Download MTH 232 Practice Test Problems (7.1-7.3, 10.1-10.5).tst

Practice Test Problems (Sections 7.1-7.3 10.1-10.5)
Name___________________________________
Express the ratio in simplest form.
1) $80 to $104
15) Matt bought a 32 oz can of fuel additive for
$43.52. Roger bought the 16 oz size for $26.24.
Who made the better buy? What was the lowest
price per ounce?
2) 24 inches to 15 inches
16) Which is the better buy: one yard of ribbon for
$0.67 or three feet of ribbon at $0.36 per foot.
3) The ratio of wins to games played if a baseball
team wins 25 games and loses 60 games
Solve the proportion.
10
6
17) = x x + 20
4) 6 feet to 60 inches
5) 8 minutes to 3 hours
18)
6) 14 hours to 96 days
1
1
7) 3 days to 5 weeks
2
2
5 x - 10
= 3
10
Use a proportion to solve the problem. Round answers to the
nearest tenth if necessary.
19) Dr. Wong can see 9 patients in 2 hours. At this
rate, how long would it take her to see 72
patients?
Solve the problem.
8) The ratio of staff to patients at Lakeview is 4 to 7.
If total staff plus patients is 1430 people, how
many staff are at Lakeview?
20) The 12th hole at the Riverwoods Golf Course is
440 yards long. How long would it be on a model
with a scale of 0.5 inches to 100 yards?
9) Carl wants to make some furniture stripper. The
stripper is a mixture of chemicals A and B in the
ratio of 11 to 4. How many ounces of chemical A
are needed to make 150 ounces of stripper?
21) Jim drove 336 miles in 7 hours. If he can keep the
same pace, how long will it take him to drive 1392
miles?
10) The ratio of the distances a pitching wedge and an
8-iron will drive a golf ball is 4 to 5. If a golfer
averages 137 yards with a pitching wedge, how
far should she average with an 8-iron?
22) In a sample of 94 widgets, 2 were defective. How
many defective widgets would you expect in a
sample of 188 widgets?
Use a proportion to solve the problem.
23) If a spring stretches 8 meters when a weight of
3-kilograms is attached to it, how much will it
stretch when a weight of 21-kilograms is attached
to it?
11) The trim for a costume costs $11.25 for 4.5 yd.
Find the unit price in dollars per yard.
12) A 3-lb package of ground beef costs $5.37. What
is the unit price in cents per ounce? Round to the
nearest hundredth of a cent.
24) The ratio of the lengths of strings that play the
notes F and G is 9 to 8. If a string 80 centimeters
long plays a G, what is the length of the string
that plays an F?
13) Find the best buy.
Brand X 8 oz for $0.56
Brand Y 6 oz for $0.36
25) On a map of the Fox River, 1 centimeter
represents 7 kilometers. If a trail by the river is
actually 28.00 kilometers long, what is the length
of the river on the map?
14) Find the best buy.
Brand A 20 oz for $14.60
Brand B 24 oz for $17.76
1
38) 366%
Provide an appropriate response.
26) Explain the process you would use to determine
the best buy.
2
39) 38 %
3
27) Suppose that Jody drove 80 miles in 2 hours.
Dividing 80 by 2 tells us how many miles Jody
drove in each hour. The units for this rate are
miles per hour (mi/hr). If we divide 2 by 80 what
information would this give us? Give an
2
interpretation of the rate = 0.025. What units
80
40)
4
%
9
41) 0.04%
would be used for this rate?
Solve the problem.
42) On a biology test, a student got 25 questions
correct but did not pass. On a second attempt, the
student got 34 questions correct. What was the
percent of increase?
Find the percent of the figure that is shaded.
28)
43) Enrollment in a business seminar increased from
62 people to 81 people. What was the percent of
increase?
44) By switching service providers, a familyʹs
telephone bill decreased from about $50 a month
to about $45. What was the percent of decrease?
29)
45) All 33 of the students in a mathematics class
attended class on Monday. On Tuesday only 25
students attended. What was the percent of
decrease?
Write the ratio as a percent.
7
30)
36
31)
46) A carpeted living room and dining room area
measures 32 ft by 13 ft. Mark decides to install
wood flooring in the 15 ft by 13 ft dining room. By
what percent has he reduced the area that is
carpeted?
25
40
Solve the problem. If the answer is an amount of money,
round to the nearest dollar.
47) The parking lot at a grocery store has 64 cars in it.
75% of the cars are blue. How many cars are blue?
8.36
32)
7.82
Write as a percent.
33) 0.47
48) The Perrones have saved $20,400 for a down
payment. If a 31% down payment is required,
what price house can they buy?
34) 0.953
49) Alex and Juana went on a 100-mile canoe trip
with their class. On the first day they traveled 26
miles. What percent of the total distance did they
canoe?
35) 4.8
36) 1
Write the percent as a fraction in the lowest terms.
37) 6%
2
50) Which is the best investment for three consecutive
years?
a. A growth of 2% followed by a growth of 4%
followed by a growth of 6%
b. A growth of 6% followed by a growth of 4%
followed by a growth of 2%
c. Three years of growth at 4% per year.
59) What is the vertex of ∠DEI?
Describe the figure.
60)
A) Simple nonconvex polygon
B) Nonsimple closed curve
C) Simple polygon
D) Simple closed curve
51) If a number is increased by 11%, by what percent
must it be decreased to obtain the original
number? Round to the nearest hundredth if
necessary.
61)
Use the following figure to verify if statement is true or false.
A) Simple closed curve
B) Simple curve
C) Closed curve
D) None of the above
62)
52) AB and GF are skew lines.
A) Simple polygon
C) Closed polygon
53) AB and CG are intersecting lines.
B) Convex polygon
D) All of the above
63)
54) AK and EK are perpendicular to the plane BEF.
55) AD and BC are coplanar lines.
Refer to this figure to answer the question.
A) Simple convex polygon
B) Nonconvex polygon
C) Nonsimple polygon
D) Convex polygon
64)
A) Simple closed curve
B) Closed curve
C) Simple curve
D) None of the above
56) What are the endpoints of HI ?
57) What are the endpoints on DE ?
Decide whether the figure is convex or not convex.
65)
58) Are HD and HA the same line?
3
66)
72)
Classify the triangle as equilateral, isosceles, or scalene.
Then classify it as right, obtuse, or acute.
67)
73)
10
8
4
68)
74)
6
5
3
69)
15
Find the requested angle.
75) Complement of 3°
15
76) Supplement of 68.5°
15
27
70)
19
77) Supplement of 129°
19
1
78) Complement of 41 °
2
Classify the polygon by name.
71)
Decide whether or not the network is traversable.
79)
80)
4
81)
Given the floor plan, determine whether a person could
traverse through each unit by passing through each door
only once.
85)
82)
86)
Give an appropriate answer.
83) Use the following graph to find a traversable path
that begins with vertex A.
87)
A) A → C → D → A → B → D
B) No traversable path exists.
C) B → A → D → C
D) A → B → D → C
84) Use the following graph to find a traversable path
that begins with vertex B.
A) B → A → C → D
B) B → A → D → C
C) B → A → D → C → A → B
D) No traversable path exists.
Give the appropriate answer.
88) What is the name for the point where the three
medians are concurrent?
89) Can a triangle be both obtuse and scalene?
90) Decide whether the statement is true or false. Two
lines in the same plane are called skew.
5
91) Decide whether the statement is true or false. The
three angles of a triangle are always
supplementary.
96) Identify all pairs of alternate interior angles.
92) Decide whether the statement is true or false. In
every triangle, the centroid, orthocenter, and
circumcenter are collinear.
Refer to the figure and provide an appropriate name for the
indicated angles.
97) Identify all pairs of alternate interior angles.
93) ∠6 and ∠7
A) Right angle
B) Alternate interior angles
C) Supplementary angles
D) Complementary angles
94) ∠3 and ∠7
A) Alternate exterior angles
B) Alternate interior angles
C) Supplementary angles
D) Complementary angles
Refer to this figure to answer the question. Line DH is
parallel to line IM. Line BO is perpendicular to line DH.
Identify the specified angles.
95) Identify all pairs of corresponding angles.
98) m∠IJN is 59°. What is the measure of ∠DEA?
99) m∠IJN is 54°. What is the measure of ∠DEJ?
100) Are ∠MLG and ∠FGC supplementary?
101) Choose the true statement.
6
Use the properties of parallel lines to solve the problem.
102) If p  q and m∠8 = 59°, what are the measures of
the other angles?
105) In the figure, GH  DE . Identify any pairs of
congruent angles.
103) In the figure, AB  CD . Identify all pairs of
congruent angles.
Solve the problem.
106) Find the measure of the indicated exterior angle.
∠x = (5n - 17)°, ∠y = (n + 9)°, ∠z = (157 - 5n)°
107) Find the measure of the indicated exterior angle.
104) In the figure, BC  DE . Identify any pairs of
congruent angles.
∠x = (198 - 5n)°, ∠y = (6n + 8)°, ∠z = (n + 10)°
108) What is the angle sum of a regular polygon with 4
sides?
109) What is the angle sum of a regular polygon with
10 sides?
110) If each angle of a regular polygon measures 108°,
how many sides does it have?
111) If each angle of a regular polygon measures 150°,
how many sides does it have?
Answer the question.
112) What is the measure of the central angle of a
regular polygon with 16 sides?
113) How many triangles are formed in a polygon
with 15 sides?
7
119)
Answer the question. Figures not drawn to scale.
114) Find the measure of ∠P
60°
140°
115) Find the measure of ∠P
200°
120)
70°
121)
12
116) Find the measure of ∠P
8
8
260°
12
100°
122)
117) Find the measure of ∠P
Find the missing length in the right triangle. If necessary,
round to the nearest tenth.
123)
50°
5 cm
Which property (if any), should be used to show that the pair
of triangles is congruent?
118)
12
5
8 cm
124)
13 cm
9 cm
5
125)
7
12
18 in.
7
20 in.
8
132) The length of a rectangle is 72 meters, and the
width is 21 meters. Find the measure of the
diagonal of the rectangle.
72 meters
126)
10 mi
5 mi
21 meters
Find d in simplest radical form.
127)
Find d in simplest radical form.
133)
3
3
128)
7
2
134)
2
2
Cube
12
Solve the problem. Give the answer to the nearest
thousandth if necessary.
129) A long-distance runner runs 3 miles south and
then 9 miles east. How far is the runner from the
starting point?
135)
7 2
South
↓
3 mi
East --9 mi-->
130) A boat travels 4 miles south and then 8 miles east.
How far is the boat from its starting point?
136)
South
↓
4 mi
2 2
East --8 mi-->
131) A painter leans a ladder against one wall of a
house (as shown below). The ladder is 29 ft long.
The base of the ladder is 23 ft from the house.
How high is the wall?
29 ft
?
23 ft
9
140) PM = 32 and LP = 46. Find the length of each
diagonal.
Find the measures of the indicated sides, angles, or diagonals
of the given parallelogram.
137) Find the measures of the angles of the
parallelogram when m∠D = 61°.
Answer the question.
141) What type of figure is formed by joining the
midpoints of the sides of a kite?
138) Two side lengths of a parallelogram are given.
Find the lengths of the other sides of the
parallelogram.
142) Choose the word ʺparallelogram,ʺ ʺrectangle,ʺ
ʺsquare,ʺ or ʺrhombusʺ that could be used in the
blank to make the statement true. If none of the
words can be used, write ʺnone.ʺ
A quadrilateral is a ___ if and only if all of its
diagonals bisect its angles.
19
10
143) Choose the word ʺrectangle,ʺ ʺsquare,ʺ or
ʺrhombus,ʺ that could be used in the blank to
make the statement true. If none of the words
can be used, write ʺnone.ʺ
A parallelogram is a ___ if and only if
its diagonals are congruent.
139) One side length of a parallelogram is given. The
perimeter of ▱HIJK is 75. Find the lengths of the
other sides of the parallelogram.
15
144) Choose the word ʺrectangle,ʺ ʺsquare,ʺ or
ʺrhombus,ʺ that could be used in the blank to
make the statement true. If none of the words
can be used, write ʺnone.ʺ
A parallelogram is a ___ if and only if
it has at least one right angle and four congruent si
.
1
2
145) Choose the word ʺrectangle,ʺ ʺsquare,ʺ or
ʺrhombus,ʺ that could be used in the blank to
make the statement true. If none of the words
can be used, write ʺnone.ʺ
A parallelogram is a ___ if and only if
it has four congruent sides,its diagonals bisect the a
.
146) Choose the word ʺrectangle,ʺ ʺsquare,ʺ or
ʺrhombus,ʺ that could be used in the blank to
make the statement true. If none of the words
can be used, write ʺnone.ʺ
A parallelogram is a ___ if and only if
it has exactly one pair of parallel side.
10
147) Choose the word ʺkite,ʺ ʺtrapezoid,ʺ or
ʺparallelogram,ʺ that could be used in the blank to
make the statement true. If none of the words
can be used, write ʺnone.ʺ
A quadrilateral is a ___ if and only if one pair of
opposite sides are parallel.
148) Choose the word ʺkite,ʺ ʺtrapezoid,ʺ or
ʺparallelogramʺ that could be used in the blank to
make the statement true. If none of the words
can be used, write ʺnone.ʺ
A quadrilateral is a ___ if and only if
a pair of adjacent angles are congruent.
149) Does the following condition ensure that a
quadrilateral is a parallelogram?
One pair of opposite sides are both parallel and con
.
150) Does the following condition ensure that a
quadrilateral is a parallelogram?
One pair of opposite sides are congruent.
11
Answer Key
Testname: MTH 232 PRACTICE TEST PROBLEMS (7.1‐7.3, 10.1‐10.5)
1) 10 : 13
2) 8 : 5
3) 5 : 17
4) 6 : 5
5) 2 : 45
6) 7 : 1152
7) 1 : 11
8) 520
9) 110
10) 171.25 yd
11) $2.50 per yd
12) 11.19 cents per
oz
13) Brand Y
14) Brand A
15) Matt, $1.36
16) One yard
17) 30
80
18)
3
19) 16 hours
20) 2.2 in.
21) 29 hr
22) 4 widgets
23) 56 meters
24) 90 centimeters
25) 4.0 centimeters
26) Answers will
vary. The best
buy is the
container with
the lowest cost
per unit. To
determine the
cost per unit,
divide the price
of the container
by the number
of units in it.
27) Answers will
vary. The rate
2
= 0.025 tells
80
us how many
hours it took
Jody to drive
each mile. The
units are hours
per mile (hr/mi).
28) 1%
29) 12%
4
30) 19 %
9
31) 62.5%
32) 106.91%
33) 47%
34) 95.3%
35) 480%
36) 100%
3
37)
50
38) 3
33
50
39)
29
75
40)
1
225
41)
1
2500
42) 36%
43) 30.6%
44) 10%
45) 24.2%
46) 46.9%
47) 48 cars
48) $65,806
49) 26%
50) c
51) 9.91%
52) TRUE
53) FALSE
54) FALSE
55) TRUE
56) H
57) None
58) Yes
59) E
60) D
61) C
62) D
63) B
64) D
65) Not convex
66) Convex
67) Scalene; obtuse
68) Scalene; acute
69) Equilateral;
acute
70) Isosceles; obtuse
71) quadrilateral
72) heptagon
73) octagon
74) decagon
75) 87°
76) 111.5°
77) 51°
1
78) 48 °
2
79) Traversable
80) Traversable
81) Not traversable
82) Traversable
83) A
84) D
85) No
86) No
87) Yes
88) centroid
89) yes
90) False
91) False
92) True
93) D
94) B
95) ∠1 and∠5, ∠2
and∠6, ∠4 and
∠8, ∠3 and∠7
96) ∠4 and∠6, ∠3
and∠5
97) ∠2 and∠6, ∠3
and∠7
98) 121°
99) 54°
100) Yes
101) ∠FGL and
∠GLK are
supplementary.
102) m∠2 = m∠4 = m
∠6 = 59°, m∠1 =
m∠3 = m∠5 = m
∠7 = 121°
103) ∠ABE and
∠FCD , ∠ABC
and ∠BCD
104) ∠ABC and
∠ADE, ∠ACB
and ∠AED
105) ∠EDF ≅ ∠GHF,
∠DFE ≅ ∠HFG,
∠DEF ≅ ∠FGH,
∠DFG ≅ ∠EFH
106) 82°
107) 123°
108) 360°
109) 1440°
110) 5 sides
12
111)
112)
113)
114)
115)
116)
117)
118)
119)
120)
121)
122)
123)
124)
125)
126)
127)
128)
129)
130)
131)
132)
133)
134)
135)
12 sides
22.5°
13
100°
65°
80°
50°
SSS
SAS
None
SAS
HA
9.4 cm
9.4 cm
26.9 in.
8.7 mi
3 2
2 3
9.487 mi
8.944 mi
17.664 ft
75 meters
14
6 3
14
2 3
136)
3
137) m∠F = 61°, m
∠G = m∠E =
119°
138) PS = 10, SR = 19
1
139) HK = 15 , HI =
2
JK = 22
140) LN = 92, MO =
64
141) rectangle
142) rhombus
143) rectangle
144) square
145) rhombus
146) none
147) trapezoid
148) none
149) Yes
150) No