a checkbook.
c. Investigate terminology and the process of filing personal income tax.
d. Investigate and explore all the components necessary to own and operate a car.
e. Analyze the options of housing alternatives.
f. Connect and apply appropriate algebraic formulas to personal finance situations.
2. Compute, analyze, and develop a variety of personal and business
investments. (P, D, M, N)
a. Analyze information to make wise decisions regarding personal savings.
b. Investigate life and health insurance.
c. Study and investigate the economics of the stock market.
d. Connect and apply appropriate algebraic formulas to personal and business
investments.
3. Analyze and illustrate the practices that affect employer and employee
decision-making. (P, D, M, G, N)
a. Compute and compare various forms of earnings and calculate gross pay,
deductions, and net pay.
b. Analyze the relationships among cost, revenue, and profit.
c. Apply linear programming to business decisions.
d. Connect and apply appropriate algebraic formulas to employer and employee
practices.
4. Demonstrate an understanding of the impact of consumer credit. (P, D, M, G,
N)
a. Compare and contrast the finances of credit cards.
b. Explore the pros and cons of installment loans.
c. Connect and apply appropriate algebraic formulas to consumer credit.
66 Collect and apply information in planning a trip. (P, D, M, G, N)
a. Investigate and evaluate modes of transportation.
b. Create a travel budget.
c. Make travel plans based upon airline schedules.
d. Utilize map-reading skills.
e. Connect and apply appropriate algebraic formulas to planning a trip.
67
Course: Survey of Mathematical Topics
Unit Theme: Personal Finance
Suggested Suggested
Comp. Obj. Teaching Strategies Assessment
1 a Create a budget for a family of four with a given yearly Student work sample
income.
1 b Use simulated checks, check registers, and Portfolio
reconciliation forms to maintain a checking account
and to reconcile the checkbook with the bank
statement.
1 c Obtain copies of 1040EZ and 1040A forms and Discussion
instruction booklets from the IRS or local library. In
groups, discuss the forms and provide sample
information for students to complete both forms.
1 d Create a poster with the following headings for six Project;
used cars cut out from newspaper advertisements: Rubric
Sticker price
Down payment (use 10% )
Loan amount
Monthly payments (use current interest rate and
three years for loan)
Total payments
Total amount including down payment
Use a calculator and the monthly payment formula to
complete the poster. Justify which car would be the
best buy after verifying the condition of the car by
visiting the dealership offering the car.
1 e Investigate the following for each of ten local Presentation
apartments for rent:
Square footage
Monthly rent
Number of bathrooms
Number of bedrooms
Using a graphing calculator, calculate linear regression
and find the line of best fit to compare any two
apartments. Use this information to make predictions.
1 f Use a calculator and the appropriate formula to Student work sample
compute monthly payments when buying a car or
house.
68
Course: Survey of Mathematical Topics
Unit Theme: Personal and Business Investments
Suggested Suggested
Comp. Obj. Teaching Strategies Assessment
2 a Visit local banks to gather information on savings Project
accounts. Prepare a poster, which compares the data.
2 b Invite an actuary or local insurance agent to speak to Teacher observation
the class concerning life and health insurance policies.
2 c Contact the Mississippi Economic Council (MEC) for Portfolio
information on participating in the state Stock Market
Game.
2 d Suppose that ancestors deposited $1 in a savings Discussion
account 200 years ago. Using simple interest of 3% ,
calculate the value of that account today. Repeat
using compound interest. Discuss the results.
(Extend: Vary the amount originally deposited and/or
the interest rate.)
2 d Use the Rule of 72 to estimate how long it would take Student work sample
to become a millionaire with an initial deposit of $1000
with an interest rate of 10% . Repeat varying interest
rates and initial deposit.
69
Course: Survey of Mathematical Topics
Unit Theme: Employer/Employee Practices
Suggested Suggested
Comp. Obj. Teaching Strategies Assessment
3 a Find gross pay based on commission sales and hourly Short answer
rate. Use federal and/or state tax tables and FICA questions
percentage rate to calculate deductions and net pay.
3 b Find the break even point given cost and revenue Constructed response
equations. Analyze the regions between the two
curves when graphed.
3 c Use the method of linear programming to maximize or Student work sample
minimize certain factors in a business situation.
3 d Research different types and financial amounts of Checklist
fringe benefits offered by local employers. Using this
data, compute additional costs associated with
employment.
70
Course: Survey of Mathematical Topics
Unit Theme: Consumer Credit
Suggested Suggested
Comp. Obj. Teaching Strategies Assessment
4 a Collect several credit card applications. Compare ● Discussion
terms, finance charges, APR, etc. Determine which
application is the most advantageous to the consumer
4 b Create an amortization schedule to illustrate the ● Student work sample
concept of installment loans.
4 b Investigate car buying options involving rebates versus ● Discussion
the offer of an extremely low interest rate. Discuss the
advantages/disadvantages of each option for the
dealer, loan institution, and buyer.
4 c Use the Rule of 78 to estimate the savings when a ● Short answer question
loan of $1000 for 12 months at 7% is paid off after
four months.
71
Course: Survey of Mathematical Topics
Unit Theme: Travel
Suggested Suggested
Comp. Obj. Teaching Strategies Assessment
5 a, b, c Plan a trip to a far away city within the 48 contiguous Presentation;
United States. Decide on destination and length of Project;
trip. Call a travel agent (or use the Internet) to Rubric
compare various modes of transportation for cost and
time constraints. Prepare a budget of anticipated
expenses.
5 d, e Obtain state maps for each student. Given two Teacher observation;
locations on the map, discuss the best route to travel Discussion
from one location to another. Calculate the costs of
driving a car to this destination. Discuss the pros and
cons of driving versus other modes of transportation.
72
ALGEBRA II
The Algebra II course is to serve as an extension of Algebra I with a variety of
topics explored in greater depth. It will continue to provide opportunities for students to
become mathematical problem solvers, to gain confidence in their ability to use
mathematics, to learn to communicate and reason mathematically, to generalize when
appropriate, and to make mathematical connections. Technology, especially graphing
calculators, should be incorporated throughout this course. This course is designed for
students who have successfully completed Algebra I and/or Geometry. This is a one-
73 Explore the relationships among coefficients, exponents, degree and roots of
equations. (P, M, G, N)
a. Use acronyms such as SOPPS (Square, Opposite sign, Product, Plus, Square)
to teach the sum/difference of cubes.
b. Solve and explore equations using the quadratic formula, completing the square,
synthetic division, graphing, and technology.+
c. Classify solutions of quadratic equations through observations of graphs and
through use of the discriminant.
d. Write a polynomial equation when given its roots.
2. Solve systems of equations and inequalities and interpret solutions. (P, D, M, G,
N)
a. Explore methods of solving systems of equations to include algebraic methods
and matrices.
b. Write a system of equations to solve a problem.
c. Interpret by graphing, and solve systems of inequalities.
d. Introduce linear programming as a method to solve problems.
3. Recognize, classify, and perform operations with irrational and complex
numbers. (P, G, N)
a. Explore and describe the complex number system.
b. Explain and apply complex conjugate methods to simplify problems.
c. Perform operations with complex numbers and review radicals.
74 and investigate relations and functions. (P, D, M, G, N)
a. Determine the domain, range, roots, and inverse of a function.
b. Recognize and determine graphs of linear, quadratic, absolute value, greatest
integer, and piece-wise functions.
c. Develop a complex coordinate plane for complex numbers (a + bi) where reals
are represented on the x-axis and imaginary units are represented on the y-axis
and model operations of complex numbers.
d. Evaluate functions including composite functions.
e. Explore and investigate solutions to compound and absolute value inequalities to
include interval notation.
f. Use scatter plots and apply regression analysis to data.
5. Investigate rational expressions and equations. (P, D, M, G, N)
a. Perform basic operations and simplify rational expressions to include complex
fractions.
b. Solve and verify solutions to equations involving rational expressions.
c. Analyze problems involving direct, inverse, joint, and combined variations.
6. Solve, graph, and apply the properties of exponential and logarithmic
expressions and equations. (P, D, M, G, N)
a. Illustrate and apply the relationships between exponential and logarithmic
functions.
b. Simplify radical, exponential, and logarithmic expressions.
c. Solve equations involving radicals, exponents, and logarithms.
d. Collect, organize, and interpret data from exponential, logarithmic, and power
functions.
757. Identify characteristics and extend operations and applications of matrices.
(P, D, N)
a. Explain dimensions of a matrix.
b. Find the inverse and determinant of a matrix.
c. Solve for unknown values in corresponding elements of equal matrices.
d. Perform basic operations and apply to matrices.
76
Grade Level: Algebra II
Unit Theme: Equations
Suggested Suggested
Comp. Obj. Teaching Strategies Assessment
1 a Work problems and explain the process of factoring ● Small group
sum/difference of cubes. observation
1 b Divide the class into groups. On individual cards, list Small group
steps for deriving the quadratic formula by completing observation
the square. Distribute one set each to be ordered in
the proper sequence.
1 b In small groups, solve a given equation using at least Teacher observation
four different methods. Have each student write a
report explaining steps involved in each method.
Designate and justify the preferred method.
1 c Provide to each student a list of quadratic equations. Self-evaluation using
Using a graphing calculator, graph equations, observe graphing calculators
the number of times the graph crosses the x-axis, then
relate to roots and x-intercepts.
1 d Create a matching set of cards (one with equations Teacher observation
and one with corresponding roots). Divide class into
groups and provide each a set of cards to match each
equation with its roots.
77
Grade Level: Algebra II
Unit Theme: Systems of Equations
Suggested Suggested
Comp. Obj. Teaching Strategies Assessment
2 a In groups, solve systems of equations simultaneously Teacher observation
using different methods. Compare and discuss
solutions and the preferred process. Exchange
methods and repeat until each student has used every
method at least once.
2 b Fill a bag with two types of candy bars costing x Student work sample
amount and y amount. On the outside of the bag,
write the total number of candy bars and the dollar
amount. Determine the number of each type.
2 c, d As an introduction to cost and profit linear Teacher observation
programming problems, invite a businessman from
industry to speak to the class.
78
Grade Level: Algebra II
Unit Theme: Irrational and Complex Numbers
Suggested Suggested
Comp. Obj. Teaching Strategies Assessment
3 a Given 1 sheet of cardboard, design and decorate a Rubric
4
math flag to represent the different sets of numbers to
show how each set relates. Tape to the bottom of a
wire hanger and display in the classroom.
3 b Given a problem that has been simplified incorrectly, ● Constructed response
find the mistake and explain how to correct it.
3 c Discuss the history of complex numbers and their ● Teacher observation
relationship to the Fundamental Theorem of Algebra.
Extension: Discuss the relationship of complex
numbers and fractals.
79
Grade Level: Algebra II
Unit Theme: Relations and Functions
Suggested Suggested
Comp. Obj. Teaching Strategies Assessment
4 a, b Given the transformation of parent graphs, match the Teacher observation;
graphs with equations and word descriptions. Write Rubric
observations and predictions based on the
transformation.
4 a, b Give groups a function and its inverse. Have part of Presentation;
the group algebraically justify the inverse of the Rubric
function and have the remaining group justify
graphically.
4 c Model the complex coordinate plane using a floor Teacher observation
graph and students as coordinates.
4 d chchc h
Explore the meaning of f 3 , f 1 , f x 1 as applied to a Teacher evaluation;
function. Teacher test
4 e Write statements involving inequalities and absolute Rubric
values that model finding the gas tank capacity,
average city miles per gallon, and highway miles per
gallon of a car.
4 f Collect data on any two situations related to the Teacher observation
students in the class (e.g., education and salary, age
and speeding tickets in a year). Graph the data and
determine the line of best-fit. From the equation, make
predictions based on this equation.
4 f Collect data on forearm length and height of students ● Teacher observation
in the class. Use technology to draw a scatter plot and
perform regression analysis.
80
Grade Level: Algebra II
Unit Theme: Rational Expressions and Equations
Suggested Suggested
Comp. Obj. Teaching Strategies Assessment
5 a Make a set of cards with rational expressions and a Teacher observation
second set of cards with the expression simplified;
distribute cards and find the match.
5 b Explain why it is necessary to verify solutions to Teacher test;
rational equations. Rubric
5 c Interview a science teacher on how the world of Presentation
science uses variations. Present to the class the main
ideas of the interview to include examples of how
variations are used in science.
81
Grade Level: Algebra II
Unit Theme: Exponential and Logarithmic Expressions and Equations
Suggested Suggested
Comp. Obj. Teaching Strategies Assessment
6 a, c Use paper and pencil to draw graphs of exponentials Teacher observation
and logarithms. Verify using a graphing calculator and
compare and contrast the graphs.
6 b Show and explain the relationship between exponents Student evaluation
and logarithms.
6 d Use technology to investigate the function which would Observation
explain the process of cooling liquid in a cup.
82
Grade Level: Algebra II
Unit Theme: Matrices
Suggested Suggested
Comp. Obj. Teaching Strategies Assessment
7 a, b Investigate the relationship among dimensions, Teacher test
inverses, and determinants of matrices.
7 c List the necessary requirements for two matrices to be Checklist
equal.
7 d Collect prices for individual orders of medium soda, Teacher test
medium fries, and hamburgers from different fast food
restaurants. Model through matrix multiplication the
total cost for ordering 5 fries, 10 sodas, and 7
hamburgers. Determine the best deal.
83
ADVANCED ALGEBRA
The Advanced Algebra course serves as an extension of algebraic concepts.
Through a more in-depth study of algebra, students will further enhance their
mathematical confidence and reasoning ability. This course will be an extension of
Algebra II, and may be used as a prerequisite to Pre-Calculus. The use of graphing
calculators and other appropriate tools of technology is strongly recommended. This is
a84 Analyze and extend patterns of graphs in families of functions. (P, D, M, G, N)
a. Determine domain and range.
b. Relate symmetry to the behavior of even and odd functions.
c. Use technology to analyze and sketch the graphs of polynomial, rational,
exponential, and logarithmic functions.
d. Explore properties of composites and inverses and their graphs as they relate
to functions.
e. Use linear programming to solve problems.
2. Investigate and apply Explore the relationships of Pascal's triangle.
3. Explore and apply fundamental principles of probability and statistics. (P, D, G,
N)
a. Use summation () and factorial notation to solve problems.
b. Expand and apply the Binomial Theorem to problem-solving situations.
c. Draw inferences from and construct charts, tables, and/or graphs that summarize
data.
d. Use and apply the Fundamental Counting Principle, permutations, and
combinations as a preface to probability.
e. Use theoretical or experimental experiences to determine simple probability.
f. Use curve-fitting to predict from data.
85, explore, and predict equations and graphs of conic sections. (P, M,
G, N)
a. Identify the parts essential to the graphs of the circle, parabola, ellipse, and
hyperbola.
b. Analyze and sketch the graphs of conics.
c. Recognize conic sections by their graphs and equations.
d. Apply algebraic techniques to write conics in standard form.
e. Graph conic sections using translations.
5. Extend algebraic techniques to higher degree polynomial and complex
rational problems. (P, D, N)
a. Factor and find zeros of polynomial equations.
b. Solve quadratic and simple polynomial inequalities.
c. Solve inequalities containing simple rational expressions.
6. Explore and extend properties and applications of exponential and logarithmic
equations. (P, D, M, G, N)
a. Explore and simplify exponential expressions and solve exponential equations.
b. Evaluate logarithmic expressions and solve logarithmic equations.
c. Explore applications of logarithms.
86
Course: Advanced Algebra
Unit Theme: Functions
Suggested Suggested
Comp. Obj. Teaching Strategies Assessment
1 a, c Using a graphing calculator or computer simulation, Teacher evaluation
investigate and discuss the domain and range of
families of functions by comparing the equation, graph,
and table of values.
1 b Using a 6" x 6" graph grid and pipe cleaner, model Teacher observation
even and odd functions.
1 d Using a graphing calculator or computer simulation, Self evaluation
compare the graphs of two functions to their composite
function. Predict the graph and verify using
technology.
1 e Create, construct, and solve a linear programming Peer evaluation
problem with at least four equations.
87
Course: Advanced Algebra
Unit Theme: Sequences and Series
Suggested Suggested
Comp. Obj. Teaching Strategies Assessment
2 a, b, d Using a calculator, take the square root of a positive Student evaluation
integer. Continue to take the square root of the
answer. Discuss the results and model the pattern.
2 c Explain the difference between a geometric and Constructed response
arithmetic series and give an example of each.
2 e Using the Internet, explore and investigate the patterns Student work sample
of Pascal's Triangle.
88
Course: Advanced Algebra
Unit Theme: Probability and Statistics
Suggested Suggested
Comp. Obj. Teaching Strategies Assessment
3 a Given a pattern of one whole, a half, one-sixth, and Teacher evaluation
one twenty-fourth, investigate and relate to n.
3 b Work problems involving batting averages and coin Teacher evaluation
tossing using the Binomial Theorem or Pascal's
Triangle.
3 c, f Students will plot their shoe size and wrist Peer evaluation
measurement on a large graph. After drawing the line
of best fit, predict a professional athlete's wrist size
based on a given shoe size.
3 d Given the school lunch menu for the day, determine Teacher evaluation
the number of possible combinations of meals.
3 e Flip coins repeatedly or draw objects from a sack to Peer evaluation
compare the outcomes to the expected probability.
3 f Using a graphing calculator, use curve fitting to find the Self-evaluation
equation of the curve of best fit containing three or
more non-linear points. Make predictions using the
equation and the graph.
89
Course: Advanced Algebra
Unit Theme: Conic Sections
Suggested Suggested
Comp. Obj. Teaching Strategies Assessment
4 a, b, c, d Given a list of quadratic equations, determine the type Teacher evaluation
of conic section. Write each equation in standard form
and identify specific characteristics.
4 b, c, e Graph parent conic sections and predict translations. Self-evaluation
Verify using a graphing calculator or computer
simulation.
90
Course: Advanced Algebra
Unit Theme: Polynomial Equations
Suggested Suggested
Comp. Obj. Teaching Strategies Assessment
5 a Create an equation given the zeros to see the Self-evaluation
relationship between the zeros and the equation. Use
technology to verify the zeros.
5 b, c Given a polynomial inequality or a rational inequality, Teacher evaluation
find and verify the values of x and express the solution
in inequality notation, interval notation, and graph form.
91
Course: Advanced Algebra
Unit Theme: Exponential and Logarithmic Equations
Suggested Suggested
Comp. Obj. Teaching Strategies Assessment
6 a, c Using pb to represent the beginning population, pe to Teacher evaluation
represent the ending population, and t to represent
growth time intervals, use the following formula to
aft
determine bacteria growth: p e p b 2 . Given
values for any two unknowns, solve for the third.
Construct and complete a two-day chart logging total
bacteria at specific time intervals for growth.
6 b, c Given logarithmic and exponential expressions, Teacher evaluation
explain the process of converting from one form to the
other and make connections for solving exponential
and logarithmic equations such as
log2 x 4 or 5 x 71 . Work application
examples that include growth and decay problems
involving half-life.
92
PRE-CALCULUS
The Pre-Calculus course serves as a bridge between Algebra II or Advanced
Algebra and Calculus. It will extend students' knowledge of concepts mastered in
Algebra II or Advanced Algebra. This course will increase analysis skills and enhance
students' reasoning ability and mathematical confidence. The use of technology,
especially graphing calculators, should be an integral part of this course. This course is
designed to prepare students for Calculus/Advanced Placement Calculus93 Investigate, predict, and extend patterns of graphs in families of functions. (P,
D, M, G, N)
a. Demonstrate proficiency in determining domain and range.
b. Relate powers and coefficients to the end behavior of graphs of functions.
c. Relate symmetry to the behavior of even and odd functions.
d. Analyze and sketch the graphs of polynomials, rational, piece-wise, greatest
integer, exponential, and logarithmic functions, and verify using technology.
e. Explore properties of composites and inverses and their graphs as they relate
to functions.
2. Illustrate and explore Use the Principle of Mathematical Induction as a form of mathematical proof.
3. Explore and apply fundamental principles of probability. (P, D, G, N)
a. Use summation () and factorial notations to solve problems.
b. Expand and apply the Binomial Theorem to problem-solving situations.
c. Use and apply the fundamental counting principle, permutations, and
combinations as a preface to probability.
d. Use theoretical or experimental experiences to determine simple probability.
94 Extend algebraic problem-solving techniques to higher degree polynomial and
complex rational equations. (P, D, G, N)
a. Factor and find zeros of polynomial equations.
b. Graph and write equations using the behavior of linear, even, and odd factors.
c. Solve simple polynomial inequalities to include quadratic inequalities.
d. Solve inequalities containing simple rational expressions.
e. Investigate optimization problems.
5. Extend operations and applications of matrices. (P, N)
a. Calculate determinants of matrices to include expansion of minors.
b. Solve systems of n equations and explain the solutions.
6. Extend properties and applications of exponential and logarithmic equations.
(P, D, M, G, N)
a. Explore and simplify exponential expressions and solve exponential equations.
b. Evaluate logarithmic expressions and solve logarithmic equations.
c. Explore the application of logarithms to problem-solving situations.
95
Course: Pre-Calculus
Unit Theme: Families of Functions
Suggested Suggested
Comp. Obj. Teaching Strategies Assessment
1 a Given a function, predict the domain and range. Enter Teacher evaluation
the function on the graphing calculator. Use a piece of
spaghetti to find the domain and range. Compare the
prediction to the spaghetti results.
1 b Using the graphing calculator, determine the end Rubric;
behavior of a function and write a paragraph explaining Teacher evaluation
the results. Discuss how the degree of the function
affected the end behaviors. Create a spreadsheet of
values to determine the end behavior of a graph.
1 c Discuss the properties of linear, even and odd factors. Self-evaluation
4 b In small groups, discuss the following situation: If
f x is an even function and g x is an odd function,
is f x g x an even function, an odd function, or
neither. Draw the graph of an even function and of an
odd function. Demonstrate symmetry with respect to
the x-axis, the y-axis, the line y x and the line
y x . Verify using the graphing calculator.
1 e In small groups, determine if families of functions have Teacher observation
the same symmetry as the parent function and justify
the answer.
1 e Fold graph paper about the line y x . Draw the Self-evaluation
graph of any function. Trace the graph on the other
side of the fold to reveal the inverse.
1 e Create and graph a function. Find and graph the Report
inverse. Write a paragraph describing the relationship
between a relation and its inverse. Include how to
determine if a relation is a function and whether the
function has an inverse.
96
Course: Pre-Calculus
Unit Theme: Sequences and Series
Suggested Suggested
Comp. Obj. Teaching Strategies Assessment
2 a, b, c On the first day of January, Bob ate one candy bar. Class discussion
Each day thereafter he ate one more candy bar than
the previous day. Determine the number of candy
bars he ate during the month of January.
2 a, b, c Find the number of calories in a candy bar of your ● Class discussion
choice. Calculate the caloric intake for that month.
Estimate the possible weight gain by the end of the
month.
2 c Tear a square piece of paper with an area of one, in Demonstration
half. Tear it in half again. Predict the area of one of
the resulting rectangles after six tears.
2 d Divide the class into groups and provide each group Teacher observation
with a ball. As the ball is thrown or dropped, use
technology to record the path of the ball.
2 e Use mathematical induction to prove that a formula is Teacher evaluation
valid for all positive integral values of n.
97
Course: Pre-Calculus
Unit Theme: Probability
Suggested Suggested
Comp. Obj. Teaching Strategies Assessment
2 b In small groups, create a geometric series which can Student evaluation
3 a be expressed in sigma notation. Exchange papers
and write the series in sigma notation form.
3 b Give an example involving a baseball player's batting Teacher evaluation
average. In small groups, use the Binomial Theorem
to determine the probability of getting at least three hits
in the next five times at bat.
3 c Write a paragraph explaining the difference between Report;
permutations and combinations. Create problems Rubric
involving each.
3 d In small groups, provide each group with a different Demonstration
type of manipulative (e.g., cards, number cubes, coins,
spinners, and slips of paper with numbers). Given a
probability problem, determine the theoretical
probability. Perform the experiment to compare
theoretical prediction to the experimental result.
98
Course: Pre-Calculus
Unit Theme: Polynomial Equations
Suggested Suggested
Comp. Obj. Teaching Strategies Assessment
4 a, b Create and graph an equation of a polynomial function. Teacher evaluation
Write a paragraph explaining the zeros of a function
and how to determine where they are located on the
graph.
4 b Provide small groups or individuals with pictures of 10 Rubric
functions which have varying degrees, but all of which
c c
ch c h h h
are factorable. For example, f x x 1 x 2 x 3 .
Have each group come up with the equation for the
function, using the smallest possible degree. Students
can expand the factors or leave them in factored form.
Have them justify why they chose the degree they did
for each factor.
4 c, d, e In small groups, create, solve, and graph rational and Student evaluation
polynomial inequalities. Extend to graphing systems of
inequalities by shading solutions with colored pencils.
Given a function, find the maximum and minimum of
the shaded region.
99
Course: Pre-Calculus
Unit Theme: Matrices
Suggested Suggested
Comp. Obj. Teaching Strategies Assessment
5 a Write a paragraph discussing the process to find the Rubric
determinant of a 3 x 3 matrix. Include both the lattice
method and expansion by minors.
5 b In small groups, create a word problem involving a Class discussion
2 x 2 matrix. Solve the system of equations by
matrices and explain the results.
100
Course: Pre-Calculus
Unit Theme: Exponential and Logarithmic Equations
Suggested Suggested
Comp. Obj. Teaching Strategies Assessment
6 a In small groups, create, explain, and verify specific Student evaluation
examples for each of the properties of exponents.
6 b Compare the relationships of a logarithmic function Student evaluation
and the inverse of an exponential function. Write an
equation in one form, exchange papers, and write the
inverse form.
6 c Solve growth and decay problems involving half-life Teacher evaluation
using logarithms.
101
TRIGONOMETRY
The Trigonometry course forms a foundation for later development of Calculus
concepts. This course is a comprehensive study of trigonometric functions with
emphasis on applications. The study of trigonometry extends algebraic concepts to the
exploration of circular and triangular functions with their properties and graphs. The use
of graphing calculators is an essential part of this course. This course is designed for
students who have successfully completed Algebra I, Geometry, and Algebra II, and is a
prerequisite for Calculus/Advanced Placement Calculus. This is a one-half credit102 Identify, locate, and apply trigonometric functions to the unit circle. (P, M, G,
N)
a. Identify and locate angles in radians and degrees based on the unit circle.
b. Convert between degree and radian measurements of angles.
c. Use the definition of the six trigonometric functions to find missing parts of a
triangle.
d. Determine the values of inverse trigonometric functions.
e. Utilize special right triangle relationships and symmetry as they apply to the unit
circle.
f. Relate the unit circle to the right triangle.
2. Explore, communicate, and apply the connections between the patterns of
trigonometric functions and graphing with and without appropriate
technology. (P, D, M, G, N)
a. Recognize, sketch, and interpret the graphs of the six basic trigonometric
functions and their inverses to include restrictions on the domain.
b. Recognize, sketch, and interpret graphs of the trigonometric functions using all
transformations.
3. Utilize and extend algebraic and geometric techniques to trigonometric
equations and applications. (P, D, M, G, N)
a. Solve for unknown parts of triangles to include Law of Sines and Law of Cosines.
b. State, verify, and utilize trigonometric identities.
c. Find arc length and area of a sector of a circle.
d. Find the area of a triangle using Heron's Formula and/or 2 bc sin A .
1
e. Solve trigonometric equations, using both radians and degrees.
f. Model and apply right triangle formulas, Law of Sines, and Law of Cosines to
problem-solving situations.
103 Introduce and investigate basic concepts of vectors and operations with
vectors. (P, M, G, N)
a. Recognize different notations for vectors.
b. Apply addition to vector sums and resultants.
c. Determine the norm (magnitude) of a vector.
d. Create a unit vector in the same and in the opposite direction of a given vector.
e. Draw a vector to represent a quantity.
104
Course: Trigonometry
Unit Theme: Circle
Suggested Suggested
Comp. Obj. Teaching Strategies Assessment
1 a, b, e, f Using a protractor and a paper plate, show the Project;
multiples of 30, 45 , and 60 and quadrantals in all four Rubric
quadrants labeling each in degrees and radians.
1
b, d Cards marked with two sides in degree measure and Demonstration
two sides in radian measure are dealt with the last
card placed face up in the middle of the table. Playing
left to right, match cards with degree/radian
equivalents. Design a similar game using inverses.
1 c, d, e With a protractor and string, use angle of elevation and Demonstration
distance from the tree to compute the height of the
tree.
1 d, e Use bow tie visuals with 30 , 45 , and 60 angles Student work sample
marked to determine the values of inverse
trigonometric functions.
1 2 2 1
3
3
0
30
-1 2 2 -1
1 f Use the acronym, All Students Take Calculus, for Demonstration
finding the sign of the six trigonometric functions in all
four quadrants. Begin with ―A" in the first quadrant, all
functions are positive. With ―S‖ in the second
quadrant, only sin x and its reciprocal are positive.
With ―T‖ in the third quadrant, only tan x and its
reciprocal are positive. With ―C‖ in the fourth quadrant,
only cos x and its reciprocal are positive.
105
Course: Trigonometry
Unit Theme: Graphs
Suggested Suggested
Comp. Obj. Teaching Strategies Assessment
2 a Review inverses of algebraic equations and discuss Self-evaluation
reflections about the line y = x. Predict and sketch the
inverse of the six basic trigonometric functions. Verify
using the graphing calculator.
2 a Using the definitions of cos 0 and sin 0 (x and y Self-evaluation
coordinate of corresponding point on the unit circle)
determine the values of the six trigonometric functions
for the quadrantal angles.
(0, 1) ● (1, 0)
● ●
(-1, 0)
● (0, -1)
2 b Using a graphing calculator or computer simulation ● Discussion;
program, investigate the phase shift, amplitude, and Self-evaluation
period changes of trigonometric graphs.
106
Course: Trigonometry
Unit Theme: Identities
Suggested Suggested
Comp. Obj. Teaching Strategies Assessment
3 a Given a set of equally spaced points on a circle of a Self-evaluation
given radius, use the Law of Sines and Law of Cosines
to find horizontal and vertical distances from point to
point to the nearest thousandth. Use a computer
program to verify solutions.
3 b Write each trigonometric function in terms of all the Teacher evaluation
other trigonometric functions. For example:
sin x = 1 cos2 x
3 b The hexagon demonstrates the following relationships: Demonstration
Functions across the heavy lines are reciprocals.
Functions across horizontal lines (heavy and light
lines) are co-functions.
Going around the hexagon, choose any three
consecutive functions. The product of the outer
two functions results in the middle function.
Within a shaded triangle, begin at the left vertex,
move right, then down. The Pythagorean
identities are formed.
3 c Using several different size balls, determine the radius Student evaluation
of each. Find the arc length of a cross-section of each
ball with a central angle of 30, 90 , 135 . Find the
area of each cross-section.
3 c, d, f Find the area of a piece of irregularly shaped land Self-evaluation
given the legal land description, and compare to the
area listed in the deed.
3 e Starting with a degree or radian measure, write a Student evaluation
trigonometric equation with that solution (e.g., given
x 45 , an equation would be tan tan x = 1 ) Justify
the value for x.
107
Course: Trigonometry
Unit Theme: Vectors
Suggested Suggested
Comp. Obj. Teaching Strategies Assessment
4 a Research different notations for vectors using the Rubric
Internet or the library. Compare and contrast the
different notations.
4 b Using necessary directional tools, locate selected Self-evaluation
items on the school campus by finding the resultant of
two given vectors from a given point.
4 c Use the Pythagorean Theorem to calculate the norm Teacher observation
(magnitude) of a vector.
4 d Draw examples of equal, opposite, parallel, and Short answer
perpendicular vectors on an overhead transparency
and investigate their relationships.
4 e Using a protractor and ruler, construct vectors given Student work sample
the magnitude and direction.
108
CALCULUS
ADVANCED PLACEMENT CALCULUS AB
ADVANCED PLACEMENT CALCULUS BC
Calculus is the study of the mathematics of change. The major focus is on
differential and integral calculus. The Calculus course provides a survey of calculus
without the theory and rigor necessary to receive advanced placement credit. The
Advanced Placement Calculus courses are intended for those students who wish to
seek college credit and/or placement from institutions of higher learning. Topics marked
by an asterisk (*) are for the additional topics to be taught in Advanced Placement
Calculus BC. The use of graphing calculators and other technologies are integral parts
of each calculus course. These courses are designed for the student who has a
thorough knowledge of college preparatory mathematics. Calculus, Advanced
Placement Calculus AB and Advanced Placement Calculus BC are each one-credit
coursesPlease adjust the course content and kind and use of the calculator as outlined in the
latest version of AP Course Description, published by the College Board each year. For
more information contact: The College Board, Advanced Placement Program, P. O. Box
6670, Princeton, New Jersey, 08541-6670.
109 basic knowledge of functions, their behavior, and
characteristics. (P, D, G, N)
a. Predict and explain the characteristics and behavior of functions and their
graphs.
b. Investigate, describe, and determine asymptotic behavior.
c. Discuss and determine continuity and discontinuity of functions.
d. *Analyze parametric, polar, and vector functions.
2. Evaluate limits and communicate an understanding of the limiting process.
(P, D, G, N)
a. State and apply properties of limits.
b. Calculate limits using algebra.
c. Estimate limits from graphs or tables of data.
d. Verify the behavior and direction of non-determinable limits.
e.
Use L'Hopital's Rule to evaluate simple indeterminate forms.
f.
*Apply L'Hopital's Rule to determine convergence of improper integrals and
series.
3. Use the definition and formal rules of differentiation to compute derivatives.
(P, G, N)
a. State and apply the formal definition of a derivative.
b. Apply differentiation rules to sums, products, quotients, and powers of
functions.
c. Discuss and demonstrate the differences between average and instantaneous
rates of change.
d. Use the chain rule and implicit differentiation.
e. Extend knowledge of derivatives to include exponential, logarithmic,
trigonometric and inverse trigonometric functions.
f. *Calculate derivatives of parametric, polar and vector functions.
110 Apply derivatives to find solutions in a variety of situations. (P, D, M, G, N)
a. Interpret and communicate the purposes of the derivatives.
b. Interpret the derivative as a rate of change in varied applied contexts, including
velocity, speed and acceleration.
c. Apply the derivative to find tangent lines and normal lines to given curves at
given points.
d. Apply Rolle's Theorem and the Mean Value Theorem and their geometric
consequences.
e. Apply differentiation techniques to curve sketching.
f. Explain and predict the relationships between functions and their derivatives.
g. Model rates of change to solve related rate problems.
h. Solve optimization problems.
i. Determine an understanding of Newton's Method to approximate roots.
j. Investigate local linear approximations.
k. *Interpret differential equations using slope fields.
l. *Solve differential equations by Euler's Method.
m. *Analyze planar curves given in parametric, polar and vector form including
velocity and acceleration vectors.
5. Employ various integration properties and techniques to evaluate integrals.
(P, D, M, G, N)
a. Demonstrate the concept of the integral as an accumulator.
b. Use Reimann's Sum and the Trapezoidal Rule to approximate definite
integrals.
c. State and apply the First and Second Fundamental Theorem of Calculus.
d. Evaluate the average value of a function on an interval.
e. Apply the power rule and u-substitution to evaluate indefinite integrals.
f. *Extend techniques of integration to include integration by parts and simple
partial fractions.
1116. Adapt integration methods to model solutions to problems. (P, D, M, G, N)
a. Investigate and apply integration to solve problems including area, volume, and
cross sections.
b. Employ integration to compute distance traveled by a particle along a line.
c. Solve differential equations using integration and separation of variables.
d. Utilize integrals to model solutions to real-world problems.
e. *Solve logistic differential equations and use them in modeling.
f. *Apply integration to find length of a curve.
7. *Explore the concepts affecting relationships among different kinds of series.
(P, D, G, N)
a. *Identify different types of series and their characteristics.
b. *Apply different types of tests to create valid arguments to determine
convergence or divergence of series.
c. *Use Lagrange's Method for computing errors of Taylor polynomials.
d. *Formulate new series from known series to include Maclaurin and Taylor
series.
* Topics marked by an asterisk (*) are for the additional topics to be taught in Advanced
Placement Calculus BC.
112
Course: Calculus/Advanced Placement Calculus AB/
Advanced Placement Calculus BC
Unit Theme: Functions
Suggested Suggested
Comp. Obj. Teaching Strategies Assessment
1 a, b, c Distribute examples of graphed functions. For each Short answer
example:
a. Use the graph to identify intervals where the
function is continuous.
b. Discuss and identify the values of the function
where failure occurs for each of the three tests of
continuity.
1 c Explore Layman's version of continuity: A function is Teacher observation
continuous if you can draw it without ever lifting your
pencil.
1 d Use technology to model parametrics by revisiting an Peer evaluation
old algebra problem of two trains traveling on the same
track.
113
Course: Calculus/Advanced Placement Calculus AB/ Placement
Advanced Calculus BC
Unit Theme: Functions
Suggested Suggested
Comp. Obj. Teaching Strategies Assessment
2 a, b, c Divide the class into groups. Each group will Group work;
investigate the function: Class discussion
3
ch xx 11
f x
Group assignments:
1) Have one group create a table of 10 to 20
function values for 1, 2
2) Create table values for 0, 1 .
3) Graph function using a decimal (friendly)
calculator window. List five (5) observations
about what happens to y values as x gets closer
to 1.
4) Predict what graph will look like and list at least
five characteristics.
5) Algebraically explore the function: ―Can it be
factored? ―
2 c, d Compare the graphs of several rational functions to Rubric
table values for behavior at points near where the
denominator is undefined.
2 d Compare a list of indeterminate forms and discuss why Student work sample
they are indeterminant.
2 d Use
x
b g
lim 1 1
x
x
to show/explore why 1 is an Short answer
indeterminant form.
114
Course: Calculus/Advanced Placement Calculus AB/ Advanced
Placement Calculus BC
Unit Theme: Derivatives
Suggested Suggested
Comp. Obj. Teaching Strategies Assessment
3 a Using an overhead graphing calculator to create Presentation
overheads of different functions, create two bugs (from
hole punched dots) to travel along the overhead
functions. Get students to predict what will happen as
both bugs walk along the curve toward each other and
the two bugs are connected by a string—one bug
stays still and the other approaches the first bug.
3 b Quotient Rule Hi = Numerator Demonstration
Lo = Denominator
Lo de Hi – Hi de Lo
And down below the denominator squared must go.
3 c Provide students with a table of values of time and Discussion
speed. Have them calculate the average speed. What
method(s) were used? Compare to instantaneous
rates.
3 b, d, e After basic differentation rules have been introduced, Test
provide memory tools. For example, PI (Power then
do the Inside), and PTA (Power, Trig, Angle).
3 f Make a set of match cards with derivatives, graphs, Free response
and different forms (parametrics, polar, and vector)
and have groups match and sort.
4 a, b Given the graph of a function draw the tangent line at a Student work sample
variety of points on the function. Estimate the slope
and analyze in terms of rate of change.
4 c Determine the tangents to the curve Short answer
4x2 9y2 36
at the ends of each axis. Describe the relationship
between the two sets of tangents.
4 d Explain the similarities and differences between Rolle's Essay
Theorem and the Mean Value Theorem.
115
Course: Calculus/Advanced Placement Calculus AB/
Advanced Placement Calculus BC
Unit Theme: Derivatives
Suggested Suggested
Comp. Obj. Teaching Strategies Assessment
4 e, f Give students a function like f bg x5 3x4 4x3 12x2
x Group work
a) Where are the zeros for f'(x)?
b) Identify intervals where graph is
increasing/decreasing.
c) Have students compute derivative and graph the
ch
derivative. Where is f x above the x-axis; Below
the x-axis?
d) State x coordinates of max/min points for f x . ch
4 e, f Make a set of match-cards to include f x, f ' , x, f " f Group investigation
'(x), f― (x) for each group of students. (Extend: Critical
number cards) Have groups match all the parts, then
present one complete solution to the class.
4 g Use a table approach to organizing student work in Student work sample
solving related rates.
Know What to Find
(lots of things) (only one here)
4 h Find examples of real-world situations that involve Project
solving optimization problems. Follow-up with a class
discussion.
4 h Investigate why a soda can is the shape and size it is? Project
4 i Use technology to demonstrate finding roots using Demonstration
Newton's Method.
4 j Justify how linear approximations are used to model Short answer
local linearity of different functions.
4 k Create an overhead with families of curves that are Small groups
solutions to a particular differential equation. Give
each group a copy of an extra transparency. Have
groups draw tangent lines at given points for different
curves. Bring all group transparencies and place on
overhead. Discuss the meaning of the slope field.
4 l Get a copy of an Euler method program or use a Discussion
spreadsheet. Investigate what happens for different
functions and different step sizes when using Euler's
method.
4 m Model tossing a baseball to a person sitting on a ferris Self assessment using
wheel using parameter equations and/or vectors. graphing calculator
116
Course: Calculus/Advanced Placement Calculus AB/
Advanced Placement Calculus BC
Unit Theme: Integrals
Suggested Suggested
Comp. Obj. Teaching Strategies Assessment
5 a Provide a data set where an over-estimate and an Constructed response
under-estimate of an integral could be computed.
Relate to an example of velocity data and estimate
distance traveled.
5 b Use technology to investigate numerical methods such Teacher observation
as the Trapezoidal Rule.
5 c Use the Fundamental Theorem of Calculus to explain Constructed response
the difference between definite and indefinite integrals.
5 d Create a graph that would model the average value Short answer
formula.
5 e, f Divide the class into two teams. Use a football field to Constructed response
score points. Team 1 has four chances to move +0
yards (correct answer = 10 yards). The team
quarterback will designate a player to answer a
question. All class members will work on the problem.
If the designated player misses the question, the side
of the room that has the most correct answers either
wins the play or blocks the play.
117
Course: Calculus/Advanced Placement Calculus AB/
Advanced Placement Calculus BC
Unit Theme: Integrals
Suggested Suggested
Comp. Obj. Teaching Strategies Assessment
6 a Compute the area between a curve and the x-axis Group investigation
using geometric shapes and rectangular areas (from
grid).
6 a Use playdough to create solids formed by revolving a Teacher observation
region about an axis. Slice into discs to demonstrate
where the disc formula for volumes is derived.
6 b Use a graph to explain how an integral would model Class discussion
distance traveled.
6 c Explain the process for solving differential equations Essay
by separation of variables.
6 d, e Investigate exponential decay and/or logistic functions Test
as they apply to integrals.
6 f Derive the formula for arc length. Demonstration
118
Course: Calculus/Advanced Placement Calculus AB/
Advanced Placement Calculus BC
Unit Theme: Series
Suggested Suggested
Comp. Obj. Teaching Strategies Assessment
7 a, b Create a set of matching cards with all the tests for Student work sample
convergence, sample series, and blank index cards.
Students will match tests with examples, then use
index cards to write an appropriate argument proving
convergence or divergence.
7 c Discuss how to find a value for c on a specific interval Class discussion
as it relates to errors of Taylor polynomials.
7 d Obtain either a computer or calculator program that will Constructed response
compute the Taylor polynomial. Explain the
computer/calculator results for the examples given.
119
DISCRETE MATHEMATICS
Discrete Mathematics is the study of mathematics as it applies to systems that have
a finite number of elements. A few of the topics that will be explored are set and binary
systems, logic, graph theory, simple games, and the geometry of fractals. Technology
will be used when appropriate throughout the course. Discrete Mathematics is usually
considered important for potential application to computer science, but is not limited to
that area. This course is designed for students who have successfully completed
Algebra II. It may be an alternative to pre-calculus, trigonometry, or calculus120 Perform operations on sets and investigate properties of fields. (P, G, N)
a. Define and recognize binary operations.
b. Perform operations on a set.
c. Identify properties of fields.
d. Identify simple operations using set theory to include Venn diagrams.
2. Apply the rules of logic to discuss the validity of arguments. (P, G, N)
a. Investigate and apply rules of logic to include negations, connectives,
conditionals, inverses, and patterns of inference.
b. Construct truth tables.
c. Apply the principles of logic to determine the validity of arguments.
d. Use basic Boolean Algebra to create elementary logic circuits.
3. Explore and investigate graph theory and its applications. (P, M, G)
a. Define and identify the basic terminology of graph theory.
b. Recognize properties of graphs having Eulerian and Hamiltonian paths and
circuits.
c. Construct and use tree diagrams to solve graph theory problems.
d. Apply graph theory techniques to determine shortest paths and scheduling
situations.
4. Investigate and explain strategies for solving simple games. (P, D, N)
a. Determine the characteristics that result in a fair game.
b. Identify winning strategies for basic games.
121 Apply and compare approaches to problem-solving situations. (P, D, M, G, N)
a. Perform basic operations with matrices.
b. Explain and represent a relation (on a finite set) by a digraph or by a matrix.
c. Apply matrices to solving problems.
d. Use difference equations to model real-life problems.
e. Investigate and apply fair division concepts to problem-solving situations.
f. Use and compare recursive approaches to problem-solving and identifying
numerical patterns.
g. Apply algorithms to solving problems.
h. Analyze networks and their applications including roads and airline routes.
6. Investigate the geometry of fractals. (P, D, G, N)
a. Identify fundamental characteristics of fractals.
b. Explain the outcomes of the Chaos game.
c. Determine patterns in area and perimeter of simple fractal patterns.
d. Explore and determine the concepts of fractal dimension.
122
Course: Discrete Mathematics
Unit Theme: Operations of Sets
Suggested Suggested
Comp. Obj. Teaching Strategies Assessment
1 a, b, c Create an operation rule: a # b 3a 2b . Investigate Teacher observation
the characteristics, properties, and which set of
numbers work with the rule.
1 d Locate examples of Lewis Carroll puzzles that use Project
Venn diagram solutions (Web investigation). Discuss
the characteristics of the examples.
123
Course: Discrete Mathematics
Unit Theme: Rules of Logic
Suggested Suggested
Comp. Obj. Teaching Strategies Assessment
2 a, b, c, d Gather materials to build a simple circuit (battery, Small groups
switch, light bulb, alligator clips). Create situations like
―The seat belt must be secure before the car will start,‖
and model with the circuit and logic.
124
Course: Discrete Mathematics
Unit Theme: Graph Theory
Suggested Suggested
Comp. Obj. Teaching Strategies Assessment
3 a, b, d Use the game ―Instant Insanity‖ to show how graph Class discussion;
theory makes solutions easy. Teacher observation
3 c Obtain a map of a five-block downtown area or within a Project
five-block radius of the school. Design a graph of all
possible paths from a designated starting point to a
specific location (school). Display options using tree
diagrams.
125
Course: Discrete Mathematics
Unit Theme: Strategies and Simple Games
Suggested Suggested
Comp. Obj. Teaching Strategies Assessment
4 a, b Use ―Master Mind‖ to teach terminology and basic Rubric
game strategies.
126
Course: Discrete Mathematics
Unit Theme: Problem Solving
Suggested Suggested
Comp. Obj. Teaching Strategies Assessment
5 a Record scores for foul shots and goals for five Student work sample
basketball players during one game. Model each
player's total scores by matrix multiplication.
5 b, c Research different mathematical methods that have Report
been used throughout history to code message,
specifically role of matrices.
5 d Consider a circular shaped pizza. If size or shape do Constructed response
not matter, what is the pattern to the number of pieces
produced by cutting once, twice, three times, etc.?
5 e Divide the class into groups of three to four students. Discussion
Give each group a circle with 10" diameter that
represents a cake. Have a group develop a method of
cutting the cake for class members that would be ―fair.‖
5 f Take the square root of a positive number on the Short answer
calculator, then take square root of answer . . .
ENTER, ENTER . . . What happens? Why?
5 g Divide class into groups. Devise a plan for dividing a Constructed response
cake among 3, 4, or more people. Solutions should be
in the form of algorithms.
5 h Find a copy of course offerings for the freshman class. Project
Design a network that would model possible
schedules.
127
Course: Discrete Mathematics
Unit Theme: Fractals
Suggested Suggested
Comp. Obj. Teaching Strategies Assessment
6 a, c, d Enlarge a Mississippi map of the coastline. Apply Student work sample
techniques for evaluating fractal dimensions to the
Mississippi map.
6 b Form groups. Play the Chaos game with equal Class discussion
probabilities of one-third. Change probabilities and
discuss similarities and differences of the outcomes.
128
PROBABILITY AND STATISTICS
The Probability and Statistics course is intended for those students who would like
to explore more closely the topics of probability and statistics. Probability provides
concepts and methods for dealing with uncertainty and for interpreting predictions
based on uncertainty. Statistics deepens and builds understanding of the methods of
data analysis. Use of appropriate tools of technology should be an integral part of this
course. This course is designed for students who have successfully completed Algebra
II. This is a129 Collect, read, interpret, and analyze data as it relates to the real world.
(P, D, M, G, N)
a. Draw inferences from charts, tables, and graphs that summarize data.
b. Find mean, median, mode, and percentile information from a given set of data.
c. Use curve-fitting to predict from collected data.
d. Explain and defend regression models using correlation coefficients and
residuals.
e. Use an understanding of algebraic concepts to determine mathematical models
of best fit.
2. Collect and decide on the most appropriate form of displaying data and be
able to create tables and different kinds of graphs to represent data. (D, M, G)
a. Collect and organize data using frequency distributions, stem-and-leaf plots, and
histograms.
b. Choose the graph type, such as bar, circle, pictograph, line, or x-y, that best
represents a given set of data.
c. Create graphs with scales which fairly display the data.
3. Demonstrate how patterns can be used to explain probability. (P, D, M, G)
a. Represent probability as a rational number.
b. Explain the relationship between theoretical and experimental probability.
c. Apply the counting principles, including permutations and combinations.
d. Construct and interpret sample spaces, events, and tree diagrams.
e. Identify types of events, including mutually exclusive, independent, and
complementary.
f. Calculate geometric probability using two-dimensional models, and explain the
processes used.
g. Create simulations and experiments that correlate to theoretical probability.
h. Use Markov Chains to calculate probability by constructing matrix models.
i. Apply the concept of a random variable to generate and interpret probability
distributions.
130 Investigate algebraic concepts as they apply to one and two variable data. (P,
D, M, G, N)
a. Describe the sampling process and effects of sampling on outcomes of statistical
processes.
b. Calculate mean, median, mode, standard deviation, z-scores, t-test, t-scores,
quartiles, and ranges, and explain their applications.
c. Apply statistics in decision-making and hypothesis testing.
d. Design, execute, make conclusions, and communicate the results of a statistical
experiment.
131
Course: Probability and Statistics
Unit Theme: Data Analysis
Suggested Suggested
Comp. Obj. Teaching Strategies Assessment
1 a, b, c, d, e Gather information on closing prices of selected stocks Rubric;
for a one-year period. In small groups and using Teacher observation;
different companies: Class discussion;
Examine differences in percentile growth from Report
month to month.
Interpret and analyze data using the necessary
formulas.
Communicate results in written and oral form to
the class.
After discussion, make conclusions about which
stock would be the best investment based upon
one year's growth.
1 b Explore to find the possible differences between the Short answer
largest and smallest of five integers whose mean is 5,
median is 5, and whose mode is 8.
1 a, c, d, e Time 30 periods of a pendulum swing for different Project
string lengths. Analyze results. Predict how tall a
pendulum is in a science museum.
132
Course: Probability and Statistics
Unit Theme: Representing Data
Suggested Suggested
Comp. Obj. Teaching Strategies Assessment
2 a, b, c Analyze monthly income/expenses using current Student graphs;
market values, which are independently and Rubric
realistically determined. Use the following categories
of expenses:
Taxes: federal income tax, state income tax, FICA
Housing: mortgage or rent, insurance, taxes
Groceries
Utilities: water, electric, gas, phone, sanitation fee,
cable
Automobile: payment, insurance, tag, gas
Entertainment
Savings
Charitable contributions
Insurance: medical, life
Clothing
Collect and organize data, then choose the graph type
that represents the data and construct this graph.
Analyze results to see if future adjustment should be
made in expense patterns.
2 a Gather nutritional data about favorite cereals. Decide Presentation
on best means to organize information; frequency,
stem-leaf plots, and/or histograms.
2 b, c Provide each group with a different data set. Each Peer evaluation
group decides on best type of graph to display data.
Groups share graphs and justification to the class.
133
Course: Probability and Statistics
Unit Theme: Probability
Suggested Suggested
Comp. Obj. Teaching Strategies Assessment
3 a, b Discuss the probability of tossing a coin. Conduct Teacher observation
experiments varying the number of tosses. Compare
and contrast theoretical and experimental probability.
3 a, b, g Reasearch the Buffon Needle Problem and perform Small groups;
the classic experiment by dropping pipe cleanerss on a Class discussion
tiled floor. Use data to compare with actual formulas
involving n.
3 c Investigate how a state, like Mississippi, determines Report
the sequence patterns of numbers and letters for
license plates or how the phone company decides to
issue new area codes.
3 d Use the school lunch menu and construct a tree Portfolio
diagram to determine the number of possible meals.
3 e Discuss whether the following example is a mutually Teacher observation;
exclusive event. Discussion;
Given a standard deck of 52 cards, find the probability Student response
of drawing a card that is a red card or a face card.
Validate by randomly pulling the red card and the face
cards and count the total number. Then change the
situation to drawing two cards from the deck that are
red cards or face cards and illustrate differences with
cards and explain use of combination formula for this
example.
3 e Discuss the differences between independent and Rubric
dependent events. Present the class with a bag of
marbles consisting of 5 red, 6 blue, and 4 green
marbles. Ask students to determine the probability of
drawing out a blue, a red, and another blue marble in
that order without replacement. Then, perform the
experiment again with replacement. Divide the class
into groups and discuss whether ―with replacement‖ or
―without replacement‖ has the greatest probability of
success. The large group will then discuss results of
the experiment and will explain their conclusions.
3 f Design a target with five sections so that the Project
probability of hitting only one particular section is 25%.
134
Course: Probability and Statistics
Unit Theme: Probability
Suggested Suggested
Comp. Obj. Teaching Strategies Assessment
3 g Using dice and decks of cards, work in small groups to Teacher observation
create a theoretical/experimental probability simulation
for one of the other groups to carry out.
3 h Suppose a presidential election has just taken place. Teacher-made test
A large sample of voters were interviewed on whether item
or not they switched party affiliations. The following
contains the probability data resulting from this survey.
Democrat Republican
L0.8
M.6
0.2 O
P
N0 0.4 Q
Given that a voter is a Democrat at this election, what
is the probability that party affiliation will be switched in
the election after the next two transitions? According
to statistics, at the time the survey was taken, 60% of
the voters were Democrat and 40% were
Republicans. Based on the survey results, what
percent of the population will be Democrats in the
election after two transitions?
3 i Repeatedly toss four coins and record the number of Class activity and
heads obtained on each trial. Find the mean number discussion
of heads in 5, 10, 25, 50, and 100 trials of the
experiment. For each number of trials, find the
probability distribution for the number of heads
obtained. (The mean of the random variable is 2.)
The mean number of heads observed when four coins
are tossed many times approaches the population
mean of the probability distribution.
135
Course: Probability and Statistics
Unit Theme: Inferential Statistics
Suggested Suggested
Comp. Obj. Teaching Strategies Assessment
4 a Design a method for obtaining a simple random Teacher Critique
sample of students. Sample to determine the
typical number of hours studied each week-night
by students in grades 11 and 12 at your school.
4 a Design a method for obtaining a stratified Teacher Critique
sample to determine who among three
hypothetical candidates will be elected
Homecoming Queen at your school.
4 b The teacher writes down all scores on the last Class discussion
major test. Each student will standardize his/her
score. Students will discuss measures of center
for the test scores and also measures of spread.
4 c, d Design an experiment to compare the means of Teacher grades
two samples. Write hypotheses, collect and project
analyze data, draw appropriate conclusions, and
communicate the results
136
ADVANCED PLACEMENT STATISTICS
The Advanced Placement Statistics course introduces students to the major
concepts and tools for collecting, analyzing, and drawing conclusions from data. Four
major areas of concentration include data explorations, design of experiments,
production of models using probability and simulation and statistical inference. The use
of technology will be an integral part of the course. This course is designed for students
who have successfully completed teaching137 Use graphical and numerical techniques to study patterns and to explore,
describe, and interpret data. (P, D, M, G, N)
a. Interpret graphical displays of distributions of univariate data (dot plots, stem
plots, histograms, box plots).
b. Summarize distribution of univariate data and correctly find and use measures of
center (mean, median, mode); measures of spread (range, interquartile range,
standard deviation); and measures of position (quartiles, percentiles,
standardized scores).
c. Explore bivariate data by analyzing patterns in scatterplots and residual plots,
performing logarithmic and power transformations to achieve linearity, finding
least squares regression lines, and finding correlation coefficients.
d. Explore categorical data, construct, and interpret frequency tables.
2. Plan a study by clarifying a question and deciding upon a method of data
collection and analysis. (P, D, N)
a. Know the characteristics of a well-designed and well-conducted study and be
able to distinguish between observational studies, surveys, and experiments.
b. Design a method for obtaining a simple random sample for a population of
interest and for obtaining a stratified sample when appropriate.
c. Identify sources of bias and discuss the concept of sampling error in studies.
d. Design experiments, to include the concepts of confounding variables, control
groups, placebo effects, blinding, randomization, replication, blocking, and
generalizability of results.
1383. Use probability to predict what the distribution of data should look like under a
given method. (P, D, M, G, N)
a. Use concepts of independent and mutually exclusive events, and apply the
addition, multiplication, and conditional probability rules to find the probability of
events.
b. Produce models using probability and simulation, and explain the ―law of large
numbers.‖
c. Find the mean and standard deviation of a random variable and the mean and
standard deviation for the sums and differences of independent random
variables.
d. Know properties of the normal distribution, use normal distribution tables, and
make inferences from these tables.
e. Simulate sampling distributions (distributions of a sample proportion, distribution
of a sample mean, distribution of a difference between two independent sampling
proportions, distribution of a difference between two independent sample
means).
f. Discuss and illustrate the Central Limit Theorem.
4. Use statistical inference to analyze data, draw appropriate conclusions, and
effectively communicate those conclusions. (P, D, G, N)
a. Find and interpret large sample confidence intervals for a proportion, a mean, a
difference between two proportions, and a difference between two means.
b. Appropriately use the following tests of significance: large sample tests for a
proportion, a mean, a difference between two proportions, and a difference
between two means (unpaired and paired); Chi-square test for goodness of fit,
homogeneity of proportions, and independence; single sample and two sample
t-procedures; and inference for slope of least squares line.
c. Write null and alternate hypotheses for studies, distinguish between one and two-
sided tests, calculate appropriate test statistics, find p-values, arrive at
appropriate conclusions, and communicate those conclusions effectively.
139
Grade Level: Advanced Placement Statistics
Unit Theme: Patterns and Data Interpretation
Suggested Suggested
Comp. Obj. Teaching Strategies Assessment
1 a Open a magazine arbitrarily and record the lengths of Check students'
all words in the first complete paragraph on the page. graphs and written
Create a dot plot of the lengths (number of letters) of description
words that were recorded. Write a few sentences
describing this distribution of word lengths. (Students
may choose various magazines and compare results.)
1 a, b Reconsider the data collected with word lengths. Check students' graph
Calculate the five number summary of this distribution and related comments
and draw a boxplot. Comment on what the boxplot
reveals about the distribution of word lengths. Are
there outliers?
1 a Consult the Farmer's Almanac or U. S. Census Report Check students'
to find a data set of interest. The Internet is also a graphs and analysis of
source for interesting data sets. Choose a one- graphs
variable data set such as percentage of residents 65
years of age or older in each of the fifty states. Draw a
histogram for the data. Make a stem plot for this data.
Describe the main features of the distribution. Is it
symmetric, right skewed, or left skewed? Single or
double peaked? Are there gaps or outliers?
1 b Write down all scores on the last major test. Each Class discussion;
student will standardize his/her score. Discuss Teacher observation
measures of center for the test scores and also
measures of spread.
1 c Collect data for number of students' siblings, and Check scatter plots
number of students' mothers' siblings. Draw a scatter
plot of students' siblings versus mothers' siblings.
Analyze patterns found in the scatter plot.
1 c Obtain from a favorite fast food restaurant nutritional Check scatter plot,
information about their sandwiches. List all regression line,
sandwiches, serving size (in ounces) of each residual plot, and
sandwich, and calories for each sandwich. Draw a analysis
scatter plot and reveal an association between a
sandwich's serving size and its calories? Determine
the least squares regression line for predicting calories
from serving size. Find the correlation coefficient.
Sketch a plot of residuals. How well does the least-
squares regression line fit the data?
140
Grade Level: Advanced Placement Statistics
Unit Theme: Patterns and Data Interpretation
Suggested Suggested
Comp. Obj. Teaching Strategies Assessment
1 c A courtier was offered a reward by an ancient king of Self-check
Persia. He asked for a grain of rice on the first square
of a chessboard, two grains on the second square,
then 4, 8, 16, etc. Plot the number of grains on each
square against the number of the square for squares 1
to 10 and connect the points with a smooth curve
(exponential curve). Take the logarithm of each of the
numbers of grains. Plot these logarithms against the
numbers of squares from 1 to 10. (straight line) Find
the least squares regression line for the logarithms of
the number of grains versus the number of squares.
Use this equation to predict the number of grains for
the 64th square.
1 d Classify each member of Congress according to Whole class
his/her gender and political party. Construct a assessment;
frequency table with row headings of Republican, Peer assessment
Democrat or other. Use column heading of male or
female. Interpret the frequency table.
141
Grade Level: Advanced Placement Statistics
Unit Theme: Sampling and Experimental Design
Suggested Suggested
Comp. Obj. Teaching Strategies Assessment
2 a, c Consult a scientific journal. Find an example of an Class discussion;
observational study, a survey, and an experiment. Peer assessment
Critique each study to determine if it is a well-designed
and well-conducted study. Identify any sources of
bias.
2 b Design a method of obtaining a simple random sample Teacher observation
to determine the typical number of hours studied each and critique
week night by students in grades 11 and 12 at your
school.
2 b Design a method for obtaining a stratified sample to Teacher critique
determine who among three hypothetical candidates
will be elected Homecoming Queen at your school.
2 d Divide class into groups of three. Each group will Teacher and peer
design an experiment, keeping in mind the concepts of critique of
confounding variables, control groups, placebo effects, experimental design
blinding, randomization, and replication.
142
Grade Level: Advanced Placement Statistics
Unit Theme: Probability and Data Distributions
Suggested Suggested
Comp. Obj. Teaching Strategies Assessment
3 a Using M&Ms, obtain probabilities for various colors. ● Class activity and
Apply the addition principle to compute the probability discussion
of choosing a red or blue M&M, when selecting one at
random.
3 a Use the multiplication and conditional probability rules ● Class activity and
to find the probability of selecting at random two male discussion
members of the class. (Assuming all names of class
members were put in a hat and two names were drawn
without replacement.) Find the conditional probability
of selecting a male member of the class, given the
student chosen has blonde hair.
3 b, c Repeatedly toss four coins and record the number of ● Class activity and
heads obtained on each trial. Find the mean number discussion
of heads in 5, 10, 25, 50, and 100 trials of the
experiment. (The mean number of heads x observed
when four coins are tossed many times approaches
the population mean of the probability distribution.)
The mean of the random variable = 2.) An illustration
of the ―Law of Large Numbers‖ follows. x will
approach 2 more closely as the number of trials
grow.
3 d Each student should calculate the ratio of his height ● Student and whole
and his arm span (e.g., height divided by arm span). class activity;
Produce a dotplot of the distribution of these ratios (for Teacher critique of
all students in class). Does the distribution appear to work
be roughly normal? Calculate the mean and standard
deviation of these ratios. Suppose that these ratios in
the population of all college students do in fact follow a
normal distribution with mean and standard deviation
equal to those found in your classroom sample. Under
this assumption, calculate the proportion of all students
who have a ratio greater than one (height greater than
arm span).
3 e Consider the population of the Reese's Pieces candies ● Individual and whole
made by Hershey. Suppose you want to learn about class activity
the distribution of colors of these candies but you can
only afford to take a sample of 25 candies. Record the
number and proportion of each color in your sample.
Each student should calculate the proportion of orange
candies obtained by the students in the class. If every
student estimated the population proportion of orange
candies by the proportion of orange candies in his
sample, would everyone arrive at the same
conclusion? Observing the sample results from the
entire class, estimate the population proportion of
orange candies. Observe the variation of the sample
proportions from sample to sample—the sampling
distribution of the sample proportion.
143
Grade Level: Advanced Placement Statistics
Unit Theme: Probability and Data Distributions
Suggested Suggested
Comp. Obj. Teaching Strategies Assessment
3 f Suppose a population consists of five employees for a ● Teacher critique of
firm. The number of years of employment are 5, 3, 6, answers
2, 4. Compute the mean length of employment for the
c h
population 4 . Select all possible samples of
size two from the population. Compute the mean of
each sample. Does the mean of the sample means
equal the population mean? Give the sampling
distribution of the means. Plot the probability
distribution of the sample means and the population.
Is the population normally or non-normally distributed?
Does the sampling distribution tend to approximate a
normal distribution? (Central Limit Theorem)
144
Grade Level: Advanced Placement Statistics
Unit Theme: Statistical Inference
Suggested Suggested
Comp. Obj. Teaching Strategies Assessment
4 a Have students think of a real situation in which they Teacher critique
would be interested in producing a confidence interval
to estimate a population proportion. Have them
describe how they would compute a 95% confidence
interval.
4 a, b, c Select one page from the white pages of a telephone Teacher grades
book. Disregard all listing of businesses, which project
provide only initials, and listing with first names that
are not gender-specific (like Pat or Chris). For the
listings, which can be identified as male or female,
count how many are male and how many are female.
What is the sample proportion of females in the
sample? Use the sample data to form a
95% confidence interval for the actual proportion of all
humans who are female. Does the confidence interval
provide a reasonable estimate of the actual proportion
of all humans who are female? (No) Explain. Using
your sample data, perform a test of significance to
address whether the sample data support the theory
that less than half of all of the telephone books'
individual listings carry female names. Write null and
alternate hypotheses. Calculate appropriate test
statistics, find p-value, and write a paragraph
describing your findings and explain how conclusions
follow from the test results.
145
| 677.169 | 1 |
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Over the last several years I have worked with a total of nine students who had a particular difficulty with math. This set has explained algebra in a clear and easy to understand way. I began with Key to Fractions and then moved to Key to Algebra. At the moment, I'm teaching six 8th and 9th grade students in a self-paced classroom. Each week I hear, "Oh. I never understood that before," about three times.
Every concept is explained well and demonstrated clearly. Each booklet has 37 pages with plenty of practice for each step. Because the books are short, the student has a sense of progress. It is encouraging to finish a book and get a new one. A separate book contains end of book tests. The notes and answers books are handy for fast grading.
My only challenge (though it has not been a problem), has been to get my students to read the actual words on each page. They believe they understand the instructions and try to fly through the work. When someone hits a snag, and asks for help, I always start with the instructions. That clears up 90% of our problems. I only get a real math question about twice a week. That's how good these books are!
I would not recommend this curriculum for fast paced students who want to move quickly.
Each student needs his or her own set of books. These are not copy masters. They are workbooks. You only need one copy of the notes and answers, and you only need one test booklet, as it is a copy master.
I used this series when homeschooling my daughter. The information was clearly explained and posed no problems in understanding any of the basic algebra concepts. She was able to complete almost a year of algebra before she entered public school in eighth grade and was placed in the "advanced" group.
We liked that each concept had lots of opportunity for practice if needed. The print was large enough for those students who have trouble with small, crowded print. Many activities are also "boxed off", helping the students keep their numerals lined up more easily and giving lots of room for those with large hand writing. This is helpful for students with learning disabilities.
These books are good but are lacking in explanations on how they get some of their answers. I even used a school text book and could not come up with the right answers on some of the problems. If you are looking to get extra practice on your Alg. work they are a good resource. Teachers do not let the kids get a hold of your answer books that is the only key you have some times.
These are excellent for the homeschooled student who just doesn't get math. All the foregoing reviews are accurate, regarding progression, clarity, presentation. We tried several traditional texts but none of them worked. They were confusing, moved to quick, presented too much at once, put too much on the page, tried to review everything every day. I am finally looking forward to my daughter actually learning algebra!
No Common Core. We searched a long time trying to find math books that didn't go Common Core for doing home school. My wife was familiar with these so we got them and love them. Don't go the Common Core route.
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Math Function Mania Desciption:
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Math Function Mania is a fun multimedia game that teaches functions, algebra and problem solving skills. Functions are very important in math! By mastering them, you will greatly increase your math skills. This game teaches you by the "hands on" method - you will discover how functions work by playing the game. In the "Mania" game you must first detect which function is being used, and then solve it by clicking on the correct multiple choice answer. There are 20 levels of play, with a virtually unlimited number of problems. Level one is easy, but by level twenty you will have to choose from among 20 different functions! Hints are available to help you learn; there are also over 20 practice rounds. An exciting Combat! option is included. In the Combat! game, you play head to head against another player. Whichever player "buzzes in" first gets to click on the answer - but if he/she fails the other player can steal! This can make learning math fun. Topics covered include equations, algebra, problem solving, critical thinking, polynomials, factoring, remainders, number bases, and prime numbers. After mastering this program, your understanding of math will improve and your SAT math scores will benefit. Requirements: 100 mhz pentium
Review Math Function ManiaEnjoy new game on your Palm.Clobber is a fascinating game that's easy to learn and fun to play. The game are full of opportunities for creating interesting positions to be solved.You can play against computer or play solitaire version.xClobber supports......
Fret Fun is the interactive guitar flash card game that helps you learn the note names for the guitar and get you on your way to reading music. It's very simple and fun to play! Each game presents a random selection of 20 notes, displayed one at a...
Splash Math is a fun and innovative way to practice math. With 11 chapters covering over 185 math skills and an endless supply of problems, it is by far the most comprehensive math workbook in the app store.
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Summary: Viewing stained glass from different angles or in various lights is necessary to discover its many qualities. Likewise, viewing solutions of differential equations from several points of view is essential to fully understand their behavior. Lomen and Lovelock provide an active environment for students to explore differential equations by using analytical, numerical, graphical, and descriptive techniques, and for students to use ODEs as a natural tool for modeling man...show morey interesting processes in science and engineering. ...show less
Basic Concepts. Autonomous Differential Equations. First Order Differential Equations - Qualitative and Quantitative Aspects. Models and Applications Leading to New Techniques. First Order Linear Differential Equations and Models. Interplay Between First Order Systems and Second Order Equations. Second Order Linear Differential Equations with Forcing Functions. Second Order Linear Differential Equations - Qualitative and Quantitative Aspects. Linear Autonomous Systems. Nonlinear Autonomous Systems. Using Laplace Transforms. Using Power Series5496.20 +$3.99 s/h
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Power Maths - A pre-calculus project - Sidney Schuman
A pre-calculus investigation designed to enable students to discover each calculus power rule independently (albeit in simplified form), and hence their inverse relationship. Students are required only to do simple arithmetic and some elementary algebra,
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The Power of One - Robert Matthews, The New Scientist
Benford's law demands that around 30 per cent of the numbers in a given data set will start with a 1, 18 per cent with a 2, right down to just 4.6 per cent starting with a 9. This essay provides a mathematical history behind the counterintuitive law,
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Powersim
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PQRST Puzzle Competition - Cihan Altay
PQRST is a quarterly online puzzle competition open to all, with competitions in January, April, July and October. Download the test as PDF, then solve and rate the puzzles within seven days. The PQRST site highlights top competitiors and puzzles receiving
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Practical Foundations of Mathematics - Paul Taylor
The full text (online, in HTML) of the book (some diagrams may be missing), published by Cambridge University Press in March, 1999 as number 59 in their series Cambridge Studies in Advanced Mathematics. Practical Foundations collects the methods of construction
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The Precalculus Algebra TI-83 Tutorial - Mark Turner
An online tutorial for using the TI-83 graphing calculator to solve the
kinds of problems typically encountered in a college algebra or
precalculus algebra course. Step-by-step instructions with full key
sequences and animated screen images. Includes
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Pretty Functions - Ivars Peterson (MathTrek)
About graphing calculators, and the software Graphing Calculator, a computer program for quickly visualizing two- and three-dimensional mathematical objects. Graphs illustrate plotting a given function, then seeing what happens when you
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Preuve Proof Prueba
A newsletter in French, Spanish, and English, the theme of which is teaching and learning mathematical proofs. Includes an extensive bibliography consisting of books, chapters in books, journal articles, and theses.
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Prime Curios! - G. L. Honaker, Jr., Chris K. Caldwell
A collection of curiosities, wonders and trivia related to prime numbers. Look up a number (up to 10^21+) and find what connections it has to the primes. The database has over 3400 curios corresponding to more than 1960 different numbers. The number of
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primegen - D. J. Bernstein
Download primegen, a small, fast library to generate prime numbers in order. Using the Sieve of Atkin instead of the traditional Sieve of Eratosthenes, it generates the 50847534 primes up to 1000000000 in just 8 seconds on a Pentium II-350; it prints
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Prime Listening - Ivars Peterson (MathTrek)
Mathematician Chris K. Caldwell of the University of Tennessee in Martin has developed a scheme for listening to sequences of primes - to hear both simple patterns and perplexing irregularities found among those numbers. "Multimedia allows the use of
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Prime Number List - James Brennan
A page with a script that generates a list of prime numbers. Once started, it will run until you click 'Stop' or your computer runs out of memory. A second page writes the list to a new Web page suitable for printing.
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Prime Numbers and Factors - Machinery's Handbook 25
Tables give factoring information on numbers from 9600 to 21600. Reprinted from Machinery's Handbook, 25th Edition ("The Bible of the Mechanical Industries"). Prime numbers in the tables are indicated by the letter P. If a number is not prime, the table
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Prime Numbers - MacTutor Math History Archives
Linked essay describing the work on primes from Pythagoras through Gauss, Legendre, Riemann, and Valee Poussin, with additional sections on still unsolved problems, the latest prime records, and other web sites, as well as 21 references (books/articles).
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A Prime Surprise - Ivars Peterson (MathTrek)
Many of the 100 or so people who had helped with the nine-prime effort immediately signed up for the new quest and began checking numbers. To everyone's surprise, Manfred Toplic (the same!) set the new record, reporting on March 2 that he had found 10
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Prime Talent - Ivars Peterson (MathTrek)
Whole numbers have all sorts of curious properties. Consider, for example, the integer 1998. It turns out that 1998 is equal to the sum of its digits plus the cubes of those digits (1 + 9 + 9 + 8 + 13 + 93 + 93 + 83). What's the largest number for which
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This book is designed for use by independent study students. There are five chapters in this book: (1) Fractions, (2) Decimals, (3) Percents, (4) Calculator Skills/Formulas/Proportions (5) Algebra.... More > In each chapter the student begins by studying the basic concepts, then progresses through computational skills involving both pencil/paper and calculator approaches. Applied problems are presented throughout the book to illustrate the relevance of each topic. Included in each chapter are numerous examples, practice problems with full answer keys, and quizzes for self-evaluation. At SWTC this textbook is used for Math Review, and Occupational Math.< Less
Sett i gang I consists of 15 chapters organized
around five main themes. The textbook is 229
pages and suitable for the first semester of a
university course or during the first year of a
community... More > education classThis is a prealgebra textbook, used by the Department of Mathematics at College of the Redwoods, Eureka, California, in their Math 376 course.
Errata and Individual chapter and solutions are... More > available at: J-M Institute Private/Home High School Workbook III is the secondThe J-M Institute Private/Home High School Workbook IV is the fourthFrom the Heart of a Teacher exposes the ugly truth about the current educational system in the United States from a man who was once the student no teacher wanted in their classroom but is now the... More > teacher that all students want to be in his.
In this breath-taking, eye-opening, "oh no he didn't" literary work, author Rodney Jordan holds no punches when it comes to the breakdown of American schools and all parties involved, which has left those who truly care about the futures of our children, scratching their heads.
With refreshing honesty, From the Heart of a Teacher not only raises awareness of the ineffective policymaking, teaching, and parenting impacting the lives of our students in grades K-12, but also offers solutions on how to fix this crisis. Jordan, a back-to-back Teacher of the Year award winner in 2010 and 2011, brings the truth to light in this book from beginning to end, challenging all who are involved when it comes to student achievement.< Less
The challenges that face African American students seeking a higher education are well documented, but high-performing and gifted students continue to succeed in going to college and thriving once... More > they arrive there. In this study, author Stacey Price Brown, PhD, looks at the educational experience through the eyes of a selection of these students. For them, the college planning process begins in early childhood, and it does not end until high school graduation.
Through these students' stories, Brown offers practical recommendations on how to create a culture that promotes the value of higher education. Learn how to help students
develop competitive college applications;
gain admittance to the college of their choice;
set high expectations for themselves; and
leverage supportive environments.
Designed to help students, parents, and educators, Stories Untold presents the journeys of talented students who have navigated the curves in the long road that leads to college.< Less
A graphing calculate can be used to bridge the communication gap between teachers and students. Concepts and vocabulary come alive when a graphing calculator is implemented properly. Change how we... More > are educated one student at a time.< Less
The study of High School Geometry is largely about understanding the attributes of different terms and rules. In this workbook, students have the opportunity to creatively describe those attributes... More > using the "Pattern Puzzle" approach inspired by the work of Russian computer scientist, Mikhail Bongard. His Bongard Problems described situations by displaying six figures that all contained a common attribute along with six accompanying figures, none of which contained that defining attrribute.
Students can use this principle to describe Geometry terms, theorems, postulates, constructions, properties and laws in ways that will be meaningful to them.
The workbook allows instructors to adapt the content to the particular needs of their own course, and is aligned with the Common Core State Standards for Mathematics.
For more information, feedback or suggestions, please contact the author, Bill Doherty, at [email protected]< Less
The mindfish Guide to the SAT and ACT is a comprehensive preparation tool from an industry leader in standardized test prep. Written by two graduates of Stanford University, the mindfish Guide covers... More > every strategy necessary for success on the SAT and ACT.< Less
Rogue Shakespeare was Mary Baldwin College's 2013-14 Shakespeare and Performance MFA class. Twelve students embarked on a one-year journey to put scholarship into practice by collaboratively... More > producing and performing in six early modern or early modern inspired theatrical works in a range of venues and in a variety of styles. Our home venue was the recreated Blackfriars Playhouse, benefiting from the college's partnership with internationally acclaimed American Shakespeare Center and combining academic and applied aspects of Shakespearean theatrical studies. Our diverse interests and backgrounds coalesced into an ambitious "Season of Treason" which roguishly challenged textual authenticity, cultural gender norms, and modern Shakespearean theatrical practice. The twelve essays in this book collectively discuss and debate the processes and results of our one-year MFA theatre company.< Less
AutPlay Therapy is a play therapy and behavioral therapy based approach to working with children and adolescents dealing with Autism Spectrum Disorder and other developmental disabilities. AutPlay is... More > a comprehensive model to assist children and adolescents in gaining needed skills and abilities. The best selling AutPlay Therapy book serves as a treatment manual and describes the AutPlay process, provides the phases of treatment in AutPlay, assessment materials, and directive play therapy techniques.< Less
Broadcast journalist, Maria Dorfner shares a behind-the-scenes glimpse into working in the competitive field of television news. Drawing on three decades of experience, she shares challenges and... More > insightful tips research, writing, reporting, producing, pitching and storytelling.< Less
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ARadicalEqn is a powerful learning aid to help students master the solving of radical equations.Interactive Coaching Calculators and Guides combine to speed the learning process.The Coaching Calculator covers equations such as :6?(x ) = 33?(2x - ...
Manufactured Analytical Solution Abstraction (MASA): a library for applying the Method of Manufactured Solutions to verification of numerical software used for solving systems of nonlinear algebraic and differential equations.
These 19 lessons provide initial instruction or intervention on linear equations and inequalities of two variables and functions. The first 4 lessons define those equations and their solutions, provide instruction on graphing those equations and ...
The ISOLDE package (Integration of Systems of Ordinary Linear Differential Equations) is a Maple package for the symbolic resolution of linear differential systems, such as the formal reduction and finding closed-form solutions.
Maxima is a system for the manipulation of symbolic and numerical expressions, including differentiation, integration, Taylor series, Laplace transforms, ordinary differential equations, systems of linear equations, polynomials, and sets, lists, vect
ALL-IN-ONE MULTI-PHYSICS FINITE ELEMENT MODELING Ever wish there was a flexible system for solving all the partial differential equation problems that come up in science and engineering, so you didn't have to buy and learn a new software tool for eac 19292 trigonometric equations with guided solutions, and encourages to learn through in-depth understanding of each solution step and repetition rather than through rote m
Learn IT lessons are designed in a way that is easy to understand and improve problem solving skills. It makes math friendlier for students who struggle with math. The Mathematical concepts are explained through Animated examples and Voice
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Math.NET aims to provide a self contained clean framework for symbolic mathematical (Computer Algebra System) and numerical/scientific computations, including a parser and support for linear algebra, complex differential analysis, system solving and more
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Graphing Systems of Linear Inequalities In this video, the instructor goes through the steps needed to graph a system of linear inequalities. He discusses slope, shows how to draw the line on the coordinate plane, and explains what section of the graph should be shaded. There is some shadow on the white board which makes it a little more difficult to see at times during the instruction. (04:49)
AuthorThe Works of Salvador Dali This video shows the most important works of the artist with photographs of him interspersed throughout. Dali lived from 1904-1989. He was a surrealist but was greatly influenced by Resnaissance artists. He loved to paint bizarre but striking images with ornate clothing. There is no narration and it is set to the music of Mogwsi. (5:01) Author(s): No creator set
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Bible Book Bop Memorize the books of the Bible with the Go Fish Guys! Song will help kids learn the books of the Bible. Author(s): No creator set
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Half Lion, Half Tiger - It's a Liger This short film features ligers at a German Zoo. (Ligers are only bred and raised in captivity. Scientists are doubtful that a liger could exist in the wild.) Run time 01:22. Author(s): No creator set
18.125 Measure and Integration (MIT) This graduate-level course covers Lebesgue's integration theory with applications to analysis, including an introduction to convolution and the Fourier transformHow to Give a Funny Speech : Funny Speeches: Practice Humor In this video you are reminded that it isn't always easy to get a laugh when making a speech. Tracy Goodwin, professional speaker and communications instructor, gives you tips on how to be better prepared for sharing humor through speech. Author(s): No creator set
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Practicing Speeches: Study Outline In this video, professional speaker and communications instructor Tracy Goodwin, teaches that it is best to work from an outline. She provides you with numerous tips including that you need to read over your outline multiple times so that your speech practice will be profitable. This is a great video to get you started on the path to a fabulous speech. (01:07)
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The Frog Prince Part 3 This is part 3 of 11 of the very cute musical / movie, The Frog Prince, featuring many great actors and actresses from the 1980's. Author(s): No creator set
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Who Leads, Who Follows? A Multi-level Perspective of Energy Transitions in the Transport Sector Part of the Transitioning towards Electric Vehicles seminar series held at the Transport Studies Unit of the Oxford University Centre for the Environment. The electrification of the vehicle fleet involves a mass of actions to be taken by European, national and local government, a range of industries and consumers. It involves coordination between transport and energy policy if the benefits of decarbonisation are to be realised. The changes must also fit (and compete for resources) with broader p Author(s): No creator set
A&E Biography. In 1883, Wilde arrived in Paris and "put his aesthetic posing behind him." He wrote the play "The Duchess of Padua" for Mary Anderson; she turns it down. He goes back to London and continues to lecture. There he meets Constance Lloyd and marries her. Apparently unaware of his homosexuality, they have two sons, Cyril in 1885 and Vyvyan in 1886. At 32 he accepts a job as an editor with a popular magaz Author(s): No creator set
United Nations Economic and Social Commission for Western Asia The United Nations Economic and Social Commission for Western Asia (UNESCWA) is one of five regional commissions created by the United Nations (UN) in order to fulfil the economic and social goals set out in the UN Charter by promoting cooperation and integration between the countries in each region of the world. The UNESCWA website provides details of its activities including its focus acreas of sustainable development and productivity, social development, economic development and globalisation Author(s): No creator set
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Precalculus : With LimitsEngineers looking for an accessible approach to calculus will appreciate Young's introduction. The book offers a clear writing style that helps reduce any math anxiety they may have while developing their problem-solving skills. It incorporates Parallel Words and Math boxes that provide detailed annotations which follow a multi-modal approach. Your Turn exercises reinforce concepts by allowing them to see the connection between the exercises and examples. A five-step problem solving method is also used to help engineers gain a stronger understanding of word problems.
Review: Equations and Inequalities
Linear Equations
Quadratic Equations
Other Types of Equations
Inequalities
Graphing Equations
Lines
Modeling Variation
Functions and Their Graphs
Functions
Graphs of Functions
Graphing Techniques: Transformations
Combining Functions
One-to-One Functions and Inverse Functions
Polynomial and Rational Functions
Quadratic Functions
Polynomial Functions of Higher Degree
Dividing Polynomials
The Real Zeros of a Polynomial Function
Complex Zeros: The Fundamental Theorem of Algebra
Rational Functions
Exponential and Logarithmic Functions
Exponential Functions and Their Graphs
Logarithmic Functions and Their Graphs
Properties of Logarithms
Exponential and Logarithmic Equations
Exponential and Logarithmic Models
Trigonometric Functions of Angles
Angle Measure
Right Triangle Trigonometry
Trigonometric Functions of Angles
The Law of Sines
The Law of Cosines
Trigonometric Functions of Real Numbers
Trigonometric Functions: The Unit Circle Approach
Graphs of Sine and Cosine Functions
Graphs of Other Trigonometric Functions
Analytic Trigonometry
Verifying Trigonometric Identities
Sum and Difference Identities
Double-Angle and Half-Angle Identities
Product-to-Sum and Sum-to-Product Identities
Inverse Trigonometric Functions
Trigonometric Equations
Vectors, the Complex Plane, and Polar Coordinates
Vectors
The Dot Product
Polar (Trigonometric) Form of Complex Numbers
Products, Quotients, Powers, and Roots of Complex Numbers
Polar Coordinates and Graphs of Polar Equations
Systems of Linear Equations and Inequalities
Systems of Linear Equations in Two Variables
Systems of Linear Equations in Three Variables
Systems of Linear Equations and Matrices
Matrix Algebra
The Determinant of a Square Matrix and Cramer's Rule
Partial Fractions
Systems of Linear Inequalities in Two Variables
Conics, Systems of Nonlinear Equations and Inequalities, and Parametric Equations
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mathematics pmr past year question with answer
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Modules Explore Real-Life Calculus
04/01/96
Calculus Connections explores mathematical theory and its applications in the world around us through richly produced video, sound and interactive simulations. Each volume consists of eight multimedia modules and a corresponding workbook. Modules begin by presenting a real-life application of a calculus concept -- a plane taking off, a bridge collapsing, a skydiver jumping, etc. Students discover how changing variables or conditions will affect the model and consequently the physical application. Predefined routes through the material take approximately 45 minutes to complete. One can also plot, manipulate and save 2D or 3D graphs, or obtain additional information through online references. John Wiley & Sons, New York, NY, (800) 225-5945, W
This article originally appeared in the 04
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This site is the entry list to a collection of short, engaging text/graphic modules on standard topics in Elementary...
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This site is the entry list to a collection of short, engaging text/graphic modules on standard topics in Elementary Algebra. They are available as Youtube videos for free classroom or download by instructors and students. Basic formulas, sample problems and standard applications are included. Format is text, audio and graphics.
Although commercials turn me off, too, I thought this short collection of some notable exercises from my text would be worth...
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Although commercials turn me off, too, I thought this short collection of some notable exercises from my text would be worth posting. This is a printable pdf with exercises from precalculus and first year calculus. Most exercises show that the tools available in these classes already give access to a surprising level of sophistication. Some other exercises are specifically designed to make a point about an important skill or a frequently observed mistakeThis project, dedicated to producing electronic materials for use within courses has developed 71 Java Applets demonstrating...
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This project, dedicated to producing electronic materials for use within courses has developed 71 Java Applets demonstrating concepts in science and mathematics. The materials are for college and graduate teaching. Materials have no searchable metadata.
FREE makes it easier to find teaching and learning resources from the federal government. There are teaching resources...
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FREE makes it easier to find teaching and learning resources from the federal government. There are teaching resources in K-12 for Arts & Music, Language Arts, Mathematics, History, Science, and special collection materials.There are more than 1,500 federally supported teaching and learning resources are included from dozens of federal agencies. New sites are added regularly.
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Calculus is a discipline in mathematics focused on limits, functions, derivatives, integrals, and infinite series, and which constitutes a major part of modern university education. It has two major branches, differential... Full article >>>
Integration is an important concept in mathematics, specifically in the field of calculus and, more broadly, mathematical analysis. Given a function ƒ of a real variable x and an interval of the real line, the integral Full article >>>
An overview of the background to calculus and a list of some applications. ... Calculus is concerned with comparing quantities which vary in a non-linear way. ... Full article >>>
Calculus, Prerequistes and Applications: a Flowchart. Possible ways to Use this Text ... Basic Calculus: From Archimedes to Newton, 2001, and ... Full article >>>
Features topic summaries with practice exercises for derivative and integral calculus. Includes solutions. Authored by D. A. Kouba. Full article >>>
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New Scientist full online access is exclusive to subscribers. Registered users are given limited access to content, find out more. To read the full article, log in or subscribe to New Scientist.
Student Review: The changing face of mathematics
MATHEMATICS is changing. Not at its deepest levels: today's newest mathematical ideas fit comfortably into the mainstream of mathematical thought. If Newton, Gauss or Hilbert were suddenly resurrected, each would still recognise the activity as mathematics. The change is one of emphasis and style, with more overt attention to the relationship between theory and applications, and more use of the computer as an experimental aid.
These changes have appeared from two directions: research and schoolteaching. The subject is simultaneously changing from the top down and from the bottom up. The task, therefore, that is facing the authors of undergraduate texts, and the designers of undergraduate curricula, is to make sure the changes meet in the middle. I have been worrying that they may not succeed, but this year's new texts offer some grounds for optimism. I hope next year will confirm the trend.
Starting from the bottom: one
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...Thomas and received an A in the course. Linear Algebra is the study of matrices and their properties. The applications for linear algebra are far reaching whether you want to continue studying advanced algebra or computer science.
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Tutorial fee-based software for PCs that must be downloaded to the user's computer. It covers topics from pre-algebra through pre-calculus, including trigonometry and some statistics. The software pos... More: lessons, discussions, ratings, reviews,...
Algebra Concepts is an interactive learning system designed to provide instruction in mathematics at the 7th grade enrichment through adult levels. The instructional goals for Algebra Concepts include... More: lessons, discussions, ratings, reviews,...
Algebra Concepts is a tool for introducing many of the difficult concepts that are necessary for success in higher level math courses. This program includes a special feature, the Algebra Tool Kit, whStudents will investigate rational roots of polynomials graphically and numerically. Students will use the Rational Zero Theorem and test roots by plugging them into the given function using spreadsh... More: lessons, discussions, ratings, reviews,...
This collection of free worksheets provides practice in a variety of algebra topics, generating ten problems at a time for users to solve. Each worksheet is printable and comes with an answer key.
To
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Basic Topology
9780387908397
ISBN:
0387908390
Pub Date: 1983 Publisher: Springer Verlag
Summary: In this broad introduction to topology, the author searches for topological invariants of spaces, together with techniques for calculating them. Students with knowledge of real analysis, elementary group theory, and linear algebra will quickly become familiar with a wide variety of techniques and applications involving point-set, geometric, and algebraic topology. Over 139 illustrations and more than 350 problems of ...various difficulties will help students gain a rounded understanding of the subject.
Armstrong, M. A. is the author of Basic Topology, published 1983 under ISBN 9780387908397 and 0387908390. Four hundred forty five Basic Topology textbooks are available for sale on ValoreBooks.com, fifty one used from the cheapest price of $46.85, or buy new starting at $61.53
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Oak Ridge N, TX Algebra worked with algebra extensively and understand what we need to do to master it. Calculus introduces abstract mathematical concepts that often require significant explanation in to understand its fundamental concepts. Calculus becomes even more complex in the second half of the basic course
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About the book:
Designed for the three-semester course for math and science majors, the Larson/Hostetler/Edwards series continues its tradition of success by being the first to offer both an Early Transcendental version as well as a new Calculus with Precalculus text. This was also the first calculus text to use computer-generated graphics (Third Edition), to include exercises involving the use of computers and graphing calculators (Fourth Edition), to be available in an interactive CD-ROM format (Fifth Edition), and to be offered as a complete, online calculus course (Sixth Edition). Every edition of the book has made the mastery of traditional calculus skills a priority, while embracing the best features of new technology and, when appropriate, calculus reform ideas. The Seventh Edition also expands its support package with an all-new set of text-specific videos.
P.S. Problem-Solving Sections, an additional set of thought-provoking exercises added to the end of each chapter, require students to use a variety of problem-solving skills and provide a challenging arena for students to work with calculus concepts.
Getting at the Concept Exercises added to each section exercise set check students' understanding of the basic concepts. Located midway through the exercise set, they are both boxed and titled for easy reference.
Review Exercises at the end of each chapter have been reorganized to provide students with a more effective study tool. The exercises are now grouped and correlated by text section, enabling students to target concepts requiring review.
The icon "IC" in the text identifies examples that appear in the Interactive Calculus 3.0 CD-ROM and Internet Calculus 2.0 web site with enhanced opportunities for exploration and visualization using the program itself and/or a Computer Algebra System.
Think About It conceptual exercises require students to use their critical-thinking skills and help them develop an intuitive understanding of the underlying theory of the calculus.
Modeling Data multi-part questions ask students to find and interpret mathematical models to fit real-life data, often through the use of a graphing utility.
Section Projects, extended applications that appear at the end of selected exercise sets. may be used for individual, collaborative, or peer-assisted assignments.
True or False? Exercises, included toward the end of many exercises sets, help students understand the logical structure of calculus and highlight concepts, common errors, and the correct statements of definitions and theorems.
Motivating the Chapter sections opening each chapter present data-driven applications that explore the concepts to be covered in the context of a real-world settingBookworm0963 via United States
Hardcover, ISBN 0669095680 Publisher: D.C. Heath, 1985 Usually ships in 1-2 business days
Hardcover, ISBN 0669095680 Publisher: D.C. Heath, 1985 Usually ships in 1-2 business days, A brand NEW book barely opened.This interesting copy is in excellent condition in both price and value. We deliver within 4 - 10 working days with USPS and free tracking / delivery confirmation. Great Customer satisfaction with money back guaranteed.
Hardcover, ISBN 0669095680 Publisher: D.C. Heath, 1985 Usually dispatched within 1-2 business days, An interesting new book on Calculus with Analytic Geometry barely opened. Despite storage dust, the book remain new and in excellent condition for both the price and value. We deliver within 10 - 16 working days with First Class Mail. Great Customer satisfaction with money back guaranteed.669095680 Publisher: D.C. Heath, 1985 Used - Acceptable. A used book that may have some cosmetic wear (i.e. shelf-wear, slightly torn or missing dust jacket, dented corner.) All text in great shape!
Softcover, ISBN 0669095680 Publisher: D.C. Heath, 1985 Used - Good. A great value for the avid reader! GOOD can range from a well cared for book in great condition to average with signs of slight wear. Overall, All text in great shape! 1986 3rd ed. Illustrated.. Hardcover. Used - Good Good . Only lightly used. Book has minimal wear to cover and binding. A few pages may have small creases and minimal underlining. Book selection as BIG as Texas. 3rd ed. Illustrated.
Hardcover, ISBN 0669095680 Publisher: D.C. Heath, 1985 Used - Good. Shipped within 24 hours. 100% Refund Guaranteed. Good copy with average wear. Comes with dust jacket if published with one - DJ may have some tears and rubbing.
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Math for the Sciences
If you need help with the math part of a science topic, you have come to the right place. Note that this will not help you with direct science topics, but will help you with the math required to solve various science problems.
You do not have to be a student at WTAMU to use this site. It is accessible 24/7 to anyone that has access to the Internet.
If this is your first visit to our website, please read
the disclaimer.
Please click on the type of science for which you need math help:
If you have any comments about this website email Kim Seward at [email protected]
This site is brought to you by West Texas A&M University (WTAMU). It was created by Kim Seward with the assistance of Jennifer Puckett. It is currently being maintained by Kim Seward.
Disclaimer:
WTAMU and Kim Seward are not responsible for how a student does on any test or any class for any reason including not being able to access the website due to any technology problems. We cannot guarantee that you will pass your math class after you go through this website. However, it will definitely help you to better understand the topics covered.
Throughout this website, we link to various outside sources. WTAMU and Kim Seward do not have any ownership to any of these outside websites and cannot give you permission to make any kind of copies of anything found at any of these websites that we link to. It is purely for you to link to for information or fun as you go through the study session. Each of these websites have a copy right clause that you need to read carefully if you are wanting to do anything other than go to the website and read it. We discourage any illegal use of the webpages found at these sites.
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This ebook is available for the following devices:
iPad
Windows
Mac
Sony Reader
Cool-er Reader
Nook
Kobo Reader
iRiver Story
Tips for simplifying tricky operations
Get the skills you need to solve problems and equations and be ready for algebra class
Whether you're a student preparing to take algebra or a parent who wants to brush up on basic math, this fun, friendly guide has the tools you need to get in gear. From positive, negative, and whole numbers to fractions, decimals, and percents, you'll build necessary skills to tackle more advanced topics, such as imaginary numbers, variables, and algebraic equations.
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Hwei Hsu, Schaum's Outline of SignalsandSystems. B.P. Lathi, Signal Processing andLinearSystems, Oxford (this book is excellent but very expensive). Student Learning Objectives: after having completed EE210 students should have acquired the
Understand use of different transforms and analyze the discrete time signalsandsystems. 2. Realize the use of LTI filters for filtering different real world signals. 3. Capable of calibrating and resolving different frequencies existing in any signal.
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Enter your mobile number or email address below and we'll send you a link to download the free Kindle Reading App. Then you can start reading Kindle books on your smartphone, tablet, or computer - no Kindle device required.
Number theory is concerned with the properties of the natural numbers: 1,2,3,.... During the seventeenth and eighteenth centuries, number theory became established through the work of Fermat, Euler and Gauss. With the hand calculators and computers of today, the results of extensive numerical work are instantly available and mathematicians may traverse the road leading to their discoveries with comparative ease. Now in its second edition, this book consists of a sequence of exercises that will lead readers from quite simple number work to the point where they can prove algebraically the classical results of elementary number theory for themselves. A modern high school course in mathematics is sufficient background for the whole book which, as a whole, is designed to be used as an undergraduate course in number theory to be pursued by independent study without supporting lectures.
{"currencyCode":"USD","itemData":[{"priceBreaksMAP":null,"buyingPrice":53.53,"ASIN":"0521575400","isPreorder":0},{"priceBreaksMAP":null,"buyingPrice":66.52,"ASIN":"0521788366","isPreorder":0}],"shippingId":"0521575400::OJrCryhfxLArwqwDc8YCcI0lTrCZyFjy8b2F8pvmsd3UV5gKn5wVs6jj%2B6yRvKXX0%2B2FfOMr1t7g1Wy7wraeWp1GvIoCv5L1NLMDFL54t%2BM%3D,0521788366::AYxQPod%2Ba6O%2Bwqs2%2BvM3EXOXmvIxdMXlHa3HZ%2F50%2FMid6xE63FrHV0mzXI7fxRdGC1HvcIRZDNyc2j7NWFqBveRkP%2BrlQvPZEXDr6%2BFmII'm pleased to report there is a new edition of R. Burn's A Pathway into Number Theory, a book that takes readers quickly and painlessly from simple facts about whole numbers to the wonders of the quadratic forms, Pell's equation and Minkowski's theorem.' Ian Stewart, New Scientist
'... admirably suitable for those meeting number theory for the first time and for unsupported individual study.' Nick Lord, The Mathematical Gazette
Book Description
Now in its second edition, this book consists of a sequence of exercises that will lead readers from simple number work to the point where they can prove algebraically the classical results of elementary number theory for themselves. A high-school course in mathematics is the only requirement.
Most Helpful Customer Reviews
This book is a carefully sequenced set of problems along with answers and a few comments. Burn uses those problems to introduce important number theory ideas. I enjoyed working through the problems to learn more about number theory. Most problems are accessible to those with a good high school mathematics background.
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Description:Readers who use this text are motivated to learn mathematics. They become more confident and are better able to appreciate the beauty and excitement of the mathematical world. That's why the new Ninth Edition of Musser, Burger, and Peterson's best-selling textbook focuses on one primary goal: helping students develop a true understanding of central concepts using solid mathematical content in an accessible and appealing format. The components in this complete learning program--from the textbook, to the eManipulative activities, to the online problem-solving tools and the resource-rich website--work in harmony to help achieve this goal.
Description:Abigail Mercer was breathless with anticipation at being reunited with Spencer Law, whom she met once and later married by proxy. But now the dashing Viscount Ravenswood denies all knowledge of their union! Far too many witnesses have made it impossible for the secretive Spencer to reject his "bride" without causing a scandal. So he has proposed a marriage in-name-only until they can locate his mysteriously absent younger brother who is responsible for everything! and untangle this messy affair. Abigail is incensed, irate . . . and irresistibly attracted to this handsome, infuriating man who hides his smoldering passion behind a proper exterior. So the lady will agree to his terms on one condition: Spencer must seal their bargain with a kiss. But he finds that one deep, lingering, unforgettable kiss isn't nearly enough. And keeping his hands off his pretty wife is going to be much harder than he thought . . .
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Elementary Algebra: Algebra Within Reach-Text Only - 6th edition
Summary: Larson IS student success. ELEMENTARY ALGEBRA: ALGEBRA WITHIN REACH owes its success to the hallmark features for which the Larson team is known: learning by example, a straightforward and accessible writing style, emphasis on visualization through the use of graphs to reinforce algebraic and numeric solutions and to interpret data, and comprehensive exercise sets. These pedagogical features are carefully coordinated to ensure that students are better able to make connections between...show more mathematical concepts and understand the content. With a bright, appealing design, the new Sixth Edition builds on the Larson tradition of guided learning by incorporating a comprehensive range of student success materials to help develop students' proficiency and conceptual understanding of algebra. The text also continues coverage and integration of geometry in examples and exercisesINSTRUCTOR EDITION. ALL ANSWERS INCLUDED. Identical to student edition.NO ACCESS CODE or CD. May have tape on cover. SHIPS FAST! ! SAME DAY or w/in 24 hours.EXPEDITED SHIPPING AVAILABLE TOO!!
$119.90 +$3.99 s/h
New
Environment Recycle Books Denham Springs, LA
Please read description before purchase >>> instructor annotated version printed on cover with all identical Students content with teaching tips, and all solutions text only no access code. satisfacti...show moreon guarantee Quicker shipper with tracking # Expedited shipping available with Priority mail for fastest delivery ...show less
Hardcover New 128508747
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DescriptionThis fresh new approach fully covers the Extended Cambridge IGCSE in Mathematics and supports students to achieve the strongest results in exams. Providing a sequential and logical teaching path through the full syllabus, it thoroughly and euqally addresses all the four curriculum areas. Focused on active learning, it includes lots of worked examples and graduated exercises that will develop confidence as students progress. A full set of answers is included, and a free CD loaded with conceptual support for every part of the book further confirms understanding. EAL-friendly, with clear pictures and diagrams, a Teacher Resource Kit is also available, providing ideas, lesson plans and support. Endorsed by Cambridge International Examinations.
Reviews for Essential Mathematics for Cambridge IGCSE Student Book
Quality of AnswersBook rating: 2
Okay so I paid a lot of money for this book assuming it's a good book. But I'm WRONG. A lot of the answers in the answer sheet is printed wrong (they think 10 x 10= 110)......... Do NOT buy this book unless you're looking for paper to recycle. by Bevan King
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This section contains free e-books and guides on Linear Algebra, some of the resources in this section can be viewed online and some of them can be downloaded.
This textbook is meant to be a
mathematically complete and rigorous introduction to abstract linear algebra for
undergraduates, possibly even first year students, specializing in mathematics.
Author tried very hard to emphasize the fascinating and important interplay
between algebra and geometry.
Linear algebra
pervades and is fundamental to algebra, geometry, analysis, applied mathematics,
statistics, and indeed most of mathematics. This course note lays the
foundations, concentrating mainly on vector spaces and matrices over the real
and complex numbers.
This lecture note
explains the concepts of projective space and curves in the projective plane.
Covered topics are: Projective spaces, Plane curves, Intersections of curves,
The genus of a curves and Riemann-Roch theorem.
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More About
This Textbook
Overview
An introduction to the mathematical skills needed to understand finance and make better financial decisions
Mathematical Finance enables readers to develop the mathematical skills needed to better understand and solve financial problems that arise in business, from small entrepreneurial operations to large corporations, and to also make better personal financial decisions. Despite the availability of automated tools to perform financial calculations, the author demonstrates that a basic grasp of the underlying mathematical formulas and tables is essential to truly understand finance.
The book begins with an introduction to the most fundamental mathematical concepts, including numbers, exponents, and logarithms; mathematical progressions; and statistical measures. Next, the author explores the mathematics of the time value of money through a discussion of simple interest, bank discount, compound interest, and annuities. Subsequent chapters explore the mathematical aspects of various financial scenarios, including:
Return and risk, along with a discussion of the Capital Asset Pricing Model (CAPM)
Life annuities as well as life, property, and casualty insurance
Throughout the book, numerous examples and exercises present realistic financial scenarios that aid readers in applying their newfound mathematical skills to devise solutions. The author does not promote the use of financial calculators and computers, but rather guides readers through problem solving using formulas and tables with little emphasis on derivations and proofs.
Extensively class-tested to ensure an easy-to-follow presentation, Mathematical Finance is an excellent book for courses in business, economics, and mathematics of finance at the upper-undergraduate and graduate levels. The book is also appropriate for consumers and entrepreneurs who need to build their mathematical skills in order to better understand financial problems and make better financial choices.
Product Details
ISBN-13: 9780470641842
Publisher: Wiley
Publication date: 7/31/2012
Edition description: New Edition
Edition number: 1
Pages: 554
Product dimensions: 9.20 (w) x 6.10 (h) x 1.40 (d)
Meet the Author
M. J. ALHABEEB, PhD, is Professor of Economics and Finance at the University of Massachusetts Amherst. A recipient of the Academy of Educational Leadership's Outstanding Teaching Award for Innovative and Creative Teaching, Dr. Alhabeeb has been teaching finance and various courses in economics for more than
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Basic College Mathematics - 2nd edition
ISBN13:978-0077281137 ISBN10: 0077281136 This edition has also been released as: ISBN13: 978-0073406114 ISBN10: 0073406112
Summary: Basic College Mathematicsoffers a refreshing approach to the traditional content of the course. Presented in worktext format,Basic College Mathematicsfocuses on basic number skills: operations and problem-solving with whole numbers, fractions, and decimals. Other topics include geometry, measurement, ratios, proportions, percents, and the real number system (with an introduction to algebra). The text reflects the compassion and insight of its experienced author team with features dev...show moreeloped to address the specific needs of developmental level students. .24.17 +$3.99 s/h
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BookCellar-NH Nashua, NH
0077281136132
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Abstract: The mathematics underlying the construction of perspective images of
three-dimensional objects. Discussion of hands-on applications and the use
of algebraic reasoning to create perspective art in a way that is accessible to
secondary teachers and their students. Includes procedures for drawing a
perspective cube.
The National Council of Teachers of Mathematics is the public voice of mathematics education, supporting teachers to ensure equitable mathematics learning of the highest quality for all students through vision, leadership, professional development, and research.
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Melrose Park Precal and expand problem solving skills (creatively and analytically) in order to solve word problems. Use manipulatives and calculators. Successful completion of this course prepares students for success in Algebra 1
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This is a short eBook that describes how to get free high school Algebra 1 help online without having to spend any money, buy anything, join any free trials, or anything like that. Free High School Algebra 1 Help Online | Algebra 1 Help.org.
A short ebook explaining a simple way to subtract integers for people who have trouble subtracting integers. This uses a method based on simply changing a subtraction problem to an addition problem based on helping people with algebra. How to Subtract Integers Without Getting Confused | Algebra 1 Help
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This third edition of the perennial bestseller defines the recent changes in how the discipline is taught and introduces a new perspective on the discipline. New material in this third edition includes:
A modernized section on trigonometry
An introduction to mathematical modeling
Instruction in use of the graphing calculator
2,000 solved... more...
MASTER ONE LIFE'S MOST USEFUL SKILLS--EVEN IF YOU'VE NEVER BEEN GOOD AT MATH Knowing algebra gives you a better choice of jobs, helps you perform better in science, computing, and math courses, ups your score on competitive exams, and improves your ability to do daily computations. And there's no faster or more painless way to master the subject... more...
This book contains nine refereed research papers in various areas, from combinatorics to dynamical systems, with computer algebra as an underlying and unifying theme. Topics covered are irregular connections, summability of solutions and rank reduction of differential systems, asymptotic behaviour of divergent series, integrability of Hamiltonian systems,... more...
This insightful book combines the history, pedagogy, and popularization of algebra to present a unified discussion of the subject. Classical Algebra provides a complete and contemporary perspective on classical polynomial algebra through the exploration of how it was developed and how it exists today. With a focus on prominent areas such as the numerical... more...
This is the softcover reprint of the English translation of 1974 (available from Springer since 1989) of the first 3 chapters of Bourbaki's 'Algèbre'. It gives a thorough exposition of the fundamentals of general, linear and multilinear algebra. The first chapter introduces the basic objects: groups, actions, rings, fields. The second chapter studies... more...
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Beginning and Intermediate Algebra - 4th edition
Summary: Get Better Results with high quality content, exercise sets, and step-by-step pedagogy! The Miller/O'Neill/Hyde author team continues to offer an enlightened approach grounded in the fundamentals of classroom experience in Beginning and Intermediate Algebra 4e. The text reflects the compassion and insight of its experienced author team with features developed to address the specific needs of developmental level students. Throughout the text, the authors communicate to students the ve...show morery points their instructors are likely to make during lecture, and this helps to reinforce the concepts and provide instruction that leads students to mastery and success. Also included are Problem Recognition Exercises, designed to help students recognize which solution strategies are most appropriate for a given exercise. These types of exercises, along with the number of practice problems and group activities available, permit instructors to choose from a wealth of problems, allowing ample opportunity for students to practice what they learn in lecture to hone their skills. In this way, the book perfectly complements any learning platform, whether traditional lecture or distance-learning; its instruction is so reflective of what comes from lecture, that students will feel as comfortable outside of class as they do inside class with their instructor79.08 +$3.99 s/h
Acceptable
SellBackYourBook Aurora, IL
0073384518116.79200.81
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Programmed Mathematics for Nurses - 8th edition
Summary: Provides students with an enjoyable way of learning the math skills requried to solve the many types of problems that may be encountered in the giving of medications and in the preparation of solutions. The secret lies in a small group of psychological principles that make up the reinforced learning system. Unlike an ordinary text that must be studied and memorized, this reinforced learning system asks the student to solve a logical series of problems. Each problem is designed to sti...show moremulate the student to think out the correct answer on the basis of information already learned. After responding to each problem students can immediately check their work against the correct answer. ...show less
A tradition of southern quality and service. All books guaranteed at the Atlanta Book Company. Our mailers are 100% recyclable.
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Books Revisited Chatham, NJ
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Junior Maths (Junior Book 1)
Description
Junior Maths Book 1 builds an excellent foundation for Mathematical study and covers the basics of addition, subtraction, multiplication and division, before moving onto more advanced material. - Covers the new numeracy framework to ensure pupils are learning the most up to date material - Combines the traditional standard method with the mental approach to challenge all abilities and satisfy all needs - Features end of chapter activities and summary exercises to engage pupils and consolidate information learned throughout each chapter - Includes a huge bank of practice material, including problem solving exercises, to ensure pupils have plenty of practice material Answer book available separately. See Junior Maths Book 1 Answer Book. Also available from Galore Park: - Junior Maths Book 2 - Junior Maths Book 3 - 11+ Maths Practice Exercises - 11+ Maths Practice Exercises Answer Book - 11+ Maths Revision Guide
Create a review
About Author
David Hillard has spent more than 45 years teaching mathematics in two preparatory schools. Since 1980 he has been associated with the Common Entrance examination at 11+, 12+ and 13+ levels in the role of either advisor, assessor or setter. He played a significant part in the revision of the syllabus in 2003 when the present format of the Common Entrance examination was introduced.
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Find a Mountain View, CA PrecalculusLong division is learned during the primary years and an introduction to basic problem solving is also included. Elementary mathematics is used in everyday life in activities such as making change, cooking, and buying in a store. It is also an essential step on the path to understanding science
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Abstract: Describes middle school students' understanding of the equal sign and the relationship between their understanding and performance when solving algebraic equations. Students are given prompts about the meaning and how they understand the equal sign; these results are highlighted. Improving students' understanding of the equal sign and their preparation for algebra may require changes in instructional practices and middle school mathematics curricula.
The National Council of Teachers of Mathematics is the public voice of mathematics education, supporting teachers to ensure equitable mathematics learning of the highest quality for all students through vision, leadership, professional development, and research.
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A1.1.3 Explain the relationship between real numbers and the number line (including the density property) and compare and order real numbers with and without the number line;
A1.1.4 Solve simple equations in one variable using inverse relationships between operations such as addition and subtraction (taking the opposite), multiplication and division (multiplying by the reciprocal), raising to a power and taking a root;
A1.3.2 Describe and calculate the slope of a line given a data set or graph of a line, recognizing that the slope is the rate of change;
A1.3.3 For bivariate data that appear to form a linear pattern, find the line of best fit by estimating visually and/or using appropriate technology to determine the least squares regression equation. Interpret the slope of the equation for a regression line within the context of the data and use the equation to make predictions;
A1.3.5 Describe and analyze lines that have positive, negative, zero and undefined slopes;
A1.3.6 Represent linear relationships graphically, algebraically (including the slope-intercept form) and verbally and relate a change in the slope or the y-intercept to its effect on the various representations;
A1.3.12 Represent and solve problems that can be modeled using a system of linear equations and/or inequalities in two variables, sketch the solution sets, and interpret the results within the context of the problem.
A1.4.3 Graph a quadratic polynomial and explain the relationship among the solutions, the zeros, the x-intercepts, and the factors;
A1.4.4 Translate between the standard form of a quadratic equation, the vertex form, and the factored form. Graph and interpret the relationships between the equation and the graph for each form.
A1.5 Students display data in a variety of forms and approximate linear models for appropriate data.
A1.5.1 Select, create, and interpret an appropriate graphical representation (e.g., scatterplot, table, stem-and-leaf plots, histogram, circle graph, etc) for a set of data and use appropriate statistics (e.g., mean, median, range, and mode) to communicate information about the data. Use these notions to compare different sets of data;
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Problem Solving Experiences : Making Sense of Mathematics
9780769032641
ISBN:
0769032648
Pub Date: 2005 Publisher: Seymour Publications, Dale
Summary: A revision of a popular series, Problem Solving Experiences: Making Sense of Mathematics is updated to reflect the most current research on learning and addresses the writing requirements of new state standards. It carefully maintains the same consistent, instructional model that has helped so many students become successful problem solvers over the years. Consisting of a consumable Student Book and a comprehensive w...raparound annotated Teacher's Edition for each of the six levels, Problem Solving Experiences: Making Sense of Mathematics offers a step-by-step approach to skill-building.
Charles, Randall I. is the author of Problem Solving Experiences : Making Sense of Mathematics, published 2005 under ISBN 9780769032641 and 0769032648. Thirty Problem Solving Experiences : Making Sense of Mathematics textbooks are available for sale on ValoreBooks.com, or buy new starting at $199.65.[read more]
Ships From:Woodland Hills, CAShipping:StandardComments:Premium Books are Like New or Brand New books direct from the publisher sometimes at a discount. ... [more]Premium Books are Like New or Brand New books direct from the publisher sometimes at a discount. These books are not available for expedited shipping and may take up to 14 business days to receive.
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This lesson received an honorable mention for the 2011 SoftChalk Lesson Challenge.'Differential equations show up in many...
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This lesson received an honorable mention for the 2011 SoftChalk Lesson Challenge.'Differential equations show up in many areas of science and technology. In fact, they turn up any time there is a relation involving some continuously varying quantities and ther rates of change. We have actually dealt with differntial equations before. A common modeling problem involving differential equations is the determination of the velocity of a ball falling which has an acceleration which is the acceleration due to gravity minus the acceleration due to air resistance. This is a differential equation because the derivative of the velocity of the ball depends on the velocity, thus finding the velocity as a function of time involves.' solving a differential equation.'In this section we willExamine the basic form of differential equationsVerify solutions to differential equationsDetermine slope fields for differential equationsFind solutions to differential equations numerically using Euler's methodFind solutions to differential equations using seperation of variables.'
This is a resource that can be used in conjunction with an Abstract Algebra class. It contains definitions and theorems...
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This is a resource that can be used in conjunction with an Abstract Algebra class. It contains definitions and theorems regarding abstract algebra. Included is a Table of Contents that lists the topics such as Integers, Functions, Groups, Polynomials, Galois Theory, Unique Factorization, etc. There is also a link to an online study guide for the topic.
This is a free online textbook designed for the Advanced Algebra instructor. According to the author, he "developed a set of...
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This is a free online textbook designed for the Advanced Algebra instructor. According to the author, he "developed a set of in-class assignments, homework and lesson plans, that work for me and for other people who have tried them. The complete set comprises three separate books that work together:•The Homework and Activities Book contains in-class and homework assignments that are given to the students day-by-day." "•The" target=״_blank״ Concepts Book provides conceptual explanations, and is intended as a reference or review guide for students; it is not used when teaching the class." •The" target=״_blank״ Teacher's Guide provides detailed lesson plans; it is your guide to how the author "envisioned these materials being used when I created them (and how I use them myself) " target=״_blank״ Instructors should note that this book probably contains more information than you will be able to cover in a single school year."
" Algebra for College Students is designed to be used as an intermediate level text for students who have had some prior...
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" Algebra for College Students is designed to be used as an intermediate level text for students who have had some prior exposure to beginning algebra in either high school or college. This text explains the why's of algebra, rather than simply expecting students to imitate examples.״Please note that this site will try to sell supplements and you must create an account. However, there is no charge for the download of the textbook. As noted on the website, "Free access to the online book. Includes StudyBreak Ads (advertising placed in natural subject breaks)."
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Visualization: Data Visualization Quick Start (German)
Harness the power of Mathematica to interactively visualize your data. This video features a series of examples that show how to create a rich interface for exploring data in depth. Includes German audio.
Mathematica's strong 3D format support and graphics features make it a prime candidate for performing 3D geometric manipulations and creative modeling. This example-driven course features a demonstration ...
The Wolfram Computable Document Format (CDF) provides a new streamlined way for creating dynamic educational content. This course from the Wolfram Mathematica Virtual Conference 2012 shows how to use ...
Mathematica provides many approaches to producing dynamic visualizations. This talk uses a number of examples to illustrate the principles involved in constructing graphics sequences, manipulating simulated cameras, building ...
In this project course from the Wolfram SystemModeler Virtual Conference 2012, a complete house-heating system is constructed in Wolfram SystemModeler. The course shows how measurement data from Mathematica
This course from the Wolfram SystemModeler Virtual Conference 2012 provides an introduction to the BioChem library and the Systems Biology Add-On and teaches you how you can build, simulate, and analyze biochemical models using SystemModeler ...
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Product Description
This Saxon Math Homeschool 7/6 Solutions Manual provides answers for all problems in the textbook lesson (including warm-up, lesson practice, and mixed practice exercises), as well as solutions for the investigations and supplemental practice found in the back of the student text. It also includes answers for the facts practice tests, activity sheets, and tests in the tests & worksheets book. Answers are line-listed, and are organized by type (lessons & investigations, facts practice tests, tests, etc.).
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In the OpenLearn unit on Developing modelling skills (MSXR209_3), the idea of revising a model was introduced. In this unit you will be taken through the whole modelling process in detail, from creating a first simple model, through evaluating it, to the subsequent revision of the model by changing one of the assumptions. The new aspect here is the emphasis on a revised model, which comes in Section 2. The problem that will be examined is one based on heat transfer.
This unit, the four provides an overview of the processes involved in developing models. It starts by explaining how to specify the purpose of the model and moves on to look at aspects involved in creating models, such as simplifying problems, choosing variables and parameters, formulating relationships and finding solutions. You will also look at interpreting results and evaluating models.
This unit, the third in a series of five, builds on the ideas introduced and developed in Modelling poll explores a real-world system – the Great Lakes – where mathematical modelling has been used to understand what is happening and to predict what will happen if changes are made. The system concerned is extremely complex but, by keeping things as simple as possible, sufficient information will be extracted to allow a mathematical model of the system to be obtained.
At the end of Section 1, we discussed the decimals
and asked whether it is possible to add and multiply these numbers to obtain another real number. We now explain how this can be done using the Least Upper Bound Property of examples just given, it was straightforward to guess the values of sup E and inf E. Sometimes, however, this is not the case. For example, if
then it can be shown that E is bounded above by 3, but it is not so easy to guess the least upper bound of E.
In such cases, it i have seen that the set [0, 2) has no maximum element. However, [0, 2) has many upper bounds, for example, 2, 3, 3.5 and 157.1. Among all these upper bounds, the number 2 is the least upper bound because any number less than 2 is not an upper bound of [0, 2 can do arithmetic with recurring decimals by first converting the decimals to fractions. However, it is not obvious how to do arithmetic with non-recurring decimals. For example, assuming that we can represent and decimal system enables us to represent all the natural numbers using only the ten integers
which are called digits. We now remind you of the basic facts about the representation of rational numbers by decimals calculator does not make mistakes in the way that human brains tend to. Human fingers do, however, make mistakes sometimes; and the calculator may not be doing what you think you have told it to do. So correcting errors and estimating the approximate size of answers are important skills in double-checking your calculator calculations. (Just as they are for checking calculations done in your head or on paper!) explores reasons for studying mathematics, practical applications of mathematical ideas and aims to help you to recognize
In order to complete this unit you will need 4 we prove that some of the properties of the groups appearing earlier in the unit are, in fact, general properties shared by all groups. In particular, we prove that in any group the identity element is unique, and that each element has a unique inverse.
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Packed with practical examples, graphs, and Q&As, this complete self-teaching guide from the best-selling author of Algebra Demystified covers all the essential topics, including: absolute value, nonlinear inequalities, functions and their graphs, inverses, proportion and ratio, and much more.
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This programme offers an approach to handwriting which develops the muscles of the hand. It includes over 400 graded exercises and activities to develop hand-eye co-ordination, form constancy, spatial organization...
This text combines a lively writing style with a diverse range of electronic tools guaranteed to excite and stimulate. Through providing interviews with real-life practitioners from organizations such as Innocent...
Shows students how to apply traditional mathematical skills in real-world contexts. This title focuses on skill building and applications engage students as they master algebraic concepts, problem solving, and communication...
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Tagged Questions
Mathematics education consists in the practice of teaching and learning mathematics, along with the associated research. Research in mathematics education concerns the tools, methods and approaches that facilitate the practice of mathematics or the study of this practice.
Why is the euler characteristic of non-convex polyhedra $\neq 2$ in general? If one removes an edge do we lose one face as in the convex case? Why does the general proof of projecting to a sphere not ...
It is well-known that a sequence has a limit if and only if it is bounded and has a unique limit point. I think this is a better definition of the limit of a sequnece, comparing with the $\epsilon-N$ ...
Does anyone find it doable to use Latex in a classroom setup instead of blackboard? I would think it is tempting except for the input speed one can reach. But considering the messiness of chalks, and ...
This winter I am planning on teaching a small seminar (20 lectures 45 minutes each) for high school students. I was was given the freedom to choose the topic of the seminar, but it is supposed to be ...
I'm a TA with Advanced Algebra in school and teach the Jordan Form now. There are three questions about eigenvalues in this chapter:
Given matrix $A$, $B$ and polynome $f$, consider the eigenvalues' ...
My mother is teaching a high school course on multivariable calculus, and they were studying linear differential equations of the form $$y' + P(x) y = Q(x),$$ and the question of why this equation is ...
One of the main obstacles in understanding the tensor product is that, unlike many other algebraic structures, you cannot really get hold of its element structure. This confuses many beginners. The ...
I just got interview to teach college (of applied science) compsci student math. This is the first time I get this type of interview. The type of interview is called a "hearing" where a dozen people ...
I need a rational function/equation beyond the contrived d=rt and work problems typically given in beginner algebra.
I am teaching such a class and would like to motivate the study of techniques for ...
I am writing a first handout on determinants. The intended audience is confident with basic matrix algebra and the basic definitions of vector space theory. I just wondered if someone would comment on ...
When I was about 17 our teacher showed us how polynomial identities had equal coefficients.
I remember him showing that this was so by moving one polynomial "over to the other side" and showing that ...
Number theory is known to be a field in which many questions that can be understood by secondary-school pupils have defied the most formidable mathematicians' attempts to answer them.
Calculus is not ...
I am having an argument with someone who thinks that it's never justified to teach something that is not strictly correct. I disagree: often, the pedagogically most efficient way to make progress is ...
Does anyone have some good, classic, counting problems? I want things that are interesting, as well as instructive- more than just compute the number of way to get a flush, etc. (Not that those aren't ...
crossposted to
I hold a PhD in pure mathematics and am looking for mathematics teaching positions in the UK, ...
I will help teach in a introductory class in mathematics for engineers in applied math at the University.
Anyone have any good and cool favorite questions or know where I can find some?
Anything is ...
Why is factorization of integers important on a first number theory course? Where is factorization used in real life? Are there examples which have a real impact? I am looking for examples which will ...
I teach A-Level maths, and in the second year we do the general binomial expansion, which is even provided for the students in the formula book.
For values of $n$ that are not positive integers: (I ...
As a student one sometimes encounters exercises which ask you to solve a rather funny "real life problem", e.g. I recall an exercise on the Krein-Milman theorem which was something like:
"You have a ...
This is a follow-up question to Why does the definition of addition require proofs? In Landau's Foundations of Analysis, his definition of addition on the natural numbers seems a bit strange to me -- ...
So I am currently a graduate student at the University of Colorado. I love math. From calculus to category theory to everything in between, I have tried and, for the most part, loved it. However, I ...
I need some math Youtube channels (or any other visual media, movies maybe...) that I can recommend to High School students, not solely as a method of learning math but more to illustrate the beauty ...
Having taken Real Analysis I before (the seven first chapters of baby Rudin) I have the option to take Measure Theory now. However I am torn between that and Set Theory. Which course would you go for ...
In my algebra class we are being taught that there are only the 3 basic trig functions (cosine, sine, and tangent). But my friend who is 2 math grade levels ahead of me is saying that there is 6 trig ...
I am kind of TAing for a class of real analysis, and I would like to speak a little about convex sets tomorrow, and explain why they are important. What kind of examples could I give? I was thinking ...
I'm introducing the Classification Theorem on closed and orientable surfaces in a talk on (intuitive) topology, and to motivate it I'd like an example of an embedding of a surface in $\mathbb{R}^3$ ...
I'm teaching the section 4.7 on optimization in Stewart Calculus. It has a subsection on "Applications to Business and Economics." There the author defines the price function $p(x)$ to be the price ...
Recently, I was teaching maxima, minima and inflection points to first year engineering students. I motived extrema by giving practical examples of optimization problems, but when a colleague asked me ...
I became a better reader when I stopped sub-vocalizing (hearing the words in my head). I still do that when I read math. I tried not to do that when I read an expression today. I felt less confident ...
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Need more help with math problems than a calculator can provide? There's now an app for that. PhotoMath promises to help solve simple linear equations and other math problems by "reading" questions with the help of your smartphone camera. But an answer isn't all you'll get from this free app. PhotoMath also provides a step-by-step guide of how each problem
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I am postponing understanding them fully until later so I skipped the chapter, but want to have a good backup in-case I need a second opinion on another area.
06-20-2008
VirtualAce
Quaternions are not simple math. I think the first book does a good job of explaining them. Every other explanation I've seen is about ten times as difficult.
06-21-2008
indigo0086
I understand the concept, but it's hard to visualize them like say Euler angles or even matrices. So when the book goes to doing he proofs for some of the calculation I get pretty lost. I'm no math wiz but I've gone through my rounds but still, I have some trouble.
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Saxon Math 76 comes in a basic set of three books, the solutions manual, student textbook, and the tests and worksheets.
The second number in Math 76 refers to the grade level that the book is normally recommended for (for average to bright students). So Math 76 is normally used in the 6th grade. The first number refers to the grade the book should be studied by slow students.
The general format of each lesson in the upper grade Saxon Math books is very consistent. First, an explanation of the lesson, with worked out example problems. This might be 2-3 pages. Next, a practice set with some problems of that particular type for students to practice on. Finally, there is a problem set with some 30 problems taken from previous lessons. The review is cumulative, so any type of problem that students have ever learned about could possibly be in the problem set.
Topics and Methodology
The topics covered in Saxon Math 76 include review and reinforcement of concepts and skills from 54 and 65. New concepts include some that will be needed in upper level algebra and geometry courses. Some new concepts include simplifying expressions containing parentheses; exponents and square roots; geometric formulae; adding, subtracting, multiplying, and dividing signed numbers.
Saxon's signature incremental approach and spiral review is also used in Saxon Math 76. New concepts are broken into small incremental parts and introduced gradually, one part at a time. There is daily review in the problem sets, which consist of a mixture of previously introduced problem types. Anything from previous lessons or even previous books is fair game.
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Algebra :
a complete introduction /
A comprehensive yet easy-to-use introduction to using algebra. This book covers all the key areas of algebra, and is useful in studying for an exam or if you simply want to improve your knowledge. Full description
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For Your Information/Products/Publications For Your Information: September 2006
September 2006, Volume 100, Issue 2, Page 157
Abstract: "The Definitive Guide to How Computers Do Math: Featuring the Virtual DIY Calculator," "From Calculus to Computers: Using the Last 200 Years of Mathematics History in the Classroom," "The Handy math Answer Book," "Innovative Approaches to Undergraduate Mathematics Courses Beyond Calculus," "It's About Time: Understanding Einstein's Relativity," "Mathematical Apocrypha Redux: More Stories and Anecdots of Mathematicians and the Mathematical," "Negative Math: How Mathematical Rules Can Be Positively Bent," and "New Mexico Mathematics Contest Problem Book" are reviewed in this month's issue of Mathematics Teacher. These texts cover the diverse topics of computers, this history of mathematics, answers to mathematical questions, teaching methodologies for undergraduate courses, the theory of relativity, stories of mathematicians, the history of negative numbers, and problem solving. For Your Information is a regular department of the journal that aims to review books, media, and other products.
The National Council of Teachers of Mathematics is the public voice of mathematics education, supporting teachers to ensure equitable mathematics learning of the highest quality for all students through vision, leadership, professional development, and research.
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Career Research
Math 102: College Mathematics
This Math 102: College Mathematics course guides you through a variety of mathematics topics with the help of engaging videos and self-assessment quizzes. Watch video lessons and learn about a variety of mathematical concepts, including exponents, polynomials, complex numbers and statistics.
About This Course
This course covers topics ranging from real number systems to probability and statistics. You'll learn to use the midpoint and distance formulas, graph inequalities and multiply binomials. You'll also explore the properties of various shapes and learn to determine their area and perimeter. Our lessons are taught by professional educators with experience in mathematics. In addition to designing the videos in this course, these educators have developed written transcripts and self-assessment quizzes to round out your learning experience.
Course Topics
Category
Objectives
Math Foundations
Learn about the different types of numbers, prime factorization, greatest common factors, least common factors and different parts of a graph. Study how to use the midpoint formula and the distance formula.
Linear Equations
Study intercepts, standard form and graphing. See how to graph an undefined slope and zero slope and use a system of equations.
Solving and Graphing Inequalities
Discover the definition of an inequality and how to graph them. Take a look at set notation, compound inequalities and systems of inequalities.
Graphing and Factoring Quadratic Equations
Examine parabolas in standard, intercept and vertex form. Learn about multiplying binomials using FOIL and the area method. See how to complete the square.
Complex and Imaginary Numbers
Learn about imaginary numbers and how they relate to complex numbers. Find out how to add, subtract, multiply, divide and graph complex numbers.
Properties of Exponents
Study the five main exponent properties and learn how to define a zero and negative exponent, simplify expressions with exponents and simplify expressions with rational exponents.
Properties of Polynomial Functions
Take a look at how to graph cubics, quartics and quintics. Discover how to add and subtract polynomials, multiply polynomials, divide polynomials with long division and use synthetic division to divide polynomials.
Simplifying and Solving Rational Expressions
Learn how to multiply and divide rational expressions, add and subtract rational expressions and solve a rational equation.
Properties of Functions
Study the basics and key terms of functions and domain and range in a function. Look at how to shift graphs on a plane, compose functions and apply function operations. Find out how to add, subtract, multiply and divide functions.
Logarithms and Exponential Equations
Learn the definition of an exponential function and a logarithm. Study how to evaluate logarithms, solve exponential equations and solve logarithmic equations.
Logic
Take a look at critical thinking and logic in mathematics, logical fallacies, propositions, truth values and truth tables. Find out about conjunctions, disjunctions, conditional statements in math, converse, inverse, contrapositive and counterexample.
Learn how to calculate percent increase with relative and cumulative frequency tables and calculate mean, median, mode and range. Discover methods for calculating simple conditional probabilities, the probability of combinations, permutations and the probability of permutations. Learn about math combinations, shifts in the mean and the probability of independent and dependent events.
Geometry
Study the properties of shapes (triangles, circles and rectangles), including perimeter, area and circumference. Look at how to identify similar triangles and the types of angles
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Essentials of College Algebra with Modeling and Visualization (4th Edition)
Categories:
Description:
Gary Rockswold teaches algebra in context, answering the question, "Why am I learning this?" By experiencing math through applications, students see how it fits into their lives, and they become motivated to succeed. Rockswold's focus on conceptual understanding helps students make connections between the concepts and as a result, students see the bigger picture of math and are prepared for future courses. This streamlined text covers linear, quadratic, nonlinear, exponential, and logarithmic functions and systems of equations and inequalities, which gets to the heart of what students need from this course. A more comprehensive college algebra text is also available
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General Information· Dynamic full-color display with backlit capability.· Thin and lightweight with easy touchpad navigation.· Use digital images or your own photos and overlay with graphical elements on the screen.· Student Software allows students to continue and/or complete assigned work outside of the classroom. Product Description: Handheld graphing calculator lets you visualize in dynamic graphing with the high-resolution full-color, backlit display. Ideal for Algebra, Trigonometry, Geometry, Statistics, Business/Finance, Biology, Physics, Chemistry, and Engineering. Touchpad navigation works more like a laptop computer. You can even transfer class assignments from this handheld to your PC or Mac computer. Calculator also lets you color-code equations, objects, points and lines...
Less
Free Delivery Worldwide : Graphing Calculator Manual for Stats : Paperback : Pearson Education (US) : 9780321570949 : 0321570944 : 30 Mar 2009 : Organized to follow the sequence of topics in the text, this manual is an easy-to-follow, step-by-step guide on how to use the TI-83/84 Plus and TI-89 graphing calculators. It provides worked-out examples to help students fully understand and use their graphing calculator
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Slay the calculus monster with this user-friendly guide Calculus For Dummies, 2 nd Edition makes calculus manageable—even if you're one of the many students who sweat at the thought of it. By breaking down differentiation and integration into digestible concepts, this guide helps you build a stronger foundation with a solid understanding... more...
Mathematics and engineering are inevitably interrelated, and this interaction will steadily increase as the use of mathematical modelling grows. Although mathematicians and engineers often misunderstand one another, their basic approach is quite similar, as is the historical development of their respective disciplines. The purpose of this Math Primer... more...
This collection of peer-reviewed conference papers provides comprehensive coverage of cutting-edge research in topological approaches to data analysis and visualization. It encompasses the full range of new algorithms and insights, including fast homology computation, comparative analysis of simplification techniques, and key applications in materials... more...
From differentiation to integration - solve problems with ease Got a grasp on the terms and concepts you need to know, but get lost halfway through a problem or, worse yet, not know where to begin? Have no fear! This hands-on guide focuses on helping you solve the many types of calculus problems you encounter in a focused, step-by-step manner. With... more...
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Study Skills Resources
If you have reviewed the material on the study skills links on the left, you have a good understanding of what actions you need to take to promote your success in mathematics. If you wish to continue to explore more ideas on studying, time-management and testing, below are additional resources: courses, books and websites.
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Too often high school math is presented as a bunch of topics whose relationships to each other is sometimes left as tenuous or non-existent
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PAPERBACK New 11115688981111568898Ships from: Agoura Hills, CA
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Overview
Providing the perfect head start, the Student Workbook contains all of the assessments, activities, and worksheets from the Instructor's Resource Binder for classroom discussions, in-class activities, and group work.
Product Details
ISBN-13: 9781111568894
Publisher: Cengage Learning
Publication date: 1/1/2011
Edition description: New Edition
Pages: 414
Product dimensions: 8.50 (w) x 10.70 (h) x 1.00 (d)
Meet the Author
Mark Clark graduated from California State University, Long Beach, with a Bachelor's and Master's in Mathematics. He is a full-time Associate Professor at Palomar College and has taught there for the past 13 years. He is committed to teaching his students through applications and using technology to help them both understand the mathematics in context and communicate their results clearly. Intermediate algebra is one of his favorite courses to teach, and he continues to teach several sections of this course each year. He has collaborated with his colleague Cynthia Anfinson to write a new intermediate and beginning algebra text published by Cengage Learning—Brooks/Cole. It is an applications-first approach to algebra; applications and concepts drive the material, supported by traditional skills and techniques.
Cynthia (Cindy) Anfinson graduated from UCSD's Revelle College in 1985, summa cum laude, with a Bachelor of Arts Degree in Mathematics and is a member of Phi Beta Kappa. She went to graduate school at Cornell University under the Army Science and Technology Graduate Fellowship. She graduated from Cornell in 1989 with a Master of Science Degree in Applied Mathematics. She is currently an Associate Professor of Mathematics at Palomar College and has been teaching there since 1995. Cindy Anfinson was a finalist in Palomar College's 2002 Distinguished Faculty
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Microsoft Mathematics 4.0
Equip students with the tools needed to grasp mathematical concepts by complementing your teaching with Microsoft Mathematics 4.0. This powerful computer algebra system has a friendly user interface and a step-by-step equation solver, helping students understand the path to a correct answer. Its powerful visualization tools also help to capture students' imaginations and keep them engaged, allowing their comprehension to rise exponentially.
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Visualize math concepts to promote better understanding
Mathematics 4.0 can help students understand mathematics, science, and tech-related concepts with powerful, easy-to use tools including a graphing calculator, unit converter, triangle solver, and equation solver. Step-by-step solutions are provided for each problem, so students can learn problem solving skills fast and easy. An improved Computer Algebra System (CAS) helps teachers share and solve more complex equations and functions. It's capable of handling many subjects, including pre-algebra, algebra, trigonometry, calculus, physics, and chemistry. Handwriting recognition is included so all students can write out problems by hand.
Present concepts in an engaging way while zeroing in on answers
Visualize many complex concepts with the powerful Graphing Calculator
Use the Triangle Solver to help students understand the relationship of sides, angles, values, and formulas
Use the Conversion Tool to spend more time exploring and testing, and less time calculating
Use the Equation Solver to work through step-by-step solutions to many mathematical problems
Keep track of insights anytime using Ink Handwriting Support for Tablets and ultra-mobile PCs
Comments(50
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Belmont's General Education requirements for the BELL Core Quantitative Reasoning courses are different from similar requirements at most other universities. At many universities, students take typical algebra, calculus, or sometimes programming courses to fulfill their general education mathematics requirement. In our BELL Core, we take a different path: instead, we ask that each student complete a course specifically designed to align with Belmont's overall General Education goals. These courses present a richer view of quantitative reasoning than typical algebra and calculus course by exposing students to logic, in-depth problem solving, and modern topics in mathematics and computing.
The specific BELL Core QR requirement (with rare exception for one or two programs) is that each student must complete one of the following three courses in their first 60 hours of study:
MTH 1020: Introduction to Mathematical Reasoning
MTH 1080: Mathematical Inquiry, or
CSC 1020: Inquiry through Computer Science.
Why is Belmont's requirement so different from many other universities' mathematics general education requirements?
Developing skills in effective writing; recognizing, evaluating, and constructing written arguments; and effective use of technology.
Developing an understanding of the conceptual frameworks and achievements in the natural sciences.
Developing an understanding of the complex nature of the world, including the consequences of individual decisions in an interdependent world.
2. Our BELL Core QR courses focus on skills (problem solving and logic in particular) that are more directly applicable and transferable beyond the classroom than would be true for algebra and calculus skills for most students.
3. Our Bell Core QR Courses incorporate more of an element of true quantitative reasoning than would algebra, calculus, or introductory programming, courses which typically focus on symbolic manipulation. Quantitative reasoning, broadly conceived, includes more than just skill at calculation; it includes the propensity and ability to use quantitative information to support sound decision-making.
4. Our Bell Core QR courses lend themselves to inclusion of accessible and relevant modern topics. That such a thing is desirable is suggested both by our own General Education Learning Goals (noted above) and curriculum recommendations from the professional societies in mathematics and computing. Even mathematics majors report that they benefitted from our BELL Core QR courses and feel they are a valuable part of their curriculum. We think this speaks to the richness of the experience we have created for students in these courses.
5. Our Bell Core QR courses are better aligned with recent curriculum guidelines from professional organizations in mathematics and computing than typical courses in algebra, calculus, and programming.
Which of the three BELL Core QR Courses should I take?
As with any college-level mathematics course, choosing the correct BELL Core course is important. Students want to take care to match their previous experiences and preparation in mathematics and their interests to one of the three courses. It is as important to choose a course that is challenging enough as it is to choose a course that is not too challenging.
At Belmont, our first criterion for placement is a Math ACT or Math SAT score; students without ACT/SAT scores, or who believe their ACT/SAT scores do not place them correctly, are welcome to take our Mathematics Placement Test. The specific placement requirements for the courses are:
MTH 1020—No placement requirements; open to all; however, we strongly recommend that any student with a Math ACT of 25 or higher, or a Math SAT of 570 or higher, enroll in MTH 1080 or CSC 1020.
MTH 1080—Math ACT of 25 or higher; Math SAT of 570 or higher.
CSC 1020—Math ACT of 22 or higher; Math SAT of 520 or higher.
Speaking just of MTH 1020 and MTH 1080 for now, in general, we recommend that all students take the highest math class for which they qualify. MTH 1020 and MTH 1080 are similar in design philosophy, but they differ in intended audience, and, to a lesser degree, in content. Students who are prepared for MTH 1080 are likely not to be sufficiently challenged in MTH 1020; consequently, such students may end up feeling bored or unsatisfied with their mathematics course if they choose MTH 1020. Any student with an interest in computing and with the proper prerequisites should consider taking CSC 1020. CSC 1020 is designed to teach logic and problem-solving skills though a broad look at computing, including both introductory programming and also general computing concepts and the impact of computing on society. CSC 1020 can serve as a good way for a student to explore a potential major or minor in a computing discipline -- several past CSC 1020 students have become computer science majors.
What transfer courses will satisfy my BELL Core QR requirement?
If you wish to transfer a course in as your BELL Core QR credit, then (unless you begin your studies at Belmont as a transfer student with 30 or more hours of transfer credit) you will need to find a course equivalent to our MTH 1020, MTH 1080, or CSC 1020. Because of their unique designs, it is very difficult to find courses at other institutions that are equivalent to MTH 1080 or CSC 1020. However, many institutions offer courses similar in content and approach to our MTH 1020. Look for courses with titles like "Math for Liberal Arts" or, sometimes, "Mathematical Reasoning." As always, seek prior approval from the Mathematics & Computer Science Department before taking any course which you hope to transfer in as your BELL Core QR course.
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UL offers algebra-free math class
Yipee! No more algebra for non-science majors.
UL Lafayette has added a new math course, Math 102, for freshmen majoring in non-science areas. Beginning this fall, students can take the course, which emphasizes quantitative reasoning, as an alternative to college algebra.
Three faculty members created the course: Dr. Kathleen Lopez, an associate professor of mathematics; Melissa Myers, a master instructor; and Christy Sue Langley, a mathematics instructor.
In a press release, Myers says universities across the country are moving away from formula-based teaching to concept-oriented, practical applications of mathematics. Myers, who is also director of freshman mathematics at the university, says this course will likely appeal to the majority of students enrolled in the College of the Arts and the College of Liberal Arts.
In the past, college algebra was the first math course taken by all undergraduates.
There are two paths students follow upon completion of their initial math course. One path is taken primarily by business and science-oriented majors, who are required to take advanced mathematics courses. The other path is for non-science majors, with the courses they take emphasizing applied mathematics.
"Creating a college algebra alternative designed specifically for non-science majors will enable us to better serve these two different populations," notes Myers.
Course topics in Math 102 include traditional concepts, such as linear and exponential functions, as well as topics designed to increase students' ability to reason quantitatively. The course emphasizes critical thinking.
"Our primary goal is to make students better educated," Myers continues. "As consumers, for instance, we're constantly exposed to advertisements. Upon completion of this course, our students will be better educated consumers who are able to recognize misleading advertisements."
Some of the skills students will learn include:
mentally estimating the sale price of an item that has been discounted;
determining which of two possible financial situations is most advantageous;
applying deductive and inductive reasoning, such as understanding the error of statements such as "All services not available in all areas."
reading and interpreting graphs, particularly recognizing graphs which have been designed to intentionally mislead;
computing the consequences of not paying off a "no-money down, two-years interest free" purchase during the interest-free period;
comparing a flat-rate subscription movie site to a service which charges an initial fee plus per-movie charge;
using proportional reasoning to determine which size of product is the best deal; and
recognizing when it is appropriate to use the phrase "growing exponentially."
"Students will be able to use the reasoning and mathematical skills they learn in this course to enhance their decision-making skills, both personally and professionally," Myers
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5: first year course glencoe accounting answer book: holt algebra one. glencoegeometrychapter 11 test form 2b answers free PDF. CMSI High School Algebra I for Middle Grade Students. Students were highly challenged in all but one Glencoe classroom.
Copy this to my account. E-mail to a friend. Find other activities. Start over. Help. Flashcards. Java or HTML. MatchingConcentrationWord Search. See a list of terms used in these activities. This activity was created by a Quia Web subscriber.
Hi gals and guys I would really value some guidance with glencoegeometry online answers on which I'm really stuck. I have this math assignment and don't know how to solve system of equations, adding exponents and subtracting exponents .
For example, standard 4.G.6 is ... criterion-referenced or standardized tests, chapter or unit tests from textbooks
Teoma search engine users found us by typing in these search phrases: "glencoegeometryanswers", answers to math problems from mcdougal littell combination and permutation math.
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Typical used book with moderate shelf-wear to dust jacket or cover, edges, corners, and spine. Book is ready to ship same or next business day. ELIGIBLE FOR FREE SHIPPING! Buy with confidence and please leave feedback after your purchase! It helps22053284::,0470880287::84lAIFp83RvWKatv72EiAhpG%2F8h43FmaLwVO5iBziYRP4W3jUQQoWYppifKWHDw7So21lkwebk3J%2By2yFgpvu7HOOIPAUZd9L8IGbF6QsAM5BNAWCMW7sA%3D%3D,0470876344::iWE2AyA1vDX1PiKRzQQddTLPZjPiGxFUZZlKS4o4%2BP4Cyzr%2BKiEHvGINwI1sGovPl%2Bvsizim6vVDYJpy8DRfTYw7TOraOOtn8WjSutaZv4N%2FUQKbNiR review of geometry is exceptional. It is quick, simple, and easy to use. It provides access to all the common postulates and theorems of geometry. This book is designed to be read straight through as a review. In fact, it does not even have an index. Because of this, I found myself searching through the book hunting for small pieces of information. But through the use of the table of contents, I could find the desired information.
Reading this book is an excellent way to prep for any geometry midterm/final or any standardized test (ACT, PSAT, SAT I, SAT II, etc.). It helped me greatly for the SAT, and in a lot less time than studing a text book or reading SAT prep books. If you need to review geometry in a short amount of time, this is the book to get.
As a long-time teacher of mathematics at the college level, I am always trolling for additional/better materials to help students learn mathematics. Since I am not a fan of the Cliffs Notes series, I hesitated before purchasing this book in a used book store. However, once I started looking through it, I realized that it is a very good review of basic geometry. It begins with the fundamental postulates and immediately goes to some basic theorems, although no proofs are offered. The chapters are:
There are a small number of exercises at the end of each chapter and a summary exam at the end of the book. Solutions to all exercises are included. If you need a fast, complete review of geometry, then this is an excellent selection. However, it has little value if you are trying to learn geometry.
After several years in a corporate engineering job, I started moonlighting as a math tutor. The Cliff's Quick Review Guides are wonderful to have in my "back pocket" when I need to quickly look something up that is covered in dust in the "archives of my brain."
This book is stripped down and to the point, which is exactly what I needed to do a thorough review. I would have rated it a "5" if it had more "Test Yourself" questions...but that's a personal preference (don't let it stop you from ordering this book).
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Logarithms are very handy when dealing with numbers at different scales but they are also useful helping us average measurements of physical phenomena that have nonlinear behavior. In this example, students learn about cloud albedo and calculating cloud optical depth. This resource is from PUMAS - Practical Uses of Math and Science - a collection of brief examples created by scientists and engineers showing how math and science topics taught in K-12 classes have real world applications.
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MoorestownFor example, the fundamental principle of equations that was introduced to you in Basic Algebra I that a + b = c is the same principle that applies in advanced courses. The only difference is that higher-level courses become more and more complex as you advance in your education. This means that, the little things may have overlooked and considered as easy becomes your nemesis in the future.
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... with DIY projects and handiwork. The original concept of BricoCalculette permits workers to easily complete various calculations, which often prove difficult, with the help of many different calculators and converters. After a short ...
... to equation sets with a snap. A set of equations can be passed in as text, while AutoAbacus ... find a solution that satisfies all constraints. The equations are not limited to be only linear, but ...
... create photo-realistic images. In doing so, Indigo uses equations that simulate the behavior of light, with no approximations or guesses taken. By accurately simulating all the interactions of light, Indigo is capable of producing effects such ...
With Linear Algebra, you can solve systems of linear equations using the LU factorization of the matrix of coefficients. You can also perform different operations (add, ... LU factors, eigenvalues and eigenvectors, establish the definiteness of a symmetric matrix, perform scalar multiplication, transposition, shift, ...
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More About
This Textbook
Overview
Introduction to
Mathematical Proofs: A Transition facilitates a smooth transition from courses designed to develop computational skills and problem solving abilities to courses that emphasize theorem proving. It helps students develop the skills necessary to write clear, correct, and concise proofs.
Unlike similar textbooks, this one begins with logic since it is the underlying language of mathematics and the basis of reasoned arguments. The text then discusses deductive mathematical systems and the systems of natural numbers, integers, rational numbers, and real numbers. It also covers elementary topics in set theory, explores various properties of relations and functions, and proves several theorems using induction. The final chapters introduce the concept of cardinalities of sets and the concepts and proofs of real analysis and group theory. In the appendix, the author includes some basic guidelines to follow when writing proofs.
Written in a conversational style, yet maintaining the proper level of mathematical rigor, this accessible book teaches students to reason logically, read proofs critically, and write valid mathematical proofs. It will prepare them to succeed in more advanced mathematics courses,
such as abstract algebra and
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Rocket science starts here.View scientific notation with the proper superscripted exponents, see output in scientific notation
Easily explore an (x,y) table of values for a given function, automatically or manuallyRocket science starts here.Supporting Documents
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An in-depth study of basic algebra concepts for those intending to further their mathematics studies. Includes linear and quadratic equations, inequalities, functions, graphing, and the more advanced topics of logarithms and matrices.
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bravo!
Bravo is a comprehensive calculator utility for Windows 95. It resembles a standard hand-held calculator and contains virtually all the functions you could possibly want in a calculator. It includes all the normal mathematic and trigonometric, as well as a built-in calendar. You can convert any number between 120 different measurement units grouped in 12 categories, compute all the values of a triangle (sides, angles, area, height) from any three known values, do vectorial and complex calculations, and more. Bravo is even multilingual and can be set to display in English, Italian, German, or Spanish.
Polynomial1 Do you know how much important to understand polynomial manipulation in algebra? Most of prealgebra and algebra problems involve polynomials.
Numera Numera (pronounced new-mare-ruh) was designed to be an affordable, expressive and flexible way to work with numbers.
Prime Derivatives This attractive, handy little prime number calculator takes any number up to twenty digits, and then factorizes all the unique prime numbers that evenly divide into the number that was entered into the field.
MathCards MathCards helps students reinforce their mathematical skills through the building of math equations or matching of facts. Kids can play against the computer or a partner, starting at various proficiency levels.
STFMath STFMath is a multipurpose math utility, suitable not only for students, but also for engineers, professors, or anyone interested in math: functions (draw, analyze, evaluate), calculators (complex, matrix, geometry, scientific) and more.
Inverse Matrices 1.03 The program gives a complete, step-by-step solution of the following problem: Given a 2x2, or 3x3, or 4x4, or 5x5 matrix. Find its inverse matrix by using the Gauss-Jordan elimination method. The program is designed for university students and professors.
LeoReport Statistical analysis and report-ready chart in almost no time. Instantly import or read data, prepare artistic graphic presentation with statistical analysis and place it in the document. Curve fit, distribution histogram, 3D and color map and more.
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Los Altos Hills, CA Microsoft ExcelPrecalculus (or Algebra 3) is an advanced form of secondary school algebra and is a foundation mathematical discipline. Precalculus prepares students for calculus and explores topics which will be applied in calculus. The topics that are studied in precalculus are real and complex numbers; solA knowledge of history is essential in the modern world in terms of policy and decision making. I like to trace the threads of a given aspect through to the present time. As an electronics engineer, I've used computers throughout my career.
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Richard Stanley's two-volume basic introduction to enumerative combinatorics has become the standard guide to the topic for students and experts alike. This thoroughly revised second edition of Volume 1 includes ten new sections and more than 300 new exercises, most with solutions, reflecting numerous new developments since the publication of the first edition in 1986. The author brings the coverage up to date and includes a wide variety of additional applications and examples, as well as updated and expanded chapter bibliographies. Many of the less difficult new exercises have no solutions so that they can more easily be assigned to students. The material on P-partitions has been rearranged and generalized; the treatment of permutation statistics has been greatly enlarged; and there are also new sections on q-analogues of permutations, hyperplane arrangements, the cd-index, promotion and evacuation and differential posets.
Author Biography
Richard P. Stanley is a professor of applied mathematics at the Massachusetts Institute of Technology. He is universally recognized as a leading expert in the field of combinatorics and its applications to a variety of other mathematical disciplines. In addition to the seminal two-volume book Enumerative Combinatories, he is the author of Combinatories and Commutative Algebra (1983) and more than 100 research articles in National Academy of Sciences (elected in 1995), the 2001 Leroy P. Steele Prize for mathematical exposition, and the 2003 Schock Prize.
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Starting at $19022mediate Algebra, 1e,authored by Sherri Messersmith presents content in bite-size pieces, focusing not only on learning mathematical concepts, but also explaining the why behind those concepts. For students, learning mathematics is not just about the memorization of concepts and formulas, but it is also about the journey of learning how to problem solve. By breaking the sections down into manageable chunks, the author has identified the core places where students traditionally struggle, and then assists them in understanding that material to be successful moving forward. Proven pedagogical features, such as You Try problems after each example, reinforce a student's mastery of a concept. While teaching in the classroom, Messersmith has created worksheets for each section that fall into three categories: review worksheets/basic skills, worksheets to teach new content, and worksheets to reinforce/pull together different concepts. These worksheets are a great way to both enhance instruction and to give the students more tools to be successful in studying a given topic. The author is also an extremely popular lecturer, and finds it important to be in the video series that accompany her texts. Finally, the author finds it important to not only provide quality, but also an abundant quantity of exercises and applications. The book is accompanied by numerous useful supplements, including McGraw-Hill's online homework management system, MathZone as well as ALEKS. MESSERSMITH is rigorous enough to prepare students for the next level yet easy to read and understand. The exposition is written as if a professor is teaching in a lecture to be more accessible to students. The language is mathematically sound yet easy enough for students to understand.
Table of Contents
1 The Real Number System and Geometry 1.1 Sets of Numbers 1.2 Operations on Real Numbers 1.3 Algebraic Expressions and Properties of Real Numbers
3 Linear Equations in Two Variables and Functions 3.1 Introduction to Linear Equations in Two Variables 3.2 Slope of a Line and Slope-Intercept Form 3.3 Writing an Equation of a Line 3.4 Linear Inequalities in Two Variables 3.5 Introduction to Functions
5 Polynomials and Polynomial Functions 5.1 The Rules of Exponents 5.2 More on Exponents and Scientific Notation 5.3 Addition and Subtraction of Polynomials and Graphing 5.4 Multiplication of Polynomials and Polynomial Functions 5.5 Division of Polynomials and Polynomial Functions
9 Quadratic Equations 9.1 The Square Root Property and Completing the Square 9.2 The Quadratic Formula Putting It All Together 9.3 Equations in Quadratic Form 9.4 Formulas and Applications 9.5 Quadratic Functions and Their Graphs 9.6 Applications of Quadratic Functions and Graphing Other Parabolas 9.7 Quadratic and Rational Inequalities
11 Nonlinear Functions, Conic Sections, and Nonlinear Systems 11.1 Graphs of Other Useful Functions 11.2 The Distance Formula, Midpoint, and Circle 11.2 The Ellipse 11.3 The Hyperbola Putting It All Together 11.4 Nonlinear Systems of Equations 11.5 Second-Degree Inequalities and Systems of Inequalities 12 Sequences and Series (Online Only) 12.1 Sequences and Series 12.2 Arithmetic Sequences and Series 12.3 Geometric Sequences and Series 12.4 The Binomial Theorem
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Discrete Mathematics
Designed for students majoring in mathematics or computer science, this course introduces discrete mathematics, including logic, methods of proof, number theory, sets, counting, relations, recursion, recurrence relations, and Boolean algebra. Topics are illustrated with applications to computer science, including design and analysis of algorithms, undecidability, program correctness, and digital logic design.
Subject:MATH Units:3
Instructor information about this course
Learning Management System (LMS) for this course:Blackboard LMS link: Course start page: Course email:[email protected] Office:OC3620 Office hours:M,W 1-2 (OC 3620) , TTh 9:30-10:30 (SEC cafeteria) Phone:(760)757-2121 ext 6256 Instructor notes:We also plan to organize online office hours through Blackboard Collaborate.
We advise you to login to blackboard.miracosta.edu during the week before the start of instruction (1/6-1/12) to become familiar with the course setup and requirements.
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Spectrum Geometry for grade 6, is designed to completely support and challenge sixthFree Delivery Worldwide : Geometry : Hardback : Glencoe : 9780078651069 : 0078651069 : 01 Jan 2005 : A flexible program with the solid content students need Glencoe Geometry is the leading geometry program on the market. Algebra and applications are embedded throughout the program and an introduction to geometry proofs begins in Chapter 2...
Spectrum Geometry for grade 5, is designed to completely support and challenge fifthThis auction is for Glencoe McGraw-Hill's GEOMETRY - Concepts and Applications math text and Teacher's Edition (TE), copyright 2008. Quoting from Glencoe's website about this title is the following: An ideal program for struggling students Geometry: Concepts and Applications covers all geometry concepts using an informal approach. Help students obtain better understanding of geometry with the many detailed examples and clear and concise explanations found throughout each lesson.Student Text -
Increase fourth- to fifth-grade students' interest in and understanding of geometry using Skills for Success: Geometry. This 128-page book features high-interest activities and lessons that prepare students to take their studies to the next level. It covers fundamental geometry topics, including points, lines, angles, geometric figures, area, perimeter, volume, congruence, symmetry, transformation, and coordinate graphing. The book includes assessments, an answer key, reproducibles, and a glossary of geometric terms. It supports NCTM standards and aligns with state, national, and Canadian provincial standards.
A top-selling teacher resource line, The 100+ Series features over 100 reproducible activities in each book!Geometry links all the activities to the NCTM Standards and provides students with practice in the skill areas required to understand geometry concepts. Reviewing concepts presented in beginning geometry plus exercises involving symmetry, rotations, translations, fractals, the coordinate plane, parallel lines, two-column proofs, intersections, bisecting angles, sectors and arcs, tangents, properties of geometric figures, surface area and volume, and trigonometry are all included. Examples of solution methods are presented at the top of each page and puzzles and riddles help gauge the success of the concepts learned. Each activity has been linked to the related NCTM standard and is...
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The K'NEX Education Elementary Math and Geometry kids' building set allows students to build, investigate and explore geometry concepts, vocabulary and structures in a 2-D and 3-D world. Students live in a 3-D world, so it makes sense for them to connect with geometry on a 3-D level. K'NEX allows them do just that. The teacher's guide, designed as a resource, provides a glossary of key terms and definitions, and it also includes vocabulary card masters to support instruction and understanding when using this K'NEX building set. The activities are standards based and designed around best practices in mathematics instruction. They build upon one another as they lead students towards a greater understanding of mathematics and geometric concepts. The set includes 142 K'NEX parts, which is...
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A welcome addition to Saxon's curriculum line, Saxon Geometry is the perfect solution for students and parents who prefer a dedicated geometry course...yet want Saxon's proven methods! Presented in the familiar Saxon approach of incremental development and continual review, topics are continually kept fresh in students' minds. Covering triangle congruence, postulates and theorems, surface area and volume, two-column proofs, vector addition, and slopes and equations of lines, Saxon features all the topics covered in a standard high school geometry course. Two-tone illustrations help students really see the geometric concepts, while sidebars provide additional notes, hints, and topics to think about. Parents will be able to easily help their students with the solutions manual, which...
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Spectrum Geometry helps students apply essential math skills to everyday life! The lessons, perfect for students in grades 6-8, strengthen math skills by focusing on points, lines, rays, angles, triangles, polygons, circles, perimeter, area, and more! The variety of activities also help extend problem-solving and analytical abilitiesFree Delivery Worldwide : College Geometry : Paperback : Pearson Education (US) : 9780131879690 : 0131879693 : 01 Mar 2007 : For courses in Geometry or Geometry for Future Teachers. This popular book has four main goals: 1. to help students become better problem solvers, especially in solving common application problems involving geometry; 2. to help students learn many properties of geometric figures, to verify them using proofs, and to use them to solve applied problems; 3. to expose students to the axiomatic method of synthetic Euclidean geometry at an appropriate level of sophistication; and 4. to provide students...
Free Delivery Worldwide : Geometry : Hardback : Pearson Education (US) : 9780201217957 : 0201217953 : 31 May 1992 : This second edition effectively prepares education students, elementary or secondary school teachers, or college instructors to teach geometry. It can also serve as a useful reference for anyone in these fields. This book can also serve as a textbook in an elementary plane geometry course having an investigative emphasis. The text explores geometric concepts inductively first and then presents deductive proof. Students are encouraged to explore geometric ideas using constructions, laboratory materials...
Perfect for students in a co-op setting, or additional siblings using the same curriculum, this extra workbook & answer key set is designed to be used along with the not-included Teaching Textbooks Geometry Version 2.0 CD-ROM Set; this book is not designed to be used without the CDs. Teaching Textbooks Geometry Version 2.0 includes 16 chapters and 110 lessons that teach students the fundamental basics of geometry up through more difficult topics such as coordinate geometry, theorems, properties, and postulates. Chapters cover lines and angles, parallel lines, triangles, quadrilaterals, circles, area, solid geometry, non-Euclidean geometries, and more. Problems modeled on questions found in the SAT/ACT are also included to help prepare students for standardized testing. This applauded...
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The 100+ Series, Intro to Geometry, offers in-depth practice and review for challenging middle school math topics such as angles and triangles; graphing lines; and area, volume, and surface area. Bonus activities on each page help extend the learning and activities, making these books perfect for daily review in the classroom or at home. Common Core State Standards have raised expectations for math learning, and many students in grades 6–8 are studying more accelerated math at younger ages. The 100+ Series provides the solution with titles that include over 100 targeted practice activities for learning algebra, geometry, and other advanced math topics. It also features over 100 reproducible, subject specific practice pages to support standards-based instruction.
Free Delivery Worldwide : Diagram Geometries : Hardback : Oxford University Press : 9780198534976 : 0198534973 : 24 Nov 1994 : Diagram geometry lies in the interaction between group theory and geometry and is an active area of research as it provides interesting combinatorial structures in geometry and shows how these can be applied to the classification of complex groups. This book provides a survey of research.
Free Delivery Worldwide : Geometry : Hardback : Oxford University Press : 9780198507581 : 0198507585 : 21 Jun 2001 : For students who studied no geometry at school. This problem-based course starts with some history and moves on to constructions, plane geometry, circles and conics to end with an introduction to algebraic geometry based on national standards for sixth through eighth grade to help ensure that children master geometry math skills before progressingNEW Hardcover -- - This book may or may not have some slight cover scuff/slightly bent corners only due to its inventory shelf life otherwise this book is in EXCELLENT CONDITION.ISBN: 0028348176 Actual Copyright Year: 2001 Publisher: Glencoe **Please note that choosing USPS Media Mail can take up to 21 business days to receive. Choose USPS Priority mail which usually delivers in 2-6 days if you expect this to be delivered sooner.s7d /ntnt 5b Powered by eBay Turbo Lister
Introduce your 7th graders to Geometry with AGS Publishing: Geometry from Pearson Learning. The content provides learners of all abilities with essential preparation in problem solving, calculator usage, and application lessons Geometry chapters will introduce students to concepts such as: ruler postulates, parallel lines, congruent triangles,...
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Free Delivery Worldwide : The Geometry of Type : Hardback : Thames & Hudson Ltd : 9780500241424 : 0500241422 : 01 Jul 2013 : Explores 100 traditional and modern typefaces in loving detail, with a full spread devoted to each entry. In this title, characters from each typeface are enlarged and annotated to reveal key features, anatomical details, and the finer, often-overlooked elements of type design, which shows how these attributes affect mood and readability.
Free Delivery Worldwide : Challenges in Geometry : Hardback : Oxford University Press : 9780198566915 : 0198566913 : 01 Apr 2005 : Containing many exercises, illustrations, hints and solutions, this text provides a range of skills required in competitions, such as the Mathematical Olympiad. Featuring many problems in Euclidean geometry, it is useful for Mathematical Olympiad training, and also serves as a supplementary text for students in pure mathematics.
Kumon Math Workbooks Geometry Measurement Grade 5 will help your child understand and apply more advanced concepts regarding lines, angles and symmetry, and will introduce them to measurement formulas for area, perimeter and volume. Workbook includes Compare and order whole numbers, fractions, and decimals on a number line, Understand and apply concepts of lines and angles (e.g. parallel and perpendicular), Identify polygons, Understand the relationship of the circumference of a circle, its diameter, and pi (tt 3.14 ), Measure and find the area and the perimeter of twodimensional shapes using formulae, Measure and find the volumes of cubes and rectangular prisms using formulae, Coordinate Geometry, Convert measurement units within a system and Identify factors and common factors
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This volume features a complete set of problems, hints, and solutions based on Stanford University's well-known competitive examination in mathematics. It offers high school and college students an excellent mathematics workbook of rigorous problems that will assist in developing and cultivating their logic and probability skills.These 20 sets of intriguing problems test originality and insight rather than routine competence. They involve theorizing and verifying mathematical facts; examining the results of general statements; discovering that highly plausible conjectures can be incorrect; solving sequences of subproblems to reveal theory construction; and recognizing "red herrings," in which obvious relationships among the data prove irrelevant to solutions. Hints for each problem appear in a separate section, and a final section features solutions that outline the appropriate procedures.Ideal for teachers seeking challenging practice math problems for their gifted students, this book will also help students prepare for mathematics, science, and engineering programs. Mathematics buffs of all ages will also find it a source of captivating challenges.
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The collection of problems is complete. The Stanford examination started in 1946 and ended in 1965. All exams are collected in the book; none is missing. The problems appear harder than traditional high school problems for two reasons: First they are based on what a student should be known by the end of his/her high school studies, not what he/she was taught during these years. Second, the problems are written to check the aptitude of students in mathematics, not if they can carry out routine calculations. Therefore, high school students from countries where the curriculum is rigorous and robust will recognize problems based on the material they have been taught although the problems may not be exactly the ones they have solved as homework. (Some of these problems can often be encountered as advanced-level problems in such rigorous curricula.) Students countries where the system is looser regarding the mathematical curriculum can find these problem quite challenging, unless the students have an interest in mathematics and math competitions.
The book is just a collection of problems. It contains hints for those who want to try to solve them on their own. It also contains the solutions for those who do not want to try them or tried and failed to solve them. However, it contains nothing else. No related theory and no methodology. It is a very cheap book and worth having but you should not expect it to serve as a tutorial book that teaches problem-solving techniques.
My 17 year-old son loves this book so much, that when his bookbag was stolen from his locker during gym he asked me to replace this book! He's on a math team, and they work on problems like this all the time. It must be good!
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Romeoville CalculusPre-Algebra/Elementary Algebra
Pre-Algebra (23%). Questions in this content area are based on basic operations using whole numbers, decimals, fractions, and integers; place value; square roots and approximations; the concept of exponents; scientific notation; factors; ratio, proportion, and perce...
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Contemporary Abstract Algebra - 7th edition
Summary: The seventh edition of Contemporary Abstract Algebra, by Joseph A. Gallian, Provides a solid introduction to the traditional topics in abstract algebra while conveying that it is a contemporary subject used daily by working mathematicians, computer scientist, and chemists. The text includes numerous theoretical and computational exercises, figures, and tables to teach you how to work out problems, as well as to write proofs. Additionally, the author provides biographies, poems, song ...show moreLyrics, historical notes, and much more to make reading the text an interesting, accessible and enjoyable experience. Contemporary Abstract Algebra will keep you engaged and gives you a great introduction to an important subject
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.. elimination.. .. ..
This eBook introduces the subjects of indices and surds, ranging from introducing both indices and the laws of indices, surds and the laws of surds, to developing the students skills in manipulation such numbers through setting a wide range of questions.
This eBook introduces the subject of differentiation, across this wide-ranging subject, starting with definitions and first principles to developing an understanding and appreciation of the first and second order differentials of the equation y = xn through a development of the equations of the gradient and normal to a curve at a particular point as well as a thorough review of maximum, minimum ..
This eBook introduces the subjects of co-ordinate geometry and graphs, ranging from finding the equations of the straight-line joining two points for which the co-ordinates are known, to calculating both the mid-point and length of a line between two known co-ordinates to plotting equations of the form y = kxn where n is even or odd for various values of k, as well as y = k√(x) where x is ..
This eBook introduces the subject of circle and circle geometry, introduces the equation of a circle, explores circle geometry, examines tangential lines to circles and their properties and equations, as well as exploring arc-length and sector area of circles where angles are represented in radians. Further, we include some elementary questions for the student to enjoy.
This eBook reviews some advanced topics in algebra, including exploring the nature of polynomials, functions, equations and identity's, examining the mathematical nomenclature used in multiplication and division. We consider multiplying out brackets, taking out common factors, manipulating algebraic fractions and simplifying expressions. Further, we include an extensive selection of questions..
GOALS OF THIS BOOK…
To identify deception in modern Christianity.
To call for correction.
HOW TO REACH THE GOALS…
Compare modern teachings with the truth of God's word.
Show the differences and publish the truth.
PERILOUS TIMES ARE COMING…
Morality and godliness are declining in Christian nations. Corruption, violence, and greed are increasing.
The book is virtually unique in providing, in a single volume, a comprehensive analysis of The General Prologue. It places the work in the context of the social change in late fourteenth century England and analyzes each pilgrim's description in socio-historical terms. The poem is supported by the author's own modernization of the text to enable the reader to understand Chaucer's Middle English.
... elimim. ... ... ...
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