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Multiple Representations
On one hand, GeoGebra is a Dynamic Geometry Software (DGS) that supports constructions with points, lines and all conic sections. On the other hand, it provides typical features of a Computer Algebra System (CAS) such as function plotting, root finding, derivatives and integrals. That's why we call GeoGebra a Dynamic Mathematics Software (DMS) for geometry, algebra and calculus.
There is no other way of gaining access to the mathematical objects but to produce some semiotic presentations. [...] There is no true understanding in mathematics for students who do not incorporate into their cognitive architecture the various registers of semiotic representations used to do mathematics. (Duval, 1999)
The basic idea of GeoGebra is to provide two representations of each mathematical object in its algebra and graphics windows. If you change an object in one of these windows, its representation in the other one will be immediately updated. Let's take the example of a quadratic polynomial f and its tangent t through a given point A. Below you see this situation in GeoGebra. When you drag point A with the mouse along the graph of f, its tangent t will change and adapt to your modifications. In the algebra window you will see how the representations of the affected objects are updated accordingly.
Brief Descriptions
Graphics window (right):
Click and drag point A with your mouse.
Click and drag function f with your mouse.
Click on the icon to reset the applet to its initial state
Algebra window (left):
Double click on point A, change the x-coordinate and press Enter.
Click on point A and press the right and left arrow keys on your keyboard.
Right click (Mac OS: apple click) on tangent t to change its equation to "Equation ax + by = c" or "Parametric Form".
| 677.169 | 1 |
Develop Algebraic Thinking 3-5 - MAT-925Use manipulatives, real-world problem-solving, and captivating activities to engage your students in developmentally appropriate algebraic thinking. This ONLINE course will provide you with numerous opportunities to reflect on current research and pedagogy related to algebraic thinking in the intermediate grades. Make direct application to your own classroom through the design and development of lessons that explore growth patterns, tables, variables, and coordinate graphs. All of the readings and activities are built upon the Common Core standards. Teachers may complete this course with or without students
| 677.169 | 1 |
gorithms
This text, extensively class-tested over a decade at UC Berkeley and UC San Diego, explains the fundamentals of algorithms in a story line that makes ...Show synopsisThis text, extensively class-tested over a decade at UC Berkeley and UC San Diego, explains the fundamentals of algorithms in a story line that makes the material enjoyable and easy to digest. Emphasis is placed on understanding the crisp mathematical idea behind each algorithm, in a manner that is intuitive and rigorous without being unduly formal. Features include: The use of boxes to strengthen the narrative: pieces that provide historical context, descriptions of how the algorithms are used in practice, and excursions for the mathematically sophisticated. Carefully chosen advanced topics that can be skipped in a standard one-semester course, but can be covered in an advanced algorithms course or in a more leisurely two-semester sequence. An accessible treatment of linear programming introduces students to one of the greatest achievements in algorithms. An optional chapter on the quantum algorithm for factoring provides a unique peephole into this exciting topic. In addition to the text, DasGupta also offers a Solutions Manual, which is available on the Online Learning Center. ""Algorithms" is an outstanding undergraduate text, equally informed by the historical roots and contemporary applications of its subject. Like a captivating novel, it is a joy to read." Tim Roughgarden Stanford University23402 Brand New International edition. 100% Same...New. 0073523402
| 677.169 | 1 |
XV. Mathematics, Grade 10
Grade 10 Mathematics Test
The spring 2008 grade 10 MCAS Mathematics test was based on learning standards in the
Massachusetts Mathematics Curriculum Framework (2000). The Framework identifies five major
content strands listed below.
Number Sense and Operations
Patterns, Relations, and Algebra
Geometry
Measurement
Data Analysis, Statistics, and Probability
The grades 9–10 learning standards for each of these strands appear on pages 72–75 of the
Mathematics Curriculum Framework, which is available on the Department Web site at
In Test Item Analysis Reports and on the Subject Area Subscore pages of the MCAS School Reports
and District Reports, Mathematics test results are reported under five MCAS reporting categories,
which are identical to the five Framework content strands listed above.
Test Sessions
The MCAS grade 10 Mathematics test included two separate test sessions, which were administered
on consecutive days. Each session included multiple-choice and open-response questions. Session 1 also
included short-answer questions.
Reference Materials and Tools
Each student taking the grade 10 Mathematics test was provided with a grade 10 Mathematics
Reference Sheet. A copy of the reference sheet follows the final question in this chapter.
During session 2, each student had sole access to a calculator with at least four functions and a square
root key. Calculator use was not allowed during session 1.
The use of bilingual word-to-word dictionaries was allowed for current and former limited English
proficient students only, during both Mathematics test sessions. No other reference tools or materials
were allowed.
Cross-Reference Information
The table at the conclusion of this chapter indicates each item's reporting category and the Framework
learning standard it assesses. The correct answers for multiple-choice and short-answer questions are
also displayed in the table.
384
Mathematics
SeSSion 1
You may use your reference sheet during this session.
You may not use a calculator during this session.
DIRECTIONS
This session contains fourteen multiple-choice questions, four short-answer questions, and
three open-response questions. Mark your answers to these questions in the spaces provided in your
Student Answer Booklet.
ID:250907 335s_10ma_s07MCAS.eps B Common ID:254546 C Common
●
1 The table below shows a linear
relationship between the values of
●
2 Which of the following is closest to the
value of the expression below?
x and y.
52 8
x y
A. 1.4
1 1
B. 2.2
2 6 C. 4.1
3 11 D. 8.5
4 16
Item: TBD Art: TBD
Based on the relationship in the table,
Source: MP
?
what is the value of y when x = 7
MCAS\07-08\Gr10\Math\335s_10ma_s07MCAS.ai (10/16/2007, 11:47 am)
A. 35
B. 31
C. 28
D. 21
385
Mathematics Session 1
ID:250896 545S_10ma_s07MCAS.eps C Common ID:261521 B Common
●
3 Sharon took 24 nighttime photographs.
The exposure times, in seconds, for her
●
4 Which of the following is equivalent to
the expression below?
photographs are represented in the stem-
and-leaf plot below. 100 3 109
A. 1010
Exposure Times (in seconds)
B. 1011
1 8 9 9 C. 1012
2 0 2 3 3 4 4 4 4 6 8 9 9 D. 1018
3 0 1 2 4 5 6 7
4 2 3
ID:273058 A Common
Key
●
5 The first five numbers of a quadratic
sequence are shown below.
3 2 represents 32
4, 6, 11, 19, 30, . . .
What is the median exposure time for
her photographs? What is the next number in the
sequence?
A. 24 seconds
A. 44
B. 25 seconds
B. 43
C. 27 seconds
C. 42
D. 28 seconds
D. 41
386
Mathematics Session 1
ID:253151 CMH015_quadrilateral.eps C Common ID:273059 C Common
●
6 A polygon and expressions representing
its dimensions, in meters, are shown
●
7 A square has an area of 75 square meters.
Which of the following is closest to the
below. length of a side of the square?
2x A. 7.8 meters
B. 8.2 meters
5 – x
C. 8.7 meters
D. 9.1 meters
3x
x + 5
ID:253160 A Common
●
8 What are the solutions of the equation
below?
Which of the following represents the
perimeter, in meters, of the polygon? 2n(3n 12) 0
A. 5x A. 0 and 4
B. 15x B. 0 and 12
C. 5x 10 C. 2 and 4
D. 7x 10 D. 2 and 12
387
Mathematics Session 1
ID:273061 CMH001_points.eps C Common ID:254620 C Common
●
9 Shantel made the line plot below to show
the numbers of points she and the other
●
10 What is the value of the expression below?
members of her team scored. 2 ( 3 2 ) 2 (1) 2
A. 18
X
X X X X B. 22
X X X X X C. 49
0 1 2 3 4 5 6 D. 51
Numbers of Points Scored by Team Members
Exactly three players scored more points ID:253851 A Common
than Shantel. Based on the line plot, ●
11 Jessica wrote the equations below.
what is the number of points that
Shantel scored? r 27 • n
s 45 • n
A. 2
Which of the following expressions is
B. 3 equivalent to s r ?
C. 4
A. (45 27)n
D. 5
B. 45(27 n)
C. (45 n)(27 n)
D. (45 27)(n n)
388
Mathematics Session 1
ID:250911 589s_10ma_s07MCAS.eps D Common ID:254607 C Common
●
12 A line is shown on the coordinate grid
below.
●
13 What is the value of the expression below?
3 8 5 (2 )
y
A. 14
6
5 B. 2
4 C. 4
3 D. 8
2
1
x
–6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6
–1 ID:254292 A Common
–2
–3
●
14 The heights, in inches, of the members
of a soccer team are listed below.
–4
–5
66, 61, 71, 62, 64, 70, 64, 63, 72, 68
–6
After a new member joined the team,
Which of the following best represents the median height of all the members
an equation of the line? was 66 inches.
Which of the following could be the
A. y 2x 2
height, in inches, of the new member?
B. y 1 x 4 A. 68
2
B. 65
C. y 1 x 2
2 C. 64
D. y 2x 4 D. 61
389
Mathematics Session 1
Questions 15 and 16 are short-answer questions. Write your answers to these questions in the boxes
provided in your Student Answer Booklet. Do not write your answers in this test booklet. You may do
your figuring in the test booklet.
ID:254582 Common
●
15 Laila is having shirts made with a logo printed on them to promote her band. The total cost
consists of a one-time fee of $75 to have the logo designed plus $8 per shirt to print the logo.
Write an equation that Laila can use to determine the total cost, C, in dollars, to make
x shirts.
ID:253231 CMH033_KLMN.eps Common
●
16 Rectangle KLMN and its dimensions are shown below. Point P lies on KL .
K P L
15 cm
N 20 cm M
What is the area, in square centimeters, of NPM ?
390
Mathematics Session 1
Question 17 17 in the space provided in your Student Answer Booklet.
ID:254600 Common
●
17 Line j is represented by the equation below.
line j: y 2 x 4
a. What is the slope of line j? Show or explain how you got your answer.
b. What is the slope of any line that is parallel to line j? Explain your reasoning.
c. Write an equation for the line, k, that is parallel to line j and passes through the point
with coordinates (3, 7). Show or explain how you got your answer.
d. Write an equation for the line, h, that is perpendicular to line j and passes through
the point with coordinates (8, 10). Show or explain how you got your answer.
391
Mathematics Session 1
Questions 18 and 19 are short-answer questions. Write your answers to these questions in the boxes
provided in your Student Answer Booklet. Do not write your answers in this test booklet. You may do
your figuring in the test booklet.
ID:229969 Common
●
18 Davis is on the high school track team. The table below shows the number of laps he ran around the
school's track each day for 7 consecutive days.
Number of Laps Each Day
Day Mon. Tue. Wed. Thu. Fri. Sat. Sun.
Number of Laps 8 11 7 9 10 11 12
What is the numerical difference between the median of the number of laps and the mode of the
number of laps?
ID:254135 Common
●
19 What is the value of the expression below?
3 26
392
Mathematics Session 1
Questions 20 and 21 are open-response questions.
• BE SURE TO ANSWER AND LABEL ALL PARTS OF EACH QUESTION.
• Show all your work (diagrams, tables, or computations) in your Student Answer Booklet.
• If you do the work in your head, explain in writing how you did the work.
Write your answer to question 20 in the space provided in your Student Answer Booklet.
ID:258329 Common
●
20 Glenn sells clothing at his store. He changes some prices each month.
a. The original price of a jacket was $30. Glenn increased the price by 10%. What is the
new price of the jacket after the increase? Show or explain how you got your answer.
b. The original price of a pair of sneakers was $50.
• Glenn increased the price by 20% in April.
• He then increased the price again by 20% in July.
What is the new price of the sneakers after both increases? Show or explain how you got
your answer.
c. The original price of a shirt was $16.
• Glenn increased the price by 25% in April.
• He then decreased the price by 30% in July.
Is the final price of the shirt the same as if the original price had been decreased by 5%?
Show or explain how you got your answer.
d. The original price of a coat was $80. Glenn increased the price to $100. By what percent
did the price increase? Show or explain how you got your answer.
393
Mathematics Session 1
Write your answer to question 21 in the space provided in your Student Answer Booklet.
ID:254373 Common
●
21 Jason launched a model rocket from the ground. The formula below can be used to determine
the height of the rocket above the ground at any time during the rocket's flight.
h 16 t ( 7 t )
In the formula, h and t are defined as follows:
• t = the time, in seconds, that has elapsed since the rocket was launched
• h = the height, in feet, of the rocket above the ground at time t
Use the formula to answer the following questions.
a. What was the height, in feet, of the rocket 1 second after it was launched? Show
your work.
b. What was the height, in feet, of the rocket 6 seconds after it was launched? Show
your work.
c. The value of h was 0 when the rocket hit the ground. How many seconds after the rocket
was launched did it hit the ground? Show your work.
d. How many seconds after the rocket was launched was the height of the rocket 160 feet?
Show your work.
394
Mathematics
SeSSion 2
You may use your reference sheet during this session.
You may use a calculator during this session.
DIRECTIONS
This session contains eighteen multiple-choice questions and three open-response questions.
Mark your answers to these questions in the spaces provided in your Student Answer Booklet.
ID:253202 CMH005_parallelogram.eps A Common ID:250983 503s_10ma_s07MCAS.eps D Common
●
22 A parallelogram and its dimensions are
shown below.
●
23 In the diagram below, line l is parallel to
line m, and line k intersects both lines.
k
6 in. l
4 in. 37°
3 in.
What is the area of the parallelogram? m
x°
A. 12 sq. in.
B. 13 sq. in.
Based on the angle measure in the
C. 18 sq. in. diagram, what is the value of x?
D. 24 sq. in.
A. 37
B. 53
C. 127
D. 143
395
Mathematics Session 2
ID:253143 CMH008_zero_slope.eps [op A Common ID:253188 D Common
●
24 In which of the following graphs does
line k best represent a line with a slope
●
25 A large organization uses a phone tree
to contact members.
of 0?
• The director first contacts
3 members. This is the 1st set
A. y of calls.
• Each member who was contacted
in the 1st set of calls then contacts
x 3 different members who were
k not previously contacted. This is
the 2nd set of calls.
• The pattern continues with each
member contacting 3 different
B. y members who were not
previously contacted.
x The table below shows the number of
members contacted in each set of calls.
k Phone Tree Calls
Number of
C. y
k Set of Calls Members Contacted
in This Set of Calls
1st 3
x
2nd 9
3rd 27
4th 81
D. k y If the pattern continues, what is the
number of members who would be
contacted in the 6th set of calls?
x
A. 216
B. 324
C. 486
D. 729
396
Mathematics Session 2
ID:273056 CMH019_cross.eps D Common ID:229576 3207734_AR1.eps B Common
●
26 The rectangle below is a cross section
of a three-dimensional object.
●
27 An international basketball court has a
region called the free-throw lane, shown
as the shaded part in the diagram below.
• The free-throw lane is shaped like
an isosceles trapezoid.
• A semicircle, shown as the unshaded
part in the diagram, is attached to
the shorter base of the trapezoid.
The rectangle could not be a cross • The radius of the semicircle is
section of which of the following 1.8 meters.
objects?
A. a cylinder
B. a prism
C. a cube
D. a cone 1.8 m
6.0 m
5.8 m
Based on the dimensions in the
diagram, what is the area of the
shaded free-throw lane?
A. 22.62 square meters
B. 27.84 square meters
C. 34.80 square meters
D. 55.68 square meters
397
Mathematics Session 2
ID:261482 295S_10ma_s06MCAS.eps D Common
●
28 The box-and-whisker plot below shows the distribution of the daily high temperatures, in
degrees Fahrenheit, in the town of Clifton during the year 2004.
Daily High Temperatures (in degrees Fahrenheit)
30 35 40 45 50 55 60 65 70 75 80 85 90 95 100
Based on the box-and-whisker plot, in which of the following intervals of temperatures is it
most likely that exactly 50% of the daily high temperatures are located?
A. 38°F to 54°F
B. 38°F to 81°F
C. 54°F to 72°F
D. 54°F to 81°F
ID:253841 C Common ID:273062 A Common
●
29 For all nonzero values of x and y, which of
the following expressions must equal 0?
●
30 The circumference of Sophie's circular
flower garden is 75 feet. Which of the
following is closest to the diameter of
A. x0( y0 ) her flower garden?
B. x y y x A. 24 feet
B. 12 feet
C. xy yx C. 10 feet
D. 5 feet
D. (x y) (x y)
398
Mathematics Session 2
Question 31 31 in the space provided in your Student Answer Booklet.
ID:261495 278S1_10ma_s06MCAS.eps, 2 Common
●
31 The first six rows of a pattern are shown in the triangular array below.
Row 1 2
Row 2 2 2
Row 3 2 4 2
Row 4 2 6 6 2
Row 5 2 8 12 8 2
Row 6 2 10 20 20 10 2
Row 7 ? ? ? ? ? ? ?
Each number in the array, other than 2, can be found by adding the two numbers in the
preceding row that are diagonally above it. For example, 6 2 4, as shown in the
triangular array.
a. If the pattern continues, what are the seven numbers in Row 7? Show or explain how you
got your answer.
Copy the table below into your Student Answer Booklet.
Sum of the
Numbers in Each Row
Row Sum
1
2
3
4
5
6
7
b. Determine the sum of the numbers in each of the first seven rows of the pattern. Complete
your table with these sums.
c. If the pattern continues, what row will be the first row in which the sum of the numbers is
greater than 600? Show or explain how you got your answer.
d. Write a rule in terms of n that can be used to find the sum of the numbers in Row n.
Show or explain how you got your answer.
399
Mathematics Session 2
Mark your answers to multiple-choice questions 32 through 40 in the spaces provided in your Student
Answer Booklet. Do not write your answers in this test booklet. You may do your figuring in the test
booklet.
ID:253219 B Common ID:261490 248S_10ma_s06MCAS.eps A Common
●
32 Each of two different-sized boxes is in ●
33 On the spinner shown below, the sizes
of the sections are as follows:
the shape of a right rectangular prism.
The volume of the larger box is • Sections S and U are equal in size.
4 times the volume of the smaller box.
The dimensions of the smaller box are • Sections R and T are equal in size.
represented below. • The size of section S is half the
size of section T.
• length: l
• width: w
• height: h S
T
Which of the following could represent
the dimensions of the larger box?
R
A. l, 4w, 4h U
B. 2l, 2w, h
C. 2l, 2w, 4h
D. 4l, 4w, 4h If Darryl spins the arrow one time, what
is the probability that it will land on
section S?
A. 1
6
B. 1
4
C. 1
3
D. 1
2
400
Mathematics Session 2
ID:273057 C Common ID:253181 B Common
●
34 Manuel is using a small paper rectangle
and a large paper rectangle for an art
●
35 Melinda invested $1000 in a retirement
account. The formula below shows the
project. amount of money, A, that will be in her
account at the end of t years.
• The length of the small rectangle
is half the length of the large A 1000(1 r)t
rectangle. In the formula, r is the interest rate,
• The width of the small rectangle expressed as a decimal. Melinda's
is half the width of the large account has an interest rate of 6%.
rectangle. Which of the following is closest to the
amount that will be in Melinda's account
The area of the small rectangle is
at the end of 2 years?
how many times the area of the large
rectangle? A. $1120
B. $1124
A. 1
16
C. $1256
B. 1 D. $1360
8
C. 1
4
ID:227872 3007141_AR1.eps A Common
D. 1
2 ●
36 In circle D, BC is a diameter, DA is a
radius, and m AB 60°.
A
B
D
C
What is mCAD ?
A. 30°
B. 50°
C. 60°
D. 70°
401
Mathematics Session 2
ID:253264 CMH012_eq_triangle.eps B Common ID:227925 D Common
●
37 In the diagram below, ST is equilateral,
R ●
38 Jeremy calculates his car's gas mileage
every time he buys gas for his car. The
and U is the midpoint of RT .
chart below shows the data from the last
S 5 times he bought gas.
Gas Mileage for Jeremy's Car
Gas Mileage
Miles Gallons of Gas
(miles per gallon)
20 cm
370 11.3 32.74
352 9.5 37.05
303 8.9 34.04
298 9.7 30.72
R U T 398 11.2 35.54
If the length of ST is 20 centimeters, Based on the data in the chart, what is the
range of gas mileage for Jeremy's car?
what is the length of SU ?
A. 2.80 miles per gallon
A. 10 cm
B. 4.31 miles per gallon
B. 10 3 cm
C. 4.82 miles per gallon
C. 20 cm D. 6.33 miles per gallon
D. 20 3 cm
402
Mathematics Session 2
ID:250619 588S_10ma_s07MCAS.eps B Common ID:253189 D Common
●
39 The vertex-edge graph below represents
all the paths in a park.
●
40 The only coins that Alexis has are
dimes and quarters.
N • Her coins have a total value
of $5.80.
M • She has a total of 40 coins.
P
Which of the following systems of
K equations can be used to find the
number of dimes, d, and the number
J of quarters, q, that Alexis has?
Mike is at point J and wants to walk A. d q 5.80
along each path exactly one time. At 40d 40q 5.80
which point will Mike finish his walk?
B. d q 40
A. point K 5
.80d 5.80q 40
B. point M
C. d q 5.80
C. point N 0
.10d 0.25q 40
D. point P
D. d q 40
0
.10d 0.25q 5.80
403
Mathematics Session 2
Questions 41 and 42 are open-response questions.
• BE SURE TO ANSWER AND LABEL ALL PARTS OF EACH 41 in the space provided in your Student Answer Booklet.
ID:251149 072S_10ma_s07MCAS.eps Common
●
41 A water dunking tank at a carnival is in the shape of a right circular cylinder. Its height is 5 feet,
and the radius of each base is 3 feet, as shown in the picture below.
a. What is the lateral surface area, in square feet, of the tank? Show your work.
b. On the first day of the carnival, the dunking tank was filled with water to a height of
4 feet. What was the volume, in cubic feet, of the water in the tank on the first day of
the carnival? Show your work.
At the end of the second day of the carnival, some water was drained from the tank. The
volume of water drained was 35.3 cubic feet.
c. Using your answer from part (b), determine the height, in feet, of the water remaining in
the tank after the water was drained at the end of the second day. Show your work.
The water that was drained from the tank was poured into containers, each in the shape of
a right rectangular prism. Each container was 2 feet in length, 1.5 feet in width, and 3 feet
in height.
d. What was the least number of containers needed to hold all the water that was drained at
the end of the second day? Show your work.
404
Mathematics Session 2
Write your answer to question 42 in the space provided in your Student Answer Booklet.
ID:251661 324S1_10ma_s07MCAS.eps, 3 Common
●
42 Felicity's class helped scientists study monarch butterflies. The students caught butterflies, put
an identifying tag on each one, and then released them.
The next year scientists caught 24 of the tagged butterflies. They sent Felicity's class the table
below, which shows the distance flown by each of the 24 butterflies.
Distances Flown by Butterflies
(in miles)
613 1366 1600 1371 1696 884
842 1886 239 1779 1604 2122
1090 1678 1885 1476 1803 1662
104 1665 1697 1669 120 857
a. What is the range of the distances, in miles, that the 24 butterflies flew? Show or explain
how you got your answer.
b. Copy the table below into your Student Answer Booklet. Complete your table by
determining the number of butterflies that flew within each distance interval.
Distance Intervals
Flown by Butterflies
Distance Interval Number of
(in miles) Butterflies
0 –600
601–1200
1201–1800
1801–2400
c. In your Student Answer Booklet, create a circle graph that shows the information in your
table from part (b). Be sure to do the following:
• Draw the sectors in your circle graph so that their sizes are reasonably accurate.
• Label each sector of your graph with the distance interval it represents and the
percent of the butterflies that flew within that distance interval.
• Show how you determined each percent.
• Include a title for your graph.
405
Massachusetts Comprehensive Assessment System
Grade 10 Mathematics Reference Sheet
AREA FORMULAS VOLUME FORMULAS
square ..................... A = s2 cube .........................................V = s3
(s = length of an edge)
rectangle ................. A = bh
right rectangular prism ............V = lwh
parallelogram ......... A = bh OR
V = Bh
triangle ................... A = 1 h
b (B = area of a base)
2
4
trapezoid ................. A = 1 (b1 + b2)
h sphere ......................................V = 3 pr3
2
circle ....................... A = pr2 right circular cylinder ............V = pr2h
.
1
right circular cone ...................V = 3 pr2h
LATERAL SURFACE AREA FORMULAS
1
right rectangular prism .......... LA = 2(hw) + 2(lh) right square pyramid ...............V = 3 s2h
right circular cylinder ........... LA = 2prh
right circular cone ................. LA = pr CIRCLE FORMULAS
( = slant height)
right square pyramid ............. LA = 2s C = 2pr
( = slant height) A = pr2
SPECIAL RIGHT TRIANGLES
TOTAL SURFACE AREA FORMULAS
cube ....................................... SA = 6s2
45˚ x
2
right rectangular prism ......... SA = 2(lw) + 2(hw) + 2(lh) x
sphere .................................... SA = 4pr2
45˚
right circular cylinder ........... SA = 2pr2 + 2prh x
right circular cone ................. SA = pr2 +pr
( = slant height) 60˚ 2y
right square pyramid ............. SA = s2 + 2s y
( = slant height)
30˚
y
3
406
Grade 10 Mathematics
Spring 2008 Released Items:
Reporting Categories, Standards, and Correct Answers*
Correct Answer
Item No. Page No. Reporting Category Standard
(MC/SA)*
1 385 Patterns, Relations, and Algebra 10.P.1 B
2 385 Number Sense and Operations 10.N.3 C
3 386 Data Analysis, Statistics, and Probability 10.D.1 C
4 386 Number Sense and Operations 10.N.2 B
5 386 Patterns, Relations, and Algebra 10.P.1 A
6 387 Patterns, Relations, and Algebra 10.P.3 C
7 387 Number Sense and Operations 10.N.3 C
8 387 Patterns, Relations, and Algebra 10.P.5 A
9 388 Data Analysis, Statistics, and Probability 10.D.1 C
10 388 Number Sense and Operations 10.N.2 C
11 388 Number Sense and Operations 10.N.1 A
12 389 Patterns, Relations, and Algebra 10.P.2 D
13 389 Number Sense and Operations 10.N.2 C
14 389 Data Analysis, Statistics, and Probability 10.D.1 A
C 8x 75
15 390 Patterns, Relations, and Algebra 10.P.7 or equivalent
16 390 Measurement 10.M.1 150 cm2
17 391 Geometry 10.G.8
18 392 Data Analysis, Statistics, and Probability 10.D.1 1
19 392 Number Sense and Operations 10.N.2 12
20 393 Number Sense and Operations 8.N.12
21 394 Patterns, Relations, and Algebra 10.P.7
22 395 Measurement 10.M.1 A
23 395 Geometry 10.G.3 D
24 396 Patterns, Relations, and Algebra 10.P.2 A
25 396 Patterns, Relations, and Algebra 10.P.7 D
26 397 Geometry 10.G.10 D
27 397 Measurement 10.M.1 B
28 398 Data Analysis, Statistics, and Probability 10.D.1 D
29 398 Number Sense and Operations 10.N.1 C
30 398 Measurement 10.M.1 A
31 399 Patterns, Relations, and Algebra 10.P.1
32 400 Measurement 10.M.3 B
33 400 Data Analysis, Statistics, and Probability 8.D.4 A
34 401 Measurement 10.M.3 C
35 401 Patterns, Relations, and Algebra 10.P.7 B
36 401 Geometry 10.G.3 A
37 402 Geometry 10.G.6 B
38 402 Data Analysis, Statistics, and Probability 10.D.1 D
39 403 Geometry 10.G.11 B
40 403 Patterns, Relations, and Algebra 10.P.8 D
41 404 Measurement 10.M.2
42 405 Data Analysis, Statistics, and Probability 10.D.1
* nswers are provided here for multiple-choice items and short-answer items only. Sample responses and scoring guidelines for
A
open-response items, which are indicated by shaded cells, will be posted to the Department's Web site later this year.
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PAPERBACK Fair 0130676993 Student Edition. Missing many pages. Heavy wrinkling from liquid damage. Does not affect the text. Heavy wear, wrinkling, creasing, Curling or tears ...on the cover and spine May be missing front or back cover. May have used stickers or residue. Poor binding causing loose and torn pages. Heavy writing, highlighting and marker.Read moreShow Less
More About
This Textbook
Overview
The engaging Martin-Gay workbook series presents a user-friendly approach to the concepts of basic math and algebra, giving readers ample opportunity to practice skills and see how those skills relate to both their lives and the real world. The goals of the workbooks are to build confidence, increase motivation, and encourage mastery of basic skills and concepts. Martin-Gay enhances readers' perception of math by exposing them to real-life situations through graphs and applications and ensures that readers have an organized, integrated learning system at their fingertips. The integrated learning resources program features book-specific supplements including Martin-Gay's acclaimed tutorial videotapes, CD videos, and MathPro 5. This book covers topics such as multiplying and dividing fractions, decimals, ratios and proportion, percent, geometry, statistics and probability, as well as an introduction to algebra. For anyone who wishing to brush up on their basic mathematical skills.
Editorial Reviews
Booknews
An introductory textbook for students needing math in non-mathematical courses. The author covers standard math topics from place value and adding; through statistics and geometry, to basic algebra. Annotation c. by Book News, Inc., Portland, Or.
From The Critics
This text provides a foundation in basic college mathematics, covering whole numbers, fractions and decimals, ratio and proportion, percent, and measurement, and introducing geometry, statistics and probability, and algebra. Emphasis is on applications, interpretation, problem solving, writing, use of technology, and critical thinking. Learning features include worked examples following a four-step process of understanding, translation, solving, and interpretation. This second edition contains new material on study skills integrated throughout, and an increased integration of geometry concepts. The author teaches mathematics at the University of New Orleans. Annotation c. Book News, Inc., Portland, OR (booknews.com)
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Meet the Author
An award-winning instructor and best-selling author, Elayn Martin-Gay has taught mathematics at the University of New Orleans for more than 25 years. Her numerous teaching awards include the local University Alumni Association's Award for Excellence in Teaching, and Outstanding Developmental Educator at University of New Orleans, presented by the Louisiana Association of Developmental Educators.
Prior to writing textbooks, Elayn developed an acclaimed series of lecture videos to support developmental mathematics students in their quest for success. These highly successful videos originally served as the foundation material for her texts. Today, the videos are specific to each book in the Martin-Gay series. Elayn also originated the Chapter Test Prep Video CDs to help students during their most "teachable moment" ---as they prepare for a test.
Elayn's experience has made her aware of how busy instructors are and what a difference quality supports make. For this reason, she created the Instructor-to-Instructor video series. These videos provide instructors with suggestions for presenting specific math topic and concepts in basic mathematics, prealgebra,beginning algebra, and intermediate algebra. Seasoned instructors can use them as a source for alternate approaches in the classroom. New or adjunct faculty may find the CDs useful for review. They are a great resource for suggestions regarding areas they may wish to emphasize, or common trouble areas students experience, that instructors my wish to highlight.
With her textbooks series, the Chapter Test Prep Video Cd, and CD Lecture series, Elayn has sought to put success within the reach of every student and instructor.
Prefacedevelop student proficiency in algebra and problem solving, and to prepare students for future courses.
Introduction developstudent proficiency in algebra and problem solving, and to prepare students for future courses.
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Course Description: This is the first course in the college preparatory math sequence. Students will review the language of algebra, operations with signed numbers, and the basic properties for simplifying and solving equations. Students will learn techniques to solve first and second degree algebraic sentences. Students will use problem-solving techniques in working with word problems involving fractions, decimals, and percents. Students will be introduced to graphing first-degree equations and inequalities in one and two variables. Students will also be introduced to basic geometrical terminology and problems.
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MATLAB及其在理工课程中的应用指南 (第3版)
Written for undergraduate students in science and engineering, this book provides a comprehensive introduction to MATLAB. The revised third edition contains three sections. The first section introduces the student to MATLAB language and environment. The second section focuses on mathematics and shows how to use MATLAB to solve calculus, linear algebra, and statistics problems. The third section focuses on applications, and contains numerous examples using MATLAB to solve problems in physics, mechanics, electronics, and signals and systems.
The book includes an introduction to MATLAB. In addition, a supplemental set of MATLAB M-files is available for download.
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CliffsQuickReview course guides cover the essentials of your toughest classes. Get a firm grip on core concepts and key material, and test your newfound knowledge with review questions.<p>Whether you're new to fractions, decimals, and percentages or just brushing up on those topics, <i>CliffsQuickReview Basic Math and Pre-Algebra</i>... more...
Your complete guide to a higher score on the CSET: Mathematics. Features information about certification requirements, an overview of the test - with a scoring scale, description of the test structure and format and proven test-taking strategies Approaches for answering the three types of questions: multiple-choice... more...
CliffsQuickReview course guides cover the essentials of your toughest subjects. Get a firm grip on core concepts and key material, and test your newfound knowledge with review questions. Whether you're new to limits, derivatives, and integrals or just brushing up on your knowledge of the subject, CliffsQuickReview Calculus can help. This guide covers... more...
CliffsQuickReview course guides cover the essentials of your toughest classes. Get a firm grip on core concepts and key material, and test your newfound knowledge with review questions. From planes, points, and postulates to squares, spheres, and slopes — and everything in between — CliffsQuickReview Geometry can help... more...
Boost Your grades with this illustrated quick-study guide. You will use it from college to graduate school and beyond. FREE Geometry Background and Triangles chapters in the trial version. Clear and concise explanations. Difficult concepts are explained in simple terms. Illustrated with graphs and diagrams. Table of Contents. Geometry Background. Euclidean... more...
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Imported EditionPrinciples Of Mathematical Analysis is the first in Walter Rudin's series of books on mathematical analysis and is a leading introductory text on the subject.
Summary of the Book
Principles of Mathematical Analysis provides a comprehensive introduction to some of the major theories of mathematical analysis. First published in 1953, the book is a standard text for undergraduate and first year graduate students.
The book begins with a discussion on Real and Complex numbers and Basic Topology. Here, students are introduced to the background required to understand rest of the topics in the book. The book goes on to discuss Numerical Sequences and Series, Continuity, Differentiation, Riemann-Stieltjes Integral, Integration of Differential Forms, and The Lebesgue Theory. Appropriate appendices and exercises follow each chapter. The book, in its third edition, includes a new section on the gamma function, and interesting, new exercises.
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Nice
The Good thing about this book is that there is a detailed solution manual of the exercises in this book available on the internet. So you can tackle the exercises with assurance. The book is not written in the most simplest language there is a great deal of intuition required from the reader but hey that is mathematics. Enjoy
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Good book for Real Analysis
It's not a particularly easy read, as is widely known, but with some patience and work, it's very useful and rewarding. Starts basic and reaches advanced topics; better to have some experience with a proof-based course before-hand.
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Description of Algebra 1: Test Forms by Saxon
Geared specifically toward the homeschool classroom, Saxon Algebra 1 is a college-prep course designed to build the mathematical foundation necessary for students to transition successfully into higher-level math courses.
Ideal for additional students joining the Algebra 1 course, this set includes 30 test forms with step-by-step test solutions, plus an answer key with answers to all student textbook practices and problem sets.
This helped my first two children to be ready for calculus in college--they were able to test out of college algebra. My youngest child needed to go at a slower rate and had to take college Math in college. So it is great for those who have a bent for math and science.
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The Complete Idiot's Guide to Calculus
Book Description: According to figures released by ACT Inc., many more U.S. high school students are taking courses in mathematics than was the case a decade ago. In fact, the portion of college-bound students taking calculus increased from 16 percent in 1987 to 27 percent in 2000. Let's face it, most students and adults who take calculus do so not for the fun of it, but rather to advance within a job or fulfill a degree requirement. The Complete Idiot's Guide(R) to Calculus will take the sting out of this complex math by putting it's uses, functions and limitations in perspective of what is already familiar to readers-algebra. Once readers have brushed up on their algebra and trigonometry skills, they'll be eased into the fundamentals of calculus
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Media, PA Cal explain it all simply so that students understand. Calculus can be a difficult topic at first. Like most math classes it has a few elementary parts that once grasped lend incite to the rest of the topic.
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Bob Miller's Algebra for the Clueless - 2nd edition
Summary: A is for Algebra-and that's the grade you'll pull when you use Bob Miller's simple guide to the math course every college-bound kid must take
With eight books and more than 30 years of hard-core classroom experience, Bob Miller is the frustrated student's best friend. He breaks down the complexities of every problem into easy-to-understand pieces that any math-phobe can understand-and this fully updated second edition of Bob Miller's Algebra for the Clueless c...show moreovers everything a you need to know to excel in Algebra I and IIShopbookaholic Wichita, KS
2006 Paperback Good Ex-library General Used Condiiton. Minor Defects may Exist. Minimal Shelf wear. Text may contain minor marking or highlighting, Binding Tight. Previous owners name or bookplate...show more may be present. Like New, May have remainder mark (black line generally made acrossed bottom page edge to indicate close out by publisher)
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syllabus and support materia (e)/pdf/4037_y13_sy.pdf
22 pages000
O Level Mathematics (syllabus D) (4024)O Level Mathematics (syllabus D) (4024) 1/1 O Level Mathematics (syllabus D) (4024) Will students be given a formula sheet to help them in the exam or do they need to
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Courses
MATH 099. Developmental Mathematics, 1-2 credits Online developmental course to prepare students for college-level mathematics courses. Topics include algebraic operations, expressions, and equations; factoring; graphing and solving linear equations. Students will develop mastery of the course outcomes by solving exercises on an adaptive, online learning system. MATH 099 is a Pass/Fail course and the credit hours do not count towards the 120-hour requirement. Placement: ACT Math score of 21 or less
MATH 131. Thinking Mathematically, 3 credits This course is a survey of topics in applied mathematics stressing the connections between contemporary mathematics and modern society. Topics include critical thinking, financial management, statistical reasoning, probability, math in politics, and math in art. This course meets the general education requirement in mathematics. Prerequisite: MATH 099 or ACT Math score of at least 22
MATH 211. Mathematics Concepts for Teachers, 3 credits The course gives prospective elementary school teachers insights into the application of mathematical reasoning, critical thinking skills, and topics related to mathematical content standards -- algebra, geometry, measurement, and data analysis and probability. This includes the process standards of problem solving, reasoning and proof, connections, communication and representation within each content standard identified in "Principles and Standards for School Mathematics" (NCTM, 2000). Prerequisite: MATH 210; EDUC 284; admission to Teacher Education Program
MATH 220. Introduction to Logic & Proof, 3 credits, Writing Intensive Introduction to Logic and Proof is designed to help students develop skills in reading and understanding elementary mathematical proofs, and in expressing their own mathematical ideas through formal writing. Emphasis will be on precision and style. Math topics include: Logical connectives and quantifiers; types of proof; elementary set theory; functions; integers and induction; equivalence relations; modular arithmetic; matrices. Prerequisite: MATH 171 or ACT Math score of at least 28
MATH/CSCI 281. Discrete Structures, 3 credits Introduction to discrete mathematics as it is used in computer science. Topics include propositional and the predicate logic, simple circuit logic, elementary number theory, sequences and summations, methods of proof (direct, by contradiction, by contraposition, by induction), set theory, graph theory, combinatorics, and discrete probability.
MATH/STAT 300. Modern Probability & Statistics, 3 credits A Calculus-based introduction to probability and the application of mathematical principles to the collection, analysis, and presentation of data. Modern probability concepts, discrete/continuous models, and applications; estimation and statistical inference through modern parametric, nonparametric, and simulation/randomization methods; maximum likelihood; Bayesian methods. This course prepares students for the preliminary P/1 exam of the Society of Actuaries (SOA) and Casualty Actuarial Society (CAS). Prerequisite: MATH 191
MATH 340. Secondary Math Methods, 3 credits Limited to secondary teaching certificate candidates. Current issues, approaches, and materials in school mathematics teaching, including philosophy and objectives, curricula, local/state/national standards, evaluation of current research. Students are required to complete a field component of 25 class contact hours. A minimum of two field components (80 hours) is required after field experience and before student teaching. Prerequisite: MATH 192; EDUC 205, 284, 309
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More About
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Overview
BUSINESS MATH, 17E provides comprehensive coverage of personal and business-related mathematics. In addition to reviewing the basic operations of arithmetic, students are prepared to understand and manage their personal finances, as well as grasp the fundamentals of business finances. BUSINESS MATH, 17E prepares students to be smart shoppers, informed taxpayers, and valued employees. Basic math skills are covered in a step-by-step manner, building confidence in users before they try it alone. Spreadsheet applications are available on the Data Activities CD, and a simulation activity begins every chapter. Chapters are organized into short lessons for ease of instruction and include algebra connections, group and class activities, communication skills, and career spotlights.
Related Subjects
Meet the Author
Mary Hansen received her B.A. in mathematics and M.A.T in education from Trinity University in San Antonio Texas. She has taught mathematics and special education and the elementary, high school and college level in Texas, North Carolina and Kansas. She is the author of Business Math, 17e, and the co-author of three high school mathematics textbooks. She currently works as an educational consultant
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Numerical Methods for Roots of Polynomials - Part II along with Part I (9780444527295) covers most of the traditional methods for polynomial root-finding such as interpolation and methods due to Graeffe, Laguerre, and Jenkins and Traub. It includes many other methods and topics as well and has a chapter devoted to certain modern virtually optimal methods. Additionally, there are pointers to robust and efficient programs. This book is invaluable to anyone doing research in polynomial roots, or teaching a graduate course on that topic. First comprehensive treatment of Root-Finding in...
Mathematical Formulas For Industrial and Mechanical Engineering serves the needs of students and teachers as well as professional workers in engineering who use mathematics. The contents and size make it especially convenient and portable. The widespread availability and low price of scientific calculators have greatly reduced the need for many numerical tables that make most handbooks bulky. However, most calculators do not give integrals, derivatives, series and other mathematical formulas and figures that are often needed. Accordingly, this book contains that information in an easy...
Exterior analysis uses differential forms (a mathematical technique) to analyze curves, surfaces, and structures. Exterior Analysis is a first-of-its-kind resource that uses applications of differential forms, offering a mathematical approach to solve problems in defining a precise measurement to ensure structural integrity. The book provides methods to study different types of equations and offers detailed explanations of fundamental theories and techniques to obtain concrete solutions to determine symmetry. It is a useful tool for structural, mechanical and electrical engineers, as...
Mathematical Concepts and Methods in Modern Biology offers a quantitative framework for analyzing, predicting, and modulating the behavior of complex biological systems. The book presents important mathematical concepts, methods and tools in the context of essential questions raised in modern biology. Designed around the principles of project-based learning and problem-solving, the book considers biological topics such as neuronal networks, plant population growth, metabolic pathways, and phylogenetic tree reconstruction. The mathematical modeling tools brought to bear on these...
Calculus of Thought: Neuromorphic Logistic Regression in Cognitive Machines is a must-read for all scientists about a very simple computation method designed to simulate big-data neural processing. This book is inspired by the Calculus Ratiocinator idea of Gottfried Leibniz, which is that machine computation should be developed to simulate human cognitive processes, thus avoiding problematic subjective bias in analytic solutions to practical and scientific problems. The reduced error logistic regression (RELR) method is proposed as such a "Calculus of Thought." This book reviews how...
This book addresses one of the key problems in signal processing, the problem of identifying statistical properties of excursions in a random process in order to simplify the theoretical analysis and make it suitable for engineering applications. Precise and approximate formulas are explained, which are relatively simple and can be used for engineering applications such as the design of devices which can overcome the high initial uncertainty of the self-training period. The information presented in the monograph can be used to implement adaptive signal processing devices capable of...
Markov processes are processes that have limited memory. In particular, their dependence on the past is only through the previous state. They are used to model the behavior of many systems including communications systems, transportation networks, image segmentation and analysis, biological systems and DNA sequence analysis, random atomic motion and diffusion in physics, social mobility, population studies, epidemiology, animal and insect migration, queueing systems, resource management, dams, financial engineering, actuarial science, and decision systems. Covering a wide range...
Are you developing strategies for a future sustainable energy supply? Are you designing policies to deploy renewable energy technologies in your country? Are you looking for new tools and measures to make your policies more effective? Are you planning to make decisions on renewable energy investments in certain countries and are you checking their policy robustness? Let the IEA guide you into successful, efficient and effective policies and decisions for accelerating deployment of renewable energy. Learn about the six policy actions that are essential ingredients for your policy...
Swarm Intelligence and bio-inspired computation have become increasing popular in the last two decades. Bio-inspired algorithms such as ant colony algorithms, bat algorithms, bee algorithms, firefly algorithms, cuckoo search and particle swarm optimization have been applied in almost every area of science and engineering with a dramatic increase of number of relevant publications. This book reviews the latest developments in swarm intelligence and bio-inspired computation from both the theory and application side, providing a complete resource that analyzes and discusses the latest and...
Mathematical Models for Society and Biology , 2e, is a useful resource for researchers, graduate students, and post-docs in the applied mathematics and life science fields. Mathematical modeling is one of the major subfields of mathematical biology. A mathematical model may be used to help explain a system, to study the effects of different components, and to make predictions about behavior. Mathematical Models for Society and Biology , 2e, draws on current issues to engagingly relate how to use mathematics to gain insight into problems in biology and contemporary society. For this...
Mereon is an approach to the unification of knowledge that relies on whole systems modelling. It is a scientific framework that charts the sequential, emergent growth process of systems. A dynamic structure, Mereon provides insight and a new approach to General Systems Theory and non-linear science. Mereon evolved through a new approach to polyhedral geometry and topology that is related to the dynamics of the polyhedra. It is related to a large number of systems, physical, mathematical, and philosophical. In linking these systems, Mereon provides access to new relationships among them...
Probability theory is a rapidly expanding field and is used in many areas of science and technology. Beginning from a basis of abstract analysis, this mathematics book develops the knowledge needed for advanced students to develop a complex understanding of probability. The first part of the book systematically presents concepts and results from analysis before embarking on the study of probability theory. The initial section will also be useful for those interested in topology, measure theory, real analysis and functional analysis. The second part of the book presents the concepts,...
Get the latest on rapidly evolving global electricity markets direct from the scholars and thought leaders who are shaping reform. In this volume, dozens of world-class experts from diverse regions provide a comprehensive assessment of the relevant issues in today's electricity markets. Amid a seething backdrop of rising energy prices, concerns about environmental degradation, and the introduction of distributed sources and smart grids, increasingly stringent demands are being placed on the electric power sector to provide a more reliable, efficient delivery infrastructure, and more...
Energy Efficiency: Towards the End of Demand Growth is a detailed guide to new energy efficiency technologies and policy frameworks affecting the profitability of efficiency projects. The contributions drawn together by F.P. Sioshansi feature insights from recognized thought leaders, detailed examinations of evolving technologies, and practical case studies yielding best practices for project planners, implementers and financiers. This volume challenges the "more is better" paradigm in energy production, examining efficiency technologies and measurement across the supply chain. ...
This book is the first on the topic and explains the most cutting-edge methods needed for precise calculations and explores the development of powerful algorithms to solve research problems. Multipoint methods have an extensive range of practical applications significant in research areas such as signal processing, analysis of convergence rate, fluid mechanics, solid state physics, and many others. The book takes an introductory approach in making qualitative comparisons of different multipoint methods from various viewpoints to help the reader understand applications of more complex...
MATLAB for Neuroscientists serves as the only complete study manual and teaching resource for MATLAB, the globally accepted standard for scientific computing, in the neurosciences and psychology. This unique introduction can be used to learn the entire empirical and experimental process (including stimulus generation, experimental control, data collection, data analysis, modeling, and more), and the 2nd Edition continues to ensure that many computational problems can be addressed in a single programming environment. This updated edition features additional material on the creation of...
Practical 3D physics simulation experience with modern feature-rich graphics and physics APIs
Create your own physics simulations and understand the various design concepts of modern games
Build a real-time complete game application, implementing 3D graphics and physics entirely from scratch
Learn the fundamental and advanced concepts of game programming using step-by-step instructions and examples
In Detail
Physics simulation is an integral part of almost all game development projects as it is essential to the rules and feel of the game (gameplay) regardless of the...
Leonardo da Vinci was a brilliant artist, scientist, engineer, mathematician, architect, inventor, writer, and even musician—the archetypal Renaissance man. But he was also, Fritjof Capra argues, a profoundly modern man.
Not only did Leonardo invent the empirical scientific method over a century before Galileo and Francis Bacon, but Capra's decade-long study of Leonardo's fabled notebooks reveal him as a systems thinker centuries before the term was coined. He believed the key to truly understanding the world was in perceiving the connections between phenomena and the larger patterns formed...
Master the PhysX 3 Physics Engine and learn how to program your very own physics simulation
Learn everything you need to know about PhysX programming from scratch
Master the most advanced features of the PhysX Physics Engine
Code examples are included in each chapter to help you learn quickly and efficiently
In Detail
In this day and age, physics engines play a very critical role in the success of a sophisticated game. PhysX is a state-of-the-art cross-platform physics engine widely used by top game studios and developers. It contains all the physics-related...
The behavior of acoustic or electromagnetic waves reflecting off, and scattering from, intercepted bodies of any size and kind can make determinations about the materials of those bodies and help in better understanding how to manipulate such materials for desired characteristics. This book offers analytical formulas which allow you to calculate acoustic and electromagnetic waves, scattered by one and many small bodies of an arbitrary shape under various boundary conditions. Equations for the effective (self-consistent) field in media consisting of many small bodies are derived. These...
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The abstract of this presentation is on solving for minimum values of multivariable functions using Lagrange's Theorem. The problem was proposed in the October 2008 issue of Mathematics Magazine. The problem stated let x, y, and z be positive real numbers with x+y+z = xyz. Find the minimum value of √1+x^2 + √1+y^2 + √1+z^2. The solution of the stated problem was found to be x=y=z=√3, which gave a minimum value of 6.
The model drawing approach to problem solving is used extensively in the math curriculum of Singapore. It takes students from the concrete to the abstract via an intermediary pictorial stage. Students create bars and break them down into "units." The units create a bridge to the concept of an "unknown" quantity that must be found. Students can learn to use this strategy in the primary grades and continue with it through the middle grades. At Worcester State College, we teach this technique to our pre-service elementary teachers.
Mathematics is an integral part of the educational experience of all students. Students arrive at Worcester State College with varying levels of mathematical preparation and are given tests so they are placed into a class for which they are well prepared. This poster presents results of investigations studying the mathematical experience of WSC students. How does a student's level of mathematical preparation affect his or her success in college? How does a student's mathematical achievement while at WSC relate to his or her likelihood of college completion?
FLIGHTS FROM ORLANDO: IS THERE A CONNECTION BETWEEN DISTANCE AND PRICE?
The objective of this problem is to find z/(y + z), given that z/(x + y)= a and y/(x + z)= b. There are two cases for solving this problem: y = z and y ≠ z. In the trivial case, y = z, it is easy to show z/(y + z)=1/2. For the second case, y ≠ z, with algebraic transformations on z/(y + z), and by recognizing algebraic similarities between a + 1 and b + 1 it can be shown that z/(y + z) = (ab + a)/(a + 2ab + b).
In Graph Theory, we can define the "Weiner Index," which is the sum of all the shortest paths in a given graph. Given two specific indexed sets of graphs, namely the Grid and Comb graphs on 2n vertices, the aim of this paper was to characterize the Weiner Index for all the Grid and Comb graphs. In this paper, we do this by using techniques from signal analysis and from the theory of recurrence relations.
Moiré Fringes, which are most often noticed as interference patterns on a TV screen or through a window screen, are the small bands caused by the interference of two iterated patterns. We can describe this interference as a function of the gradients of two iterated functions. This gradient does not only predict the existence of Moiré Fringes, but also their periodicity and density. In this project, we describe how this metric for Moiré fringes works, and provide some examples including mathematical code, which generates images, and associated informational graphs, which show Moiré Fringes. Math majors Jonathan Lussier and Richard Ouellette collaborated on this project.
This is a conference presentation given at the Northwest Mathematics Conference for middle and high school teachers. We consider the Sock Drawer and the Chuck-a-Luck classic probability problems. We illustrate ways to turn them into successful activities for the middle and high school classroom.
We discuss how the Oregon Mathematics Leadership Institute (OMLI) enabled a team of five instructors, including a master teacher and four mathematics faculty, to design and implement a course on non-Euclidean geometry for K-12 teachers. We focus on the intense structure of the course, which was delivered in 15 sessions of two hours each. We also discuss the content of the course, which included units on both taxicab and spherical geometry. Finally, we emphasize the pedagogy of the course, which included hands-on cooperative learning that was carefully orchestrated to ensure everyone's participation, as well as skilled facilitation that was aimed at eliciting productive mathematics discourse, and thus at improving understanding of mathematical concepts.
Mathematicians throughout the years have developed many powerful inequalities relating to acute triangles. One of the more famous is Euler's Inequality, published in 1765, relating a triangle's inradius to its circumradius. Consider an acute triangle with side-lengths a, b, and c, with inradius r and semiperimeter p. James Keenan, a 2008 WSC graduate, and I proved that (1-cosA)(1- cosB)(1- cosC) ≥ cosAcosBcosC(2- (3√3r)/p). In this PowerPoint presentation, I describe our proof, which was accomplished using Euler's Inequality, Heron's
Most of us use cryptography every day without even realizing it. Every time you use your cell phone and every time you buy a book online, you are using cryptography to send encrypted messages. In this poster we outline the basics of the cryptography involved and indicate how advanced mathematics is used in these everyday transactions.
THE TRIVIALITY AND NONTRIVIALITY OF TATE-LICHTENBAUM SELF PAIRINGS ON JACOBIANS OF CURVES
Let E be an elliptic curve defined over a finite field F and suppose that E[n] is defined over F. For attacking the elliptic curve discrete logarithm problem it is useful to know when points pair with themselves nontrivially under the Tate-Lichtenbaum pairing. In this paper we characterize when all points in E[n] have trivial self pairings. This result is expressed in terms of the action of the Frobenius endomorphism on E[n^2]. We give examples of how this result can be used to derive some well-known residuacity laws. We then generalize the elliptic curve result to Jacobians of algebraic curves of arbitrary genus.
This paper addresses the study of the homogenization problem associated with propagation of long wave disturbances in materials whose properties exhibit not only spatial but also temporal inhomogeneities (called dynamic materials). Homogenization theory is employed to replace an equation with oscillating coefficients by a homogenized equation. Two typical examples of periodic homogenization are considered: the wave equation and Maxwell's system coefficients oscillating rapidly not only in space but also in time. Conditions that generate applicability of the homogenization procedure to dynamic materials composites are developed. The effective tensors of rank-one laminates for one-dimensional wave equation and the full Maxwell's system are computed explicitly. We also note some dramatic differences between the hyperbolic and the elliptic cases.
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Elements of Number Theory - 02 edition
Summary: This book is a concise introduction to number theory and some related algebra, with an emphasis on solving equations in integers. Finding integer solutions led to two fundamental ideas of number theory in ancient times - the Euclidean algorithm and unique prime factorization - and in modern times to two fundamental ideas of algebra - rings and ideals. The development of these ideas, and the transition from ancient to modern, is the main theme of the book. The histori...show morecal development has been followed where it helps to motivate the introduction of new concepts, but modern proofs have been used where they are simpler, more natural, or more interesting. These include some that have not yet appeared in textbooks, such as a treatment of the Pell equation using Conway's theory of quadratic forms. Also, this is the only elementary number theory book that includes significant applications of ideal theory. It is clearly written, well illustrated, and supplied with carefully designed exercises, making it a pleasure to use as an undergraduate textbook or for independent study
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OverviewBlitzer continues to raise the bar with his engaging applications developed to motivate readers from diverse majors and backgrounds. Thinking Mathematically, Fifth Edition, draws from the author's unique background in art, psychology, and math to present math in the context of real-world applications. The author understands the needs of nervous readers and provides helpful tools in every chapter to help them master the material. Voice balloons are strategically placed throughout the book, showing what an instructor would say when leading a student through a problem. Study tips, chapter review grids, Chapter Tests, and abundant exercises provide ample review and practice.
Product Details
ISBN-13: 9780321691125
Publisher: Pearson
Publication date: 1/28/2010
Edition number: 5
Pages: 960
Sales rank: 1,093,984
Product dimensions: 8.30 (w) x 10.90 (h) x 1.20 (d)'s love for teaching mathematics was nourished for nearly 30 years at Miami Dade College, where he received numerous teaching awards, including Innovator of the Year from the League for Innovations in the Community College and an endowed chair based on excellence in the classroom. In addition to Thinking Mathematically, Bob has written textbooks covering introductory algebra, college algebra, algebra and trigonometry, and precalculus, all published by Prentice Hall. When not secluded in his Northern California writer's cabin, Bob can be found hiking the beaches and trails of Point Reyes National Seashore, and tending to the chores required by his beloved entourage of horses, chickens, and irritable roosters
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First Course in Wavelets with Fourier Analysis
This book fills the gap between volumes on wavelets that are either "too advanced" (in terms of mathematical background required) or that contain ...Show synopsisThis book fills the gap between volumes on wavelets that are either "too advanced" (in terms of mathematical background required) or that contain "too little" mathematical theory underlying wavelets. It presents most of the theory underlying Fourier analysis and wavelets in a clear and comprehensive fashion-- "without" requiring advanced background in real analysis. Provides a careful balance between theory and practical algorithms, and features a clear presentation of applications to digital signal processing--e.g., data compression, digital filtering and singularity detection. Includes illustrations and MATLAB code used in many of the algorithms. Inner Product Spaces. Fourier Series. The Fourier Transform. Discrete Fourier Analysis. Wavelet Analysis. Multiresolution Analysis. The Daubechies Wavelets. For anyone interested in Wavelets and Fourier Analysis
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05217536 and Assessing Skills in Mathematics (Cambridge International Examinations)
The handbooks provide clear practical and up-to-date adviceon teaching and assessing skills across a range of core subject areas for IGCSE and O Level;they can also be used by teachers delivering local syllabuses in the subject. They offer ideas and strategies for effective classroom practice, the setting of coursework, assessing students' work and the integration of different skills. Readers can 'dip into' the books to read up on a particular topic or approach and the material is relevant to both new and experienced teachers alike. All authors are experienced teachers, teacher trainers and examiners
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Complete Mathematics for GCSE and Standard Grade (Mathematics)
Description: Written by an experienced teacher and examiner, Complete Mathematics for GCSE and Standard Grade is an ideal book for average-ability students. Groundwork is covered in the first section and then thoroughly revised in the second section beforeMore...
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Written by an experienced teacher and examiner, Complete Mathematics for GCSE and Standard Grade is an ideal book for average-ability students. Groundwork is covered in the first section and then thoroughly revised in the second section before harder topics are approached. Key Points: · Carefully graded practice questions to consolidate basic techniques · Problems and investigations to develop skills required for coursework · Emphasis on everyday situations relevant to the demands of future employment · Complete set of answers
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Precise Calculator has arbitrary precision and can calculate with complex numbers, fractions, vectors and matrices. Has more than 150 mathematical functions and statistical functions and is programmable (if, goto, print, return, for).
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In this unit you will see first how to convert vectors from geometric form, in terms of a magnitude and direction, to component form, and then how conversion in the opposite sense is accomplished. The ability to convert between these different forms of a vector is useful in certain problems involving displacement and velocity, as shown in Section 2, in which you will also work with bearings.
Assuming that both the content of mathematics and the processes need to be included in programmes and curricula, the problem becomes one of how a suitable curriculum can be structured. One possibility is to construct a very specific curriculum with clearly defined objectives for both content and processes separately, and possibly with suggested learning activities. However, content and process are two complementary ways of viewing the subject.
An alternative is to see the curriculum aimed at teachers who wish to review how they go about the practice of teaching maths, those who are considering becoming maths teachers, or those who are studying maths courses and would like to understand more about the teaching process.
This unit is from our archive and is an adapted extract from Teaching mathematical thinking at Key Stage 3 (ME624) which is no longer taught by The Open University. If you want to study formally with us, you may wish to explore other cour main teaching text of this unit is provided in the workbook below. The answers to the exercises that you'll find throughout the workbook are given in the answer book. You can access it by clicking on the link under the workbook. Section 4.2 of the unit requires you to listen to some audio files. You'll find these on the next page of this unit.
RSS ('Really Simple Syndication' or 'Rich Site Summary') newsfeeds supply headlines, links, and article summaries from various websites. By using RSS 'feedreader' software you can gather together a range of feeds and read them in one place: they come to you, rather than you having to go out and look for breaking news. The range of RSS feeds on offer is growing daily. There is probably a feed to cover all aspects of your life where you might need the latest information, and you mayReferencing is not only useful as a way of sharing information, but also as a means of ensuring that due credit is given to other people's work. In the electronic information age, it is easy to copy and paste from journal articles and web pages into your own work. But if you do use someone else's work, you should acknowledge the source by giving a correct reference.
Taking someone's work and not indicating where you took it from is termed plagiarism and is regarded as an infringemenIf you are considering taking your studies further you might like to consider using bibliographic software. Bibliographic software can be used to sort references, annotate them, manage quotations or create reading lists.
There are several software packages on the market. Some are listed below.
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If you are not sure87% of items that are filed into a filing cabinet are never looked at again. STANFORD UNIVERSITY
The world is producing nearly two exabytes of new and unique information every year – an exabyte is a new term that had to be coined for a billion gigabytes. All the words ever spoken by human beings comes to five exabytes. UNIVERSITY OF CALIFORNIA (BERKELEY)
More new information has been produ both search engines and subject gateways will help you find the resources that you need, the types of information that you find will differ.
Search engines such as Google and Yahoo! search the internet for keywords or phrases, and then show you the results. These results are not mediated by the search engines, and therefore you need to use your own judgement on the reliability of the results. You may, for example, find websites written by experts, alongside websites written byComplementary currencies also demand a rethink of our economy, but have a more imaginative and radical edge. Because of the difficulties with conventional monetary systems, various alternatives are being tried. These are usually restricted to a particular group of people, and so are called 'local' or 'complementary' currencies. They are generally based in a local community and enable people to exchange goods and services without resorting to 'traditional' currency. Some areCommunities such as Findhorn already behave as if natural resources need careful management: they work hard to reduce fossil fuel use. A central assumption of this way of thinking is that people need to root economies more locally (Figure 15). To see the same impulse spread through the mainstream economy would require that th will the decisions be made that will result in meaningful action on climate change, and who will make them stick? Following climate change politics in the media can give the impression that most of the action on climate change is going on between national decision makers in international forums. It is important to keep in mind that these forums have resulted from persistent pressure from a combination of grassroots environmental activists and a global network of science and policy exper thing is common to all three attempts to find a route to a sustainable economy and society: in different ways they all assume that people will get actively involved in making human societies more sustainable. But this transformation will not take place through the corporate world's promises, by local protectionism, a return to 'strong states' or the publication of numerous indicators. Any of the three positions outlined above requires interactions and feedbacks created by a vibrantNot for the first time in this book, you are faced with a term that is important but difficult to define precisely. Although the fact that plenty of people from different standpoints are using the term 'globalisation' is some measure of its importance, it can be confusing to find that there are different ways of framing what it means for humans and the environment today and in the future. In this section, the range of political responses to climate change and environment–economy interacHuman societies have to take urgent action to end their dependence on fossil fuels. They also have to prepare to adapt to the uncertainties inherent in global environmental changes, particularly climatic ones. We have to alter the whole path of our development and decision making in order to make our societies both environmentally adaptable and sustainable. This unit takes on the task of trying to chart some of the ways in which this might come about.
The context for these changes by g part I have presented evidence showing that even apparently remote regions of our planet are intimately connected through physical processes. For example, once an organic POP is transported to the poles, then biological processes can take over and through bioaccumulation perhaps cause harm. But this physical connection has allowed the ice to preserve unique proxy records of the past climate of our planet. Directly measuring the gases trapped in the ice has enabled histories of past at
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Maths TutorOpen. To bridge the gap from school to university study, to revise or find the
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Properties of straight line segments - Maths TutorIn this unit a system of co-ordinates is described, and is used to find various
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Simplifying Algebraic Fractions - Maths TutorSimplifying Algebraic Fractions. The ability to simplify fractions and to write them
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Using Graphs to Identify Relationships: Graphing Functions
PDF (Acrobat) Document File
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1.97 MB | 14 pages
PRODUCT DESCRIPTION
This is a 14 page bundle that teaches students how to use graphs to identify relationships, as well as to make connections between graphs and their meanings. This bundle includes a warmup, notes, practice, and an exit ticket. Students will need to connect real world word problems to their graphs and function tables. Students will also be asked to recognize an increasing, decreasing, or no changing line on a graph and determine the meaning. Answer key is included
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Probability : An Introduction - 87 edition
Summary: Excellent basic text covers set theory, probability theory for finite sample spaces, binomial theorem, probability distributions, means, standard deviations, probability function of binomial distribution, and other key concepts and methods essential to a thorough understanding of probability. Designed for use by math or statistics departments offering a first course in probability. 360 illustrative problems with answers for half. Only high school algebra needed. Chap...show moreter bibliographies. ...show less
01/01/1987 Paperback Used-Good Book in good or better condition. Dispatched same day from US or UK warehouse. Fair 0486652521
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This is a Smart Worksheet covering circles, parabolas and ellipses. The sheet consists of nearly 80 questions with each having an individualized on-line video solution. I've also included a host of tools and resets so that you can track of your progress, Hope you enjoy the live worksheet and if you have any questions, then by all means give us a buzz and send us an email. Cheers, MarkParabola" tells you everything you ever needed to know about parabolas but were afraid to ask.
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books.google.com - Bridging the gap between elementary number theory and the systematic study of advanced topics, A Classical Introduction to Modern Number Theory is a well-developed and accessible text that requires only a familiarity with basic abstract algebra. Historical development is stressed throughout, along with... Classical Introduction to Modern Number Theory
A Classical Introduction to Modern Number Theory
Bridging the gap between elementary number theory and the systematic study of advanced topics, A Classical Introduction to Modern Number Theory is a well-developed and accessible text that requires only a familiarity with basic abstract algebra. Historical development is stressed throughout, along with wide-ranging coverage of significant results with comparatively elementary proofs, some of them new. An extensive bibliography and many challenging exercises are also included. This second edition has been corrected and contains two new chapters which provide a complete proof of the Mordell-Weil theorem for elliptic curves over the rational numbers, and an overview of recent progress on the arithmetic of elliptic curves.
Review: A Classical Introduction to Modern Number Theory (Graduate Texts in Mathematics) (Graduate Texts in Mathematics #84)
User Review - Dan - Goodreads
I just read the chapter about the elliptic curve y^2 = x^3 + Dx, it was pretty good.Read full review
Review: A Classical Introduction to Modern Number Theory (Graduate Texts in Mathematics) (Graduate Texts in Mathematics #84)
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The most difficult book I have read up to now ;).For me it took more than an hour to read one page of this book ! This book devotes some parts about historical comments in number theory, have you ever ...Read full review
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FDMAT 108
Prerequisite: Math 100B with a grade of "B" or higher or one year of high school algebra. This class prepares students to understand, analyze, and solve real-life problems that require quantitative reasoning. Topics include the meaning of probabilities, how to read, critique, and apply statistical information found in news reports, public policy debates, consumer reports, and other daily life and professional situations; the use of mathematical models in describing, understanding, and making predictions about real world phenomena; and the mathematics of loans and investments. Other topics may be included as time permits. All topics will be illustrated by examples and applications from current events, daily life, business, and natural phenomena. (Fall, Winter Spring)
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Related Resources
OK. Let's get started, please. First, I wanted to remind you that tomorrow is the first exam in this class. It is taking place here if your last name starts with S or beyond, and it is taking place in Walker top floor if your last name starts from A-R. If you are left-handed and you prefer to have a real table, feel free to go to Walker. Otherwise, try to go to the correct room. It is better.
And, well, let's see. We will be basically grading the exam in the afternoon evening and then posting the scores on the online system, so you can check there. And there will be makeup exams on Tuesday, Wednesday and Thursday next week. For times and places, I will announce on the Web page. That is in case things don't go well or in case somehow you cannot make it tomorrow. Remember, if you have an absence for like a sports tournament or something like this, please let us know now. What else? Hopefully you have seen the two practice exams. And one of them you probably talked about in recitation yesterday. The other one we are going to see a bit now. I have had some of you comment that the practice exams are much easier than the problem sets.
And, well, let's say the problem sets are harder than the exams because they are designed to make you think and to truly help you put things together, see how you would use the concepts in a real world situation. The exams are a bit easier. The actual exam is comparable to the practice exams in difficulty. It is a little bit, maybe a tiny, tiny bit harder, especially when practice exam 1B was a little bit on the easier side of thing, but not much harder.
So, if you do fine on the practice exams, you should do fine tomorrow. As you have seen, the format is basically five or six problems that cover all the material we have seen. And, well, there is a bit of everything. Some of the problems are very easy and shouldn't take more than a minute or two to finish. Some of those will take a bit more thinking. Remember, you only have 50 minutes so you have to think about how to use your time.
The exam is designed so that most of you can finish it in 50 minutes, but don't stay stuck on the same problem for a half an hour. Switch to the next page. Let me just tell you first about the list of topics. Basically, the list of topics is simple. It is everything. I mean, everything we have seen so far is on the exam. But let me just remind you of the main topics that we have seen. First of all, we learned about vectors, how to use them, and dot-product. At this point, you probably should know that the dot-product of two vectors is obtained by summing products of components.
And geometrically it is the length of A times the length of B times the cosine of the angle between them. And, in particular, we can use dot-product to measure angles by solving for cosine theta in this equality. And most importantly to detect whether two vectors are perpendicular to each other. Two vectors are perpendicular when their dot-product is zero. Any questions about that? No. Is everyone reasonably happy with dot-product by now? I see a stunned silence. Nobody happy with dot-product so far? OK. If you want to look at Practice 1A, a good example of a typical problem with dot-product would be problem 1.
Let's see. We are going to go over the practice exam when I am done writing this list of topics. I think probably we actually will skip this problem because I think most of you know how to do it. And if not then you should run for help from me or from your recitation instructor to figure out how to do it. The second topic that we saw was cross-product. When you have two vectors in space, you can just form that cross-product by computing its determinant. So, implicitly, we should also know about determinants.
By that I mean two by two and three by three. Don't worry about larger ones, even if you are interested, they won't be on the test. And applications of cross-product, for example, finding the area of a triangle or a parallelogram in space. If you have a triangle in space with sides A and B then its area is one-half of the length of A cross B. Because the length of A cross B is length A, length B sine theta, which is the same as the area of the parallelogram formed by these two vectors. And the other application of cross-product is to find a vector that's perpendicular to two given vectors. In particular, to find the vector that is normal to a plane and then find the equation of a plane.
Another application is finding the normal vector to a plane and using that finding the equation of a plane. Basically, remember, to find the equation of a plane, ax by cz = d, what you need is the normal vector to the plane. And the components of the normal vector are exactly the coefficients that go into this. And we have seen an argument for why that happens to be the case. To find a normal vector to a plane typically what we will do is take two vectors that lie in the plane and will take their cross-product. And the cross-product will automatically be perpendicular to both of them. We are going to see an example of that when we look at problem 5 in practice 1A. I think we will try to do that one.
Another application, well, we will just mention it as a topic that goes along with this one. We have seen also about equations of lines and how to find where a line intersects a plane. Just to refresh your memories, the equation of a line, well, we will be looking at parametric equations. To know the parametric equation of a line, we need to know a point on the line and we need to know a vector that is parallel to the line. And, if we know a point on the line and a vector along the line, then we can express the parametric equations for the motion of a point that is moving on the line.
Actually, starting at point, at time zero, and moving with velocity v. To put things in symbolic form, you will get a position of that point by starting with a position of time zero and adding t times the vector v. It gives you x, y and z in terms of t. And that is how we represent lines. We will look at problem 5 in a bit, but any general questions about these topics? No. Do you have a question? Do we have to know Taylor series? That is a good question. No, not on the exam. [APPLAUSE]
Taylor series are something you should be aware of, generally speaking. It will be useful for you in real life, probably not when you go to the supermarket, but if you solve engineering problems you will need Taylor series. It would be good not to forget them entirely, but on the 18.02 exams they probably won't be there. Let me continue with more topics. And then we can see if you can think of other topics that should or should not be on the exam. Third topics would be matrices, linear systems, inverting matrices.
I know that most of you that have calculators that can invert matrices, but still you are expected at this point to know how to do it by hand. If you have looked at the practice tests, both of them have a problem that asks you to invert a matrix or at least do part of it. And so it is very likely that tomorrow there will be a problem like that as well. In general, when a kind of problem is on both practice tests it's a good indication that it might be there also on the actual exam.
Unfortunately, not with the same matrix so you cannot learn the answer by heart. Another thing that we have learned about, well, I should say this is going to be problem 3 on the test and will on the practice test. On the actual test, too, I think, actually. Anyway, we will come back to it later. A couple of things that you should remember. If you have a system of the form AX equals B then there are two cases. If a determinant of A is not zero then that means you can compute the inverse matrix and you can just solve by taking A inverse times B. And the other case is when the determinant of A is zero, and there is either no solution or there is infinitely many solutions.
In particular, if you know that there is a solution, for example, if B is zero there always is an obvious solution, X equals zero, then you will actually have infinitely many. In general, we don't really know how to tell whether it is no solution or infinitely many. Questions about that? Yes? Will we have to know how to rotate vectors and so on? Not in general, but you might still want to remember how to rotate a vector in a plane by 90 degrees because that has been useful when we have done problems about parametric equations, which is what I am coming to next.
What we have seen about rotation matrices, that was the homework part B problem, you are not supposed to remember by heart everything that was in part B of your homework. It is a good idea to have some vague knowledge because it is useful culture, I would say, useful background for later in your lives, but I won't ask you by heart to know what is the formation for a rotation matrix. And then we come to, last by not least, the problem of finding parametric equations.
And, in particular, possibly by decomposing the position vector into a sum of simpler vectors. You have seen quite an evil exam of that on the last problem set with this picture that maybe by now you have had some nightmares about. Anyway, the one on the exam will certainly be easier than that. But, as you have seen -- I mean, you should know, basically, how to analyze a motion that is being described to you and express it in terms of vectors and then figure out what the parametric equation will be. Now, again, it won't be as complicated on the exam as the one in the problem set. But there are a couple of those on the practice exam, so that gives you an idea of what is realistically expected of you.
And now once we have parametric equations for motion, so that means when we know how to find the position vector as a function of a parameter maybe of time, then we have seen also about velocity and acceleration, which the vector is obtained by taking the first and second derivatives of a position vector. And so one topic that I will add in there as well is somehow how to prove things about motions by differentiating vector identities.
One example of that, for example, is when we try to look at Kepler's law in class last time. We look at Kepler's second law of planetary motion, and we reduced it to a calculation about a derivative of the cross-product R cross v. Now, on the exam you don't need to know the details of Kepler's law, but you need to be able to manipulate vector quantities a bit in the way that we did. And so on practice exam 1A, you actually have a variety of problems on this topics because you have problems two, four and six, all about parametric motions.
Probably tomorrow there will not be three distinct problems about parametric motions, but maybe a couple of them. I think that is basically the list of topics. Anybody spot something that I have forgotten to put on the exam or questions about something that should or should not be there? You go first. Yeah? How about parametrizing weird trigonometric functions? I am not sure what you mean by that. Well, parametric curves, you need to know how to parameterize motions, and that involves a little bit of trigonometrics. When we have seen these problems about rotating wheels, say the cycloid, for example, and so on there is a bit of cosine and sine and so on.
I think not much more on that. You won't need obscure trigonometric identities. You're next. Any proofs on the exam or just like problems? Well, a problem can ask you to show things. It is not going to be a complicated proof. The proofs are going to be fairly easy. If you look at practice 1A, the last problem does have a little bit of proof. 6B says that show that blah, blah, blah. But, as you will see, it is not a difficult kind of proof. So, about the same. Yes? Are there equations of 3D shapes that we should know at this point? We should know definitely a lot about the equations of planes on lines. And you should probably know that a sphere centered at the origin is the set of points where distance to the center is equal to the radius of the sphere.
We don't need more at this point. As the semester goes on, we will start seeing cones and things like that. But at this point planes, lines. And maybe you need to know about circles and spheres, but nothing beyond that. More questions? Yes? If there is a formula that you have proved on the homework then, yes, you can assume it on the test. Maybe you want to write on your test that this is a formula you have seen in homework just so that we know that you remember it from homework and not from looking over your neighbor's shoulder or whatever. Yes, it is OK to use things that you know general-speaking. That being said, for example, probably there will be a linear system to solve.
It will say on the exam you are supposed to solve that using matrices, not by elimination. There are things like that. If a problem says solve by using vector methods, things like that, then try to use at least a vector somewhere. But, in general, you are allowed to use things that you know. Yes? Will we need to go from parametric equations to xy equations? Well, let's say only if it is very easy. If I give you a parametric curve, sin t, sin t, then you should be able to observe that it is on the line y equals x, not beyond that. Yes? Do we have to use --
Yes. I don't know if you will have to use it, but certainly you should know a little bit about the unit tangent vector. Just remember the main thing to know that the unit tangent vector is velocity divided by the speed. I mean there is not much more to it when you think about it. Yes? Kepler's law, well, you are allowed to use it if it helps you, if you find a way to squeeze it in. You don't have to know Kepler's law in detail. You just have to know how to reproduce the general steps. If I tell you R cross v is constant, you might be expected to know what to do with that. I would say --
Basically, you don't need to know Kepler's law. You need to know the kind of stuff that we saw when we derived it such as how to take the derivative of a dot-product or a cross-product. That is basically the answer. I don't see any questions anymore. Oh, you are raising your hand. Yes. How to calculate the distance between two lines and the distance between two planes? Well, you have seen, probably recently, that it is quite painful to do in general. And, no, I don't think that will be on the exam by itself. You need to know how to compute the distance between two points. That certainly you need to know. And also maybe how to find the compliment of a vector in a certain direction. And that is about it, I would say. I mean the more you know about things the better.
Things that come up on part Bs of the problem sets are interesting things, but they are usually not needed on the exams. If you have more questions then you are not raising your hand high enough for me to see it. OK. Let's try to do a bit of this practice exam 1A. Hopefully, everybody has it. If you don't have it, hopefully your neighbor has it. If you don't have it and your neighbor doesn't have it then please raise your hand. I have a couple.
If you neighbor has it then just follow with them for now. I think there are a few people behind you over there. I will stop handing them out now. If you really need one, it is on the website, it will be here at the end of class. Let's see. Well, I think we are going to just skip problems 1 and 2 because they are pretty straightforward and I hope that you know how to do them. I mean I don't know.
Let's see. How many of you have no problem with problem 1? How many of you have trouble with problem 1? OK. How many of you haven't raised your hands? OK. How many of you have trouble with problem 2? OK. Well, if you have questions about those, maybe you should just come see me at the end because that is probably more efficient that way. I am going to start right away with problem 3, actually.
Problem 3 says we have a matrix given to us |1 3 2; 2 0 - 1; 1 1 0|. And it tells us determinant of A is 2 and inverse equals something, but we are missing two values A and B and we are supposed to find them. That means we need to do the steps of the algorithm to find the inverse of A. We are told that A inverse is one-half of |1 ... ...; - 1 - 2 5; 2 2 - 6|. And here there are two unknown values.
Remember, to invert a matrix, first we compute the minors. Then we flip some signs to get the cofactors. Then we transpose. And, finally, we divide by the determinant. Let's try to be smart about this. Do we need to compute all nine minors? No. We only need to compute two of them, right? Which minors do we need to compute? Here and here or here and here? Yeah, that looks better. Because, remember, we need to transpose things so these two guys will end up here. I claim we should compute these two minors. And we will see if that is good enough. If you start doing others and you find that they don't end up in the right place then just do more, but you don't need to spend your time computing all nine of them. If you are worried about not doing it right then, of course, you can maybe compute one or two more to just double-check your answers.
But let us just do those that we think are needed. The matrix of minors. The one that goes in the middle position is obtained by deleting this row and that column, and we are left with a determinant |3 2;1 0|, 3 times 0 minus 1 times 2 should be - 2 should be - 2. Then the one in the lower left corner, we delete the last row and the first column, we are left with |3 2; 0 - 1|. 3 times (- 1) is negative 3 minus 0. We are still left with negative three. Is that step clear for everyone? Then we need to go to cofactors. That means we need to change signs. The rule is --
We change signs in basically these four places. That means we will be left with positive 2 and negative 3. Then we take the transpose. That means the first column will copy into the first row, so this guy we still don't know, but here we will have two and here we will have minus three. Finally, we have to divide by the determinant of A. And here we are actually told that the determinant of A is two.
So we will divide by two. But there is only one-half here so actually it is done for us. The values that we will put up there are going to be 2 and negative 3. Now let's see how we use that to solve a linear system. If we have to solve a linear system, Ax equals B, well, if the matrix is invertible, its determinant is not zero, so we can certainly write x equals A inverse B. So we have to multiply, that is one-half | 1 2 - 3; - 1 - 2 5; 2 2 - 6|.
Times B [ 1, - 2, 1]. Remember, to do a matrix multiplication you take the rows in here, the columns in here and you do dot-products. The first entry will be one times one plus two times minus two plus minus three times one, one minus four minus three should be negative six, except I still have, of course, a one-half in front. Then minus one plus four plus five should be 8. Two minus four minus six should be -8. That will simplify to [- 3, 4, - 5]. Any questions about that?
OK. Now we come to part C which is the harder part of this problem. It says let's take this matrix A and let's replace the two in the upper right corner by some other number C. That means we will look at 1 3 C; 2 0 - 1; 1 1 0|. And let's call that M. And it first asks you to find the value of C for which this matrix is not invertible. M is not invertible exactly when the determinant of M is zero. Let's compute the determinant.
Well, we should do one times that smaller determinant, which is zero minus negative one, which is 1 times 1 minus three times that determinant, which is zero plus one is 1. And then we have plus C times the lower left determinant which is two times one minus zero is 2. That gives us one minus three is - 2 2C. That is zero when C equals 1. For C equals 1, this matrix is not invertible. For other values it is invertible. It goes on to say let's look at this value of C and let's look at the system Mx equals zero. I am going to put value one in there.
Now, if we look at Mx equals zero, well, this has either no solution or infinitely many solutions. But here there is an obvious solution. Namely x equals zero is a solution. Maybe let me rewrite it more geometrically. X 3 y z = 0. 2x - z = 0. And x y = 0. You see we have an obvious solution, (0, 0, 0). But we have more solutions. How do we find more solutions? Well, (x, y, z) is a solution if it is in all three of these planes. That is a way to think about it.
Probably we are actually in this situation where, in fact, we have three planes that are all passing through the origin and all parallel to the same line. And so that would be the line of solutions. To find it actually we can think of this as follows. The first observation is that actually in this situation we don't need all three equations. The fact that the system has infinitely many solutions means that actually one of the equations is redundant. If you look at it long enough you will see, for example, if you multiply three times this equation and you subtract that one then you will get the first equation. Three times (x y) - (2x - z) will be x 3y z.
Now, we don't actually need to see that to solve a problem. I am just showing you that is what happens when you have a matrix with determinant zero. One of the equations is somehow a duplicate of the others. We don't actually need to figure out how exactly. What that means is really we want to solve, let's say start with two of the equations. To find the solution we can observe that the first equation says actually that <x, y, z> dot-product with <1, 3, 1> =0. And the second equation says <x, y, z> dot-product with <2, 0,- 1> is zero. And the third equation, if we really want to keep it, says we should be also having this.
Now, these equations now written like this, they are just saying we want an x, y, z that is perpendicular to these vectors. Let's forget this one and let's just look at these two. They are saying we want a vector that is perpendicular to these two given vectors. How do we find that? We do the cross-product. To find x, y, z perpendicular to <1, 3, 1> and <2, 0, - 1>, we take the cross-product. And that will give us something. Well, let me just give you the answer. I am sure you know how to do cross-products by now. I don't have the answer here, so I guess I have to do it.
That should be <- 3, probably positive 3, and then - 6>. That is the solution. And any multiple of that is a solution. If you like to neatly simplify them you could say negative one, one, negative two. If you like larger numbers you can multiply that by a million. That is also a solution. Any questions about that? Yes? That is correct. If you pick these two guys instead, you will get the same solution. Well, up to a multiple. It could be if you do the cross-product of these two guys you actually get something that is a multiple --
Actually, I think if you do the cross-product of the first and third one you will get actually minus one, one, minus two, the smaller one. But it doesn't matter. I mean it is really in the same direction. This is all because a plane has actually normal vectors of all sizes. Yes? I don't think so because -- An important thing to remember about cross-product is we compute for minors, but then we put a minus sign on the second component. The coefficient of j in here, the second component, you do one times minus two times one. That is negative three indeed. But then you actually change that to a positive three. Yes?
Well, we don't have parametric equations here. Oh, solving by elimination. Well, if it says that you have to use vector methods then you should use vector methods. If it says you should use vectors and matrices then you are expected to do it that way. Yes? It depends what the problem is asking. The question is, is it enough to find the components of a vector or do we have to find the equation of a line? Here it says find one solution using vector operations. We have found one solution. If you wanted to find the line then it would all the things that are proportional to this. It would be maybe minus 3t, 3t minus 6t, all the multiples of that vector.
We do because (0, 0, 0) is an obvious solution. Maybe I should write that on the board. You had another question? Not quite. Let me re-explain first how we get all the solutions and why I did that cross-product. First of all, why did I take that cross-product again? I took that cross-product because I looked at my three equations and I observed that my three equations can be reformulated in terms of these dot-products saying that x, y, z is actually perpendicular these guys and these guys have normal vectors to the planes. Remember, to be in all three planes it has to be perpendicular to the normal vectors.
That is how we got here. And now, if we want something that is perpendicular to a bunch of given vectors, well, to be perpendicular to two vectors, an easy way to find one is to take that cross-product. And, if you take any two of them, you will get something that is the same up to scaling. Now, what it means geometrically is that when we have our three planes and they all actually contain the same line --
And we know that is actually the smae case because they all pass through the origin. They pass through the origin because the constant terms are just zero. What happens is that the normal vectors to these planes are, in fact, all perpendicular to that line. The normal vectors -- Say this line is vertical. The normal vectors are all going to be horizontal. Well, it is kind of hard to draw. By taking the cross-product between two normal vectors we found this direction. Now, to find actually all the solutions.
What we know so far is that we have this direction <-3 3 - 6>. That is going to be parallel to the line of intersections. Let me do it here, for example, <3 3 - 6>. Now we have one particular solution. 0, 0, 0. Actually, we have found another one, too, which is <- 3, 3, - 6>. Anyway, if a line of solutions -- -- has parametric equation x = - 3t, y = 3t, z = - 6t, anything proportional to that. That is how we would find all the solutions if we wanted them.
It is almost time. I think I need to jump ahead to other problems. Let's see. I think problem 4 you can probably find for yourselves. It is a reasonably straightforward parametric equation problem. You just have to find the coordinates of point P. And for that it is a very simple trick. Problem 5. Find the area of a spaced triangle. It sounds like a cross-product. Find the equation of a plane also sounds like a cross-product. And find the intersection of this plane with a line means we find first the parametric equation of the line and then we plug that into the equation of the plane to get where they intersect. Does that sound reasonable? Who is disparate about problem 5? OK. Let me repeat problem 5.
First part we need to find the area of a triangle. And the way to do that is to just do one-half the length of a cross-product. If we have three points, P0, P1, P2 then maybe we can form vectors P0P1 and P0P2. And, if we take that cross-product and take the length of that and divide by two, that will give us the area of a triangle. Here it turns out that this guy is <1, 1, 2>, if I look at the solutions, so you will end up with square root of 6 over 2.
The second is asking you for the equation of a plane containing these three points. Well, first of all, we know that a normal vector to the plane is going to be given by this cross-product again. That means that the equation of plane will be of a form x plus y plus 2z equals something. If a coefficient is here it comes from the normal vector. And to find what goes in the right-hand side, we just plug in any of the points. If you plug in P0, which is (2, 1, 0) then two plus one seems like it is 3. And, if you want to double-check your answer, you can take P1 and P2 and check that you also get three. It is a good way to check your answer.
Then the third part. We have a line parallel to the vector v equals one, one, one through the point S, which is (- 1, 0, 0). That means you can find its parametric equation. X will start at - 1, increases at rate 1. Y starts at zero, increases at rate one. Z starts at zero, increases at rate one. You plug these into the plane equation, and that will tell you where they intersect. Is that clear? And now, in the last one minute, on that side I have one minute, let me just say very quickly --
Well, do you want to hear about problem 6 anyway very quickly? Yeah. OK. Problem 6 is one of these like vector calculations. It says we have a position vector R. And it asks you how do we find the derivative of R dot R? Well, remember we have a product rule for taking the derivative. UV prime is U prime V plus UV prime. It also applies for dot-product. That is dR by dt dot R plus R dot dR by dt. And these are both the same thing. You get two R dot dR/dt, but dR/dt is v for velocity vector. Hopefully you have seen things like that. Now, it says show that if R has constant length then they are perpendicular. All you need to write basically is we assume length R is constant.
That is what it says, R has constant length. Well, how do we get to, say, something we probably want to reduce to that? Well, if R is constant in length then R dot R is also constant. And so that means d by dt of R dot R is zero. That is what it means to be constant. And so that means R dot v is zero. That means R is perpendicular to v. That is a proof. It is not a scary proof. And then the last question of the exam says let's continue to assume that R has constant length, and let's try to find R dot v.
If there is acceleration then probably we should bring it in somewhere, maybe by taking a derivative of something. If we know that R dot v equals zero, let's take the derivative of that. That is still zero. But now, using the product rule, dR/dt is v dot v plus R dot dv/dt is going to be zero. That means that you are asked about R dot A. Well, that is equal to minus V dot V. And that is it. Simple manipulations. Good luck on the exam tomorrow. I will see you tomorrow
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Algebra I Workbook
This workbook is a collection of practice problems crucial for reinforcing Algebra I concepts necessary to exceed State expectations for required coursework and standardized... More > testing. There are a total of 117 Algebra I practice worksheets, which includes two worksheets for all 50 Bench Mark topics, designed to reinforce concepts within the Algebra I Curriculum. This workbook can also be used to supplement any textbook approved for use in the State. This is a valuable instrument for teaching and a convenient bank of problems to check for understanding and to assist in mastering Algebra I.< Less
Hands-On Algebra: Patterns, Equations, and Functions is an easy, step-by-step activity book designed for Kindergarten - Third grade teachers. The book is loaded with games, investigations, and... More > blackline masters that are quick and easy. The focus is to provide all children with hands on approaches to understanding algebraic concepts. Included in this activity book is also a diagnostic assessment on algebraic concepts according to the NCTM standards. If you are as busy, stressed and pressed for time as most teachers, this book will quickly become another best friend.< Less
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how to simplify their math problems, provides ample real-life practice problems and solutions, and gives grown-ups the necessary background in basic arithmetic to handle everyday problems quickly.
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"An antidote to the way math is taught in schools." —Library Journal
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This is not a book for people who are afraid of math, although it is presented as an antidote to the way math is often taught in school. The author expresses a fascination with mathematical principles and a joy in number manipulation that will seem entirely unfamiliar to those who dislike math in the first place. The book offers a concise overview of basic arithmetic and helpful techniques for solving story problems (the bane of every schoolchild's existence). It's not quite as much fun as a book of math puzzles, but a grade-school student who enjoys math might like this book, or it could be used as a workbook for a class. For popular math collections.-- Amy Brunvand, Fort Lewis Coll. Lib., Durango, Col.
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Published by Coast Publishing, PO Box 3399, Coos Bay, OR 97420. Basic information on how to simplify computations by reordering, rearranging, and breaking up numbers, using equivalents and identities, and approximating and rounding off 18, 2012
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Even though I was already advanced in math, this book provided me some awesome shortcuts. But if I think about it the concepts are pretty simple. In fact, I even knew some of the principles they taught me. This is a good buy.
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For examination in June and November 2014 This syllabus is available only to Centers ... Cambridge IGCSEAdditionalMathematics (US) (0459) syllabus content will cover the ... 3.1 Goals Cambridge IGCSEMathematicssyllabus is designed as a two-year course for examination at age 16-plus. The ...
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additionrationsSolving a System of Two Linear Equations. Other Systems of Equations. Solving a System of Three Linear Equations. Determinants. Properties of Determinants. Solving a System of Linear Equations Using Determinants. Partial Fractions.
The Circle. The Parabola. The Ellipse. The Hyperbola. Translation of Axes. The General Second-Degree Equation. Systems of Quadratic Equations. Polar Coordinates. Graphs in Polar Coordinates.
21. The Derivative.
Motion. The Limit. The Slope of a Tangent Line to a Curve. The Derivative. Differentiation of Polynomials. Derivatives of Products and Quotients. The Derivative of a Power. Implicit Differentiation. Proofs of Derivative Formulas. Higher Derivatives.
The Indefinite Integral. The Constant of Integration. Area Under a Curve. The Definite Integral.
25. Applications of Integrations.
Area Between Curves. Volumes of Revolution: Disk Method. Volumes of Revolution: Shell Method. Center of Mass of a System of Particles. Center of Mass of Continuous Mass Distributions. Moments of Inertia. Work, Fluid Pressure, and Average Value.
additionrations
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Finally figure out physics! Teach Yourself Physics introduces you to physics gradually by building a foundation of appropriate mathematical skills. Easy-to-understand diagrams help you understand key points
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Algebra is one of the main branches in mathematics. The book series of elementary algebra exercises includes useful problems in most topics in basic algebra.
About the book
Description
Algebra is one of the main branches in mathematics. The book series of elementary algebra exercises includes useful problems in most topics in basic algebra. The problems have a wide variation in difficulty, which is indicated by the number of stars.
Content
Author Biographies
Preface
Real numbers
Equations
Inequalities
About the Author
Mr. Wenlong Wang
Mr. Wenlong Wang is a retired mathematics educator in China. He has been working on algebra and geometry problems for many years, and has taught many students in the past few years. He is an expert and a senior researcher in mathematics education.
Professor Hao Wang
Professor Hao Wang is a faculty member in the Department of Mathematical & Statistical Sciences at the University of Alberta, an advisory board member of Centre for Mathematical Biology, an associate editor for International Journal of Numerical Analysis & Modeling – Series B, an editor for Nonlinear Dynamics and Systems Theory (an international journal of research and surveys), an editor for a special issue of The Canadian Applied Mathematics Quarterly, and an associate faculty member for Faculty of 1000 Biology. Dr. Wang has strong interests in interdisciplinary research of mathematical biology. His research group is working on areas as diverse as modeling stoichiometry-based ecological interactions, microbiology, infectious diseases, predator-prey interactions, habitat destruction and biodiversity, risk assessment of oil sands pollution. Mathematical models include ordinary differential equations, delay differential equations, partial differential equations, stochastic differential equations, integral differential/difference equations
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Paramount ChemistryAlgebra 1 or elementary algebra is very important to know as it is required for higher math courses, like geometry and algebra 2. Algebra 1 can be challenging if concepts in prealgebra were not fully understood. However some concepts in algebra 1 can be challenging as well.
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There are some mathematical problems whose significance goes beyond the ordinary - like Fermat's Last Theorem or Goldbach's Conjecture. This book explains why these problems exist, why they matter, what...
Motivating readers by making maths easier to learn, this work includes complete past exam papers and student-friendly worked solutions which build up to practice questions, for all round exam preparation
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Cotati AlgebraBuilding confidence in the concepts introduced here and the ways to express them is critical. Understanding Precalculus and Trig concepts need not be daunting. They can be explained in simple terms and there are ways to remember key concepts
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Repetition, drills and application ensure mastery of computational skills with Lifepac Math. Students will progress to higher-level cognitive reasoning and analysis as their problem solving ability increases.
Perfect for students who flourish in a self-paced, individualized learning format, each consumable LIFEPAC combines lessons, exercises, projects, reviews and tests.
Product:
Lifepac Math: Grade 9: Unit 10: Quadratic and Algebraic Equations
Vendor:
Alpha Omega
Binding Type:
Paperback
Media Type:
Book
Minimum Grade:
9th Grade
Maximum Grade:
9th Grade
Weight:
0.4 pounds
Length:
11 inches
Width:
8.5 inches
Height:
0.125 inches
Vendor Part Number:
MAT 0910
Subject:
Algebra, Calculus & Trig Math: Grade 9: Unit 10: Quadratic and Algebraic Equations.
Average Rating
Parent Rating
Comments
I would not recommend Switched on Schoolhouse. We have tried it two different years with different children and were not successful either time. It has not been a good match for my family.
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About Mathematics HL
IB Mathematics HL is a course for students with a good background in mathematics and strong analytical and technical skills. Most students will be expecting to include mathematics in their university studies, either as a subject in its own right or within courses such as physics, engineering and technology. The course is also for students who have a strong interest in mathematics and enjoy meeting its challenges.
The course is fundamentally the same as any course taught in a regular face to face school. The difference is the medium of learning. As in any face to face school, there is course content, interaction with the teacher and assessment.
Students will need to be organized and motivated as they will have much more control over when and where they learn. This has significant advantages for students, especially in a subject such as mathematics, where having the right conditions for learning are important.
This online Mathematics HL course has been written by some of the best IB mathematics teachers in the world, approved by the IB organisation itself and you will be supported by highly experienced IB teachers.
You can choose when and where you learn as well as being able to communicate with your teachers virtually around the clock.
In addition, the skills and attitudes acquired in taking a demanding, two year online course will develop your ability to work in a connected world and cope with Higher Education where more and more courses are online.
The course uses a number of mathematical software and hardware. It is strongly recommended that students buy and use a TI-nspire (non CAS) graphing calculator. The course also uses Geogebra (a free software) and students are given a license for the widely used software Autograph. Students should also have access to a scanner so that they can scan and submit handwritten assignments.
A cohort of classmates in a similar situation who you can easily communicate with.
Access to communication tools, discussion forums and a blog
Mathematics Sample Lesson
On the left is a lesson on trigonometric functions. If you have a look at the lesson, you will see that it contains engaging content, videos, interactive diagrams, blogging activities and downloadable lesson notes.
By the end of the lessons, you will be able to derive the graphs of certain trigonometric functions, explain the meaning of period and amplitude and how this relates to domain and range, and use transformations to understand the feature of the graphs of certain trigonometric functions.
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More About
This Textbook
Overview
Based on a series of lectures given at Sheffield during 1971-72, this text is designed to introduce the student to homological algebra avoiding the elaborate machinery usually associated with the subject. This book presents a number of important topics and develops the necessary tools to handle them on an ad hoc basis. The final chapter contains some previously unpublished material and will provide additional interest both for the keen student and his tutor. Some easily proven results and demonstrations are left as exercises for the reader and additional exercises are included to expand the main themes. Solutions are provided to all of these. A short bibliography provides references to other publications in which the reader may follow up the subjects treated in the book. Graduate students will find this an invaluable course text as will those undergraduates who come to this subject in their final year.
Editorial Reviews
From the Publisher
'As we have come to expect from the author the exposition is clear and straightforward. There are many nontrivial exercises with complete solutions included at the end of each chapter.' Mathematical Reviews
'A particularly useful feature of the book under review is the collection of exercises throughout the text, with full solutions at the end of chapters. This should make the book particularly well suited to the student meeting the subject for the first time.' Bulletin of the London Mathematical Society
'To sum up the book ... affords a very good introduction to the methods of Homological Algebra.' Bulletin of the Institution of Mathematics and Its Applications
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A full year 7th grade math curriculum that includes selected answers in the back of the book plus FREE online resources offered by the publisher:Program Resources. We specialize in homeschooling curri...
Prentice hall mathematics (2004) This is a full year curriculum! Reading and Math Literacy Workbook with Answer Key. The books have wear to the covers but no significant writing or highlighting is pre...
The Connected Mathematics materials were written to support teacher learning of both unfamiliar content and pedagogical strategies. The Teacher's Guides include extensive help with mathematics, pedago...
On Core Mathematics can be used with any existing math program to provide complete coverage of the Common Core State Standards in Mathematics. This program includes interactive lessons for each and ev...
The Connected Mathematics materials were written to support teacher learning of both unfamiliar content and pedagogical strategies. The Teacher's Guides include extensive help with mathematics, pedago...
Most importantly, you can be assured your child will develop valuable skills to help him be successful in future math courses. What topics are studied? Everything from number sets and estimation to an...
Parent Guide : This guide walks you through the program highlighting the main elements of the student and teacher materials and provides guidance on setting up your lesson plan, pacing, and adapting t...
Most importantly, you can be assured your child will develop valuable skills to help him be successful in future math courses. What topics are studied? Everything from number sets and estimation to an...
| 677.169 | 1 |
Plane Geometry
Description
This traditional text acquaints your student with the fundamental tools of geometry in an engaging way. Students learn the necessity of a formal proof before plunging into demonstrative geometry, with many complete example proofs to develop the thinking process. Through a well-written text and abundant exercises, your student will learn to think logically and systematically. The many "extras" include the mathematical information on several famous buildings, biographies of great mathematicians, and geometry in the world around us. Designed to be used in grade 11 and is 332
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McGraw-Hill Education Announces Interactive E-books with ALEKS 360
McGraw-Hill Education has introduced ALEKS 360, a mathematics solution that combines an artificial intelligence and personalized learning program with a fully integrated, interactive e-book package. ALEKS 360 delivers assessments of students' math knowledge, guiding them in the selection of appropriate new study material, and recording their progress toward mastery of course goals. Through adaptive questioning, ALEKS accurately assesses a student's knowledge state and delivers targeted instruction on the exact topics a student is most ready to learn.
The e-books featured within ALEKS 360 are interactive versions of their physical counterparts, which offer virtual features such as highlighting and note-taking capabilities, as well as access to multimedia assets such as images, video, and homework exercises. E-books are accessible from ALEKS Student Accounts and the ALEKS Instructor Module for convenient, direct access.
The initial e-books to be offered in ALEKS 360 include: Introductory Algebra, Second Edition, by Julie Miller and Molly O'Neill; Intermediate Algebra, Second Edition, by Miller and O'Neill; College Precalculus, Second Edition, by John W. Coburn; and College Algebra, Second Edition, by Coburn.
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This text, aimed specifically at undergraduate students, will provide the basic background in statistics and matrix algebra giving students the necessary grounding for a proper understanding of econometrics.
This text, aimed specifically at undergraduate students, will provide the basic background in statistics and matrix algebra giving students the necessary grounding for a proper understanding of econometrics.
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Best math tool for school and college! If you are a student, it will helps you to learn! Note: In linear algebra, the determinant is a value associated with a square matrix. The determinant provides important information when the matrix is that of the coefficients of a system of linear equations, or when it corresponds to a linear transformation of a vector free app is a math calculator, which is able to multiplicate a matrix with an other. The maximal number of rows and columns of a matrix is 4.
Best math tool for school and college! If you are a student, it will helps you to learn linear algebra! Note: Matrix multiplication is a binary operation of two matrices which produces another matrix. It has numerous applications in applied mathematics, physics, and engineering.
Speech to Text Translator TTS is a funny and user-friendly speech recognition, text to speech (TTS) and translator application, which allows you to take notes easily by speaking. You can copy these notes to clipboard and listen. You can send and share these notes with e-mail, SMS, social media and various instant messaging applications such as WhatsApp, Viber, Skype and vs. You can also search these notes on the web. Speech to Text, Text to Speech (TTS) and translation features are all in one application ! Speak, translate, listen, send and search using Speech to Text Translator TTS ! You can also use this software for language education. You can learn to speak all languages. Enjoy Speech to Text Translator TTS !
FOR ADS-FREE FULL VERSION, PLEASE DONATE ONLY $3 VIA PAYPAL OR CREDIT-CARD AND REQUEST LICENSE CODE WITHIN THE PROGRAM. AFTER ENTERING THE LICENCE CODE, YOU WON'T GET ANY ADVERTISEMENTS ANYMORE.
Best math tool for school and college! If you are a student, it will helps you to learn linear algebra! Note: The inverse of a matrix A is the matrix B, with AxB=I where I is the identity matrix and the multiplication used is ordinary matrix multiplication. A matrix is a nonsingular matrix if it is an invertible matrix, and the determinant of this matrix does not equal 0.
This mathematics application "Matrices and determinants" is a complete reference for matrix algebra and its mathematical operations for various applications. we tried our best effort to include almost all topics with its explanations. here you can find all topics of matrices and determinants like DEFINITIONS TYPES OF MATRICES, EQUALITY OF MATRICES, ALGEBRA OF MATRICES, PROPERTIES OF MATRIX ADDITION, MULTIPLICATION OF A MATRIX BY A SCALAR (SCALAR MULTIPLICATION), SUBTRACTION OF MATRICES (DEFINITION), MULTIPLICATION OF MATRICES, PROPERTIES OF MATRIX MULTIPLICATION., TRANSPOSE OF A MATRIX, PROPERTIES OF TRANSPOSE, SYMMETRIC AND SKEW-SYMMETRIC MATRICES, DETERMINANTS, SINGULAR MATRIX,ADJOINT OF A SQUARE MATRIX, INVERSE OF A MATRIX, ELEMENTARY TRANSFORMATIONS OR ELEMENTARY OPERATIONS OF A MATRIX, ORTHOGONAL MATRIX, SUBMATRIX, RANK OF MATRIX, SOME THEOREM ON RANK OF A MATRIX. EQUIVALENT MATRICES.ECHELON FORM OF A MATRIX, ALGORITHM FOR FINDING THE RANK OF A MATRIX., SYSTEM OF SIMULTANEOUS LINEAR EQUATIONS., SOLUTIONS OF A NON-HOMOGENEOUS SYSTEM OF LINEAR EEQUATIONS, ALGORITHM FOR SOLVING A NON-HOMOGENEOUS SYSTEM OF LINEAR EQUATIONS-RANK METHOD, SOLUTION OF A HOMOGENEOUS SYSTEM OF LINEAR EQUATIONS-MATRIX METHOD, ALGORITHM FOR SOLVING A HOMOGENEOUS SYSTEM OF LINEAR EQUATIONS.
This is application for solving mathematical problems from chapter "Matrices". Its main advantage is in the full, detailed solving a problem with all auxiliary actions, in contrast to apps-calculators. User-friendly and intuitive interface will do process of solving in several clicks. It is the best pocket assistant for student both at home and on exams. It have a solving of problems like: - Matrix addition; - Matrix multiplication; - Matrix scalar multiplication; - Determinant calculation; - Inverse of the matrix; - Transpose; - Solving of systems of linear equations (by Cramer's Rule, Gaussian Elimination and Inverse Matrix Method). This application will greatly facilitate your life!
We apologize in advance for possible errors in translation. English isn't our native language, so please let us know if we need to correct something.
Another nice feature is matrix computation of addition, subtraction and multiplication with up to 3 matrices. For this, Matrix Calculator Free provides intuitive user interface which enables you to do matrix computation with ease.
Matrix Calculator Free is a free trial version of Matrix Calculator Pro. The free version is limiting to handling matrices with dimensions less than 3. For the matrices bigger than 2 by 2, the result from various matrix operations including matrix inverse is partially shown.
If you like Matrix Calculator Free, please upgrade to the Pro version. Matrix Calculator Pro is so fast that inverse of 20 by 20 matrix can be done in a couple of seconds with my phone HTC Glacier. There's no predetermined matrix size limit. Its maximum size depends on your phone memory.
As a user of the application, you are our most important critic and commentator. We value your opinion and want to know what we are doing right, what we could do better, what features you'd like us to implement, and any other comments you are willing to pass our way.
In addition, if you experience any technical problem or bug, please feel free to send us an email describing your problem and we'll get back to you with answer as quickly as possible.
We also value your ratings on our application, because your rating is just a compact form of your opinion. If you like or dislike the application, please leave your rating actively.
Finally, we need your help in making this app multilingual. If you like this app and want to translate to your own language, please let us know including
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This website is a useful and user-friendly tool for performing statistical computation. Each of the links will show an...
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This website is a useful and user-friendly tool for performing statistical computation. Each of the links will show an annotated list of the statistical procedures available under that rubric. There is a great variety of online statistical 'tools' or applets that are ready to use and include: Utilities, Clinical Research Calculators, Probabilities, Distributions, Frequency Data, Proportions, Ordinal Data, Correlation and Regression, t-Tests and Procedures, ANOVA, ANCOVA, and Miscellanea.
GeoGebra is a dynamic mathematics software for education in secondary schools that joins geometry, algebra and calculus. On...
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GeoGebra is a dynamic mathematics software for education in secondary schools that joins geometry, algebra and calculus. On the one hand, GeoGebra is a dynamic geometry system. You can do constructions with points, vectors, segments, lines, conic sections as well as functions and change them dynamically afterwards.On the other hand, equations and coordinates can be entered directly. Thus, GeoGebra has the ability to deal with variables for numbers, vectors and points, finds derivatives and integrals of functions and offers commands like Root or Extremum.The GeoGebraWiki is a free pool of educational materials for GeoGebra. Everyone can contribute and upload materials there: International GeoGebraWiki - pool of educational materials for GeoGebra and the German GeoGebraWiki The Dynamic Worksheets GeoGebra can also be used to create dynamic worksheets:Pythagorasvisualisation of Pythagoras' theoremLadder against the Wallapplication of Pythagoras' theorem Circle and its Equationconnection between a circle's center, radius and equation Slope and Derivative of a Function (3 sheets)relation between slope, derivative and local extrema of a functionDerivative of a Polynomial interactive exercise to practice finding the derivative of a cubic polynomialUpper- and Lower Sums of a Functionvisualisation of the backgrounds of Riemann's Integral
This website is for people involved in applied social research and evaluation. You'll find lots of resources and links to...
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This website is for people involved in applied social research and evaluation. You'll find lots of resources and links to other locations on the Web that deal in applied social research methods.Some highlights of what is available: The Knowledge Base, Selecting Statistics, The Simulation Book, Concept Mapping
Möbius Transformations Revealed is a short video by Douglas Arnold and Jonathan Rogness which depicts the beauty of Möbius...
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Möbius Transformations Revealed is a short video by Douglas Arnold and Jonathan Rogness which depicts the beauty of Möbius transformations and shows how moving to a higher dimension reveals their essential unity. It was one of the winners in the 2007 Science and Visualization Challenge and was featured along with the other winning entries in the September 28, 2007 issue of journal Science. The video, which was first released on YouTube in June 2007, has been watched there by more than a million viewers and classified as a "Top Favorite of All Time" first in the Film & Animation category and later in the Education category. It has been selected for inclusion in MathFilm Festival 2008.
R is a language and environment for statistical computing and graphics. It is a GNU project which is similar to the S...
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R is a language and environment for statistical computing and graphics. It is a GNU project which is similar to the S language and environment which was developed at Bell Laboratories (formerly AT&T, now Lucent Technologies) by John Chambers and colleagues. R can be considered as a different implementation of S. There are some important differences, but much code written for S runs unaltered under R. R provides a wide variety of statistical (linear and nonlinear modelling, classical statistical tests, time-series analysis, classification, clustering, ...) and graphical techniques, and is highly extensible. The S language is often the vehicle of choice for research in statistical methodology, and R provides an Open Source route to participation in that activity. One of R's strengths is the ease with which well-designed publication-quality plots can be produced, including mathematical symbols and formulae where needed. Great care has been taken over the defaults for the minor design choices in graphics, but the user retains full control. R is available as Free Software under the terms of the Free Software Foundation's GNU General Public License in source code form. It compiles and runs on a wide variety of UNIX platforms and similar systems (including FreeBSD and Linux), Windows and MacOS.
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This book was written by an experienced maths tutor to help parents and carers to be able to tutor their child in algebra and equations. This book contains 10 lesson plans for hourly tuition sessions, which would cost £20-£25 if you paid a tutor. Written in Plain English so that even the most nervous adult can understand the concepts before explaining it to their child.
Today's society is an affluent one. Many people have more money to spend today than in any other period of history. Unfortunately, too many people do not have the ability to handle this money skilfully. Lack of this ability often results in debt, frustration, and heartache.
This book was written by an experienced maths tutor to help parents and carers to be able to tutor their child in general maths. This book contains 14 lesson plans for hourly tuition sessions (which would cost £20-£25 if you paid a tutor)on maths units ranging from basic addition to more advanced ratio questions. Also suitable for adults taking basic or functional skills exams in adult numeracy.
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Geometry: Fundamental Concepts and Applications
9780321473318
ISBN:
0321473310
Edition: 1 Pub Date: 2007 Publisher: Pearson
Summary: This Geometry workbook makes the fundamental concepts of geometry accessible and interesting for college students and incorporates a variety of basic algebra skills in order to show the connection between Geometry and Algebra.
Bass, Alan is the author of Geometry: Fundamental Concepts and Applications, published 2007 under ISBN 9780321473318 and 0321473310. Four hundred sixty Geometry: Fundamental Concepts a...nd Applications textbooks are available for sale on ValoreBooks.com, one hundred twenty one used from the cheapest price of $3.20, or buy new starting at $18.84
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Algebra and Trigonometry - 3rd edition
Summary: Written for a one- or two-term course at the freshman/sophomore level, the third edition covers the principles of college algebra, trigonometry, and analytic geometry in the concise and student-friendly style that have made Zill's texts a world-wide success. It includes all of the trademark features for which Zill is known including, lucid examples and problem sets, a rich pedagogy, a complete teaching and learning ancillary package, and much more. Throughout the text readers will fi...show morend a wide range of word problems and relevant applications, historical accounts of famous mathematicians, and a strong variety of modern exercises
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Ioannis Tziakos
πMath will be a math package to implement linear algebra methods and algorithms. The goal is to provide vectors and matrices based on abstract classes to aid the implementation, research and debugging of numerical analysis algorithms.
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Math Basics for the Healthcare Professional, Third Edition draws on comments from the field to include more applications: thus, the expanded units on metric system conversions, pre-algebra, reading drug labels, medicine cups, and syringes, parenteral dosages, intravenous administration formulas, and basic dosages by weight have been included in the text. The appendix includes an additional practice tests for each unit. A student CD offers an additional two practice tests for student use.
Features
Mnemonic devices: helps student build memory of basic skills
Easy to learn format based on a hierarchy of skills: helps student learn in a structured, repetitive manner
Pull out sheets in front and back of text and student CD: helps student locate and practice formulas
New To This Edition
The third edition of this work text provides a reorganization of the metric system unit so that it is placed with Roman numerals in the whole numbers unit with time in allied health.
Additions to the text include:
pre-algebra basics
a separate metric unit
reading drug labels
medicine cups, syringes
intravenous administration bags
parenteral dosages
basic intravenous administration
basic dosage by weight units.
Each unit has instruction, practice, and self-assessment as a structure. The context is for allied health students. This contextualization helps students appreciate the value of learning math for their careers. The unit self-tests include 15 questions, providing more practice in self-assessment. This edition has provided the odd numbers answers in the key at the end of the work text. In addition, extra practice units are added in an appendix with the answer keys for easy self-checking. The accompanying CD rom includes another set of practice tests with answers.
Table of Contents
Table of Contents
Preface
Health Occupations Matrix of Math Skills and Self-Assessment
Health Occupations Math Skills Self-Assessment Score Sheet
Math for Healthcare Professionals Pre-test
Unit 1
Whole Number Review
Addition
Subtraction
Multiplication
Division
Number Statements
Rounding
Estimation
Basics of statistical Analysis
Mean/Average
Median
Mode
Range
Roman Numerals
Concept 1
Concept 2
Concept 3
Whole Number Self-Test
Unit 2
Fractions
Part-to-Whole Relationships
Equivalent Fractions
Reducing to Lowest or Simplest Terms
Multiplication Method
Division Method
Improper Fractions
Adding Fractions with Like Denominators
Finding the Common Denominator
Ordering Fractions
Subtraction of Fractions
Borrowing in Subtraction of Fractions
Multiplication of Fractions
Multiplying a Fraction by a Whole Number
Reducing before you Multiply as a Timesaver
Multiplication of Mixed Numbers
Division of Fractions
Fraction Formula
Complex Fractions
Fraction Self-Test
Unit 3
Decimals
Rounding Decimals
Comparing Decimals
Addition of Decimals
Subtraction of Decimals
Multiplication of Decimals
Division of Decimals
Zeros as Placeholders in Decimal Division
Simplified Multiplication and Division of Decimals
Simplified Multiplication
Simplified Division
Changing Decimals to Fractions
Changing Fractions to Decimals
Temperature Conversions with Decimals
Decimal Conversion Formula
Solving Mixed Fraction and Decimal Problems
Decimal Self-Test
Unit 4
Ratio and Proportion
Ratio
Proportion
Solving for x
Word Problems Using Proportions
Solving for x in More Complex Problems Using Proportion
Nutritional Application of Proportions
Ratio and Proportion Self-Test
Unit 5
Percents
Percent-to-Decimal Conversion
Decimal-to-Percent Conversion
Using Proportion to Solve Percent Problems
Percent Strength of Solutions
Single Trade Discount
Percent Self-Test
Unit 6
Combined Applications
Conversion among Fractions, Decimals, Ratios, and Percent
Suggested Order of Operations
Using Combined Applications in Measurement Conversion
Standard Units of Measure
More Combined Applications
Combined Applications Self-Test
Unit 7
PreAlgebra Basics
Integers
Absolute Value
Integer Operations
Adding Integers with the Same Sign
Adding Integers with Different Signs
Subtracting Integers
Multiplication of Integers
Division of Integers
Exponential Notation
Scientific Notation
Square Roots
Order of Operations
Algebraic Expressions
Expressions
Writing Expressions from Word Problems
Solving Equations
Writing Equations from Word Problems
Literal Equations
Pre-Algebra Basics Self-Test
Unit 8
The Metric System
Using the Metric Symbols
Changing Unit Measures
Metric System Self-Test
Unit 9
Reading Drug Labels, Medicine Cups, Syringes, and Intravenous Fluid
Administration Bags
Reading Drug Labels
Reading medicine Cups
Reading Syringes
Reading IV Adminstration Bags
Reading Drug Labels, Medicine Cups, Syringes, and Intravenous Fluid
Administration Bags Self-Test
Unit 10
Apothecary Measurement and Conversions
Apothecary Measurement and Conversions
Apothecary System Self-Test
Unit 11
Dosage Calculations
Rounding in Dosage Calculations
Dosage Calculations Formula
Practice Practice Using Drug Labels
Dosage Calculations Self-Test
Unit 12
Parenteral Dosage
Parenteral Dosage
Parenteral Dosage Self-Test
Unit 13
The Basics of Intravenous Fluid Administration
IV Fluid Adminstration
The Basics of Intravenous Fluid Administration Self-test
Unit 14
Basic Dosage by Weight
Basic Dosage by Weight
Basic Dosage by Weight Self-Test
Practice Post-Test
Appenix
Appendix of Practice Unit Exams 1-14 and Answers
Answer Key
Index
About the Author(s)
Michele Benjamin Lesmeister is currently a full-time, tenured member of the faculty at Renton Technical College and has taught in two-year colleges for over 20 years. Michele has also been involved in developing transitional learning materials for native speakers and second language speakers for the health care fields for 18 years. As an active participant in the Universal Design for Learning initiative on the RTC campus, Michele tries to create materials that address learner barriers and improve access to learning for all students. Michele has authored several books, both of which she uses within her own classrooms. Michele is the Vice-President of the Renton Federation of Teachers as well as a member of the National Learning Disabilities Association, the League of Innovation, and the Council on Adult Basic Education. Michele also received the Faculty of the Year Award at RTC in 1989 and 2006
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Solving Math Problems: Reading Problems Carefully
Overview: It is essential to read a math problem carefully before any other steps can be taken to solve the problem. The process of reading a math problem carefully includes understanding the meaning of any unfamiliar words or symbols, paying close attention to directions, sorting out any information that is not needed, and determining if […]
Math Review of Angles and Parallel Lines
Overview: Angles and the lines that form them are an essential part of geometry. Understanding the relationship between parallel lines, lines that are not parallel, and the different types of angles within figures is important to determining their measurement. What Are the Relationships Between Angles on a Straight Line? Suppose that three points A, B, […]
Math Review of Converting between Conventional and Metric Systems
Overview: In the United States, two separate measurement systems are used, the conventional or English system and the metric system. The conventional system with inches, pounds, cups, and quarts, is in use in many aspects of everyday life, in carpentry, and in many trades, while the metric system is used in science, medicine, and many […]
Pedigree: How to determine your genetic lineage
Overview: Pedigrees are visual representations of a family's genetic history. Each pedigree focuses on one specific gene that is studied by geneticists. There are several benefits of studying a family's genetic history. By reviewing past generations, scientists can deduce the mode of inheritance for a specific gene. A person can study their family's pedigree to […]
Math Review of Rational Exponents
Overview Rational exponents are an extension of the rules of exponents. They can be solved by applying those rules and often take more than one step. What Is an Exponent? An exponent such as 32 is a direction to multiply 3 by itself twice, such as 3∙3, or 9. Similarly, an exponent such as […]
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Basic College Mathematics with Early Integers
9780321726438
ISBN:
032172643X
Edition: 2 Pub Date: 2011 Publisher: Pearson Education
Summary: Martin-Gay, Elayn is the author of Basic College Mathematics with Early Integers, published 2011 under ISBN 9780321726438 and 032172643X. Five hundred thirty four Basic College Mathematics with Early Integers textbooks are available for sale on ValoreBooks.com, one hundred seventy two used from the cheapest price of $43.47, or buy new starting at $124.97All the information used inside the book was helpful for my desire to re-learn math from the bottom up.
Developmental math appreciation, I simply took the course so I could re-learn math from the bottom due to not having had a math class in over 10 yrs as well as I don't remember ever having a math teacher that really cared if I learned and understood.
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A video instructional series on algebra for college and high school classrooms and adult learners; 26 half-hour video...
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A video instructional series on algebra for college and high school classrooms and adult learners; 26 half-hour video programs and coordinated books In this series, host Sol Garfunkel explains how algebra is used for solving real-world problems and clearly explains concepts that may baffle many students. Graphic illustrations and on-location examples help students connect mathematics to daily life. The series also has applications in geometry and calculus instruction.
Decision-Making is central to human activity. Thus, we are all decision-makers. However, a "good" decision making starts with...
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Decision-Making is central to human activity. Thus, we are all decision-makers. However, a "good" decision making starts with a consecutive-focused-thinking process that encompasses many disciplines of study. This site offers information on applied management science and an introduction to general operations research. It describes deterministic; and probabilistic models; lists books on operations research and management science; and links to related Web sites.
This site contains the learning materials for eleven online courses that are currently taught at Carnegie Mellon...
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This site contains the learning materials for eleven online courses that are currently taught at Carnegie Mellon University. Students anywhere may use these materials as learning resouces. Instructors at other learning institutions may use and even base their own courses on these materials free of charge. An instructor can create an account on OLI, select and sequence course materials, and take advantage of OLI's tracking of student progress. While all courses come in the "open and free" version, at least one course (Logic and Proofs) also comes in a version that requires payment of a fee to OLI. The available couses at this time are: Biology, Calculus, Causal Reasoning, Chemistry, Economics, Emperical Research Methods, French, Logic and Proofs, Physics, Statistics, and Statics.
EnVision is a Web-based chat program that assists in the live communication of mathematical content. It is used by the author...
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EnVision is a Web-based chat program that assists in the live communication of mathematical content. It is used by the author to conduct online office hours in introductory courses. It allows students to log in anonymously and thus reduce anxieties that they may have about seeking assistance.
Fraction Fundamentals is a Stand Alone Instructional Resource (StAIR) that teaches students basic concepts about fractions...
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Fraction Fundamentals is a Stand Alone Instructional Resource (StAIR) that teaches students basic concepts about fractions and tests their knowledge. This resource is suitable for 3rd grade students, but may be used in other grade levels if needed. By going through this PowerPoint, students learn what fractions are, where they see fractions, equivalent fractions, and comparing fractions. There are multiple choice and true/false questions throughout the presentation to assess student learning. Audio is avaliable on most slides to assist non-readers or visually impaired students.
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This course will not satisfy the general elective category for students who entered their program or study in or after the 2007 Fall semester.
Basic Algebra is considered a developmental course. A comprehensive departmental final examination is included in this course.
VI. Catalog Course Description
This is an introductory course in Algebra. Topics include operations with numerical and algebraic expressions, including rational and radical expressions, factoring, and graphing. Study skills are also emphasized.
VII. Required Course Content and Direction
Learning Goals:
Course Specific:
The student will be able to:
add, subtract, multiply, and divide signed numbers.
simplify algebraic expressions by distributive property and combining like terms.
solve linear equations and use linear equations to solve applications.
Planned Sequence of Topics and/or Learning Activities:
Solving of linear equations, inequalities, and quadratic equations by factoring
Properties and operations with radical expressions
Introduction to graphing of linear equations and slope concepts
Solving of applications using linear and quadratic equations
Assessment Methods for Core Learning Goals:
All Discipline-Specific Course Objectives will be assessed as follows:
The student will apply mathematical concepts and principles to identify and solve problems presented through informal assessment, such as oral communication among students and between teacher and students. Formal assessment will consist of open-ended questions reflecting theoretical and applied situations.
Assessment Methods for Core Learning Goals:
Reference, Resource, or Learning Materials to be used by Students:
There is a departmentally selected textbook. Details on other materials provided by the instructor of each course section. See course format. Student notebook is required and a calculator is optional.
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This popular Physical Chemistry text book is now available in electronic format. We have preserved much of the material of the former hard copy editions, making changes to improve understanding of the concepts in addition to including some of the recent discoveries in physical chemistry. Many chapters have new sections and the coverage of several chapters has been greatly expanded. The chapter on statistical mechanics, 15, has been completely rewritten.
The eBook has also been divided into smaller modules that are appropriate for specific courses in Physical Chemistry.
Easy to use Clebsch-Gordan coefficient solver for adding two angular momentums in Quantum Mechanics. This tool is created for my Quantum Mechanics II course offered by Dr. Thompson in Summer of 2007.
[Instruction]
Execute "GUI.m" script by invoking "GUI".
Inspired by a discussion with my father on how to solve sudokus, I decided to implement a GUI for MATLAB and play around with automatic solving. The result can be found here: You can use the GUI just for playing sudoku and having an online check or you may turn on the solving aids: Display tooltips showing all valid numbers so far, or have a semiautomatic or a automatic solver which evaluates the logical constraints. On top of that, a branching algorithm is implemented, which solves any arbitrary sudoku very fast.
I set out to study ruby by creating a set of scripts, together called "Solver". Solver plays and creates sudoku puzzles. It uses a command line interface and reads or produces html files. It should be cross-platform (tested on MacOSX)..
Math Solver Free for Windows 8 is a handy tool for performing frequently used operations used for solving math problems. You can use this tool for solving quadratic equations or calculating the angles of a triangle.
The app also includes a unit converter and other useful tools for dealing with math problems by using your Windows 8 device.
Worksheet Generator for Chemistry is a handy and reliable software that helps you to easily and quickly create and customize your personal chemistry worksheets.
The application provides you with various exercise templates that allow you to adjust your worksheets. You are able to insert various chemistry exercises of different areas such as units and chemical formulae, thermochemistry, chemical kinetics, Redox reactions and organic chemistry.
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The UW Math Circle is full for the year and is not admitting new students. Our other events – Math Hour and the Math Hour Open Olympiad – are open to everyone. If you are interested in joining the circle next Fall, consider coming to the Olympiad in June.
To receive up-to-date information about this and related events that we organize, please join our mailing list here.
We also invite you to check out the UW Math Hour for some fun mathematics in the spring!
What is UW Math Circle?
The UW Math Circle is intended for Seattle-area middle school and junior-high school students, and it is being offered at no cost. The program is aimed at 7th, 8th, and 9th graders with mathematical minds, with the intent of continuing their development in this direction.
The students meet weekly in the Math Circle to engage in a variety of activities. Here, we develop many areas of mathematics, including (but definitely not limited to) logic, graph theory, combinatorics, and geometry. Follow the links at the top of the page for a more detailed breakdown of what's being covered in each meeting.
To reinforce the lessons learned at each Math Circle, weekly homework assignments are given at the end of the meetings. The students are encouraged to delve even further than the problem statement, in order to really get a feel for the solution. To reinforce this behavior, the first hour of each meeting is spent by the students explaining their solutions and methods to their peers, with the listening students free to critique the solutions and offer help when things get confusing.
The last half of the meeting is spent covering new material. We introduce the concepts to the students with a major emphasis on hands-on activities. For the students, this means that much of their time is spent actively engaging in problem-solving, with ample time to ask probing questions to their colleagues and the instructors.
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Extended Studies in Mathematics 1
10 Units
This course deepens students understanding of the principles and practices of teaching and learning Mathematics in secondary schools. Students will explore ways of differentiating curriculum to meet the diverse needs of learners in the Mathematics classroom. Specific attention will be given to the literacy and numeracy demands of Mathematics as an area of study; and the incorporation of technology into the teaching and learning of Mathematics.
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Glen Ridge, FL PrecalculusThe course also gives the students a thorough introduction of functions and quadratic equations. They will learn all the operations associated with the two, such as factoring and graphing. The end of the course takes the students? knowledge of algebra 1 one step further by introducing them to some basic concepts of geometry.
...Precalculus includes algebra, coordinate geometry, trigonometry, and most of all, functions---the general concept as well as specific functions. Students come to this course familiar with basic algebra and geometry. A precalculus course builds on all of their previous mathematical knowledge and experience to understand calculus that is essential to succeed in a college
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Introduction to the Mathematics of Money: Saving and Investing - 07 edition
Summary: This is an undergraduate textbook on the basic aspects of personal savings and investing with a balanced mix of mathematical rigor and economic intuition. It uses routine financial calculations as the motivation and basis for tools of elementary real analysis rather than taking the latter as given. Proofs using induction recurrence relations and proofs by contradiction are covered. Inequalities such as the Arithmetic-Geometric Mean Inequality and the Cauchy-Schwarz Inequality are use...show mored. Basic topics in probability and statistics are presented. The student is introduced to elements of saving and investing that are of life-long practical use. These include savings and checking accounts certificates of deposit student loans credit cards mortgages buying and selling bonds and buying and selling stocks. The book is self contained and accessible. The authors follow a systematic pattern for each chapter including a variety of examples and exercises ensuring that the student deals with realities rather than theoretical idealizations. It is suitable for courses in mathematics investing banking financial engineering and related topics. ...show less
New Book from multilingual publisher. Shipped from UK within 4 to 14 business days. Please check language within??the description. Established seller since 200075.50 +$3.99 s/h
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Intermediate Algebra - With CD - 6th edition
Summary: Key Message:TheTobey/Slater seriesbuilds essential skills one at a time by breaking the mathematics down into manageable pieces. This practical ''building block'' organization makes it easy for readers to understand each topic and gain confidence as they move through each section. The authors provide a ''How am I Doing?'' guide to give readers constant reinforcement and to ensure that they understand each concept before moving on to the next. With Tobey/Slater, readers have a tutor a...show morend study companion with them every step of the way. Key Topics:Basic Concepts; Linear Equations and Inequalities; Equations and Inequalities in Two Variables and Functions; Systems of Linear Equations and Inequalities; Polynomials; Rational Expressions and Equations; Rational Exponents and Radicals; Quadratic Equations and Inequalities; The Conic Sections; Additional Properties of Functions; Logarithmic and Exponential Functions Market:For all readers interested in basic college mathematics. ...show less
6
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Discrete geometry is a relatively new development in pure mathematics, while computational geometry is an emerging area in applications-driven computer science. Their intermingling has yielded exciting advances in recent years, yet what has been lacking until now is an undergraduate textbook that bridges the gap between the two. Discrete and Computational Geometry offers a comprehensive yet accessible introduction to this cutting-edge frontier of mathematics and computer science.
Geometry in ancient Greece is said to have originated in the curiosity of mathematicians about the shapes of crystals, with that curiosity culminating in the classification of regular convex polyhedra addressed in the final volume of Euclid's Elements.
This book offers an ideal graduate-level introduction to the theory of partial differential equations. The first part of the book describes the basic mathematical problems and structures associated with elliptic, parabolic, and hyperbolic partial differential equations, and explores the connections between these fundamental types.
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Modify Your Results
As a high school student in Alabama, you know that passing the Alabama High School Graduation Exam (AHSGE) is required for graduation. The eight Countdown Tests in this book will help you prepare for the Reading Comprehension and Language areas of the test. Each multiple-choice test item relates to an AHSGE Reading Comprehension Objective or Language Objective. There are additional practice tests at the end of each unit.
Designed to meet the needs of today's classroom, Glencoe Literature has been developed with careful attention to instructional planning for teachers, strategic reading support, and universal access that meets the learning needs of all students.
This book offers sequential language instruction along with extensive drill and practice in grammar, usage, and mechanics. This important tool includes a handbook as well as vocabulary, spelling, and composition lessonsA flexible program with the solid content students need, Glencoe Algebra 1 strengthens student understanding and provides the tools students need to succeed--from the first day your students begin to learn the vocabulary of algebra until the day they take final exams and standardized tests.
The book's design is up-to-date as it underlines the real-world applications of Maths as well as its connections to other subjects like science, history and music. The Chapter Projects, Hands-On Labs, and Interdisciplinary Investigations makes the book very useful and interesting to the students.
This textbook of Glencoe Mathematics Course 1 has unit lessons on Number, Operations, and Statistics, Number and Operations: Decimals and Fractions, Patterns, Relationships, and Algebraic Thinking, Measurement and Geometry, Number, Operations, and Algebraic Thinking.
This book is talked about The Texas Prairies and Lakes region offers a wide range of attractions. Among them is the States Fair of Texas. Located in Dallas, it boasts the 212-foot Texas Star-the tallest Ferris wheel in North America. As with all circles, the ratio of the circumference of the Texas Star to its diameter is a constant, π. You'll learn more about ratios in Chapter 7 and circumference in Chapter 12.
Mathematics: Applications and Concepts is a three-course Middle School series intended to bridge the gap from Elementary Mathematics to Algebra 1"Mathematics: Applications and Concepts is
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Tour of the Calculus
This text breathes life in to the core mathematical principles and process of calculus, in its largest aspect a celestial measuring tape and man's ...Show synopsisThis text breathes life in to the core mathematical principles and process of calculus, in its largest aspect a celestial measuring tape and man's attempt to represent the world in time and space. Using clear, instructive explanations, this book explains more than a mathematical system, it also explores an instrument commensurate with humankind's limitless capacity to question and theorize about it's place in the universe
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from 100 providers and counting...
In the first six weeks of the course, we begin with an introduction to the parts of the upper limb and a discussion of the anatomic position, including the three-dimensional planes in which body movements are performed. Next, we cover the osteology of the upper limb by describing the bones of the extremity, how they articulate at synovial joints, and the movements that are possible at these joints. We explore the blood supply and innervation to the upper limb.
A revolution is underway in science classrooms. The demands of the new workplace and the ready access to information afforded by new technologies have radically changed the way we define a scientifically literate society.
More than ever teachers need professional development that provides them with the resources they need and empowers them to take the action required to build classrooms where the next generation of scientifically literate students will flourish.
Complex analysis is the study of functions that live in the complex plane, i.e. functions that have complex arguments and complex outputs. In order to study the behavior of such functions we'll need to first understand the basic objects involved, namely the complex numbers. We'll begin with some history: When and why were complex numbers invented? Was it the need for a solution of the equation x^2 = -1 that brought the field of complex analysis into being, or were there other reasons?
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Editorial projects
Projects I have worked on in my capacity as a freelance copyeditor/editor. Dec 3
In all books before Algebra 1/2 (the equivalent of a Pre-Algebra book), the book is designed for the student to complete assorted mental math problems, learn a new mathematical concept, practice problems relating to that lesson, and solve a varied number of problems which include what the students learned today and in select previous lessons—all for one day's class. This daily cycle is interrupted for tests and additional topics. In the Algebra 1/2 book and all higher books in the series, the mental math is dropped, and tests are given more frequently. The Saxon math program has a specific set of products to support homeschoolers, including solution keys and ready-made tests, which makes it popular among some homeschool families.
Saxon math
Saxon Phonics K
Saxon Phonics 1
Saxon Phonics 2
Flip to back Flip to front Listen Playing... Paused You're listening to a sample of the Audible audio edition. Learn more
When I bought this book, I knew it was to be used in conjunction with the whole Saxon Phonics Intervention program. However, it does have some super lists of vocabulary words, phonic rules, syllable division rules, spelling words, sight words, and irregular pattern words. I used Hooked On Phonics and Phonics Intervention when I home schooled my children. Both had learning difficulties, and phonics based reading helped. (They both have gone to college.) Now that I am a geezer, I work as a private tutor.
Phonics Intervention
Saxon Math 5/4
Saxon Math 6/5
Saxon Math 7/6
Saxon Math 8/7
Algebra 1: An Incremental Development
Saxon's 'Algebra 2' is the second in an integrated three books or three courses series comprised of 'Algebra 1', 'Algebra 2' and 'Advanced Mathematics' designed to prepare students for calculus. The 'Algebra 2' set covers topics that advanced math students are expected to master in 9th grade. While called a 'homeschool kit' it can be used quite effectively by parents 'after school' to supplement or enhance a child's math proficiency which is how we have been using Saxon (me and my 2 boys) ever since 4th grade.
Algebra 2: An Incremental Development
The Future of Human Spaceflight: Objectives and Policy Implications in a Global Context
United States Space Policy: Challenges and Opportunities Gone Astray
A European Approach to Space Security
A Place for One's Mat: China's Space Program, 1956–2003
Reconsidering the Rules for Space Security
Science and the Educated American
Nuclear Reactors: Generation to Generation
AAAS Bulletin
judicial independence
challenges of mass incarceration
challenges to public universities
the university and the city
future of research universities
what is missing in medical thinking
after the 2008 elections
science and technology policy problems
race in the age of Obama
the new pragmatism
election and its consequences
financial crisis and economic policy
education of an American dreamer
black humor
nanotechnology: novel applications
future of power
the nuclear future
on the future of energy
Humanities Indicators
Humanities Indicators Offering the latest information on the state of the humanities in schools, colleges, the workforce, scholarly research, and American life. Departmental Survey
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Synopses & Reviews
Publisher Comments:
While the mathematics of classical engineering and science is primarily "continuous, " the mathematics of computer science is primarily "discrete" or "combinatorial." This volume provides a useful guide to combinatorial mathematics for computer scientists and applied mathematicians. Based on a beginning graduate-level course taught by the author, it covers the two major subdivisions of combinatorics, enumeration and graph theory, with emphasis on the conceptual needs of computer science. Each part is divided into a "basic concepts" chapter that emphasizes the intuitive ideas of the subject, followed by four "topics" chapters that explore these ideas in depth. Given the rapid and continued growth of computer science today, this accessible, well-written volume will be an invaluable practical resource for graduate students, advanced undergraduates, and professionals with an interest in algorithm design and other aspects of computer science and combinatorics.
Book News Annotation:
A textbook for a beginning graduate course for students majoring in mathematics or computer science. It uses combinatorial mathematics to teach basic techniques of proof. The 1985 edition was published by Computer Science Press, Rockville, Maryland. Annotation c. Book News, Inc., Portland, OR (booknews.com)"Synopsis"
by Firebrand,
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I am going to study computer science next year. I am afraid I can't handle the mathematics in the university because I only know some basic mathematics, such as set theory, simple probability, simple matrix operation and I don't know calculus.
1 Answer
I'd suggest getting a good handle on Discrete Mathematics, first and foremost, though I'd never discourage anyone from studying calculus and linear algebra, if they desire to do so. Of more immediate use, however, would be studying Discrete Mathematics. Unfortunately, most textbooks in discrete mathematics are somewhat expensive.
One great choice, for a "beginner" (in that it presumes very little in the way of a mathematics background), is Susanna S. Epp's Discrete Mathematics with Applications. This text, however, is very expensive.
Another text which is excellent is Edward R. Scheinerman's Mathematics: A Discrete Introduction, though it is geared more for math majors than for computer science majors. I think it's less expensive than Epp's text, so I'd suggest taking a look at it, as well.
If cost is an issue, there are some well known notes that are freely accessible and free. For example, see
See also this earlier post, where the question posted sought recommendations for a great text in discrete mathematics. The "leading" answer there recommends Concrete Mathematics by Knuth and company, which is a phenomenal text, but some students may find it difficult to tackle without a more solid foundation in mathematics, including at least some Calculus. But do please do take a look at the text. If you hope to be a computer scientist, Concrete Mathematics will be, either now or later, a "must read" text book. (It is also considerably less expensive than many introductory Discrete Mathematics textbooks!)
I don't agree. I'd read Concrete Mathematics in high school, it was very friendly and the only part I would skip was about hypergeometric functions (it was tedious). True, explanations are concise, but there are many helpful examples and almost everything is done from the very basics. I would definitely recommend this book! (+1 for the other books.)
–
dtldarekJul 21 '13 at 18:53
@dtldarek I wasn't sure on that one. It's one of my "faves"! I rewrote my post to describe it more accurately.
–
amWhyJul 21 '13 at 19:00
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Elementary Linear Algebra - 6th edition
ISBN13:978-0618783762 ISBN10: 0618783768 This edition has also been released as: ISBN13: 978-0547004815 ISBN10: 0547004818
Summary: The cornerstone of Elementary Linear Algebra is the authors' clear, careful, and concise presentation of material--written so that students can fully understand how mathematics works. This program balances theory with examples, applications, and geometric intuition for a complete, step-by-step learning system.The Sixth Edition incorporates up-to-date coverage of Computer Algebra Systems (Maple/MATLAB/Mathematica); additional support is provided in a corresponding tec...show morehnology guide. Data and applications also reflect current statistics and examples to engage students and demonstrate the link between theory and practice25 +$3.99 s/h
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Book has a small amount of wear visible on the binding, cover, pages.Selection as wide as the Mississippi.
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Hardcover Very Good 0618783768 Great condition! No writing or highlighting. Amazing price, Ships fast
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La Palma TrigonometryThere are three main components of precalculus that are so vital that I suggest students must know:
1. Know how to represent functions. There are many different ways you can describe a functions, the most popular are algebraic and graphical.
2
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Papers and other writings on the SimCalc Project, which aims to democratize access to the Mathematics of Change for mainstream students: "Learning the Basics with Calculus"; "An introduction to the profound potential of connected algebra activities:issues of representation, engagement and pedagogy"; "Leveraging handhelds to increase student learning: Engaging middle school students with the mathematics of change"; "The networked classroom"; "Improving understanding of core algebra and calculus ideas in a connected SimCalc classroom"; and more.
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Considered a classic by many, A First Course in Abstract Algebra, Seventh Edition is an in-depth introduction to abstract algebra. Focused on groups, rings and fields, this text gives students a firm foundation for more specialized work by emphasizing an understanding of the nature of algebraic structures
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Elementary and Intermediate Algebra for College Students - 4th edition
Summary: Today's students are visual learners, and Angel/Runde offers a visual presentation to help them succeed in math. Visual examples and diagrams are used to explain concepts and procedures. New Understanding Algebra boxes and an innovative color coding system for variables and notation keep students focused. Short, clear sentences reinforce the presentation of each topic and help students overcome language barriers to learn math and Intermediate Algebra for College Students:
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San Quentin Algebra 2 concepts build on each other so that future topics depend on understanding previous material. Therefore, misunderstanding one topic can cause continuous problems down the road. If this is left unaddressed, knowledge gaps compound over time and the student gets further behind
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9780201726343
ISBN:
0201726343
Edition: 5 Pub Date: 2003 Publisher: Pearson
Summary: This text is organised into 4 main parts - discrete mathematics, graph theory, modern algebra and combinatorics (flexible modular structuring). It includes a large variety of elementary problems allowing students to establish skills as they practice.
Ralph P. Grimaldi is the author of Discrete and Combinatorial Mathematics: An Applied Introduction, Fifth Edition, published 2003 under ISBN 9780201726343 and 0...201726343. Six hundred ninety seven Discrete and Combinatorial Mathematics: An Applied Introduction, Fifth Edition textbooks are available for sale on ValoreBooks.com, one hundred thirty used from the cheapest price of $61.00, or buy new starting at $166.67.[read more]
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I think you might be approaching it the wrong way. At least in my experience, I've found there's not really a linear path to learning things. I've gone through various stages of my own where I thought, "I'm going to go back and re-read every physics/math book starting in the beginning and then everything will make sense!" It's never worked that way (at least for me.) The way we teach high school gives the false impression that there is a set specific order of classes that has to be followed. It was only after the fact that I learned my high school taught biology first, chemistry second, and physics third because somebody decided to do it in alphabetical order.
As far as practical advice goes, here's what I do when I want to learn something I'm unfamiliar with: Pick one thing you want to learn about today. Head to the library and go to the math/science section. (Don't spend a whole lot of money on text books unless you know they fit your learning style.) Grab about ten books on the subject and find yourself a quiet spot (preferably near a computer so you can look up any words that are unfamiliar.) You're not going to read all ten books (that wouldn't be an inefficient use of time.) Just pick the one that has the writing style you connect with the most. Make sure it has problems and answers. Read a little bit, then spend your time doing problems. Do as many as you can, and when you get stuck, read a little bit more. For the problems you get really stuck on, it's good to have an actual person to help you out. Make a note of which problems you couldn't solve, and try to have a friend that's good in math walk you through these. You can make him/her dinner as a thank you.
Above all else (and I can't stress this enough) try not to get too flustered. This stuff is hard, and it's easy to get frustrated. Try to play with the math and find examples of how it relates to things you care about. Try to come up with your own examples. (When I was learning about variational calculus, I was completely lost until I realized it's the same problem I was doing when choosing a route to class that would maximize my probability of seeing this girl I had a secret crush on.)
Finally, it takes a long time to learn, so don't put a deadline on it. Just do a little bit each day and you'll catch up. Learning is not something you do to a certain point and then say, "Yup, I'm done...that's all there is."
Disclaimer: I'm a statistical physicist not a cosmologist, so any gravity answers I give might be complete hooey.
Classically, we think of the centrifugal force as a fictitious force since you could describe the same effect using Newton's first law without any forces. That said, general relativity is a theory which states that gravity itself is a certain kind of fictitious force. It turns out gravity is more accurately described as motion in a curving 4D space time. I suppose it's possible to rewrite it in terms of centrifugal force, (I had a student earlier this semester who tried to convince me of exactly this), but I'd need to see more proof before I went along. To do so, you'd need to answer these questions. Why would gravity point in the opposite direction of centrifugal force? Why does it work even when masses aren't spinning? Most importantly, can you calculate a prediction with this model that doesn't show up in other models? If the theory can't do this, then you're doing what some physicists call "MATHturbating", (i.e. using math to make yourself feel good, but not really doing anything useful that might make the rest of the physics community feel good.)
You have 20,000 viewers in a car of mass ~2000 kg driving at 100 km/hr. That's an angular momentum change of about 7x1015 kg m2/s. Earth has an angular momentum of 1034 kg m2/s, or roughly 1019 times bigger. This would change the length of a day by about 0.00000000000000001%.
Michael Phelps swims about 2 m/s. If the water is falling slower than this rate at the bottom, I'm guessing he coud swim up it (though there's likely be some physics I'm neglecting here.) You could use g h = 0.5 v2 to find g = 0.1 m/s2.
I'm gonna assume we're just talking kinetic energy and not the energy it requires to create the hair. Let's say your hair is about inch long everywhere and 50 microns thick. If each har is separated by 1 mm, you'd have a total hair mass of 100 grams. Travelling at a speed of 1 cm every 2 weeks, the total kinetic energy lost would be 3x10-18 Joules. This is not a significant figure.
According to one source, the wars have costed about $4 trillion. I'm not an expert on cocaine cost, but a quick web search gives $70 per gram. At this cost, you could buy 57 million kilograms. At 1.2 g/cm3, it could cover the National Mall
with about 8 centimeters of blow.
Cool! This is interesting and particularly relevant to me. Having cracked more than my fair share of teeth, I've been wonder if cracked teeth could be melted back together in the same way that ceramics can. Unfortunately, I'm not an experimentalist, so I'm probably not the best on to ask about how to measure things. My best guess would be to use an extracted tooth and set up a temperature gradient by heating one side.
Using the source below, the volume of the Grand Canyon is about 4x1012 m3. A quarter is about 0.2 mL in volume. It would take about 2x1019 quarters to fill the Grand Canyon. That's about 100,000 times the national det.
Oh man. I'm so sorry. No one should be forced into the hell that is listening to that song every day.
Let's say you do 5 events per week on average. That's about 250 gigs per year and about 15,000 over the course of a lifetime. "I Gotta Feeling" is about 4.5 minutes long. If you played it once per event, you'd have listened to about 47 days of it.
I'm assuming you're interested in how well you can slice things (or possibly people.) If so, I agree with OwlPenn that you may be more interested in pressure, which is force per unit area. Still, you asked for force, so I'll try to calculate that.
Let's say you swing at a tree and the blade gets embedded 3 inches inside the trunk. If your blade is travelling at 100 mph (this is a little bit faster than a baseball bat) then the average stopping force on the blade is roughly 150 Newtons.
I'm guessing te average person watches TV about 2 hours per day. There are about roughly 10 30-second car commercials per hour. Over the course of a lifetime, this would be about 200 days of car commercials.
This is a packing problem. There's a lot of research devoted to it, though it's not aimed at chips per se.
If you smash the chips in the bag before opening, they'll fall to the bottom. If you did this until they were dust, I'm betting it'd be around the bottom 10 percent of the back. As a rough guess for the dimensions of the bag, I'd say 10 cm by 5 cm by 20 cm = 1000 cm3. This means you get an extra 900 cm3 of air with every bag of chips you buy.
"Flux" is a general term meaning the amount of something passing through some area. I could talk about the flux of baseballs through a strike zone or the flux of Kool-Aid guys through a wall. Magnetic flux is just the amount of magnetic field that passes through some area.
Solving crossword puzzles isn't very significant calorically, so you're basically expending energy at your normal resting rate of about 100 W. In contrast, a person exercising vigorously can burn energy at a rate of up to 2300 W (I calculated this for Michael Phelps's workout in Ballparking.) As such, you'd need to exercise 23 times longer than exercise guy does in his frame. I can't really do the relativity part without knowing how fast the train is moving. If the train moves fast enough, exercise guy would have to catch up to you in the burning calories department.
Are we talking fart power? If so, it depends on the speed. In Ballparking, I estimated that a sustained fart produces about 0.01 N of force upward. To have this lift you, you'd need the amount of gas to be about 90,000 times larger. Assuming a 10 mg normal fart (you get this by assuming a 10 cm3 fart with the same density as air), you'd need a fart that contained about 1 kg of air. That's almost a bath tub worth of fart air.
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The Dugopolski series in developmental mathematics has helped thousands of students succeed in their developmental math courses. Elementary & Intermediate Algebra, 4e is system between the examples and exercise sets, so no matter where the students start, they will see the connection between the two. Finally, the author finds it important to not only provide quality but also a wide variety and quantity of exercises and applications
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Elementary & Intermediate Algebra (4th edition
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Excerpt: ... ically complementary organs or parts: the nervous system; the skeletal system. A group of interacting mechanical or electrical components. A network of structures and channels, as for communication, travel, or distribution. A network of related computer software, hardware, and data transmission devices. IE316316 Lecture 1 5 Examples of Models Physical Models Simulation Models Probability Models Economic Models Biological Models Mathematical Programming Models IE316 Lecture 1 6 Mathematical Programming Models What does mathematical programming mean? Programming here means "planning." Literally, these are "mathematical models for planning." Also called optimization models. Essential elements Decision variables ...
Excerpt: ... he skeletal system. A group of interacting mechanical or electrical components. A network of structures and channels, as for communication, travel, or distribution. A network of related computer software, hardware, and data transmission devices. IE418418 Lecture 1 5 Examples of Standard Model Types Simulation Models Probability Models Economic Models Biological Models Mathematical Programming Models IE418 Lecture 1 6 Mathematical Programming Models What does mathematical programming mean? Programming here means "planning." Literally, these are "mathematical models for planning." Also called optimization models. The essential element is the existence of an objective. Some categories of mathematical programs (see the ...
Excerpt: ... Introduction to Mathematical Programming IE406 Lecture 5 Dr. Ted Ralphs IE406 Lecture 5 1 Reading for This Lecture Bertsimas 2.5-2.7 IE406 Lecture 5 2 Existence of Extreme Points Definition 1. A polyhedron P Rn contains a line if there exists a vector x P and a nonzero vector d Rn such that x + d P R. Theorem 1. Suppose that the polyhedron P = {x Rn|Ax b} is nonempty. Then the following are equivalent: The polyhedron P has at least one extreme point. The polyhedron P does not contain a line. There exist n rows of A that are linearly independent. IE406 Lecture 5 3 Optimality of Extreme Points Theorem 2. Let P Rn be a polyhedron and consider the problem minxP c x for a given c Rn. If P has at least one extreme point and there exists an optimal solution, then there exists an optimal solution that is an extreme point. Proof: IE406 Lecture 5 4 Optimality in Linear Programming For linear optimization, a finite optimal cost is equivalent to the existen ...
Excerpt: ... Findings from Observations of Mathematics Lessons in M3RP Teacher Leader Classrooms During the 2000-01 School Year Prepared by SAMPI-Western Michigan University July 2001 The Michigan Middle Schools Mathematics Reform Project (M3RP) is a four-year c ...
Excerpt: ... AEB 6182: Lecture V Transformations of Risk Aversion and E-V Versus Direct Utility Maximization I. Interpretations and Transformations of Scale for the Pratt-Arrow Absolute Risk Aversion coefficient: Implications for Generalized Stochastic Dominance A. To this point, we have discussed technical manifestations of risk aversion such as where the risk aversion coefficient comes from and how the utility of income is derived. However, I want to start turning to the question: How do we apply the concept of risk aversion? B. Several procedures exist for integrating risk into the decision making process such as direct application of expected utility, mathematical programming using the expected value-variance approximation, or the use of stochastic dominance. All of these approaches, however, require some notion of the relative size of risk aversion. 1. Risk aversion directly uses a risk aversion coefficient toparameterize the negative exponential or power utility functions. 2. Mathematical programming uses the concep ...
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0521777690
9780521777698
The Beginner's Guide to MATHEMATICA®, Version 4:This update of Jerry Glynn and Theodore Gray's hugely successful textbook covers not only the basic Mathematica features, but also the new features of Mathematica Version 4. The book teaches new Mathematica users some of the important basics of the latest release of this powerful software tool: using the typesetting features, programming palettes, defining functions, creating graphs and notebooks, and applying useful problem solving techniques. Using their skills as Mathematica experts and teachers, the authors provide a brisk but careful tutorial for the Mathematica novice. From the fundamentals of installing and running Mathematica on your computer, through to tips on how to get the most from the advanced programming features, the presentation maintains its concise and knowledgeable tone, providing indexes for both concepts and Mathematica function names. This book will be a valuable tool for both students and individual Mathematica users.
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Rent The Beginner's Guide to MATHEMATICA®, Version 4 4th edition today, or search our site for Theodore textbooks. Every textbook comes with a 21-day "Any Reason" guarantee. Published by Cambridge University Press.
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A Level Further Maths
If you get a grade A at GCSE you should seriously consider studying Further Maths. As Maths is such a vast subject it is impossible to cover it all in one A Level. Hence Further Maths develops some of the concepts met in A Level Maths and brings it to a higher plane. it attracts students who thoroughly enjoy the subject and are keen to extend their understanding and knowledge. The course is chiefly for a student who wishes to study Mathematics, Engineering or any related subject in Higher Education.
What our students say......."I have thoroughly enjoyed my time here at Carmel, especially in my Further Maths studies. The new knowledge that I have learnt throughout the course has been extremely beneficial to my Maths studies as well and I really like the way the two subjects overlap in content but feel separate because of the different class and teacher." (Tara Moran-Reeves)
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Summary: These authors understand what it takes to be successful in mathematics, the skills that students bring to this course, and the way that technology can be used to enhance learning without sacrificing math skills. As a result, they have a created a textbook with an overall learning system involving preparation, practice, and review to help students get the most out of the time they put into studying. In sum, Sullivan and Sullivan'sAlgebra and Trigonometry: Enhanced with Graphing Utilit...show moreiesgives students a model for success in mathematics. ...show less
2008-01-07 Hardcover Very Good 5TH EDITION. CD INCLUDED SEALED. Book is in very good condition but has water mark along front edge. Minor shelf/edge wear, binding tight. Text appears clean & unmark...show moreed. ...show less
Water damaged Every book shipped with tracking number. Typical worn out used book. May have bent pages, loose binding, or markings. Overall definitely readable and usable. May not include Supplements,...show more CDs or Access Codes. -Acceptable-
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You are here
Math 1172: Engineering Mathematics A - Calculus in Polar Coordinates
Wed Mar 06, 3:00pm to 4:00pm
Location:
Cockins Hall 042
This workshop has been cancelled due to instructor illness.
Polar coordinates can be confusing at first, especially to visualize graphically. Unfortunately, this is a necessary skill in order to set up integrals in polar coordinates. This workshop will use technology to help you visualize graphs in polar coordinates, and will apply that knowledge to setting up integrals over polar regions. This workshop will also show you how to graph functions in polar coordinates on your TI-84 graphing calculator.
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Chaos: Making a New Science
by James Gleick Publisher Comments
Chaos records the birth of a new science. This new science offers a way of seeing order and pattern where formerly only the random, the erratic, the unpredictable – in short, the chaotic – had been observed.
Chaos is a history of discovery... (read more)
The Beginner's Guide to Constructing the Universe
by Michael S. Schneider Publisher Comments
The universe may be a mystery, but it's no secret.
Michael Schneider leads us on a spectacular, lavishly illustrated journey along the numbers one through ten to explore the mathematical principles made visible in flowers, shells, crystals, plants... (read more)
Mathematics and the Physical World
by Morris Kline Publisher Comments
Stimulating account of development of mathematics from arithmetic, algebra, geometry and trigonometry, to calculus, differential equations and non-Euclidean geometries. Also describes how math is used in optics, astronomy, other phenomena.... (read more)
Algebra I Workbook for Dummies (For Dummies)
by Mary Jane Sterling Publisher Comments
From signed numbers to story problems — calculate equations with ease Practice is the key to improving your algebra skills, and that's what this workbook is all about. This hands-on guide focuses on helping you solve the many types of algebra... (read more)
Algebra II Workbook for Dummies (For Dummies)
by Mary Jane Sterling Publisher Comments
From radical problems to rational functions -- solve equations with ease Do you have a grasp of Algebra II terms and concepts, but can't seem to work your way through problems? No fear -- this hands-on guide focuses on helping you solve the many types of... (read more)
Differential Equations Problem Solver
by Rea Publisher Comments
... (read more)
Linear Algebra With Applications
by Otto Bretscher Book News Annotation
A text for undergraduates, stressing examples, exercises, history,
and applications, and keeping abstract exposition to a minimum.
Coverage includes linear equations and transforms, subspaces of Rn
and their dimensions, orthogonality and least squares,... (read more)
Complexity: The Emerging Science at the Edge of Order and Chaos
by M Mitchell Waldrop Publisher Comments
Why did the stock market crash more than 500 points on a single Monday in 1987? Why do ancient species often remain stable in the fossil record for millions of years and then suddenly disappear? In a world where nice guys often finish last, why do humans... (read more)
Algebra I for Dummies
by Mary Jane Sterling Publisher Comments
Get the right solution every time -- algebra the fun and easy way! Includes a great glossary of algebraic terms for easy reference The pain-free way to explore algebra--and come out smilin' Does the word polynomial make your hair stand on end? Let Mary... (read more)
Algebra II for Dummies (For Dummies)
by Mary Jane Sterling Publisher Comments
Besides being an important area of math for everyday use, algebra is a passport to studying subjects like calculus, trigonometry, number theory, and geometry, just to name a few. To understand algebra is to possess the power to grow your skills and... (read more)
Mastering Mathematics How To Be a GR 3RD Edition
by Richard Smith Publisher Comments
Providing solid tips for every stage of study, Mastering Mathematics stresses the importance of a positive attitude and gives students the tools to succeed in their math course. This practical guide will help students: avoid mental blocks during math... (read more)
The History of the Calculus and Its Conceptual Development
by Carl B Boyer Publisher Comments
This book, for the first time, provides laymen and mathematicians alike with a detailed picture of the historical development of one of the most momentous achievements of the human intellect ― the calculus. It describes with accuracy and... (read more)
A History of Pi
by Petr Beckmann Publisher Comments
The history of pi, says the author, though a small part of the history of mathematics, is nevertheless a mirror of the history of man. Petr Beckmann holds up this mirror, giving the background of the times when pi made progress -- and also when it did
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there are many useful topic in this course but truth table is one the best and useful tools for solved our problems in real world. another is probability is most useful topic , many events are probable, so that situations this tools is better way to solve the probable events. and also graphs are very easy way to convey our and solve our problems , and set theory is another use full and favorite topic
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Formules mathématiques is the French version of the Math Formulary App that covers all mathematical formulas that are usually used in the school and the university. Where necessary graphics are included to depict and explain the topic better.
SD-Card Installation is supported. Bug reports related to the content and the app itself are more than welcome. Proposals for new features would be great.
This is the free version of the Formules mathématiques Pro app that you can getBest mathematical tool for school and college! If you are a student, it will help you to learn algebra!
Note: Polynomials appear in settings ranging from basic chemistry and physics to economics and social science; they are used in calculus and numerical analysis to approximate other functions. In advanced mathematics, polynomials are used to construct polynomial rings, a central concept in algebra and algebraic geometryFórmulas Matemáticas is the Spanish version of the Math Formulary App that covers all mathematical formulas that are usually used in the school and the university. Where necessary graphics are included to depict and explain the topic better. pointsJokespedia - this hilarious app is the most comprehensive collection of the best jokes, sayings, poems, riddles, and funny quotes in the English language. You can add your best adages yourself, have them rated by other users and climb up in the ranking. So there is something new to read and chuckle at every day, just in case the 13000 entires weren't enough. Use this app to learn English with a lot of fun.
From the classic Little Johnny jokes to the nasty blonde jokes right through to the old tongue twisters, all the entries are split into over 25 categories.
With this free joke app you'll be the joker at every party. We have the best birthday quotes and pick up lines. No matter whether it's a bloke joke or a girls' gag, it never gets old.
For adults we have the adult jokes section, the dirty jokes, and the Yo Mama jokes categories. Of course the classic celebrity characters, like Chuck Norris, Bill Clinton, Al Bundy and Barney Stinson, are all in there too.
To tease your friends or your foes, we recommend the professional categories. Whether they're a civil servant, a farmer, a graduate, a student, a doctor, a lawyer, a politician, a broker, a footballer or a schoolboy, we have just the thing. The classical knock knock jokes and light bulb jokes are also included. A separated clean jokes section is available.
For those who like black comedy we have the famous, bar room and stonerPoints are given for the following: 1 point - giving a rating, 15 points - joke published (and accepted by moderator), 1 point if your joke gets a 3 star rating, 2 points for 4 star rating and 3 points for 5 star rating. will be removed by the moderators
Please leave a comment to report any bugs or submit any feedback you have.
Math Formulary Pro covers all mathematical formulas that are usually used in the school and the university. Where necessary graphics are included to depict and explain the topic better. This Pro Version contains no ads and don't require any permissions.
Formules mathématiques
Fórmulas Matemáticas
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Algebra With Spirit
PDF (Acrobat) Document File
Be sure that you have an application to open this file type before downloading and/or purchasing.
0.22 MB | 18 pages
PRODUCT DESCRIPTION
Alcohol-Themed Algebra Problems from the 18th and 19th Centuries.
There are forty of them, 10 each in the categories Drinking, Mixing, Storing and Pouring, and Buying and Selling.
As a bit of an amateur math historian I find it interesting how the problems given to students reflect the culture. The political, moral, and economic considerations surrounding alcohol use have done a lot of changing since the middle of the 18th century. This period contains the Whiskey Rebellion, the rise of the Temperance movement, and the enactment and repeal of Prohibition, just to name a few major examples.
Because authors used to treat the cultural acceptance of alcohol (as well as other issues) more matter-of-factly, old math books are full of interesting word problems that illuminate the spirit of the times from a slightly different angle than we are used to seeing
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Explore and analyze the solutions of mathematical models from diverse disciplines
As biology increasingly depends on data, algorithms, and models, it has become necessary to use a computing language, such as the user-friendly MATLAB, to focus more on building and analyzing models as opposed to configuring tedious calculations. Explorations of Mathematical Models in Biology with MATLAB provides an introduction to model creation using MATLAB, followed by the translation, analysis, interpretation, and observation of the models.
With an integrated and interdisciplinary approach that embeds...
Beyond simulation and algorithm development, many developers increasingly use MATLAB even for product deployment in computationally heavy fields. This often demands that MATLAB codes run faster by leveraging the distributed parallelism of Graphics Processing Units (GPUs). While MATLAB successfully provides high-level functions as a simulation tool for rapid prototyping, the underlying details and knowledge needed for utilizing GPUs make MATLAB users hesitate to step into it. Accelerating MATLAB with GPUs offers a primer on bridging this gap. Starting with the basics, setting up...
This book uses numerous in-depth explanations, diagrams, calculations, and tables to provide an intensive overview of modern control theory and control system design. Mathematics are kept to a minimum, and engineering applications are stressed throughout. Completely updated and packed with student-friendly features, the sixth edition presents a range of updated examples using MATLAB<SUP>®</SUP>, as well as an appendix listing MATLAB functions for optimizing control system analysis and design. Over 75 percent of the problems presented in the previous edition have been revised or replaced.
...
MATLAB By Example guides the reader through each step of writing MATLAB programs. The book assumes no previous programming experience on the part of the reader, and uses multiple examples in clear language to introduce concepts and practical tools. Straightforward and detailed instructions allow beginners to learn and develop their MATLAB skills quickly. The book consists of ten chapters, discussing in detail the integrated development environment (IDE), scalars, vectors, arrays, adopting structured programming style using functions and recursive functions, control flow, debugging,...
MATLAB for Neuroscientists serves as the only complete study manual and teaching resource for MATLAB, the globally accepted standard for scientific computing, in the neurosciences and psychology. This unique introduction can be used to learn the entire empirical and experimental process (including stimulus generation, experimental control, data collection, data analysis, modeling, and more), and the 2nd Edition continues to ensure that many computational problems can be addressed in a single programming environment. This updated edition features additional material on the creation of...
Assuming only a basic knowledge of automatic control and signals and systems, this self-contained handbook covers advanced topics in automatic control. These include the LQR and H∞ approaches as well as concepts of modeling analysis. The text deals with advanced automatic control techniques, with particular attention to their robustness. The authors explain how the Linear Matrix Inequalities (LMI) technique can be used as a unifying tool for system analysis and controller design. This easy-to-read text presents the essential theoretical background and provides numerous examples and MATLAB®...
Incorporating feedback from professors and practicing engineers, the third edition of this bestselling text reflects the state of the art in the field and restructures the material to be more convenient for course use. Reorganized, expanded, and updated, it includes several new topics and many new end-of-chapter problems. This edition also takes advantage of the new features in the latest version of MATLAB<SUP>®</SUP>, with updated MATLAB code available for download on the book's CRC Press web page.
...
This is a short, focused introduction to MATLAB, a comprehensive software system for mathematical and technical computing. It contains concise explanations of essential MATLAB commands, as well as easily understood instructions for using MATLAB's programming features, graphical capabilities, simulation models, and rich desktop interface. Written for MATLAB 7, it can also be used with earlier (and later) versions of MATLAB. This book teaches how to graph functions, solve equations, manipulate images, and much more. It contains explicit instructions for using MATLAB's companion software,...
This title provides the most important theoretical aspects of Image and Signal Processing (ISP) for both deterministic and random signals. The theory is supported by exercises and computer simulations relating to real applications.
More than 200 programs and functions are provided in the MATLAB® language, with useful comments and guidance, to enable numerical experiments to be carried out, thus allowing readers to develop a deeper understanding of both the theoretical and practical aspects of this subject.
...
Optimal filtering applied to stationary and non-stationary signals provides the most efficient means of dealing with problems arising from the extraction of noise signals. Moreover, it is a fundamental feature in a range of applications, such as in navigation in aerospace and aeronautics, filter processing in the telecommunications industry, etc. This book provides a comprehensive overview of this area, discussing random and Gaussian vectors, outlining the results necessary for the creation of Wiener and adaptive filters used for stationary signals, as well as examining Kalman filters...
This book uses MATLAB as a computing tool to explore traditional DSP topics and solve problems. This greatly expands the range and complexity of problems that students can effectively study in signal processing courses. A large number of worked examples, computer simulations and applications are provided, along with theoretical aspects that are essential in order to gain a good understanding of the main topics. Practicing engineers may also find it useful as an introductory text on the subject.
...
Computational Colour Science Using MATLAB 2nd Edition offers a practical, problem-based approach to colour physics. The book focuses on the key issues encountered in modern colour engineering, including efficient representation of colour information, Fourier analysis of reflectance spectra and advanced colorimetric computation. Emphasis is placed on the practical applications rather than the techniques themselves, with material structured around key topics. These topics include colour calibration of visual displays, computer recipe prediction and models for colour-appearance...
Classification, Parameter Estimation and State Estimation is a practical guide for data analysts and designers of measurement systems and postgraduates students that are interested in advanced measurement systems using MATLAB. 'Prtools' is a powerful MATLAB toolbox for pattern recognition and is written and owned by one of the co-authors, B. Duin of the Delft University of Technology.
After an introductory chapter, the book provides the theoretical construction for classification, estimation and state estimation. The book also deals with the skills required to bring the theoretical...
This new textbook in Signals and Systems provides a pedagogically-rich approach to what can oftentimes be a mathematically 'dry' subject. Chaparro introduces both continuous and discrete time systems, then covers each separately in depth. Careful explanations of each concept are paired with a large number of step by step worked examples. With features like historical notes, highlighted 'common mistakes,' and applications in controls, communications, and signal processing, Chaparro helps students appreciate the usefulness of the techniques described in the book. Each chapter contains a...
Quickly Engages in Applying Algorithmic Techniques to Solve Practical Signal Processing Problems
With its active, hands-on learning approach, this text enables readers to master the underlying principles of digital signal processing and its many applications in industries such as digital television, mobile and broadband communications, and medical/scientific devices. Carefully developed MATLAB® examples throughout the text illustrate the mathematical concepts and use of digital signal processing algorithms. Readers will develop a deeper understanding of how to apply the algorithms by...
Environmental Data Analysis with MatLab is for students and researchers working to analyze real data sets in the environmental sciences. One only has to consider the global warming debate to realize how critically important it is to be able to derive clear conclusions from often-noisy data drawn from a broad range of sources. This book teaches the basics of the underlying theory of data analysis, and then reinforces that knowledge with carefully chosen, realistic scenarios. MatLab, a commercial data processing environment, is used in these scenarios; significant content is devoted to...
An accompanying manual to Theodoridis/Koutroumbas, Pattern Recognition, that includes Matlab code of the most common methods and algorithms in the book, together with a descriptive summary and solved examples, and including real-life data sets in imaging and audio recognition. *Matlab code and descriptive summary of the most common methods and algorithms in Theodoridis/Koutroumbas, Pattern Recognition 4e. *Solved examples in Matlab, including real-life data sets in imaging and audio recognition *Available separately or at a special package price with the main text (ISBN for package:...
Up-to-date, technically accurate coverage of essential topics in image and video processing
This is the first book to combine image and video processing with a practical MATLAB®-oriented approach in order to demonstrate the most important image and video techniques and algorithms. Utilizing minimal math, the contents are presented in a clear, objective manner, emphasizing and encouraging experimentation.
The book has been organized into two parts. Part I: Image Processing begins with an overview of the field, then introduces the fundamental concepts, notation, and terminology...
MATLAB: An Introduction with Applications 4th Edition walks readers through the ins and outs of this powerful software for technical computing. The first chapter describes basic features of the program and shows how to use it in simple arithmetic operations with scalars. The next two chapters focus on the topic of arrays (the basis of MATLAB), while the remaining text covers a wide range of other applications.
MATLAB: An Introduction with Applications 4th Edition is presented gradually and in great detail, generously illustrated through computer screen shots and step-by-step tutorials,...
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The American Mathematical Society (AMS) was founded in 1888 in order to further mathematical research and scholarship. Since that time, they have embarked on a number of outreach programs designed to educate the public...
In this animated and interactive object, the learner uses a TI-86 calculator to solve for the magnitude of the resultant and of one of the component forces in a right triangle. Target Audience: 2-4 Year College...
The University of Akron has created these excellent algebra tutorials that review some of the main topics in the discipline. There are ten lessons, which focus on topics like radicals and exponents, basic algebra,...
The lessons, activities, and other materials at this site are designed to enable math teachers to develop a multimedia teaching approach to math. This site provides resources such as spreadsheets, calculators, and...
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OASD Mathematics Unit Frameworks
COURSE: Essentials of Math
OVERARCHING QUESTIONS:
Mathematical Processes: How can I use math knowledge, skills, and strategies to solve real-world
and non-routine problems?
Number Operations and Relationships: How can I use numbers effectively to quantify, describe,
and label things in my world?
Geometry: How can I use geometric concepts, relationships, and procedures to interpret,
represent, and solve problems?
Measurement: What appropriate tools and techniques can I use to measure things accurately?
Statistics and Probability: How can I use data collection and analysis, statistics and probability to
solve problems?
Algebraic Relationships: How can I use algebraic relationships in personal, scientific, economic,
social, medical, artistic and civic fields of inquiry?
STANDARDS:
MATHEMATICAL PROCESSES:
A1: Understand a broad body of mathematical knowledge and apply a variety of
mathematical skills and strategies, including reasoning, oral and written communication,
and the use of appropriate technology, when solving mathematical, real-world and non-
routine problems.
NUMBER OPERATIONS AND RELATIONSHIPS:
B1: Know how to use numbers effectively for various purposes, such as counting,
measuring, estimating, and problem solving.
GEOMETRY:
C1: Know how to use geometric concepts, relationships and procedures to interpret,
represent, and solve problems.
MEASUREMENT and REFERENCE FRAMES:
D1: Select and use appropriate tools (including technology) and techniques to measure
things to a specified degree of accuracy. Use measurements in problem-solving
situations.
DATA AND CHANCE:
E1: Know how to use data collection and analysis, statistics and probability in problem-
solving situations, employing technology where appropriate.
PATTERNS, FUNCTIONS and ALGEBRA:
F1: Discover, describe, and generalize simple and complex patterns and relationships. In
the context of real-world problem situations, use algebraic techniques to define and
describe the problem to determine and justify appropriate solutions.
5/23/2006 1
Essentials of Math
COURSE: Essentials of Math
UNIT: Paper and Pencil Calculations
PACING: 7-8E1.12.1 Work with data in the context of real-world situations.
• Formulate hypotheses that lead to collection and analysis of one- and two-variable data
• Design a data collection plan that considers random sampling, control groups, the role of
assumptions, etc.
• Conduct an investigation based on that plan
5/23/2006 2
Essentials of Math
• Use technology to generate displays, summary statistics, and presentations.5/23/2006 3
Essentials of Math
Mathematics
COURSE: Essentials of Math
UNIT: Using the Calculator and Estimation
PACING: 9-10 days
BENCHMARKS:Calculator
5/23/2006 4
Essentials of Math
Mathematics
COURSE: Essentials of Math
UNIT: Part Time and Summer Jobs
PACING: 8-9Can I read and write/fill out job applications?
* How can I use addition, subtraction, multiplication, and division?
How can I solve problems in this unit?
*How do I compute total earnings/tips/social security?
*How can I use the guess and check method to solve problems?
*Can I read and interpret want ads?
How can I use this in the real world?
5/23/2006 5
Essentials of Math
*How can I evaluate and apply for jobs?
KEY CONTENT LANGUAGE:
Minimum wage, tips, social security, FICA,
RESOURCES:
Classified ads, internet (WISCareers), job application forms, resume examples
5/23/2006 6
Essentials of Math
Mathematics
COURSE: Essentials of Math
UNIT: Full-Time Work
PACING: 11 Writing5/23/2006 7Can I calculate total time and wages for a particular job?
How can I use this in the real world?
*How can I evaluate jobs in terms of pay and benefits?
KEY CONTENT LANGUAGE:
Weekly/biweekly/annual pay, piecework, commission, net pay, deductibles, face value,
beneficiary, term, straight life
RESOURCES:
Internet, classified ads, job applications
5/23/2006 8
Essentials of Math
Mathematics
COURSE: Essentials of Math
UNIT: Recreation and Sports* Can I evaluate the meaning of fractions and their remainders?
How can I solve problems in this unit?
*How can I evaluate the cost of memberships, tickets, and necessary materials for
particular recreational activities?
5/23/2006 9
Essentials of Math
How can I use this in the real world?
*How can I evaluate and choose a recreational activity based on associated costs?
KEY CONTENT LANGUAGE:
Membership fee, cost per visit, all day pass, remainder
RESOURCES:
YMCA flyers with prices, Menus, Store flyers with prices, sales tax tables
5/23/2006 10
Essentials of Math
Mathematics
COURSE: Essentials of Math
UNIT: Basic Purchases How can I use addition, subtraction, multiplication, division, and percents?
How can I solve problems in this unit?
*How can I calculate the amount of discount and the discount rate?
*How can I calculate the sales tax of a purchase?
How can I use this in the real world?
*How can I evaluate the cost of buying audio/video equipment, clothing, or food?
*How do I order from a catalog/online/telephone?
5/23/2006 11
Essentials of Math
*How can I evaluate the best buy at a store using unit pricing?
KEY CONTENT LANGUAGE:
Markdown, discount, discount rate, sales tax, unit prices
RESOURCES:
Catalogs, newspaper ads
5/23/2006 12
Essentials of Math
Mathematics
COURSE: Essentials of Math
UNIT: Savings and Checking Accounts
PACING: 7 use this in the real world?
*How can I use a checking/savings account responsibly?
*How can I compute the simple/compound interest earned on investments or paid on
loans?
*How can I compare/evaluate different checking accounts to determine the best option?
5/23/2006 13
Essentials of Math
KEY CONTENT LANGUAGE:
Checking accounts, savings accounts, deposit slips, withdrawal slips, check register, bank
statement, I = prt, compound interest
RESOURCES:
"How to do your banking" handour
5/23/2006 14
Essentials of Math
Mathematics
COURSE: Essentials of Math
UNIT: Credit 15How can I use patterns to predict future payment amounts?
How can I use this in the real world?
*How can I responsibly use credit cards?
*How can I calculate finance charges so that I may calculate/estimate future balances?
*How do I take out a loan and calculate the amount of interest due?
*How can I purchase something on an installment plan, and how do I calculate the
finance charge?
KEY CONTENT LANGUAGE:
Credit card, charge receipt, credit card statement, finance charge, unpaid balance, new
balance, overdraft, annual percentage rate (APR), installment price, installment plan,
RESOURCES:
Credit card applications, credit card statements, consolidate loan flyers
5/23/2006 16
Essentials of Math
Mathematics
COURSE: Essentials of Math
UNIT: Automobile Expenses5/23/2006 17
Essentials of Math
*How can I calculate the monthly payment for a car loan?
*How can I calculate the total operating expenses for a car?
How can I use this in the real world?
*How can I evaluate the total cost and options to determine which car to purchase?
*How can I negotiate a price, and determine a finance charge?
*How can I determine the cost of renting an automobile?
KEY CONTENT LANGUAGE:
Sticker price, options, negotiated price, trade-in allowance, vehicle registration fee, title,
EPA, mpg, cpg, insurance, liability, collision, comprehensive, premiums, deductibles
RESOURCES:
Insurance info, online insurance quotes, classified ads
5/23/2006 18
Essentials of Math
Mathematics
COURSE: Essentials of Math
UNIT: Transportation
PACING: 10 19
Essentials of Math
ESSENTIAL AND TOPICAL QUESTIONS:
What math skills or knowledge will I need in this unit?
*How can I use addition, subtraction, multiplication, and division?
*How can I use charts, graphs, maps, and schedules to gain the necessary information
needed to solve problems?
How can I solve problems in this unit?
*How can I convert times to different time zones?
How can I use this in the real world?
*How can I estimate distance and travel time for a trip?
*How can I determine the cost, travel time, and distance traveled for a bus, train,
airplane, subway, and taxi?
*What factors need to be considered when choosing the most economical way to travel?
KEY CONTENT LANGUAGE:
Time Zones
RESOURCES:
Hand clocks and time zone charts, maps with scales, "mapquest", travel agent
5/23/2006 20
Essentials of Math
Mathematics
COURSE: Essentials of Math
UNIT: Taxes
PACING: 11-133 Analyze non-routine problems and arrive at solutions by various means including models and
simulations, often starting with provisional conjectures and progressing, directly or indirectly, to a solution,
justification, or counter-example.
A1.12.4 Develop effective oral and written presentations employing:
• Mathematical terminology
• Notation,
• Symbols
• Conventions for mathematical arguments
• Display of data5/23/2006 21
Essentials of Math use tax forms, booklets, and tax tables to help me complete my taxes?
How can I solve problems in this unit?
*How can I fill out the tax forms so that I correctly calculate the refund/amount owed?
How can I use this in the real world?
*How do I determine which tax form to use and then gather the necessary information for
calculating the refund/amount owed?
KEY CONTENT LANGUAGE:
W-2 form, 1099 form, IRS, deductions, exemptions, adjusted gross income, taxable
income, 1040 EZ, 1040 schedule A
RESOURCES:
Tax forms (W1-2, 1040EZ, 1040, WI) and booklets, Tax tables, W-2 forms, W-4 forms,
1099 forms
5/23/2006 22
Essentials of Math
Mathematics
COURSE: Essentials of Math
UNIT: Housing
PACING: 105/23/2006 23
Essentials of Math want ads, perimeter, area, and proportions to help solve problems?
How can I use this in the real world?
*How can I rent an apartment or buy a condo/house?
*How can I calculate what my monthly mortgage would be for a particular home?
*How can I estimate my real estate taxes and homeowners insurance?
*How can I calculate the cost of utilities, decorating, and remodeling?
*How can I compare mortgages to analyze, which is the best?
KEY CONTENT LANGUAGE:
Mortgage, real estate taxes, homeowners insurance, condominium, perimeter, area,
proportions
RESOURCES:
Rulers, tape measures, apartment ads, mortgage charts, sample utility bills
5/23/2006 24
Essentials of Math
Mathematics
COURSE: Essentials of Math
UNIT: Trade Industries• Proportional reasoning, including those involving squaring and cubing
5/23/2006 25
Essentials of Math area, perimeter, addition, subtraction, multiplication, division, and
operations with fractions to solve problems?
How can I solve problems in this unit?
*How can I draw diagrams to help solve problems?
How can I use this in the real world?
*How can I calculate costs associated with carpentry, plumbing, electrical work, painting,
and masonry, as well as utilize comparative consumerism?
KEY CONTENT LANGUAGE:
Board foot, inside/outside diameter, area, and perimeter
RESOURCES:
5/23/2006 26
Essentials of Math
Mathematics
COURSE: Essentials of Math
UNIT: Other Professions4 Develop effective oral and written presentations employing:
• Mathematical terminology
• Notation,
• Symbols
• Conventions for mathematical arguments5/23/2006 27
Essentials of Math read and create charts and tables of information and utilize proportions to
solve problems?
How can I solve problems in this unit?
*How can I read schedules and calculate to time according to hours, minutes, and
seconds?
How can I use this in the real world?
*How can I solve problems involving advertising costs, presenting data in an organized
fashion, currency exchange, quality control sampling, determining health care drug
dosages, radio and television programming, and evaluation of raises/promotions?
KEY CONTENT LANGUAGE:
Area, column inch, line graphs, bar graphs, currency exchange rate, quality control
RESOURCES:
5/23/2006 28
Essentials of Math
Mathematics
COURSE: Essentials of Math
UNIT: Personal Finance operations to solve problems?
How can I solve problems in this unit?
*How can I design a personal budget so that I may solve personal financial problems?
How can I use this in the real world?
5/23/2006 29
Essentials of Math
*How can I calculate inflation rate and/or use the inflation rate to determine purchasing
power?
*How can I determine the costs of raising a family?
*How can I determine a person's net worth based on their total assets and liabilities?
KEY CONTENT LANGUAGE:
Purchasing Power, inflation rate, fixed and variable expenses, assets, liabilities, net worth
RESOURCES:
Newspaper Articles
5/23/2006 30
Essentials of Math
Mathematics
COURSE: Essentials of Math
UNIT: Investments operations to solve problems?
How can I use this in the real world?
*How do I calculate the redemption value of a US savings bond?
*How do I calculate interest earned on a CD?
*How do I invest in stocks and calculate net profit/loss?
5/23/2006 31
Essentials of Math
*How do I invest in mutual funds?
*How do I calculate annual pension benefit?
KEY CONTENT LANGUAGE:
US Savings Bonds, certificates of deposit, stocks, shares, dividends, mutual funds,
pension plans
RESOURCES:
Investment information from newspaper, internet and financial advertisements
5/23/2006 32
Essentials of Math
Mathematics
COURSE: Essentials of Math
UNIT: Probability perform basic operations with fractions?
How can I solve problems in this unit?
*How can I calculate the probability of independent and dependent events?
*How can I draw a tree diagram in order to list the sample space?
How can I use this in the real world?
*How can I use probabilities to make predictions about real world events?
5/23/2006 33
Essentials of Math
KEY CONTENT LANGUAGE:
Simple probability, sample space, independent events, dependent events, tree diagram,
counting principle
RESOURCES:
Dice, cards, card games
5/23/2006 34
Essentials of Math
Mathematics
COURSE: Essentials of Math
UNIT: Measurement
PACING: 2-3D1.12.2 Select and use tools with appropriate degree of precision to determine measurements directly
within specified degrees of accuracy and error.
D1.12.3 Determine measurements using
• Estimation perform basic operations on integers as well as fractions?
5/23/2006 35
Essentials of Math
How can I solve problems in this unit?
*How can I measure an object with a ruler and estimate its length to the nearest 16th of an
inch/nearest mm?
How can I use this in the real world?
*How can I estimate lengths in English and metric units?
*How can I use rulers/measuring tapes to calculate area and perimeter?
KEY CONTENT LANGUAGE:
English units, metric units, area, perimeter
RESOURCES:
Rulers, micrometers, measuring tape
5/23/2006 36
Essentials of
| 677.169 | 1 |
Product Details:
Advantage provides an interactive learning experience and the tools students need to gain learning confidence and improve their grades. Help your child build a solid academic foundation with High School Advantage a complete student resource center that combines lessons exercises and quizzes with additional learning resources to support and motivate your child in reaching his or her full academic potential.The ADVANTAGE Approach to Effective Learning:. ENGAGE: Interactive learning experience engages the student.. REINFORCE: Standards-driven lesson plan reinforces classroom learning.. SUPPORT: Study aids & reference tools support the learning experience.. MOTIVATE: Brain-building games add fun to studying.Student Benefits. Learn At Your Own Pace.. Overcome Challenging Topics.. Review Lessons As Needed.. Prepare For College.MathSolidify critical math skills and prepare for college with detailed lessons that simplify complex concepts theories and equations.. Algebra II. Geometry & Trigonometry.. Plus: Calculus iPod study materials.ScienceEstablish a thorough understanding of all areas in Science with the help of multimedia presentations interactive lessons and practice exercises.. Biology.. Chemistry.. Physics.Social StudiesStudy landmark historical events to understand their impact on the development of the contemporary United States. Learn basic supply and demand principles and how they affect the marketplace.. US History.. US Government.. Economics.EnglishDevelop an aptitude for organizing and presenting information in a clear and concise manner whether on a research paper college essay or cover letter. . Research.. Writing.. Presenting.Foreign LanguageBuild and perfect basic conversational skills in Spanish French Ger
| 677.169 | 1 |
A robust bridge between high school and higher level mathematics, this text presents some of the most fundamental and beautiful ideas in pure mathematics. It covers not only standard material but also many interesting topics not usually encountered at this level, such as solving cubic equations, studying the five Platonic solids, coding secret information, and comparing the sizes of two infinite sets. This third edition contains three new chapters that provide an introduction to mathematical analysis. It also includes solutions to all of the odd-numbered exercises. A solutions manual is available for qualifying instructors.
This title will only allow
printing of 2 consecutive pages
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copying of 2 consecutive pages
at a time.
| 677.169 | 1 |
Course Summary
This course provides a brief review of introductory algebra topics. Topics to be covered include integer operations, order of operations, perimeter and area, fractions and decimals, scientific notation, ratios and rates, conversions, percents, algebraic expressions, linear equations, the Pythagorean theorem, and graphing.
Why Take This Course?
At the end of this course students will have reviewed the core topics of introductory algebra. Students will be comfortable with the concepts and procedures of introductory algebra, and be able to apply their knowledge to other coursework and real-world problems.
Instructors & Partners
Kelly Vetter
Instructor
Kelly Vetter is an instructor at Wake Technical Community College. She has a B.S. in Mathematics Education and a Certificate in E-Learning from North Carolina State University. She has taught math for a total of 17 years and has been teaching developmental math for 12 of those years. She has taught in various formats including the classroom, online, and hybrid courses.
Sue Ann Austin
Instructor
Sue Ann Austin is an instructor at Wake Technical Community College. She has taught developmental math for 4 years and prior to that was a high school math teacher. She has a B.S. in Applied Mathematics from Carnegie-Mellon University and completed the NC Teach program at North Carolina State University. She was a software engineer for 15 years prior to entering the field of education.
Andy Brown
Course Developer
After graduating from MIT with a degree in physics in 2009, Andy spent two years teaching, traveling around the world, and biking across the United States. When he heard about Udacity, he abandoned his vagabond ways to share his passion for learning and teaching with the world.
| 677.169 | 1 |
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