AnswersIC Pre-Cal - DeeringUnit Test

Unit Test — Unit test Answers

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Caleb and Emily are standing 100 yards from each other. Caleb looks up at a 45° angle to see a hot air balloon. Emily looks up at a 60° angle to see the same hot air balloon. Approximately how far is the hot air balloon off the ground?

A
44.3 yd.
B
63.4 yd.
C
73.2 yd.
D
89.7 yd.
2
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Triangle ABC is a sketch of a triangular flower bed that has an area of 65.1 square feet.Trigonometric area formula: Area =

Question illustration
A
17 feet
B
33 feet
C
40 feet
D
50 feet
3

In triangle ABC, AB = 90 in., BC = 80 in., and angle B measures 50°. What is the approximate perimeter of the triangle?

A
242.4 in.
B
265.3 in.
C
308.3 in.
D
324.1 in.
4

A plane took off at a 15° angle to the ground and flew in Sydney’s direction. She is standing at a point 25 miles from the point where the plane took off. If the plane has traveled 20 miles in the air, about how far is Sydney from the airplane? Round your answer to the nearest whole number.

A
8 mi.
B
15 mi.
C
28 mi.
D
59 mi.
5

Heron’s formula: Area =

Question illustration
A
27 square units
B
38 square units
C
364 square units
D
728 square units
6

Which of the following is the graph of ?

Question illustration
A
On a coordinate plane, the x axis ranges from negative 2 pi to 2 pi with an interval of pi units and the y axis ranges from negative 5 to 1 with an interval of 1 unit. The graph is 2 pi periodic with asymptotes at x equals plus or minus n pi. It touches the lines y equals negative 3 by 2 at (3 pi by 2, comma negative 3 by 2 ) and (negative pi by 2 by negative 3 by 2) and y equals negative 5 by 2 at ( pi by 2 comma negative 5 by 2) and (negative 3 pi by 2 comma negative 5 by 2).
Option A
B
On a coordinate plane, the x axis ranges from negative 2 pi to 2 pi with an interval of pi units and the y axis ranges from negative 5 to 1 with an interval of 1 unit. The graph is 2 pi periodic with asymptotes at x equals plus or minus n pi. It touches the lines y equals negative 1 at (3 pi by 2 comma negative 1) and (negative pi by 2 comma negative 1) and y equals negative 3 at (pi by 2 comma negative 3) and (negative 3 pi by 2 comma negative 3).
Option B
C
On a coordinate plane, the x axis ranges from negative 2 pi to 2 pi with an interval of pi units and the y axis ranges from negative 5 to 1 with an interval of 1 unit. The graph is 2 pi periodic with asymptotes at x equals plus or minus n pi. It touches the lines y equals negative 1 at (pi comma negative 1) and (negative pi comma negative 1) and y equals negative 3 at (0 comma negative 3).
Option C
D
On a coordinate plane, the x axis ranges from negative 2 pi to 2 pi with an interval of pi units and the y axis ranges from negative 5 to 1 with an interval of 1 unit. The graph is 2 pi periodic with asymptotes at x equals plus or minus n pi. It touches the lines y equals negative 1 point 8 at (0 comma negative 1 point 8) and y equals negative 2 point 2 at (pi comma negative 2 point 2) and (negative pi comma negative 2 point 2).
Option D
7

How does the graph of y = sec(x + 3) – 7 compare with the graph of y = sec(x)?

A
It is the graph of y = sec(x) shifted 3 units right and 7 units up.
B
It is the graph of y = sec(x) shifted 3 units left and 7 units up.
C
It is the graph of y = sec(x) shifted 3 units left and 7 units down.
D
It is the graph of y = sec(x) shifted 3 units right and 7 units down.
8

Review the graph.

Question illustration
A
y = tanx
B
y = cosx
C
y = tan-1x
D
y = cos-1x
9

What is the period of the function ?

Question illustration
A
units
Option A
B
units
Option B
C
units
Option C
D
units
Option D
10

Which transformation should be applied to the graph of the function to obtain the graph of the function ?

Question illustration
A
a vertical stretch, a horizontal compression to make the period , a horizontal shift of units to the right, and a vertical shift of 4 units up
Option A
B
a vertical stretch, a horizontal compression to make the period , a horizontal shift of units to the right, and a vertical shift of 4 units up
Option B
C
a vertical stretch, a horizontal compression to make the period , a horizontal shift of units to the right, and a vertical shift of 4 units up
Option C
D
a vertical stretch, a horizontal compression to make the period , a horizontal shift of units to the right, and a vertical shift of 4 units up
Option D
11

Which functions are symmetric with respect to the origin?

A
y = arcsinx and y = arccosx
B
y = arccosx and y = arctanx
C
y = arctanx and y = arccotx
D
y = arcsinx and y = arctanx
12

After a windstorm, a leaning pole makes a 75° angle with the road surface. The pole casts a 15-foot shadow when the sun is at a 45° angle of elevation. About how long is the pole?

A
11.0 ft.
B
12.2 ft.
C
16.7 ft.
D
20.5 ft.
13

A kite is made up of two isosceles triangles, KIT and KET, with the lengths shown. The top triangle of the kite, ΔKIT, is made from approximately 17 square inches of material.Heron’s formula: Area =

Question illustration
A
31 square inches
B
34 square inches
C
48 square inches
D
62 square inches
14

Which is an x-intercept of the graph of the function ?

Question illustration
A
(minus StartFraction 2pi over 3 EndFraction , 0)
Option A
B
(minus StartFraction pi over 3 EndFraction , 0)
Option B
C
(StartFraction pi over 6 EndFraction , 0)
Option C
D
(StartFraction 5pi over 6 EndFraction , 0)
Option D
15

Which expression is equivalent to 30°?

A
Inverse of cosine (StartFraction StartRoot 3 EndRoot Over 2 EndFraction)
Option A
B
Inverse of sine (StartFraction StartRoot 3 EndRoot Over 2 EndFraction)
Option B
C
Sine (StartFraction StartRoot 3 EndRoot Over 2 EndFraction)
Option C
D
Cosine (StartFraction StartRoot 3 EndRoot Over 2 EndFraction)
Option D
16

What is the equation of the graph below?

Question illustration
A
y = sec(x) + 2
B
y = csc(x) + 2
C
y = csc(x + 2)
D
y = sec(x + 2)
17

Suppose you want to transform the graph of the function into the graph of the function . Which transformations should you perform?

Question illustration
A
Reflect the graph of the first function across the x-axis, translate it units to the left, and translate it 2 units up.
Option A
B
Reflect the graph of the first function across the x-axis, translate it units to the right, and translate it 2 units up.
Option B
C
Reflect the graph of the first function across the line , translate it units to the left, and translate it 2 units up.
Option C
D
Reflect the graph of the first function across the line , translate it units to the right, and translate it 2 units up.
Option D
18

The angle measures in a triangle are in the ratio 1:3:5. The longest side of the triangle measures 5 inches. What is the approximate perimeter of the triangle?

A
9.0 in.
B
9.4 in.
C
11.1 in.
D
12.7 in.
19

What are the possible remaining angle measures in triangle ABC with ?

Question illustration
A
and
Option A
B
m angle B similar to 121 degrees, m angle C similar to 19 degrees
Option B
C
m angle B similar to 59 degrees, m angle C similar to 81 degrees
Option C
D
No triangle can be formed with these measures.
20

Let a function y represent the water level in a harbor measured in meters, and let x represent the number of hours since high tide. At time x = 0, the water level is 19.5 meters (a maximum). At time x = 6.26 hours, the water level is 10.5 meters (a minimum). The period of the function is 12.5 hours.After how many hours is the water expected to reach a depth of 17 meters for the first time? Round to the nearest tenth of an hour.

A
2.2 hours
B
6.3 hours
C
12.1 hours
D
12.5 hours

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