AnswersTX-Precalculus AUnit Test

Unit Test — Cumulative exam Answers

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1
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Which expression is equivalent to ?

Question illustration
A
Cosine (negative StartFraction pi Over 3 EndFraction)
Option A
B
Sine (negative StartFraction pi Over 3 EndFraction)
Option B
C
Cosine (StartFraction pi Over 2 EndFraction)
Option C
D
Sine (StartFraction pi Over 2 EndFraction)
Option D
2
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Which is the graph of y =-3 ?

Question illustration
A
On a coordinate plane, a curve starts at (0, 0) and curves up through (negative 3, 3).
Option A
B
On a coordinate plane, a curve starts at (0, 0) and curves down through (1, negative 1) and (4, negative 2).
Option B
C
On a coordinate plane, a curve starts at (0, 0) and curves down through (1, negative 3).
Option C
D
On a coordinate plane, a curve starts at (0, 0) and curves up through (1, 3) and (2, 4.5).
Option D
3

What is rewritten using the power property?

Question illustration
A
e log Subscript 6 Baseline f
Option A
B
f log Subscript 6 Baseline e
Option B
C
log Subscript 6 Baseline (e times f)
Option C
D
log Subscript 6 Baseline (e + f)
Option D
4

The equations and are graphed below. According to the graph, which of the following is part of the solution to the trigonometric inequality over the interval radians?

Question illustration
A
x equal to StartFraction pi over 6 EndFraction
Option A
B
x equal to StartFraction 2pi over 3 EndFraction
Option B
C
x equal to StartFraction 4pi over 3 EndFraction
Option C
D
x equal to StartFraction 3 pi over 2 EndFraction
Option D
5

Which shows a correct simplification of sin(x + )?

Question illustration
A
sin(x + )= sin(x)cos() + cos(x)sin()= sin(x) · 1 + cos(x) · 0= sin(x)
Option A
B
sin(x + )= cos(x)cos() – sin(x)sin()= cos(x) · 1 – sin(x) · 0= cos(x)
Option B
C
sin(x + )= sin(x)cos() + cos(x)sin()= sin(x) · –1 + cos(x) · 0= –sin(x)
Option C
D
sin(x + )= cos(x)cos() – sin(x)sin()= cos(x) · –1 – sin(x) · 0= –cos(x)
Option D
6

Which statement about the simplified binomial expansion of (a + b2)n, where n is a positive integer, is true?

A
The exponent of b will always be even.
B
The exponent of a will always be odd.
C
The sum of the exponents of a and b will always equal n.
D
The sum of the exponents of a and b will always equal n – 1.
7

Which of the following could be the graph of y = –xn where n is odd?

A
mc014-1.jpg
Option A
B
mc014-2.jpg
Option B
C
mc014-3.jpg
Option C
D
mc014-4.jpg
Option D
8

The side length, s, of a cube is 3x + 2y. If V = s3, what is the volume of the cube?

A
3x3 + 18x2y + 36xy2 + 8y3
B
27x3 + 54x2y + 18xy2 + 2y3
C
27x3 + 18x2y + 12xy2 + 2y3
D
27x3 + 54x2y + 36xy2 + 8y3
9

What is the solution to x 4 + 4x 3 ≤ 12x 2?

A
(–6, 2)
B
[–6, 2]
C
(–ꝏ, –6) U (2, ꝏ)
D
(–ꝏ, –6] U [2, ꝏ)
10

Annabelle’s bicycle has a wheel radius of 13 inches. She places a sticker on the wheel so that its minimum height above the ground is 0.5 inches. When she rides her bicycle, the wheel completes 90 revolutions every minute. The sticker begins at its minimum height above the ground.Which equation models the height in inches of the sticker after x minutes?

A
y = 0.5 sine (180 pi x) + 13
Option A
B
y = 12.5 sine (180 pi x) + 13
Option B
C
y = 0.5 sine (180 pi x minus StartFraction pi Over 2 EndFraction) + 13
Option C
D
y = 12.5 sine (180 pi x minus StartFraction pi over 2 EndFraction) + 13
Option D
11

What are the roots of the polynomial equation ? Use a graphing calculator and a system of equations.

Question illustration
A
–24, –3, 12
B
–12, 3, 24
C
–4, –2, 3
D
–3, 2, 4
12

Read the proof.

Question illustration
A
tangent double angle identity
Option A
B
tangent sum identity
Option B
C
tangent double angle identity
Option C
D
tangent sum identity
Option D
13

Which statements comparing the graphs of function 1 and function 2 are true? Check all that apply.

A
Function 1 has a hole, while function 2 does not.
B
Function 1 has an oblique asymptote, while function 2 does not.
C
Function 2 has a hole, while function 1 only has asymptotes.
D
Function 2 only has asymptotes, while function 1 has a hole.
E
Both functions have the same domain restriction.
F
Both functions have the same vertical asymptote.
14

Which statement comparing the oblique asymptotes of the functions f(x) and g(x) is true?

Question illustration
A
The oblique asymptote for g(x) is steeper than for f(x).
B
Both functions have the same oblique asymptote.
C
The oblique asymptote for f(x) is steeper than for g(x).
D
Both functions have parallel oblique asymptotes.
15

The time it takes a spinner to stop completely is 12 seconds. If the spinner completes 6 revolutions in this time, what was the average angular velocity of the spinner, in radians per second, for the 12-second interval?

A
π
B
2π
C
4π
D
12π
16

A rectangular prism with a volume of 400 cubic centimeters has the dimensions x + 1 centimeters, 2x centimeters, and x + 6 centimeters. The equation can be used to find x. What is the length of the longest side? Use a graphing calculator and a system of equations to find the answer.

Question illustration
A
4 centimeters
B
5 centimeters
C
8 centimeters
D
10 centimeters
17

Which expression is equivalent to ?

Question illustration
A
log Subscript 2 Baseline 9 + 3 log Subscript 2 Baseline x
Option A
B
log Subscript 2 Baseline x + 3 log Subscript 2 Baseline 9
Option B
C
3 log Subscript 2 Baseline x minus log Subscript 2 Baseline 9
Option C
D
3 log Subscript 2 Baseline 9 minus log Subscript 2 Baseline x
Option D
18

A farmer sells almonds according to the chart below. The more pounds of almonds that are sold, the lower the cost per pound is for the entire order of almonds.Almond PricesNumber of PoundsCost (per Pound)up to 10$20 more than 10, and up to 20$15 more than 20, and up to 30$10 more than 30$5 The farmer graphs a step function to model the situation, where y represents the cost per pound for an order of x pounds of almonds. Which of the following describes the farmer’s graph for the step that includes 20.75 pounds, and what is the total cost of 20.75 pounds of almonds?

A
a horizontal segment with an open circle at (20, 10) and a closed circle at (30, 10); $207.50
B
a horizontal segment with a closed circle at (20, 10) and an open circle at (30, 10); $207.50
C
a horizontal segment with an open circle at (21, 10) and a closed circle at (30, 10); $311.25
D
a horizontal segment with a closed circle at (21, 10) and an open circle at (30, 10); $311.25
19

Suppose f(x) = 2(x + 1)2 and f(g(x)) = 2(2x + 4)2. What is g(x)?

A
g(x) = x + 3
B
g(x) = x + 4
C
g(x) = 2x + 3
D
g(x) = 2x + 4
20

What is written as a single logarithm?

Question illustration
A
4 log Subscript one-half Baseline 2 Superscript 4 Baseline u squared minus v cubed
Option A
B
log Subscript one-half Baseline w Superscript 4 Baseline (StartFraction u squared Over v cubed EndFraction)
Option B
C
log Subscript one-half Baseline (StartFraction w Superscript 4 Baseline Over u squared v cubed EndFraction)
Option C
D
log Subscript one-half Baseline (w (StartFraction u squared Over v cubed EndFraction)) Superscript 4
Option D

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