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. |
( |
b. |
Cannot determine. |
c. |
( |
____ 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 5 x4 1 5 |
c. |
y = –5x + 25 |
b. |
y = –5x + 22 |
d. |
y = 1 5 x5 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: 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: 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: 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: 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. |
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 –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 –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. |
|
c. |
|
b. |
|
d. |
|
____
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. |
|
c. |
|
b. |
|
d. |
|
____
22.
Solve the equation .
a. |
|
c. |
|
b. |
|
d. |
|
____ 23. Solve the compound inequality. Then graph the solution set.
and
a. |
{s | –8 s 2}
0123456789100–1–2–3–4–5–6–7–8–9–10s |
b. |
{s | s –8 or s 2}
0123456789100–1–2–3–4–5–6–7–8–9–10s |
c. |
{s | –8 s 2}
0123456789100–1–2–3–4–5–6–7–8–9–10s |
d. |
{s | s –8 or s 2}
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 |
c. |
The expression is undefined at |
d. |
The expression is undefined at |
____ 25. Determine whether the data in the table are linear. Explain.
Session Length (min) |
1 |
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, |
b. |
Yes, the difference between successive session lengths is constant. For example, |
c. |
Yes, the rate of change is constant. For example, |
d. |
No, the ratio of the cost to the session length is not constant. For example, to the nearest hundredth, |
____
26.
Solve the equation .
a. |
There is no solution. |
c. |
|
b. |
3 2 |
d. |
|
____ 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 |
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.
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. |
|
____
35.
Order the numbers 4,
1
8
,
a. |
1 8 , 0.6632, |
c. |
1 8 |
b. |
4, 1 8 , |
d. |
1 8 , 0.6632, |
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. |
( |
b. |
Cannot determine. |
c. |
( |
____ 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 5 x4 1 5 |
c. |
y = –5x + 25 |
b. |
y = –5x + 22 |
d. |
y = 1 5 x5 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: 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: 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: 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: 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. |
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 –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 –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. |
|
c. |
|
b. |
|
d. |
|
____
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. |
|
c. |
|
b. |
|
d. |
|
____
22.
Solve the equation .
a. |
|
c. |
|
b. |
|
d. |
|
____ 23. Solve the compound inequality. Then graph the solution set.
and
a. |
{s | –8 s 2}
0123456789100–1–2–3–4–5–6–7–8–9–10s |
b. |
{s | s –8 or s 2}
0123456789100–1–2–3–4–5–6–7–8–9–10s |
c. |
{s | –8 s 2}
0123456789100–1–2–3–4–5–6–7–8–9–10s |
d. |
{s | s –8 or s 2}
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 |
c. |
The expression is undefined at |
d. |
The expression is undefined at |
____ 25. Determine whether the data in the table are linear. Explain.
Session Length (min) |
1 |
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, |
b. |
Yes, the difference between successive session lengths is constant. For example, |
c. |
Yes, the rate of change is constant. For example, |
d. |
No, the ratio of the cost to the session length is not constant. For example, to the nearest hundredth, |
____
26.
Solve the equation .
a. |
There is no solution. |
c. |
|
b. |
3 2 |
d. |
|
____ 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 |
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.
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. |
|
____
35.
Order the numbers 4,
1
8
,
a. |
1 8 , 0.6632, |
c. |
1 8 |
b. |
4, 1 8 , |
d. |
1 8 , 0.6632, |

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