AnswersTX-Mathematical Models with Applications AUnit Test

Unit Test — Unit test Answers

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1
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Fiona drew a regular polygon that first maps directly onto itself after rotating 15 degrees. How many sides does the polygon have?

A
12
B
15
C
24
D
48
2
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The two square pyramids are similar. The side length of the smaller pyramid is the side length of the larger pyramid.

Question illustration
A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
3

Michele wanted to measure the height of her school’s flagpole. She placed a mirror on the ground 48 feet from the flagpole, then walked backwards until she was able to see the top of the pole in the mirror. Her eyes were 5 feet above the ground and she was 12 feet from the mirror. Using similar triangles, find the height of the flagpole to the nearest tenth of a foot.

Question illustration
A
20 ft
B
38.4 ft
C
55 ft
D
25 ft
4

A cylinder has a radius of 2.8 inches and a height of 2.4 inches. Which cylinder is similar?

A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
5

Nina was curious about the height of the Eiffel Tower. She used a 1.2 meter model of the tower and measured its shadow at 2 P.M. The length of the shadow was 0.9 meter. Then she measured the Eiffel Tower’s shadow, and it was 240 meters. What is the height of the Eiffel Tower?

Question illustration
A
.45
B
2880 m
C
30 m
D
320 m
6

Which describes an isometric transformation?

A
dilation
B
rotation
C
side length change
D
angle change
7

Consider the reflectional symmetry of the rhombus.

Question illustration
A
0
B
1
C
2
D
4
8

Rectangle ABCD is transformed to A'B'C'D' by a dilation.

Question illustration
A
Option
Option A
B
Option
Option B
C
3
D
6
9

The height, h, in feet of a ball suspended from a spring as a function of time, t, in seconds can be modeled by the equation . Which of the following is the graph of this equation?

Question illustration
A
On a coordinate plane, a curve crosses the y-axis at (0, 5). It increases to (2, 8), and then decreases to (6, 2).
Option A
B
On a coordinate plane, a curve crosses the y-axis at (0, 8). It decreases to (4, 2), and then increases to (8, 8).
Option B
C
On a coordinate plane, a curve crosses the y-axis at (0, 5). It increases to (1, 8), and then decreases to (3, 2).
Option C
D
On a coordinate plane, a curve crosses the y-axis at (0, 5). It decreases to (2, 1), and then increases to (3, 8).
Option D
10

The graph shows parallelogram FGHJ and the location of vertex F’ after a dilation with respect to the origin.

Question illustration
A
(1, –5)
B
(3, –5)
C
(1, –6)
D
(3, -6)
11

Which shows a translation of octagon A three units right to form octagon A'?

A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
12

The height, h, in feet of the tip of the hour hand of a wall clock varies from 9 feet to 10 feet. Which of the following equations can be used to model the height as a function of time, t, in hours? Assume that the time at t = 0 is 12:00 a.m.

A
h = 0.5 cosine (StartFraction pi Over 12 EndFraction t) + 9.5
Option A
B
h = 0.5 cosine (StartFraction pi Over 6 EndFraction t) + 9.5
Option B
C
h = cosine (StartFraction pi Over 12 EndFraction t) + 9
Option C
D
h = cosine (StartFraction pi Over 6 EndFraction t) + 9
Option D
13

A right triangle is drawn on the coordinate plane.Which is a dilation of this triangle with respect to the origin by a factor of ?

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

Isosceles triangle ABC is transformed to the image, triangle A'B'C'.

Question illustration
A
A dilation could have been applied because all of the vertices decreased by 2 units.
B
An isometric transformation could have been applied because all of the vertices moved 2 units right and 2 units down.
C
A dilation could have been applied because all of the vertices increased 2 units.
D
An isometric transformation could have been applied because all of the vertices moved 2 units left and 2 units up.
15

Consider the reflectional symmetry of the shape.

Question illustration
A
2
B
3
C
4
D
5
16

The blades of a windmill turn on an axis that is 35 feet above the ground. The blades are 10 feet long and complete two rotations every minute. Which of the following equations can be used to model h, the height in feet of the end of one blade, as a function of time, t, in seconds? Assume that the blade is pointing to the right, parallel to the ground at t = 0 seconds, and that the windmill turns counterclockwise at a constant rate.

A
h = negative 10 sine (StartFraction pi Over 15 EndFraction t) + 35
Option A
B
h = negative 10 sine (Pi t) + 35
Option B
C
h = 10 sine (StartFraction pi Over 15 EndFraction t) + 35
Option C
D
h = 10 sine (Pi t) + 35
Option D
17

Which statements are true about the relationship between the figures? Select three options.

A
Quadrilateral A'B'C'D' is an isometric transformation of quadrilateral ABCD.
B
Angle D' will have the same measure as angle B.
C
Angle C' will have the same measure as angle A.
D
Segment AB can be obtained through an isometric transformation of segment BC.
E
Segment C’D’ cannot be obtained through an isometric transformation of segment AD.
18

The blades of a windmill turn on an axis that is 30 feet from the ground. The blades are 10 feet long and complete 2 rotations every minute. Write a sine model, y = asin(bt) + k, for the height (in feet) of the end of one blade as a function of time t (in seconds). Assume the blade is pointing to the right when and that the windmill turns counterclockwise at a constant rate.

Question illustration
A
y = 30 sine (StartFraction pi Over 15 EndFraction t) + 10
Option A
B
y = 30 sine (StartFraction pi Over 15 EndFraction t) + 30
Option B
C
y = 10 sine (StartFraction pi Over 15 EndFraction t) + 10
Option C
D
y = 10 sine (StartFraction pi Over 15 EndFraction t) + 30
Option D
19

Which image does not have reflective symmetry?

A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
20

The graph shows trapezoid F'G'H'J'.

Question illustration
A
FJ must be parallel to GH.
B
FG must have the same measure as HJ.
C
JH must be perpendicular to H'J'.
D
JJ' must be the same distance as HH'.

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