AnswersPARTB - EOP PGCPS ALGEBRA 2 OC SPRING2026 - 793033Cumulative Exam

Cumulative Exam — Cumulative exam Answers

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21
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How is the graph of transformed to produce the graph of ?

Question illustration
A
It is stretched horizontally by a factor of 2 and translated up 3 units.
B
It is compressed horizontally by a factor of 2 and translated up 3 units.
C
It is stretched vertically by a factor of 2 and translated up 3 units.
D
It is compressed vertically by a factor of 2 and translated up 3 units.
22
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Which expression is equivalent to ?

Question illustration
A
x Superscript one-half Baseline y Superscript 4
Option A
B
x Superscript one-eighth Baseline y Superscript 8
Option B
C
x Superscript one-fourth Baseline y Superscript 8
Option C
D
x Superscript one-fourth Baseline y Superscript 4
Option D
23

In the triangle below, represents which ratio?

Question illustration
A
tanB
B
tanC
C
sinB
D
cosC
24

Phan fills the tank of her car with gasoline before starting her road trip. The table below shows the amount of gas left in her tank as she drives.Number of Hours vs. Amount Left in TankNumber of Hours Spent Driving (h)3579Amount of Gas Left in Tank, in gallons (g)12840Which equation models the amount of gas left in the car as Phan drives, and how many gallons of gasoline does it take to fill her tank?

A
g = 18 – 2h; 18 gallons
B
g = 18 – 2h; 16 gallons
C
g = 3h + 3; 30 gallons
D
g = 3h + 3; 12 gallons
25

Which set of transformations is needed to graph f(x) = –0.1cos(x) – 4 from the parent cosine function?

A
reflection across the y-axis, vertical compression by a factor of 0.1, vertical translation 4 units up
B
reflection across the x-axis, vertical compression by a factor of 0.1, vertical translation 4 units down
C
vertical stretching by a factor of 0.1, vertical translation 4 units down, reflection across the y-axis
D
vertical stretching by a factor of 0.1, vertical translation 4 units up, reflection across the x-axis
26

Which solution finds the value of x in the triangle below?

Question illustration
A
Secant 60 degrees = StartFraction 8 Over x EndFraction. 2 = StartFraction 8 Over x EndFraction. 2 x = 8. x = 4.
Option A
B
Cosecant 60 degrees = StartFraction 8 Over x EndFraction. StartFraction 2 StartRoot 3 EndRoot Over 3 EndFraction = StartFraction 8 Over x EndFraction. x times 2 StartRoot 3 EndRoot = 24. x = StartFraction 24 Over 2 StartRoot 3 EndRoot EndFraction. x = StartFraction 12 Over StartRoot 3 EndRoot EndFraction times StartFraction StartRoot 3 EndRoot Over StartRoot 3 EndRoot EndFraction. x = StartFraction 12 StartRoot 3 EndRoot Over 3 EndFraction. x = 4 StartRoot 3 EndRoot.
Option B
C
Secant 60 degrees = StartFraction 8 Over x EndFraction. One-half = StartFraction 8 Over x Endfraction. x = 16
Option C
D
Cosecant 60 degrees = StartFraction 8 Over x EndFraction. StartFraction StartRoot 3 EndRoot Over 2 EndFraction = StartFraction 8 Over x EndFraction. x times StartRoot 3 EndRoot = 16. x = StartFraction 16 Over StartRoot 3 EndRoot EndFraction. x = StartFraction 16 Over StartRoot 3 EndRoot EndFraction times StartFraction StartRoot 3 EndRoot Over StartRoot 3 EndRoot EndFraction. x = StartFraction 16 StartRoot 3 EndRoot Over 3 EndFraction.
Option D
27

Myra uses an inverse variation function to model the data for the ordered pairs below.(2, 30), (3, 20), (4, 15), (5, 12), (6, 10)Which statement best explains whether an inverse variation function is the best model for the data?

A
An inverse function is the best model because as x increases, y decreases.
B
An inverse function is the best model because the products of corresponding x- and y-values are equal.
C
An inverse variation function is not the best model because data points approximate a straight line.
D
An inverse variation function is not the best model because the data points show an exponential decay.
28

What is the equation of the graph below?

Question illustration
A
y = cosine (StartFraction x Over 0.4 EndFraction)
Option A
B
y = cos(5x)
C
y = cos(0.4x)
D
y = cosine (StartFraction x Over 5 EndFraction)
Option D
29

The depth of the water, d, at the end of a pier changes periodically as a function of time, t, in hours as shown in the graph below. According to the model, the last low tide occurred at 5:00 a.m. When will the next low tide occur? Let t = 0 be 12:00 a.m.

Question illustration
A
3:00 a.m.
B
5:00 a.m.
C
3:00 p.m.
D
5:00 p.m.
30

For what value of x does ?

Question illustration
A
1
B
3
C
12
D
no solution
31

Which expression is equivalent to cos120°?

A
°
Option A
B
cos240°
C
cos300°
D
cos420°
32

Which of the following is the graph of ?

Question illustration
A
On a coordinate plane, 2 curves are shown. Both curves have an asymptote at x = 2. One curve opens up and to the right in quadrant 1. The other curve opens down and to the left and it crosses the x-axis at (1, 0).
Option A
B
On a coordinate plane, 2 curves are shown. Both curves have an asymptote at x = 2. One curve opens up and to the right in quadrants 1 and 4. It crosses the x-axis at (3, 0). The other curve opens down and to the left and it crosses the y-axis at (0, negative 1.5).
Option B
C
On a coordinate plane, 2 curves are shown. Both curves have an asymptote at x = negative 2. One curve opens up and to the right in quadrants 1 and 2. It crosses the y-axis at (0, 1.5). The other curve opens down and to the left and it crosses the x-axis at (negative 3, 0).
Option C
D
On a coordinate plane, 2 curves are shown. Both curves have an asymptote at x = negative 2. One curve opens up and to the right in quadrants 1, 2, and 4. It crosses the x-axis at (negative 1, 0). The other curve opens down and to the left in quadrant 3.
Option D
33

What are the domain and range of f(x) = 2(3x)?

A
domain: ; range:
Option A
B
domain: ; range:
Option B
C
domain: ; range:
Option C
D
domain: ; range:
Option D
34

Which equation is represented by the graph below?

Question illustration
A
y = one-eighth e Superscript x
Option A
B
y = one-half e Superscript x
Option B
C
y = 2 e Superscript x
Option C
D
y = 8 e Superscript x
Option D
35

How does the graph of g(x) = 3x – 2 compare to the graph of f(x) = 3x?

A
The graph of g(x) is a translation of f(x) 2 units left.
B
The graph of g(x) is a translation of f(x) 2 units right.
C
The graph of g(x) is a translation of f(x) 2 units up.
D
The graph of g(x) is a translation of f(x) 2 units down.
36

What is the following sum?

Question illustration
A
4 x (RootIndex 3 StartRoot 2 y EndRoot) + 12 x squared y (RootIndex 3 StartRoot 2 y squared EndRoot)
Option A
B
8 x (RootIndex 3 StartRoot x y EndRoot) + 12 x cubed y squared (RootIndex 3 StartRoot 6 y EndRoot)
Option B
C
16 x cubed y (RootIndex 3 StartRoot 2 y squared EndRoot)
Option C
D
48 x cubed y (RootIndex 3 StartRoot 2 y EndRoot)
Option D
37

What is the simplified form of the following expression?

Question illustration
A
2 StartRoot 2 EndRoot
Option A
B
5 StartRoot 2 EndRoot
Option B
C
9 StartRoot 2 EndRoot
Option C
D
15 StartRoot 2 EndRoot
Option D
38

For which value of is csc () undefined?

Question illustration
A
0
B
StartFraction pi Over 2 EndFraction
Option B
C
StartFraction 3 pi Over 2 EndFraction
Option C
D
StartFraction 7 pi Over 2 EndFraction
Option D
39

What is the value of ?

Question illustration
A
–4.00
B
–0.25
C
1.51
D
2.41
40

Which expression is equivalent to ?

Question illustration
A
2 log Subscript 5 Baseline x + log Subscript 5 Baseline 4
Option A
B
2 log Subscript 5 Baseline x + log Subscript 5 Baseline 16
Option B
C
2 log Subscript 5 Baseline x + 2 log Subscript 5 Baseline 4
Option C
D
2 log Subscript 5 Baseline x + log Subscript 5 Baseline 4
Option D

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