Writing Questions in Algebra II | Polynomial | Equations

Writing in Algebra II

Note: We always have talked about these questions, or a similar question, before they appear on an
assessment. I don’t want the writing/concept questions to be a gotcha! type question – that’s not what I’m
aiming for.
**
Write down a compound inequality (using AND / OR) where the solution set is: ( 2, 7] ÷
**
The expression x y © means (a) take the first number and subtract the second number, then (b) multiply that
result by the second number, and finally (c) add the first number to the result.

Part I: Calculate 5 2 ©
Part II: Jamaal claims that the only way to get an even result is to have both x and y be even. Is Jamaal’s claim
**
Some bonus points if you can say which are truths and which are lies! If it’s true, explain why it’s true. If
it’s a lie, explain why it’s a lie.
Statement I: If { , , } l q y G _ and F G _ , then q F e .
Statement II: If a C e and C F _ , then a F e .
**
Wise Miles proclaims “There is a particular number for b which will make the following equation have only one
solution: 2 4 x b + = . (In other words, once this value for b is plugged in, there is only one x value that satisfies
the equation.)”
Show Miles is correct. Algebraically find this value for b AND explain clearly, with words and equations, why
your value for b yields only one solution for the equation.
**
(a) Explain why
5 5 5
( ) xy x y = without using your exponent rules. Explain it to someone so they can
understand it simply!
(b) Explain why
8 2 16
( ) a a = without using your exponent rules. Explain it to someone so they can understand
it simply!
(c) Explain why
8
6
2
a
a
a = without using your exponent rules. Explain it to someone so they can understand it
simply!
**
Explain why
0
5 is 1 in a way that a student in Algebra I could understand. (P.S. Don’t say “because it’s 5
multiplied by itself 0 times.”)
**
Of the following equations below, identify three that are not polynomials? Explain why the ones you’ve chosen
are not polynomials?

Not a polynomial:
Reason:

Not a polynomial:
Reason:

Not a polynomial:
Reason:
**
Explain why

3
4

1
2
can be rewritten as
3 2
4 1
. (In other words, why does the “flip and multiply” technique work?)

**
What is the difference between a rational expression and a rational equation? Which one are you allowed to
use the “I hate fractions” method with and why?
**
Explain to someone why we can rewrite
5
11 as
1/5
11 . Why in the world is a radical the same as an exponent?
Remember, we’ve been practicing our writing all year. Read over your explanation – is it clear? If you read it in a
textbook, before understanding this idea, would you now understand it? TEACH the concept!
**
Is a circle a function? Explain why or why not. You may want to use a diagram to illustrate. For a complete
answer, you will have to include the definition of a function, and show how it applies or does not apply to a
circle.
**
Is a relation which maps “date of birth” to “person” a function? Why or why?
**
Is the point (2, 3) a solution to
4 5
3 2 1
y x
x y
= ÷ ¦
´
÷ =
¹
? Explain why or why not.
**
Two students attempted to solve the system of equations
2 4 38
2 2 4
x y
x y
+ = ¦
´
÷ = ÷
¹
solution is incorrect? Explain the error.

**
How many solutions does
2 1
3 6 1
x y
x y
+ = ÷ ¦
´
÷ ÷ =
¹

have, and explain how you know?
**
a. Is the sum of two linear functions also a linear function? Explain.
b. Is the product of two linear functions also a linear function? Explain.
c. Is the composition of two linear functions also a linear function? Explain.
**
Solve by completing the square:
2
10 7 0 x x ÷ + = .
Explain in a sentence what your solutions above mean:

___________________________________________________________________________________________

___________________________________________________________________________________________
**
(a) What is the vertex of a parabola?

__________________________________________________________________________________

__________________________________________________________________________________

(b) What is the minimum y value for this quadratic:
2
( 5) 2 y x = + + ? Why (pun intended!)? In other words,
explain to someone who is only in Algebra I how you know that y value is the minimum.
(c) What is the vertex of
2
( 5) 2 y x = + + ?
**
(a) Is 2 x = a solution to
2
6 10 0 x x ÷ + = ? How do you know?

(b) Is 3 x i = + a solution to
2
6 10 0 x x ÷ + = ? How do you know?
**
John and Betty stared at the quadratic equation
2
1 0 x x ÷ ÷ = , in an attempt to solve it. John said: “It may be
factorable? Let’s try!” They tried ( 1)( 1) x x + ÷ but that didn’t work. They also tried ( 1)( 1) x x ÷ + , but Betty said
“Duh! That’s the same thing as ( 1)( 1) x x + ÷ .” So they concluded there was no solution.

John and Betty are wrong. Explain to John and Betty what their misconception is.
**
The following text was recovered from a math textbook with a horrible ink stain on it:

And when we graph the quadratic
2
1 9 4 2x y x ÷ + = , we find that it has exactly one x-intercept, which means that
the quadratic comes down to and then bounces off of the x-axis – but never crosses it. In a sense, this is a very
The ink stain is annoyingly placed, because we can’t see the last term in the quadratic. Figure out a possible
value of the number under the ink stain. Explain how found your answer.
**
Solve:
2
6 8 0 x x + + >
Explain in a complete sentence (without using the word “it”) what your solution means:
**
What axis is y x = ÷ is a reflection over? ____________________
explain – but you must use words.
**
Mr. Shah has yet again confused himself. He gets confused about vertical and horizontal stretching and
shrinking. He found the following blank charts on a smartboard on the course conference, and asked you to
help him figure things out. Can you fill in the following charts, and use them to explain (using words, making
reference to the numbers in the chart you’ve filled in) horizontal and vertical stretching and shrinking to Mr.
Shah?

**
Explain why ) 1 (2 4 3
x
÷ + = does not have a solution, but why ) 1 3(2 2
x
+ = ÷ ÷ does have a solution.

NOTE: If you look back at your response and can’t underline where you explained why, you should be sure to
revise your answer. You will want to be as comprehensive as possible in your explanation. You may want to use
**
(a) Does
2
2log ( ) 5 5 x + = ÷ have a solution? If so, what is it? If not, explain why it does not have a solution.

(b) Does 2(2) 5 5
x
+ = ÷ have a solution? If so, what is it? If not, explain why it does not have a solution.
(c) Fill in the blank, and explain how you came up with the answer:
52
2
) log (2 _____ = .
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