AnswersIC Pre-Cal - DeeringUnit Test

Unit Test — Cumulative exam Answers

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The parent cosecant function is shifted 2 units down, and its period is changed to . Which of the following is the graph of the transformed function?

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A
On a coordinate plane, the x axis ranges from negative 6 pi to 6 pi with an interval of pi units and the y axis ranges from negative 6 to 2 with an interval of 2 units. A graph of a function with asymptotes at x equals plus or minus n pi is drawn. It touches the line y equals negative 1 at (3 by 2 pi comma negative 1) and (negative 9 by 2 pi comma negative 1). Another line y equals negative 3 touches at (3 by 2 pi comma negative 3) and (negative 9 by 2 pi comma negative 3).
Option A
B
On a coordinate plane, the x axis ranges from negative 6 pi to 6 pi with an interval of pi units and the y axis ranges from negative 4 to 4 with an interval of 2 units. A graph of a function with asymptotes at x equals plus or minus n pi is drawn. It touches the line y equals 1 at (3 by 2 pi comma1) and (negative 9 by 2 pi comma 1). Another line y equals negative 1 touches at (9 by 2 pi comma negative 1) and (negative 3 by 2 pi comma negative 1).
Option B
C
On a coordinate plane, the x axis ranges from negative 6 pi to 6 pi with an interval of pi units and the y axis ranges from negative 6 to 2 with an interval of 2 units. A graph of a function with asymptotes at x equals plus or minus n pi is drawn. It touches the line y equals 1 at (6 pi comma1), (0 comma 1) and (negative 6 pi comma 1). Another line y equals negative 3 touches at (3 pi comma negative 3) and (negative 3 pi comma negative 3).
Option C
D
On a coordinate plane, the x axis ranges from negative 6 pi to 6 pi with an interval of pi units and the y axis ranges from negative 4 to 4 with an interval of 2 units. A graph of a function with asymptotes at x equals plus or minus n pi is drawn. It touches the line y equals 1 at (6 pi comma1), (0 comma 1) and (negative 6 pi comma 1). Another line y equals negative 2 touches at (3 pi comma negative 1) and (negative 3 pi comma negative 1).
Option D
2
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Triangle PQR has sides measuring 9 feet and 10 feet and a perimeter of 24 feet. What is the area of triangle PQR? Round to the nearest square foot.Heron’s formula: Area

Question illustration
A
6 square feet
B
7 square feet
C
19 square feet
D
22 square feet
3

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
4

What is the following simplified product? Assume

Question illustration
A
3 x StartRoot 6 x EndRoot + x Superscript 4 Baseline StartRoot 30 x EndRoot + 24 x squared + 8 x Superscript 5 Baseline StartRoot 10 x EndRoot
Option A
B
3 x StartRoot 6 x EndRoot + x Superscript 4 Baseline StartRoot 30 x EndRoot + 24 x squared StartRoot 2 EndRoot + 8 x Superscript 5 Baseline StartRoot 10 EndRoot
Option B
C
3 x StartRoot 6 x EndRoot minus x Superscript 4 Baseline StartRoot 30 x EndRoot + 24 x squared StartRoot 2 EndRoot minus 8 x Superscript 5 Baseline StartRoot 10 EndRoot
Option C
D
3 x StartRoot 6 x EndRoot minus x Superscript 4 Baseline StartRoot 30 x EndRoot + 24 x squared StartRoot 2 x EndRoot minus 8 x Superscript 5 Baseline StartRoot 10 x EndRoot
Option D
5

On a unit circle, the vertical distance from the x-axis to a point on the perimeter of the circle is twice the horizontal distance from the y-axis to the same point. What is sin?

Question illustration
A
One-fifth
Option A
B
StartFraction StartRoot 5 EndRoot Over 5 EndFraction
Option B
C
StartFraction 2 StartRoot 5 EndRoot Over 5 EndFraction
Option C
D
2
Option D
6

A waterwheel has a radius of 5 feet. The center of the wheel is 2 feet above the waterline. You notice a white mark at the top of the wheel. How many radians would the wheel have to rotate for the white mark to be 3 feet below the waterline?

A
radians
Option A
B
radians
Option B
C
radians
Option C
D
radians
Option D
7

What is the solution of ?

Question illustration
A
x = –10
B
x = 3
C
x = –10 or x = 3
D
no solution
8

From where Kiana is standing, she must look up at a 50° angle to see the top of a building. If she backs up 50 feet, she will need to look up at a 40° angle to see the top of the same building. Approximately how tall is the building?

Question illustration
A
119.0 ft.
B
141.8 ft.
C
185.1 ft.
D
220.6 ft.
9

Which is the graph of ?

Question illustration
A
A smooth curve resembling an arctangent function. The x-axis ranges from -6 to 6, and the y-axis from -p to p. The curve approaches horizontal asymptotes at y = p/2 and y = -p/2, passing through the origin.
Option A
B
A graph of a function with asymptotic behavior. The x-axis ranges from -5 to 5, and the y-axis ranges from -p to p. The curve is located in the fourth quadrant, approaching the y-axis asymptotically as x approaches zero from both positive and negative directions. The curve also approaches zero asymptotically as x moves away from zero in both directions. The function does not intersect either axis.
Option B
C
A graph of a function with the x-axis ranging from -2.5 to 2.5 and the y-axis ranging from -p to p. The curve passes through the origin (0,0) and changes direction at y=0. It intersects the x-axis at two points, approximately at x=-1 and x=1. The curve is symmetric about the origin.
Option C
D
The image shows a mathematical graph plotted on a Cartesian coordinate system. The x-axis ranges from -2 to 2, and the y-axis ranges from -p to p. A smooth, continuous curve intersects the x-axis at approximately 1. The curve extends into both the positive and negative quadrants. The point p is labeled on the positive y-axis and -p on the negative y-axis.
Option D
10

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
11

The formula gives the length of the side, s, of a cube with a surface area, SA. How much longer is the side of a cube with a surface area of 480 square meters than a cube with the surface area of 270 square meters?

Question illustration
A
m
Option A
B
m
Option B
C
m
Option C
D
m
Option D
13

If x is a positive integer, which expression is equivalent to ? Assume .

Question illustration
A
RootIndex 20 StartRoot x Superscript 7 EndRoot
Option A
B
x (RootIndex 20 StartRoot x cubed EndRoot)
Option B
C
StartFraction RootIndex 6 StartRoot x Superscript 5 Baseline EndRoot Over x squared EndFraction
Option C
D
x cubed (RootIndex 6 StartRoot x Superscript 5 Baseline EndRoot)
Option D
14

What is the domain of the function ?

Question illustration
A
all real numbers except , where n is any integer
Option A
B
all real numbers except , where n is any integer
Option B
C
all real numbers except , where n is any integer
Option C
D
all real numbers except , where n is any integer
Option D
15

Which statement is true about the graph of the equation ?

Question illustration
A
There is a horizontal asymptote at .
Option A
B
There is a horizontal asymptote at .
Option B
C
There is a vertical asymptote at .
Option C
D
There is a vertical asymptote at .
Option D
16

What is the following product? Assume

Question illustration
A
6 y squared StartRoot 10 EndRoot + 12 StartRoot 5 y EndRoot
Option A
B
6 StartRoot 10 EndRoot + 12 StartRoot 5 y EndRoot
Option B
C
6 y squared StartRoot 10 EndRoot + 4 StartRoot 5 y EndRoot
Option C
D
3 y squared StartRoot 10 EndRoot + 12 StartRoot 5 y EndRoot
Option D
17

The mean sustained wind velocity, v, can be determined by the equation , where p is the air pressure, in millibars, at the center of the hurricane. What is the approximate air pressure at the center of a hurricane when the mean sustained wind velocity is 64 meters per second?

Question illustration
A
103 millibars
B
194 millibars
C
363 millibars
D
910 millibars
18

What restriction should be applied to y = tanx for y = arctanx to be defined?

A
Restrict the range to (negative StartFraction pi Over 2 EndFraction, StartFraction pi Over 2 EndFraction)
Option A
B
Restrict the range to left-bracket negative StartFraction pi Over 2 EndFraction, StartFraction pi Over 2 EndFraction right-bracket
Option B
C
Restrict the domain to (negative StartFraction pi Over 2 EndFraction, StartFraction pi Over 2 EndFraction)
Option C
D
Restrict the domain to left-bracket negative StartFraction pi Over 2 EndFraction, StartFraction pi Over 2 EndFraction right-bracket
Option D
19

Let cot(x) = , with 0 < x < 90°. What is sin(x)?

Question illustration
A
StartFraction 5 Over StartRoot 89 EndRoot EndFraction
Option A
B
StartFraction 8 Over StartRoot 89 EndRoot EndFraction
Option B
C
StartFraction StartRoot 89 EndRoot Over 8 EndFraction
Option C
D
StartFraction StartRoot 89 EndRoot Over 5 EndFraction
Option D
21

On which interval are both the sine and cosine functions increasing?

A
(StartFraction 3 pi Over 2 EndFraction, 2 pi)
Option A
B
(StartFraction pi Over 2 EndFraction, pi)
Option B
C
(0, pi)
Option C
D
(pi, StartFraction 3 pi Over 2 EndFraction
Option D
22

Jake and Maddie each take the closest path from their homes to the store. Based on the picture below, what is the approximate difference in the distance each person traveled to the store?

Question illustration
A
1.4 m
B
5.9 m
C
6.4 m
D
7.7 m

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