Algebra 2 Fall Final Assignment 2019 It is very important that you review for the Algebra 2 Final. Here are a few pieces of information

you want to know.

➢ Your Final is worth 15% of your overall grade

➢ The final covers concepts from the entire semester, they are the following:

Topic 1 – Linear Functions and Systems Topic 10 – Matrices

Topic 2 – Quadratic Functions Topic 3 – Polynomial Functions

➢ The final is 45 multiple choice problems, here are some tips for multiple choice problems

o Read the question before you look at the answer.

o Come up with the answer in your head before looking at the possible answers, this

way the choices given on the test won't throw you off or trick you.

o Eliminate answers you know aren't right.

o Read all the choices before choosing your answer.

o There is no penalty for wrong answers on the test; it’s to your benefit to attempt

every question.

This Assignment is due the day of your final and is worth the same as seven assignments.

Make sure you show your work for full credit; circling the correct answer is not enough.

For a video with solutions to all problems, follow the links from mathwithmills.weebly.com

Assigned problems for each day of the Finals Review

Date Problems to complete in-class/at Home

Monday, Topic 1- Linear Functions #1-12

Tuesday, Topic 2- Quadratic Functions #26-46

Wednesday, Topic 10- Matrices #13-25

Thursday, Topic 3- Polynomial Functions #47-66

Friday, Diagnostic Quiz

During Finals Week Review problems as needed

Finals Schedule

Monday, December 16th, 2019

1st period EXAM 7:45 - 9:30

2nd period 9:40 -10:19

3rd period 10:24 -11:03

4th period 11:08 -11:47

Lunch 11:47 -12:27

5th period 12:27-1:06

6th period 1:11 -1:50

7th period 1:55 -2:35

Tuesday, December 17th, 2019

2nd period EXAM 7:45 - 9:30

Break

3rd period EXAM 9:40 -11:25

Wednesday, December 18th, 2019

4th period EXAM 7:45 - 9:30

Break

5th period EXAM 9:40- 11:25

Thursday, December 19th, 2019

6th period EXAM 7:45 - 9:30

Break

7th period EXAM 9:40 -11:25

Algebra 2 Semester 1 Test Reference Sheet

Polynomial Identities: Matrices:

𝑎3 + 𝑏3 = (𝑎 + 𝑏)(𝑎2 − 𝑎𝑏 + 𝑏2) Identity Matrix: [1 00 1

]

𝑎3 − 𝑏3 = (𝑎 − 𝑏)(𝑎2 + 𝑎𝑏 + 𝑏2) Inverse Matrix: [𝑎 𝑏𝑐 𝑑

] [𝑑 𝑒𝑓 𝑔

] = [1 00 1

]

det 𝐴 = 𝑎𝑑 − 𝑏𝑐

𝐴−1 =1

det 𝐴[

𝑑 −𝑏−𝑐 𝑎

]

Student Work Area

1. What is the domain and range of the graph given below?

A. Domain: {𝑥|−5 < 𝑥 ≤ 6}

Range: {𝑦|−4 ≤ 𝑦 < 7}

B. Domain: {𝑥|−5 ≤ 𝑥 < 6}

Range: {𝑦|−4 < 𝑦 ≤ 7}

C. Domain: {𝑥|−4 ≤ 𝑥 < 7}

Range: {𝑦|−5 < 𝑦 ≤ 6}

D. Domain: {𝑥|−4 < 𝑥 ≤ 7}

Range: {𝑦|−5 ≤ 𝑦 < 6}

2. Describe the domain and range of the function graphed below.

A. Domain: [−4, 4)

Range: (−3, 2]

B. Domain: (−4, 4] Range: [−3, 2)

C. Domain: (−3, −1] Range: [−4, 4)

D. Domain: [−4, 4)

Range: (−3, −1]

3. Which graph represents the piecewise function?

𝑓(𝑥) = {

1

2𝑥 − 1, 𝑥 ≥ −3

−1

3𝑥 + 2, 𝑥 < −3

A.

C.

B.

D.

4. The table below shows the fees for renting a boat at the lake. What is the domain and

range of the function?

𝐻𝑜𝑢𝑟𝑠, 𝑥 0 < 𝑥 ≤ 2 2 < 𝑥 ≤ 4 4 < 𝑥 ≤ 8 8 < 𝑥 ≤ 10

𝐶𝑜𝑠𝑡, 𝑦 $350 $500 $800 $1000

A. 𝐷: {𝑥|0 < 𝑥 ≤ 10}

𝑅: {𝑦|350 ≤ 𝑦 ≤ 1000}

C. 𝐷: {0, 2, 4, 8, 10}

𝑅: {𝑦|350 ≤ 𝑦 ≤ 1000}

B. 𝐷: {𝑥|0 < 𝑥 ≤ 10}

𝑅: {350, 500, 800, 1000}

D. 𝐷: {0, 2, 4, 8, 10}

𝑅: {350, 500, 800, 1000}

5. Which of the following piecewise functions represents the graph below?

A. 𝑓(𝑥) = { 3

2𝑥 + 1, 𝑥 < −2

2𝑥 + 3, − 2 ≤ 𝑥 < 1−𝑥 + 2, 𝑥 ≥ 1

B. 𝑓(𝑥) = {−

3

2𝑥 + 1, 𝑥 < −2

2𝑥 + 3, − 2 ≤ 𝑥 < 1𝑥 + 2, 𝑥 ≥ 1

C. 𝑓(𝑥) = {−

3

2𝑥 + 1, 𝑥 ≤ −2

2𝑥 + 3, − 2 < 𝑥 ≤ 1𝑥 + 2, 𝑥 > 1

D. 𝑓(𝑥) = { 3

2𝑥 + 1, 𝑥 ≤ −2

2𝑥 + 3, − 2 < 𝑥 ≤ 1−𝑥 + 2, 𝑥 > 1

6. The graph of 𝑓(𝑥) is shown below. If 𝑔(𝑥) is the result of translating 𝑓(𝑥) up 5 units and

left 6 units, what is the equation of 𝑓(𝑥) ?

A. 𝑔(𝑥) = |𝑥 + 2| + 3

B. 𝑔(𝑥) = |𝑥 + 3| + 2

C. 𝑔(𝑥) = |𝑥 + 5| + 6

D. 𝑔(𝑥) = |𝑥 + 6| + 5

7. The function, 𝑓(𝑥), is graphed below. Which of the following statements are true? Select

all that apply.

F. 𝑓(𝑥) is increasing on the interval (−∞, ∞) .

G. 𝑓(𝑥) is increasing on the interval (− ∞, −3) .

H. 𝑓(𝑥) is increasing on the interval (−5, 1) .

I. 𝑓(𝑥) is decreasing on the interval (−∞, ∞) .

J. 𝑓(𝑥) is decreasing on the interval (−3, ∞) .

K. 𝑓(𝑥) is decreasing on the intervals (−∞, −5) and (− 1, ∞).

8. Given the graph below, which interval has the largest average rate of change?

A. [−14, 4]

B. [−10, 4]

C. [−8, 4]

D. [−2, 4]

9. Given 𝑓(𝑥) = 3𝑥2 − 6𝑥 + 5 and 𝑔(𝑥) = −3𝑥 + 23, complete the tables below to find

the x-values where 𝑓(𝑥) = 𝑔(𝑥).

𝑓(𝑥) = 3𝑥2 − 6𝑥 + 5

𝑥 𝑓(𝑥)

−3

−2

−1

0

1

2

3

4

5

6

7

𝑔(𝑥) = −3𝑥 + 23

𝑥 𝑔(𝑥)

−3

−2

−1

0

1

2

3

4

5

6

7

A. 𝑛𝑜 𝑠𝑜𝑙𝑢𝑡𝑖𝑜𝑛 C. 𝑥 = 0, 1, 2 ,6 ,7

B. 𝑥 = 14, 29 D. 𝑥 = −2, 3

10. Given the graph below, approximately when is −3

5𝑥2 + 5𝑥 + 8 < 0 ?

A. 𝑥 < −1.4 or 𝑥 > 9.7

B. −1.4 < 𝑥 < 9.7

C. 𝑥 < 8

D. 𝑥 > 8

11. Solve the following system for y:

{

𝑥 + 𝑦 + 𝑧 = 3−𝑥 + 𝑦 + 𝑧 = 5𝑥 + 2𝑦 − 3𝑧 = 2

A. 𝑦 = 15 C. 𝑦 = 3

B. 𝑦 = 4.6 D. 𝑦 = 2.5

12. Janessa want to get a pedicure and manicure for the homecoming dance. She sees the

following prices advertised at a salon.

Haircut and Manicure $52.00

Haircut and Pedicure $57.00

Haircut, Manicure, and Pedicure $84.00

Assume the price of each option is the same as purchasing each item separately. How

much will Janessa spend on a manicure and pedicure? Bubble your answer in the grid

below.

13. The matrix below represents the prices of backpacks and binders a company has in stock.

The backpacks and binders are offered in three different colors: red, yellow, and purple.

If the company has a 15% off sale, then which matrix shows the amount of the discount

for each item?

R Y P

Backpack [26 30 327 4 5

] Binder

A. [

3.90 30 321.05 4 5

] C. [25.85 30.85 31.85

7 4 5]

B. [3.90 4.50 4.801.05 0.60 0.75

] D. [25.85 30.85 31.856.85 3.85 4.85

]

14. If 𝑀 = [−3 69 10

], 𝑁 = [−1213

], and 𝑂 = [21 15

−17 21], then which of the following

statements is true?

A. 𝑁 − 𝑂 = [

−33 −2730 −8

] C. 𝑀 + 𝑂 = [18 24

−11 31]

B. 𝑀 + 𝑁 = [−15 −622 23

] D. 𝑂 − 𝑀 = [24 9

−26 11]

16.

Find the value of 𝑡 below:

[8 − 𝑡 0

8 −6] = [

−5 08 −4𝑦 + 2

]

Round your answer to the nearest tenth if needed. Bubble your answer in the grid below.

15. A segment with endpoints 𝐴(1, 6) and 𝐵(4, 5) can be represented by the matrix [1 46 5

].

Which of the following matrix operations will translate 𝐴𝐵̅̅ ̅̅ to the right 3 units and down

2 units?

A. [

1 46 5

] + [3 3

−2 −2] C. [

1 46 5

] + [3

−2]

B. [1 46 5

] + [3 −23 −2

] D. [1 46 5

] + [3 −2]

17. Find the product of 𝑋𝑌, given 𝑋 = [5 −2

−1 3] and 𝑌 = [

8 4−1 0

].

A. [

324

] C. [40 −81 0

]

B. [36 −4−5 2

] D. [42 20

−11 −4]

18. Teresa is given the matrices 𝐴 = [2 31 5

] and 𝐵 = [1 40 3

]. Teresa multiplied 𝐴𝐵 and 𝐵𝐴

to get 𝐴𝐵 = [2 171 19

] and 𝐵𝐴 = [6 233 15

]. Which statement below best describes

Teresa’s work?

A. Teresa’s work is incorrect because matrix multiplication is commutative.

B. Teresa’s work is correct because matrix multiplication is not commutative.

C. Teresa’s work is incorrect because matrix multiplication is not commutative.

D. Teresa’s work is correct because matrix multiplication is commutative.

19. Which of the following equations are true for the following matrices:

𝐴 = [−3 47 −9

] 𝑍 = [0 00 0

] 𝐼 = [1 00 1

]

Select all that apply.

F. 𝐴 ∙ 𝐼 = 𝐴

G. 𝐴 ∙ 𝑍 = 𝐴

H. 𝐴 + 𝐼 = 𝐴

I. 𝐴 + 𝑍 = 𝐴

J. 𝐴 ∙ 𝐼 = 𝑍

K. 𝐴 ∙ 𝑍 = 𝐼

20.

Find the value of det 𝑆, given 𝑆 = [

−2 −9−7 1

]

Round your answer to the nearest tenth if needed. Bubble your answer in the grid below.

21. A matrix equation is shown below:

[𝑎 𝑏𝑐 𝑑

] [ℎ 𝑖𝑗 𝑘

] = [1 00 1

]

Which of the following statements must be true?

A. 𝑎𝑏 − 𝑐𝑑 ≠ 0 C. 𝑎𝑏 − 𝑐𝑑 = 0

B. 𝑎𝑑 − 𝑏𝑐 = 0 D. 𝑎𝑑 − 𝑏𝑐 ≠ 0

22. Find the inverse of 𝑀 = [11 315 5

].

A. [

11

10

3

103

2

1

2

] C. [

1

2−

3

10

−3

2

11

10

]

B. [50 −30

−15 11] D. [

−11 −3−15 −5

]

23. Which matrix equation represents the system of equations below?

{4𝑥 − 14𝑦 + 3𝑧 = 17

5𝑦 − 12𝑧 = 106𝑥 − 11𝑧 = −22

A.

[4 −14 35 −12 06 −11 0

] [𝑥𝑦𝑧

] = [1710

−22]

B. [4 −14 35 −12 06 −11 0

] [1710

−22] = [

𝑥𝑦𝑧

]

C. [4 −14 30 5 −126 0 −11

] [𝑥𝑦𝑧

] = [1710

−22]

D. [4 −14 30 5 −126 0 −11

] [1710

−22] = [

𝑥𝑦𝑧

]

24. In the matrix equation below, 𝐶 represents the coefficient matrix and 𝐶−1 represents its

inverse matrix.

[5 7

10 5] [

𝑥𝑦] = [

330390

]

Which of the following statements are true? Select all that apply.

F. 𝐶−1 = [−

1

9

2

97

45−

1

9

]

G. 𝐶−1 = [−

1

9

7

452

9−

1

9

]

H. 𝐶−1 = [

1

9−

7

45

−2

9

1

9

]

I. 𝑥 = 24

J. 𝑥 = 30

K. 𝑥 = 50

26.

Compare the two functions represented below. Determine which of the following

statements is true.

Function 𝑓(𝑥) Function 𝑔(𝑥)

𝑔(𝑥) = (𝑥 − 6)2 − 4

A. The functions have the same vertex.

B. The minimum value of 𝑓(𝑥) is the same as the minimum value of 𝑔(𝑥).

C. The functions have the same axis of symmetry.

D. The minimum value of 𝑓(𝑥) is less than the minimum value of 𝑔(𝑥).

27. The graph of 𝑓(𝑥) = 𝑥2 is vertically compressed by a factor of 1

2 and translated to the

right three units and down one unit to produce the function 𝑔(𝑥). Which of the

following equations represents 𝑔(𝑥)?

A. 𝑔(𝑥) = −

1

2(𝑥 + 3)2 + 1 C. 𝑔(𝑥) =

1

2(𝑥 − 3)2 − 1

B. 𝑔(𝑥) = −1

2(𝑥 + 1)2 + 3 D. 𝑔(𝑥) =

1

2(𝑥 − 1)2 − 3

25. Every week, Milla buys bagels and donuts at a bakery. Last week, she bought 4 bagels

and 3 donuts for $5.55. This week she bought 5 bagels and 5 donuts for $8.00. The

systems of equations that represents this situation can be expressed using the matrix

equation below:

[4 35 5

] [𝑥𝑦] = [

5.558.00

]

What is the cost of a donut?

A. $0.75 C. $1.60

B. $0.85 D. $2.22

28. A parabola has a vertex of (5, 6) and passes through the point (10, −4). In the

𝑦 = 𝑎(𝑥 − ℎ)2 + 𝑘 form of the parabola, what is the value of 𝑎 ?

A. −2 C. −

2

5

B. 2

5 D. −

2

45

30. Translate 𝑦 = 𝑥2 − 4𝑥 + 6 five units to the left. What is the graph obtained after the

translation?

A.

C.

B.

D.

29. Which of the following statements describe key features of 𝑓(𝑥) = 𝑥2 + 2𝑥 + 7 ?

Select all that apply.

F. The y-intercept is (0, 7).

G. The y-intercept is (0, 2).

H. The vertex is (−1, 6).

I. The vertex is (2, 7).

J. The minimum is 𝑦 = 6.

K. The minimum is 𝑦 = 7.

L. The axis of symmetry is 𝑥 = −1.

M. The axis of symmetry is 𝑥 = 2.

31. Which of the following systems of equations could a student use to write a quadratic

function in standard form for the parabola passing through the points (1, −3), (4, 6), and (5, 9)?

A. {

𝑥2 − 3𝑥 + 𝑐 = 𝑦

4𝑥2 + 6𝑥 + 𝑐 = 𝑦

5𝑥2 + 9𝑥 + 𝑐 = 𝑦

C. {

𝑎 − 3𝑏 + 𝑐 = 𝑦16𝑎 + 6𝑏 + 𝑐 = 𝑦25𝑎 + 9𝑏 + 𝑐 = 𝑦

B. {2𝑎 + 𝑏 + 𝑐 = −38𝑎 + 4𝑏 + 𝑐 = 6

10𝑎 + 5𝑏 + 𝑐 = 9 D. {

𝑎 + 𝑏 + 𝑐 = −316𝑎 + 4𝑏 + 𝑐 = 625𝑎 + 5𝑏 + 𝑐 = 9

32. Which of following functions does not represent the parabola with a vertex at (1, 4) and

x-intercepts (−1, 0) and (3, 0).

A. 𝑓(𝑥) = −(𝑥 − 1)2 + 4 C. 𝑓(𝑥) = −𝑥2 + 2𝑥 + 3

B. 𝑓(𝑥) = −𝑥2 + 𝑥 + 4 D. 𝑓(𝑥) = −(𝑥 + 1)(𝑥 − 3)

33. Identify the interval(s) on which the function 𝑓(𝑥) = 𝑥2 − 𝑥 − 6 is positive.

A. 𝑥 < −2 and 𝑥 > 3 C. −2 < 𝑥 < 3

B. 𝑥 < −3 and 𝑥 > 2 D. −3 < 𝑥 < 2

34. A parabola has x-intercepts at 2 and 6 and goes through the point (8, 4). What other

point is on the parabola?

A. (−2, −2) C. (−3, 15)

B. (4, −2) D. (1, 15)

35. Simplify: (11 + 𝑖) + (3 − 15𝑖)

A. 14 − 14𝑖 C. 12 − 12𝑖

B. −4 + 4𝑖 D. 14 + 16𝑖

36. Simplify: (3 − 7𝑖)2

A. −40 + 0𝑖 C. 58 + 0𝑖

B. −40 − 42𝑖 D. 58 − 42𝑖

37. Simplify: 6+2𝑖

2−𝑖

A. 2 + 2𝑖 C.

6 + 2𝑖

2 − 𝑖

B. 2 + 3𝑖 D. 10 + 10𝑖

38. Which of the following functions is equivalent to 𝑓(𝑥) =1

2𝑥2 + 6𝑥 + 11 ?

A. 𝑔(𝑥) =1

2(𝑥 + 6)2 + 11 C. 𝑔(𝑥) =

1

2(𝑥 + 6)2 − 7

B. 𝑔(𝑥) =1

2(𝑥 + 6)2 + 22 D. 𝑔(𝑥) =

1

2(𝑥 + 6)2 − 14

39. If (𝑥 + 3)(𝑥 − 9) = (𝑥 − ℎ)2 + 𝑘, then what is the value of 𝑘 ?

A. 𝑘 = −36 C. 𝑘 = −18

B. 𝑘 = −27 D. 𝑘 = 9

40. Solve the following equation: 1

6(𝑥 + 5)2 = 8

A. 𝑥 = ±√23 C. 𝑥 = −5 ±

2√3

3

B. 𝑥 = ±√43 D. 𝑥 = −5 ± 4√3

41. What are the solutions to the quadratic equation, 3𝑥2 + 7𝑥 + 11 = 5𝑥 + 7?

A. 𝑥 =

−2 ± 2𝑖√11

3 C. 𝑥 =

−1 ± 𝑖√11

3

B. 𝑥 =−1 ± 2𝑖√11

3 D. 𝑥 =

±𝑖√11

3

42. The function 𝑓(𝑥) is graphed below. What are the solutions to 𝑓(𝑥) = 0?

A. 𝑥 = −4 ± 2𝑖

B. 𝑥 = 4 ± 𝑖

C. 𝑥 = −8, 0

D. 𝑥 = 3, 5

43.

A local business wants to expand the size of their rectangular parking lot that currently

measures 120 𝑓𝑡 by 200 𝑓𝑡. The project will cost less if equal amounts are added to

each side, as shown below. Zoning restrictions limit the total size of the parking lot to

35,000 𝑓𝑡2. What is the maximum amount of distance (𝑥) that can be added on to the

each side of the parking lot? Round your answer to the nearest foot. Bubble your answer

in the grid provided below.

44. What are the x-coordinates of the solution for the system given below?

{𝑥2 + 10𝑥 + 6𝑦 + 8 = 13

2𝑥 + 3𝑦 = 7

A. 𝑥 = 2 𝑎𝑛𝑑 𝑥 = 4 C. 𝑥 = −3 𝑎𝑛𝑑 𝑥 = 3

B. 𝑥 = −4 𝑎𝑛𝑑 𝑥 = −2 D. 𝑥 = −3

45. Two rockets are launched from the same point and at the same time. Rocket A’s path is

modeled by the equation ℎ = −1

4𝑡2 + 8𝑡, where ℎ is the height and 𝑡 is the time.

Rocket B’s path is modeled by the equation ℎ =3

4𝑡. When will the rockets collide?

Round your answer to the nearest tenth if necessary.

46. Graph the system {𝑦 ≥ −(𝑥 − 2)2 + 6

𝑦 ≥ −3𝑥 + 7

A.

C.

B.

D.

47. The function 𝑓(𝑥) =1

2𝑥3 +

1

4𝑥2 −

15

4𝑥 is graphed to

the right. Over which intervals of x is the graph

positive?

A.

B.

C.

D.

48. Which of the following functions has the same end behavior as the function below?

A. 𝑔(𝑥) = −6𝑥 − 7 C. 𝑔(𝑥) = 𝑥2 − 4𝑥 + 5

B. 𝑔(𝑥) = −|𝑥 + 3| − 5 D. 𝑔(𝑥) = 𝑥3 + 2𝑥

49. State where the function is increasing and decreasing.

A. Never Increasing

Decreasing: (−∞, +∞)

B. Increasing: (−8, 0) ∪ (0, + ∞)

Decreasing: (−∞, −8)

C. Increasing: (−∞, −8) ∪ (0, 8)

Decreasing: (−8, 0)

D. Increasing: (−8, −4) ∪ (0, +∞)

Decreasing: (−∞, −8) ∪ (−4, 0)

50.

Which expression must be subtracted from (4𝑥3 − 5𝑥2 + 6𝑥 − 3) to result in

(6𝑥3 − 2𝑥2 + 4𝑥 + 7) ?

A. −2𝑥3 − 3𝑥2 + 2𝑥 − 10 C. −2𝑥3 − 7𝑥2 + 10𝑥 + 4

B. 2𝑥3 + 3𝑥2 − 2𝑥 + 10 D. 2𝑥3 − 7𝑥2 + 10𝑥 + 4

51. Find the product: (𝑥 − 1)(𝑥 + 5)(𝑥 − 3)

A. 𝑥3 + 15 C. 𝑥3 − 3𝑥2 − 13𝑥 − 15

B. 𝑥3 + 𝑥2 − 17𝑥 + 15 D. 𝑥3 + 7𝑥2 − 7𝑥 + 15

52. A manufacturer is going to package their product in an open rectangular box made from

a single flat piece of cardboard. The box will be created by cutting a square out from

each corner of the rectangle and folding the flaps up to create a box. The original

rectangular piece of cardboard is 20 𝑖𝑛𝑐ℎ𝑒𝑠 long and 15 𝑖𝑛𝑐ℎ𝑒𝑠 wide. Write a function

that represents the volume of the box.

A. 𝑉(𝑥) = 𝑥3 − 35𝑥2 + 300𝑥 C. 𝑉(𝑥) = 𝑥2 − 35𝑥 + 300

B. 𝑉(𝑥) = 4𝑥3 − 70𝑥2 + 300𝑥 D. 𝑉(𝑥) = 4𝑥2 − 70𝑥 + 300

53. Factor completely: 𝑥4 − 13𝑥2 + 36

A. (𝑥2 − 9)(𝑥2 + 4) C. (𝑥 − 3)(𝑥 + 3)(𝑥 + 2)2

B. (𝑥 − 3)(𝑥 + 3)(𝑥 + 4)(𝑥 − 4) D. (𝑥 − 3)(𝑥 + 3)(𝑥 + 2)(𝑥 − 2)

54. Factor completely: 64𝑥3 − 27

A. (4𝑥 − 3)(4𝑥2 + 12𝑥 + 9) C. (4𝑥 − 3)(16𝑥2 + 12𝑥 + 9)

B. (4𝑥 − 3)(4𝑥2 + 12𝑥 − 9) D. (4𝑥 − 3)(16𝑥2 − 12𝑥 − 9)

55. If (𝑎 + 𝑏)2 = 𝑎2 + 2𝑎𝑏 + 𝑏2, then which expression is equivalent to (4𝑥2 + 6𝑦4)2 ?

A. 2(4𝑥2) + 2(4𝑥2)(6𝑦4) + 2(6𝑦4) C. (4𝑥2)2 + 2(4𝑥2)(6𝑦4) + (6𝑦4)2

B. 4𝑥2(2) + 2(4)(6) + 6𝑦4(2) D. 4𝑥2 + 2(4)(6) + 6𝑦2

56. What is the remainder in the division (−4𝑥3 + 80𝑥 − 150) ÷ (𝑥 − 5)?

57. Use synthetic or long division to find the quotient of (2𝑥2 − 33𝑥 + 16) ÷ (𝑥 − 16)?

A. 2𝑥 − 33 +

16

𝑥 − 16 C. 2𝑥 − 1 +

−32

𝑥 − 16

B. 2𝑥 − 1 D. 2𝑥 + 1

58. Given (𝑥 − 9) is a factor of the polynomial, 𝑓(𝑥) = 16𝑥3 − 144𝑥2 − 81𝑥 + 729, what

are the remaining factors?

A. (4𝑥 − 9)(4𝑥 + 9) C. (4𝑥 − 9)

B. (16𝑥2 + 81) D. (4𝑥 − 9)(4𝑥 − 9)

59. Which polynomial is graphed below?

A. 𝑓(𝑥) = (𝑥 + 1)(𝑥 − 3)

B. 𝑓(𝑥) = (𝑥 − 1)(𝑥 + 1)(𝑥 + 3)

C. 𝑓(𝑥) = 𝑥(𝑥 + 3)(𝑥 − 1)

D. 𝑓(𝑥) = 𝑥(𝑥 − 3)(𝑥 + 1)

60. The equation 𝑥3 − 3𝑥2 + 4𝑥 − 12 = 0 is graphed below. Use the graph to help solve

the equation and find all the roots of the function.

A. 𝑥 = 3, −2, 2

B. 𝑥 = −12, 1, 3

C. 𝑥 = 3, −2𝑖, 2𝑖

D. 𝑥 = 12,3 − 𝑖√7

2,3 + 𝑖√7

2

61. What is the end behavior for the function, 𝑓(𝑥) = (𝑥2 + 4𝑥 − 3)(3𝑥5 + 6𝑥3)?

A. as 𝑥 → −∞, 𝑓(𝑥) → −∞ and as 𝑥 → +∞, 𝑓(𝑥) → +∞

B. as 𝑥 → −∞, 𝑓(𝑥) → +∞ and as 𝑥 → +∞, 𝑓(𝑥) → +∞

C. as 𝑥 → −∞, 𝑓(𝑥) → −∞ and as 𝑥 → +∞, 𝑓(𝑥) → −∞

D. as 𝑥 → −∞, 𝑓(𝑥) → +∞ and as 𝑥 → +∞, 𝑓(𝑥) → −∞

62. Solve: 3𝑚3 − 2𝑚2 − 5𝑚 = 0

A. 𝑚 = −1, 𝑚 = 0, 𝑚 =

5

3 C. 𝑚 = −

5

3, 𝑚 = 0, 𝑚 = 1

B. 𝑚 = −3, 𝑚 = 0, 𝑚 = 5 D. 𝑚 = −5, 𝑚 = 0, 𝑚 = 3

63. Solve: 𝑥4 − 3𝑥2 = 10

A. 𝑥 = 5, 𝑥 = −2 C. 𝑥 = ±√5, 𝑥 = ±√2

B. 𝑥 = ±5, 𝑥 = ±2𝑖 D. 𝑥 = ±√5, 𝑥 = ±𝑖√2

64. Write the equation of a cubic function with rational coefficients that has zeros

of −4 and 3 − √5.

A. 𝑥3 − (3 + √5)𝑥2 − 16𝑥 + 48 + 16√5

B. 𝑥4 − 6𝑥3 − 12𝑥2 + 96𝑥 − 64

C. 𝑥3 − 2𝑥2 − 20𝑥 + 16

D. 𝑥2 + (1 − √5)𝑥 − 12 + 4√5

65. Given the two functions:

𝑓(𝑥) = (𝑥 + 1)(𝑥 − 4)(𝑥 + 5)

𝑔(𝑥) = 2 ∙ 𝑓(𝑥)

Determine which of the following statements is correct.

A. The function 𝑔(𝑥) has exactly one zero.

B. The function 𝑔(𝑥) has exactly six zeros.

C. The function 𝑔(𝑥) has zeros at 𝑥 = −5, −1, 4.

D. The function 𝑔(𝑥) has zeros at 𝑥 − 10, −2, 8.

66. Which of the following functions is odd?

A. 𝑓(𝑥) = 12𝑥5 − 4𝑥2 + 3 C. 𝑓(𝑥) = −𝑥6 + 3

B.

D.

Algebra 2 Semester 1

Instructional Materials 2019-20 Answers

Topic 1

Linear

Functions &

Systems

Topic 10

Matrices

Topic 2

Quadratic

Functions &

Equations

Topic 3

Polynomial Functions

1. A 13. B 26. B 47. A

2. A 14. D 27. C 48. B

3. C 15. A 28. C 49. D

4. B 16. 13 29. F, H, J, L 50. A

5. A 17. D 30. A 51. B

6. A 18. B 31. D 52. B

7. G, J 19. F, I 32. B 53. D

8. D 20. −65 33. A 54. C

9. D 21. D 34. C 55. C

10. A 22. C 35. A 56. −250

11. C 23. C 36. B 57. B

12. 59.00 24. G, I 37. A 58. A

25. B 38. C 59. D

39. A 60. C

40. D 61. A

41. C 62. A

42. A 63. D

43. 31 64. C

44. D 65. C

45. 29 66. B

46. B