So, the correct choice is D.
Standardized Test Practice - Cumulative, Chapters 1-7
1. Adrian wants to measure the width of a ravine.
He marks distances as shown in the diagram.
Using this information, what is the approximate width
of the ravine?
A 5 ft
B 6 ft
C 7 ft
D 8 ft
ANSWER: D
2. Kyle and his family are planning a vacation in
Cancun, Mexico. Kyle wants to convert 200 US
dollars to Mexican pesos for spending money. If 278
Mexican pesos are equivalent to $25, how many
pesos will Kyle get for $200?
F 2178
G 2224
H 2396
J 2504
SOLUTION: Let the unknown number of pesos be x.
Form a proportion for the given information.
SOLUTION: By AA Similarity,
Use the corresponding side lengths to write a
proportion.
So, the correct option is G.
Substitute and solve for x: ANSWER: G
4. Refer to the figures below. Which of the following
terms best describes the transformation?
So, the correct choice is D.
ANSWER: D
SOLUTION: F congruent The figures are not the same size, therefore, they are not congruent. G enlargement This is the correct choice. The image to the right of the arrow is larger than the
preimage. H reduction This is not the correct choice. The image to the right of the arrow is larger than the
preimage. J scale The figures are not the same size, therefore, they are not the same scale. G
2. Kyle and his family are planning a vacation in
Cancun, Mexico. Kyle wants to convert 200 US
dollars to Mexican pesos for spending money. If 278
Mexican pesos are equivalent to $25, how many
pesos will Kyle get for $200?
F 2178
G 2224
H 2396
J 2504
SOLUTION: Let the unknown number of pesos be x.
Form a proportion for the given information.
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ANSWER: G
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5. The ratio of North Carolina residents to Americans is
about 295 to 10,000. If there are approximately
So, the correct option is G.
ANSWER: Standardized
Test Practice - Cumulative, Chapters 1-7
G
4. Refer to the figures below. Which of the following
terms best describes the transformation?
SOLUTION: F congruent The figures are not the same size, therefore, they are not congruent. G enlargement This is the correct choice. The image to the right of the arrow is larger than the
preimage. H reduction This is not the correct choice. The image to the right of the arrow is larger than the
preimage. J scale The figures are not the same size, therefore, they are not the same scale. G
ANSWER: G
5. The ratio of North Carolina residents to Americans is
about 295 to 10,000. If there are approximately
300,000,000 Americans, how many of them are
North Carolina residents?
A 7,950,000
B 8,400,000
C 8,850,000
D 9,125,000
SOLUTION: Let the unknown number of North Carolina residents
be x.
G
ANSWER: G
5. The ratio of North Carolina residents to Americans is
about 295 to 10,000. If there are approximately
300,000,000 Americans, how many of them are
North Carolina residents?
A 7,950,000
B 8,400,000
C 8,850,000
D 9,125,000
SOLUTION: Let the unknown number of North Carolina residents
be x.
Form a proportion for the given information.
So, the correct option is C.
ANSWER: C
7. Two similar trapezoids have a scale factor of 3:2.
The perimeter of the larger trapezoid is 21 yards.
What is the perimeter of the smaller trapezoid?
A 14 yd
B 17.5 yd
C 28 yd
D 31.5 yd
SOLUTION: Let the unknown perimeter be x.
Form a proportion for the given information.
Form a proportion for the given information and solve
for x:
So, the correct option is C.
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ANSWER: C
So, the correct option is A.
ANSWER: A
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So, the correct option is C.
ANSWER: Standardized
Test Practice - Cumulative, Chapters 1-7
C
7. Two similar trapezoids have a scale factor of 3:2.
The perimeter of the larger trapezoid is 21 yards.
What is the perimeter of the smaller trapezoid?
A 14 yd
B 17.5 yd
C 28 yd
D 31.5 yd
Therefore, about 203 students in the school have
homework four nights a week. ANSWER: 203
9. GRIDDED RESPONSE In the triangle below,
Solve for x.
SOLUTION: Let the unknown perimeter be x.
Form a proportion for the given information and solve
for x:
SOLUTION: By AA Similarity,
Use the corresponding side lengths to write a
proportion.
Substitute.
Solve for x.
So, the correct option is A.
ANSWER: A
8. GRIDDED RESPONSE Colleen surveyed 50
students in her school and found that 35 of them have
homework at least four nights a week. If there are
290 students in the school altogether, how many of
them would you expect to have homework at least
four nights a week?
SOLUTION: Let x be the unknown number of students who have
homework at least four nights a week. Form a proportion for the given information and solve
for x: ANSWER: 9
10. Quadrilateral WXYZ is a rhombus. If m XYZ =
110°, find m ZWY.
Therefore, about 203 students in the school have
homework four nights a week. ANSWER: 203
9. GRIDDED RESPONSE In the triangle below,
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SOLUTION: A rhombus is a parallelogram with all four sides
congruent. So,
Then, is an isosceles triangle. Therefore,
If a parallelogram is a rhombus, then each diagonal
bisects a pair of opposite angles. So,
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.
Therefore,
ANSWER: Standardized
Test Practice - Cumulative, Chapters 1-7
9
10. Quadrilateral WXYZ is a rhombus. If m XYZ =
110°, find m ZWY.
ANSWER: 10
13. GRIDDED RESPONSE The scale of a map is 1
inch = 2.5 miles. What is the distance between two
cities that are 3.3 inches apart on the map? Round to
the nearest tenth, if necessary.
SOLUTION: Let the unknown actual distance between the two
cities be x.
SOLUTION: A rhombus is a parallelogram with all four sides
congruent. So,
Then, is an isosceles triangle. Therefore,
If a parallelogram is a rhombus, then each diagonal
bisects a pair of opposite angles. So,
Form a proportion for the given information and solve
for x: .
Therefore,
ANSWER: 55°
12. GRIDDED RESPONSE In the triangle below,
bisects VRU. Solve for x.
SOLUTION: An angle bisector in a triangle separates the opposite
side into two segments that are proportional to the
lengths of the other two sides.
Therefore, the two cities are 8.25, or 8.3, miles
apart. ANSWER: 8.3
15. Refer to triangle XYZ to answer each question.
a. Suppose
What do you know about the relationship between segments XQ, QZ, YR, and RZ?
b. If
XQ = 15, QZ = 12, and YR = 20,
what is the length of
c. Suppose
and QR = 9.5 units.
What is the length of
SOLUTION: ANSWER: 10
13. GRIDDED RESPONSE The scale of a map is 1
inch = 2.5 miles. What is the distance between two
cities that are 3.3 inches apart on the map? Round to
the nearest tenth, if necessary.
SOLUTION: Let the unknown actual distance between the two
cities be x.
a. Since
, we know that the segments cut
off by these parallel lines are proportional ( Corollary
7.1). Therefore,
.
b. Substitute and solve for RZ:
Form a proportion for the given information and solve
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Therefore, the two cities are 8.25, or 8.3, miles
apart. ANSWER: Standardized
Test Practice - Cumulative, Chapters 1-7
8.3
15. Refer to triangle XYZ to answer each question.
a. Suppose
What do you know about the relationship between segments XQ, QZ, YR, and RZ?
b. If
XQ = 15, QZ = 12, and YR = 20,
what is the length of
c. Suppose
and QR = 9.5 units.
What is the length of
SOLUTION: a. Since
, we know that the segments cut
off by these parallel lines are proportional ( Corollary
7.1). Therefore,
.
b. Substitute and solve for RZ:
c. Since
is the midsegment of the triangle XYZ. Therefore, since QR = 9.5, then
or 19.
ANSWER: a.
b. 16 units
c. 19 units
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