Algebra 2 Final Multiple Choice Identify the choice that best completes the statement or answers the question. ____ 1. Find the determinant of . a. –152 c. 152 b. 676 d. –50 ____ 2. Write a quadratic function in standard form with zeros 7 and –3. a. c. b. d. ____ 3. Use Pascal’s Triangle to expand the expression . a. b. c. d. ____ 4. Find the intercepts of , and graph the line. a. x-intercept: –4, y-intercept: 4 246810–2–4–6–8–10x 2 4 6 8 10 –2 –4 –6 –8 –10 y c. x-intercept: 3 , y-intercept: 3 246810–2–4–6–8–10x 2 4 6 8 10 –2 –4 –6 –8 –10 y b. x-intercept: 3 , y-intercept: 4 246810–2–4–6–8–10x 2 4 6 8 10 –2 –4 –6 –8 –10 y d. x-intercept: –4, y-intercept: 3 246810–2–4–6–8–10x 2 4 6 8 10 –2 –4 –6 –8 –10 y ____ 5. Write the set in set-builder notation. 024680–2–4–6–8x a. [–2, 4) c. b. d. [–2, 4] ____ 6. Graph . a. 2468–2–4–6–8–10x 2 4 6 8 10 –2 –4 –6 –8 –10 y c. 2468–2–4–6–8–10x 2 4 6 8 10 –2 –4 –6 –8 –10 y b. 2468–2–4–6–8–10x 2 4 6 8 10 –2 –4 –6 –8 –10 y d. 2468–2–4–6–8–10x 2 4 6 8 10 –2 –4 –6 –8 –10 y ____ 7. Graph the line with slope 1 that passes through (–6, 0). a. 3691215–3–6–9–12–15x 3 6 9 12 15 –3 –6 –9 –12 –15 y c. 3691215–3–6–9–12–15x 3 6 9 12 15 –3 –6 –9 –12 –15 y b. 3691215–3–6–9–12–15x 3 6 9 12 15 –3 –6 –9 –12 –15 y d. 3691215–3–6–9–12–15x 3 6 9 12 15 –3 –6 –9 –12 –15 y ____ 8. Determine whether the binomial () is a factor of the polynomial . a. () is not a factor of the polynomial . b. Cannot determine. c. () is a factor of the polynomial . ____ 9. Use Cramer’s rule to solve the system of equations. a. (–22, 37) c. (–37, 22) b. (40, 34) d. (–74, 44) ____ 10. Solve . a. c. b. d. ____ 11. In slope-intercept form, write the equation of the line that is parallel to y = –5x + 23 and passes through (4, 5). a. y = 1 5x 4 1 5 c. y = –5x + 25 b. y = –5x + 22 d. y =  1 5x 5 4 5 ____ 12. Find the absolute value . a. 9 c. 3 b. 53 d. 35 ____ 13. Translate so that the vertex is at (3, –6). Then graph. a. 2468–2–4–6–8–10x 2 4 6 8 10 –2 –4 –6 –8 –10 y c. 2468–2–4–6–8–10x 2 4 6 8 10 –2 –4 –6 –8 –10 y b. 2468–2–4–6–8–10x 2 4 6 8 10 –2 –4 –6 –8 –10 y d. 2468–2–4–6–8–10x 2 4 6 8 10 –2 –4 –6 –8 –10 y ____ 14. Write the augmented matrix for , and solve. Round your answer to the nearest tenth. a. ; , c. ; , b. ; , d. ; , ____ 15. Solve the equation by completing the square. a. x = 10 or x = –18 c. x = 7 or x = –7 b. x = –5 or x = 9 d. x = 5 or x = –9 ____ 16. Identify the zeros and asymptotes of . Then graph. a. Zeros: and 3 Vertical asymptotes: , Horizontal asymptote: 24681012–2–4–6–8–10–12x 2 4 6 8 10 12 –2 –4 –6 –8 –10 –12 y c. Zeros: and 3 Vertical asymptotes: , Horizontal asymptote: 24681012–2–4–6–8–10–12x 2 4 6 8 10 12 –2 –4 –6 –8 –10 –12 y b. Zeros: and 2 Vertical asymptotes: , Horizontal asymptote: 24681012–2–4–6–8–10–12x 2 4 6 8 10 12 –2 –4 –6 –8 –10 –12 y d. Zeros: and 2 Vertical asymptotes: , Horizontal asymptote: 246.

1. Algebra 2 Final
Multiple Choice
Identify the choice that best completes the statement or answers
the question.
____
1.
Find the determinant of .
a.
–152
c.
152
b.
676
d.
–50
____
2.
Write a quadratic function in standard form with zeros 7 and –3.
a.
c.
b.
d.
____
3.
Use Pascal’s Triangle to expand the expression .
a.

2. b.
c.
d.
____
4.
Find the intercepts of , and graph the line.
a.
x-intercept: –4, y-intercept: 4
246810–2–4–6–8–10x
2
4
6
8
10
–2
–4
–6
–8
–10
y
c.
x-intercept:
, y-intercept:
3
246810–2–4–6–8–10x

3. 2
4
6
8
10
–2
–4
–6
–8
–10
y
b.
x-intercept:
, y-intercept: 4
246810–2–4–6–8–10x
2
4
6
8
10
–2
–4
–6
–8
–10
y
d.
x-intercept: –4, y-intercept:
3

4. 246810–2–4–6–8–10x
2
4
6
8
10
–2
–4
–6
–8
–10
y
____
5.
Write the set in set-builder notation.
024680–2–4–6–8x
a.
[–2, 4)
c.
b.
d.
[–2, 4]
____
6.
Graph .
a.

5. 2468–2–4–6–8–10x
2
4
6
8
10
–2
–4
–6
–8
–10
y
c.
2468–2–4–6–8–10x
2
4
6
8
10
–2
–4
–6
–8
–10
y
b.
2468–2–4–6–8–10x
2
4
6
8
10

6. –2
–4
–6
–8
–10
y
d.
2468–2–4–6–8–10x
2
4
6
8
10
–2
–4
–6
–8
–10
y
____
7.
Graph the line with slope
1
that passes through (–6, 0).
a.
3691215–3–6–9–12–15x
3
6
9

7. 12
15
–3
–6
–9
–12
–15
y
c.
3691215–3–6–9–12–15x
3
6
9
12
15
–3
–6
–9
–12
–15
y
b.
3691215–3–6–9–12–15x
3
6
9
12
15
–3
–6
–9
–12

8. –15
y
d.
3691215–3–6–9–12–15x
3
6
9
12
15
–3
–6
–9
–12
–15
y
____
8.
Determine whether the binomial () is a factor of the polynomial
.
a.
() is not a factor of the polynomial .
b.
Cannot determine.
c.
() is a factor of the polynomial .
____
9.
Use Cramer’s rule to solve the system of equations.
a.
(–22, 37)

9. c.
(–37, 22)
b.
(40, 34)
d.
(–74, 44)
____
10.
Solve .
a.
c.
b.
d.
____
11.
In slope-intercept form, write the equation of the line that is
parallel to y = –5x + 23 and passes through (4, 5).
a.
y =
1
5x
1
5
c.
y = –5x + 25
b.
y = –5x + 22
d.

10. y =
1
5x
4
5
____
12.
Find the absolute value .
a.
9
c.
3
b.
53
d.
35
____
13.
Translate so that the vertex is at (3, –6). Then graph.
a.
2468–2–4–6–8–10x
2
4

11. 6
8
10
–2
–4
–6
–8
–10
y
c.
2468–2–4–6–8–10x
2
4
6
8
10
–2
–4
–6
–8
–10
y
b.
2468–2–4–6–8–10x
2
4
6
8
10
–2

12. –4
–6
–8
–10
y
d.
2468–2–4–6–8–10x
2
4
6
8
10
–2
–4
–6
–8
–10
y
____
14.
Write the augmented matrix for , and solve. Round your answer
to the nearest tenth.
a.
; ,
c.
; ,
b.
; ,
d.
; ,
____

13. 15.
Solve the equation by completing the square.
a.
x = 10 or x = –18
c.
x = 7 or x = –7
b.
x = –5 or x = 9
d.
x = 5 or x = –9
____
16.
Identify the zeros and asymptotes of . Then graph.
a.
Zeros: and 3
Vertical asymptotes: ,
Horizontal asymptote:
24681012–2–4–6–8–10–12x
2
4
6
8
10
12
–2
–4
–6
–8
–10
–12
y

14. c.
Zeros: and 3
Vertical asymptotes: ,
Horizontal asymptote:
24681012–2–4–6–8–10–12x
2
4
6
8
10
12
–2
–4
–6
–8
–10
–12
y
b.
Zeros: and 2
Vertical asymptotes: ,
Horizontal asymptote:
24681012–2–4–6–8–10–12x
2
4
6
8
10
12
–2
–4

15. –6
–8
–10
–12
y
d.
Zeros: and 2
Vertical asymptotes: ,
Horizontal asymptote:
24681012–2–4–6–8–10–12x
2
4
6
8
10
12
–2
–4
–6
–8
–10
–12
y
____
17.
Identify the degree of the monomial .
a.
4
c.
6
b.

16. 2
d.
–2
____
18.
Graph the function .
a.
123456–1–2–3–4–5–6x
1
2
3
4
5
6
–1
–2
–3
–4
–5
–6
y
c.
123456–1–2–3–4–5–6x
1
2
3
4
5
6
–1
–2
–3

17. –4
–5
–6
y
b.
123456–1–2–3–4–5–6x
1
2
3
4
5
6
–1
–2
–3
–4
–5
–6
y
d.
123456–1–2–3–4–5–6x
1
2
3
4
5
6
–1
–2
–3
–4
–5

18. –6
y
____
19.
Simplify the expression . Assume that all variables are positive.
a.
c.
b.
d.
____
20.
Find the zeros of the function by factoring.
a.
or
c.
or
b.
or
d.
or
____
21.
The parent function is reflected across the x-axis, vertically
stretched by a factor of 4, and translated right 9 units to create
g. Use the description to write the quadratic function in vertex
form.
a.

19. c.
b.
d.
____
22.
Solve the equation .
a.
c.
b.
d.
____
23.
Solve the compound inequality. Then graph the solution set.
and
a.
{s | –
0123456789100–1–2–3–4–5–6–7–8–9–10s
b.
–
0123456789100–1–2–3–4–5–6–7–8–9–10s
c.

20. {s | –
0123456789100–1–2–3–4–5–6–7–8–9–10s
d.
–
0123456789100–1–2–3–4–5–6–7–8–9–10s
____
24.
Simplify . Identify any x-values for which the expression is
undefined.
a.
The expression is undefined at .
b.
The expression is undefined at and .
c.
The expression is undefined at and .
d.
The expression is undefined at .
____
25.
Determine whether the data in the table are linear. Explain.
Session Length (min)
1
8
15

21. 22
30
Cost ($)
1.60
4.05
6.50
8.95
12.80
a.
No, the rate of change is not constant. For example, to the
nearest hundredth, and .
b.
Yes, the difference between successive session lengths is
constant. For example, , , and so on.
c.
Yes, the rate of change is constant. For example, , , and so on.
d.
No, the ratio of the cost to the session length is not constant.
For example, to the nearest hundredth, and .
____
26.
Solve the equation .
a.
There is no solution.
c.
b.
3
2
d.
____
27.

22. Identify the property demonstrated by the equation 4 + (5 + 8) =
(4 + 5) + 8.
a.
Distributive Property
c.
Commutative Property
b.
Closure Property
d.
Associative Property
____
28.
Solve . Check your answer.
a.
b.
c.
d.
There is no solution because the original equation is undefined
at .
____
29.
Simplify the expression .
a.
c.
16
25
b.

23. d.
4
5
____
30.
Use elimination to solve the system .
a.
(6, –2)
c.
(–2, 6)
b.
(–8, –15)
d.
(–6, –8)
____
31.
Solve the equation .
a.
x = 23
c.
x = 13
b.
x= 23 or x = –7
d.
x = 13 or x = 3
____
32.
Express as a single logarithm. Simplify, if possible.
a.

24. c.
6
b.
729
d.
____
33.
A sawyer (person who cuts down trees) wants to know the
height of a tree. The sawyer measures the shadow of his friend,
who is 5 feet tall and standing beside the tree, and measures the
shadow of the tree. If his friend’s shadow is 12 feet long and
the tree’s shadow is 60 feet long, how tall is the tree?
a.
144 feet
c.
25 feet
b.
1 foot
d.
53 feet
____
34.
Which function is vertically stretched by a factor of 5 and
translated 6 units right from the parent function?
a.
c.
b.
d.
____

25. 35.
Order the numbers 4,
1
8
, , 0.6632, from least to greatest.
a.
1
8
, 0.6632, , , 4
c.
, 4, , 0.6632,
1
8
b.
4,
1
8
, , 0.6632,
d.
1
8

26. , 0.6632, , 4,
Algebra 2 Final
Multiple Choice
Identify the choice that best completes the statement or answers
the question.
____
1.
Find the determinant of .
a.
–152
c.
152
b.
676
d.
–50
____
2.
Write a quadratic function in standard form with zeros 7 and –3.
a.
c.
b.
d.
____
3.
Use Pascal’s Triangle to expand the expression .

27. a.
b.
c.
d.
____
4.
Find the intercepts of , and graph the line.
a.
x-intercept: –4, y-intercept: 4
246810–2–4–6–8–10x
2
4
6
8
10
–2
–4
–6
–8
–10
y
c.
x-intercept:
, y-intercept:
3

28. 246810–2–4–6–8–10x
2
4
6
8
10
–2
–4
–6
–8
–10
y
b.
x-intercept:
, y-intercept: 4
246810–2–4–6–8–10x
2
4
6
8
10
–2
–4
–6
–8
–10
y
d.

29. x-intercept: –4, y-intercept:
3
246810–2–4–6–8–10x
2
4
6
8
10
–2
–4
–6
–8
–10
y
____
5.
Write the set in set-builder notation.
024680–2–4–6–8x
a.
[–2, 4)
c.
b.
d.
[–2, 4]
____
6.
Graph .

30. a.
2468–2–4–6–8–10x
2
4
6
8
10
–2
–4
–6
–8
–10
y
c.
2468–2–4–6–8–10x
2
4
6
8
10
–2
–4
–6
–8
–10
y
b.
2468–2–4–6–8–10x
2
4
6

31. 8
10
–2
–4
–6
–8
–10
y
d.
2468–2–4–6–8–10x
2
4
6
8
10
–2
–4
–6
–8
–10
y
____
7.
Graph the line with slope
1
that passes through (–6, 0).
a.
3691215–3–6–9–12–15x
3

32. 6
9
12
15
–3
–6
–9
–12
–15
y
c.
3691215–3–6–9–12–15x
3
6
9
12
15
–3
–6
–9
–12
–15
y
b.
3691215–3–6–9–12–15x
3
6
9
12
15
–3
–6

33. –9
–12
–15
y
d.
3691215–3–6–9–12–15x
3
6
9
12
15
–3
–6
–9
–12
–15
y
____
8.
Determine whether the binomial () is a factor of the polynomial
.
a.
() is not a factor of the polynomial .
b.
Cannot determine.
c.
() is a factor of the polynomial .
____
9.
Use Cramer’s rule to solve the system of equations.

34. a.
(–22, 37)
c.
(–37, 22)
b.
(40, 34)
d.
(–74, 44)
____
10.
Solve .
a.
c.
b.
d.
____
11.
In slope-intercept form, write the equation of the line that is
parallel to y = –5x + 23 and passes through (4, 5).
a.
y =
1
5x
1
5
c.
y = –5x + 25
b.

35. y = –5x + 22
d.
y =
1
5x
4
5
____
12.
Find the absolute value .
a.
9
c.
3
b.
53
d.
35
____
13.
Translate so that the vertex is at (3, –6). Then graph.
a.
2468–2–4–6–8–10x

36. 2
4
6
8
10
–2
–4
–6
–8
–10
y
c.
2468–2–4–6–8–10x
2
4
6
8
10
–2
–4
–6
–8
–10
y
b.
2468–2–4–6–8–10x
2
4
6
8

37. 10
–2
–4
–6
–8
–10
y
d.
2468–2–4–6–8–10x
2
4
6
8
10
–2
–4
–6
–8
–10
y
____
14.
Write the augmented matrix for , and solve. Round your answer
to the nearest tenth.
a.
; ,
c.
; ,
b.
; ,
d.

38. ; ,
____
15.
Solve the equation by completing the square.
a.
x = 10 or x = –18
c.
x = 7 or x = –7
b.
x = –5 or x = 9
d.
x = 5 or x = –9
____
16.
Identify the zeros and asymptotes of . Then graph.
a.
Zeros: and 3
Vertical asymptotes: ,
Horizontal asymptote:
24681012–2–4–6–8–10–12x
2
4
6
8
10
12
–2
–4
–6
–8
–10
–12

39. y
c.
Zeros: and 3
Vertical asymptotes: ,
Horizontal asymptote:
24681012–2–4–6–8–10–12x
2
4
6
8
10
12
–2
–4
–6
–8
–10
–12
y
b.
Zeros: and 2
Vertical asymptotes: ,
Horizontal asymptote:
24681012–2–4–6–8–10–12x
2
4
6
8
10
12

40. –2
–4
–6
–8
–10
–12
y
d.
Zeros: and 2
Vertical asymptotes: ,
Horizontal asymptote:
24681012–2–4–6–8–10–12x
2
4
6
8
10
12
–2
–4
–6
–8
–10
–12
y
____
17.
Identify the degree of the monomial .
a.
4
c.

41. 6
b.
2
d.
–2
____
18.
Graph the function .
a.
123456–1–2–3–4–5–6x
1
2
3
4
5
6
–1
–2
–3
–4
–5
–6
y
c.
123456–1–2–3–4–5–6x
1
2
3
4
5
6
–1

42. –2
–3
–4
–5
–6
y
b.
123456–1–2–3–4–5–6x
1
2
3
4
5
6
–1
–2
–3
–4
–5
–6
y
d.
123456–1–2–3–4–5–6x
1
2
3
4
5
6
–1
–2
–3

43. –4
–5
–6
y
____
19.
Simplify the expression . Assume that all variables are positive.
a.
c.
b.
d.
____
20.
Find the zeros of the function by factoring.
a.
or
c.
or
b.
or
d.
or
____
21.
The parent function is reflected across the x-axis, vertically
stretched by a factor of 4, and translated right 9 units to create
g. Use the description to write the quadratic function in vertex
form.

44. a.
c.
b.
d.
____
22.
Solve the equation .
a.
c.
b.
d.
____
23.
Solve the compound inequality. Then graph the solution set.
and
a.
{s | –
0123456789100–1–2–3–4–5–6–7–8–9–10s
b.
–
0123456789100–1–2–3–4–5–6–7–8–9–10s

45. c.
{s | –
0123456789100–1–2–3–4–5–6–7–8–9–10s
d.
–
0123456789100–1–2–3–4–5–6–7–8–9–10s
____
24.
Simplify . Identify any x-values for which the expression is
undefined.
a.
The expression is undefined at .
b.
The expression is undefined at and .
c.
The expression is undefined at and .
d.
The expression is undefined at .
____
25.
Determine whether the data in the table are linear. Explain.
Session Length (min)
1

46. 8
15
22
30
Cost ($)
1.60
4.05
6.50
8.95
12.80
a.
No, the rate of change is not constant. For example, to the
nearest hundredth, and .
b.
Yes, the difference between successive session lengths is
constant. For example, , , and so on.
c.
Yes, the rate of change is constant. For example, , , and so on.
d.
No, the ratio of the cost to the session length is not constant.
For example, to the nearest hundredth, and .
____
26.
Solve the equation .
a.
There is no solution.
c.
b.
3
2
d.

47. ____
27.
Identify the property demonstrated by the equation 4 + (5 + 8) =
(4 + 5) + 8.
a.
Distributive Property
c.
Commutative Property
b.
Closure Property
d.
Associative Property
____
28.
Solve . Check your answer.
a.
b.
c.
d.
There is no solution because the original equation is undefined
at .
____
29.
Simplify the expression .
a.
c.
16
25

48. b.
d.
4
5
____
30.
Use elimination to solve the system .
a.
(6, –2)
c.
(–2, 6)
b.
(–8, –15)
d.
(–6, –8)
____
31.
Solve the equation .
a.
x = 23
c.
x = 13
b.
x= 23 or x = –7
d.
x = 13 or x = 3
____
32.
Express as a single logarithm. Simplify, if possible.

49. a.
c.
6
b.
729
d.
____
33.
A sawyer (person who cuts down trees) wants to know the
height of a tree. The sawyer measures the shadow of his friend,
who is 5 feet tall and standing beside the tree, and measures the
shadow of the tree. If his friend’s shadow is 12 feet long and
the tree’s shadow is 60 feet long, how tall is the tree?
a.
144 feet
c.
25 feet
b.
1 foot
d.
53 feet
____
34.
Which function is vertically stretched by a factor of 5 and
translated 6 units right from the parent function?
a.
c.
b.
d.

50. ____
35.
Order the numbers 4,
1
8
, , 0.6632, from least to greatest.
a.
1
8
, 0.6632, , , 4
c.
, 4, , 0.6632,
1
8
b.
4,
1
8
, , 0.6632,
d.

51. 1
8
, 0.6632, , 4,