AnswersIC Pre-Cal - DeeringUnit Test

Unit Test — Unit test Answers

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A particle travels in a circle around a fixed point at 16 revolutions per minute. The linear velocity of the particle is 240π inches per minute.What is the distance, in inches, between the particle and the fixed point?

A
3.75
B
7.5
C
15
D
30
4
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During high tide around 11:00 p.m., the water level is 3 feet above a marker on a pier. The following day, during low tide around 5:12 a.m., the water level has dropped 3 feet below the marker. The height of the water is modeled by the function , where x is the time in hours since 11:00 p.m.What is the height of the water at 2:15 a.m.?

Question illustration
A
0.22 feet below the marker
B
0.07 feet below the marker
C
1.26 feet above the marker
D
1.39 feet above the marker
5

The function g(x) represents f(x) = after translating units left and 4 units up.Which equation represents g(x)?

Question illustration
A
g (x) = 9 cosine (x minus StartFraction pi Over 3 EndFraction) minus 1
Option A
B
g (x) = 9 cosine (x minus StartFraction pi Over 3 EndFraction) + 7
Option B
C
g (x) = 9 cosine (x minus StartFraction 2 pi Over 3 EndFraction) minus 1
Option C
D
g (x) = 9 cosine (x minus StartFraction 2 pi Over 3 EndFraction) + 7
Option D
6

Suppose the function h(x) = sinx is translated units left and 11 units down. Which graph represents the result?

Question illustration
A
On a coordinate plane, a function has a maximum of negative 10 and minimum of negative 12. It completes one period at 2 pi. It decreases through the y-axis at (0, negative 11).
Option A
B
On a coordinate plane, a function has a maximum of negative 10 and minimum of negative 12. It completes one period at 2 pi. It crosses the y-axis at (0, negative 10).
Option B
C
On a coordinate plane, a function has a maximum of negative 10 and minimum of negative 12. It completes one period at 2 pi. It increases through the y-axis at (0, negative 11).
Option C
D
On a coordinate plane, a function has a maximum of negative 10 and minimum of negative 12. It completes one period at 2 pi. It crosses the y-axis at (0, negative 12).
Option D
7

Which of the following is true of the location of an angle, , whose tangent value is ?

Question illustration
A
has a 30-degree reference angle and is located in Quadrant II or IV
Option A
B
has a 30-degree reference angle and is located in Quadrant II or III
Option B
C
has a 60-degree reference angle and is located in Quadrant II or IV
Option C
D
has a 60-degree reference angle and is located in Quadrant II or III
Option D
8

Which is equivalent to ? Give your answer in radians.

Question illustration
A
0
B
Option
Option B
C
Option
Option C
D
Option
Option D
9

Suppose tan(b) = –2, and the terminal side of b is located in quadrant II. What is cot(b)?

A
–2
B
Negative one-half
Option B
C
One-half
Option C
D
2
10

The angle measures associated with which set of ordered pairs share the same reference angle?

A
(Negative StartFraction StartRoot 3 EndRoot Over 2 EndFraction , negative one-half), (negative one-half, Negative StartFraction StartRoot 3 EndRoot Over 2 EndFraction)
Option A
B
(one-half, Negative StartFraction StartRoot 3 EndRoot Over 2 EndFraction), (Negative StartFraction StartRoot 3 EndRoot Over 2 EndFraction, one-half)
Option B
C
(Negative one-half, negative StartFraction StartRoot 3 EndRoot Over 2 EndFraction), (One-half, StartFraction StartRoot 3 EndRoot Over 2 EndFraction)
Option C
D
(StartFraction StartRoot 3 EndRoot Over 2 EndFraction, one-half), (one-half, StartFraction StartRoot 3 EndRoot Over 2 EndFraction)
Option D
11

The merry-go-round at the fair rotates 12 times each minute, and children are 15 feet from the center of the wheel when they are in their seats. What is the linear velocity of the children in feet per hour?

A
360π
B
720π
C
21,600π
D
43,200π
12

What is the range of ?

Question illustration
A
and
Option A
B
and
Option B
C
and
Option C
D
and
Option D
14

Over which interval is the graph of y = cos(x) strictly increasing?

A
0 less-than x less-than StartFraction pi Over 2 EndFraction
Option A
B
0 < x < π
C
StartFraction pi Over 2 EndFraction less-than x less-than StartFraction 3 pi Over 2 EndFraction
Option C
D
π < x < 2π
15

An object is attached to a spring that is stretched and released. The equation models the distance, d, of the object in inches above or below the rest position as a function of time, t, in seconds. Approximately when will the object be 6 inches above the rest position? Round to the nearest hundredth, if necessary.

Question illustration
A
0 seconds
B
1.38 seconds
C
4.62 seconds
D
8 seconds
16

In which quadrant(s) is csc(x) positive?

A
quadrant I only
B
quadrant II only
C
quadrants I and II
D
quadrants I and III
17

Which of the following best explains the value of on the unit circle below?

Question illustration
A
The length opposite the angle is the vertical distance from the x-axis on the graph.
Option A
B
The length adjacent to the angle is the vertical distance from the x-axis on the graph.
Option B
C
The length opposite the angle is the horizontal distance from the y-axis on the graph.
Option C
D
The length adjacent to the angle is the horizontal distance from the y-axis on the graph.
Option D
18

Review the graph.

Question illustration
A
y = –3cos(x)
B
y = –3sin(x)
C
y = 3cos(x)
D
y = 3sin(x)
19

At a certain location, the number of hours of sunlight is modeled by y = where x represents the number of weeks after the summer solstice.Based on the model, what is the minimum number of hours of sunlight at this location?

Question illustration
A
3.2
B
5.6
C
6.4
D
13.0
20

A seat on a Ferris wheel is level with the center of the wheel. The diameter of the wheel is 200 feet. Suppose the wheel rotates 60°, causing the height of the seat to decrease. How much closer to the ground is the seat after the rotation?

A
50 feet
B
feet
Option B
C
100 feet
D
feet
Option D
21

What are the values of m and in the diagram below?

Question illustration
A
,
Option A
B
,
Option B
C
,
Option C
D
,
Option D
22

Which shows all the exact solutions of ? Give your answer in radians.

Question illustration
A
and
Option A
B
and
Option B
C
, , , and
Option C
D
, , , and
Option D
24

The table shows the temperatures in degrees Celsius, y, inside a shed at x hours past noon. The maximum and minimum temperatures are shown.

Question illustration
A
y = 3 cosine (StartFraction pi Over 12 EndFraction x minus StartFraction pi Over 3 EndFraction) + 17
Option A
B
y = 3 cosine (StartFraction pi Over 12 EndFraction x minus StartFraction pi Over 4 EndFraction) + 17
Option B
C
y = 6 cosine (StartFraction pi Over 12 EndFraction x minus StartFraction pi Over 3 EndFraction) + 17
Option C
D
y = 6 cosine (StartFraction pi Over 12 EndFraction x minus StartFraction pi Over 4 EndFraction) + 17
Option D

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