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10th Grade Math

Multiple Choice
Identify the choice that best completes the statement or answers the question.
 

 1 

A car salesperson earns a weekly base salary of $500 plus a commission rate of 4% on his sales for the week. If last week he had gross earnings of $745, what were his sales for the week?
A
$245
C
$12,500
B
$6,125
D
$18,625
 

 2 

Three fair coins are tossed. What is the probability that the coins will show at least two heads?
A
1
C
mc002-2.jpg
B
mc002-1.jpg
D
mc002-3.jpg
 
 
Three students ran for student council secretary at a local high school The results of the election are listed by class below. Only juniors and seniors were eligible to vote.
Student Council Secretary Election Results
 
Kunio Kato
Frank Rodriguez
Rosa Smith
Juniors
170
136
108
Seniors
186
169
59
Total
356
305
167
 

 3 

Consider the Student Council Secretary Election Results. What percent of juniors voted for Kunio Kato?
A
32.9%
C
26.1%
B
41.1%
D
44.9%
 

 4 

Meredith’s quiz scores this semester are shown in the table below. Which of the following measures should she choose to make her average quiz grade appear as high as possible?
Quiz Number
1
2
3
4
5
6
7
8
9
Grade
78
78
92
81
81
78
73
80
85
A
mode
C
median
B
range
D
mean
 

 5 

Triangle ABC, shown in the diagram below, is an isosceles triangle.
mc005-1.jpg
If the measure of mc005-2.jpg is 130°, what is the measure of mc005-3.jpg?
A
220°
C
65°
B
50°
D
130°
 

 6 

Regular polygon ABCDE is shown below.
mc006-1.jpg
If each side of the polygon measures 8, then what is the measure of each interior angle of polygon ABCDE?
A
36°
C
mc006-4.jpg
B
450°
D
108°
 

 7 

Below are two triangles.
mc007-1.jpg
What additional information do you need to verify whether the two triangles are similar?
A
The sum of the angles in each triangle is 180°.
C
mc007-2.jpg measures the same as mc007-3.jpg.
B
Angle C is equal in measure to angle F.
D
mc007-4.jpg measures 23.
 

 8 

Below are two triangles.
mc008-1.jpg
What additional information do you need to verify whether the two triangles are similar?
A
The sum of the angles in each triangle is 180°.
C
Angle ACB is equal in measure to angle F.
B
mc008-2.jpg measures the same as mc008-3.jpg.
D
mc008-4.jpg measures 27.
 

 9 

In the figure below, the shaded area is a planar cross section of the conic solid.
mc009-1.jpg
What is the area, in square centimeters, of the cross-section inside of the cone?
A
78.54
C
36.65
B
19.63
D
4.91
 

 10 

In the manufacturing of a car part, the solid below is cut in half by a knife passing from its top directly through to its bottom, in the same orientation as it appears.
mc010-1.jpg
What is the most accurate representation of the resulting cross section?
A
mc010-2.jpg
C
mc010-4.jpg
B
mc010-3.jpg
D
mc010-5.jpg
 

 11 

Edgar designed a new shoe box for an athletic shoe company. The volume of the box for a pair of size 11 shoes is 518.7 cubic inches. If the box has a rectangular base measuring 13.3 inches by 7.5 inches, what is the height of the box?
mc011-1.jpg
A
4.1 inches
C
5.2 inches
B
4.7 inches
D
5.1 inches
 

 12 

A landscaper planted 50 flowers around the base of a circular fountain in front of a municipal building. The radius of the fountain is 11.5 feet, and each flower is located 4 feet away from the fountain’s base. What is the length of the arc between each pair of adjacent flowers? Round your answer to the hundredth of a foot.
A
1.45 feet
C
2.93 feet
B
1.95 feet
D
3.42 feet
 

 13 

The volume of the cone is approximately 160 cubic units. What is the radius of the cone, to the nearest hundredth?
mc013-1.jpg
A
4.01 units
C
8.02 units
B
11.99 units
D
2.98 units
 

 14 

The speed of sound is affected by temperature, humidity, and altitude. At sea level, if the temperature is 70°F and the relative humidity is 30%, sound waves travel at approximately 1,135.4 feet per second. How fast does sound travel in miles per hour in these conditions? Round your answer to the nearest tenth.
A
869 miles per hour
C
786.2 miles per hour
B
808.2 miles per hour
D
774.1 miles per hour
 

 15 

Rather than following a sidewalk, a student on her way to school cuts across a vacant lot, as shown in the diagram below. All lengths are in feet.
mc015-1.jpg
What statement best characterizes the difference between the lengths of the two paths?
A
The path across the vacant lot is about 0.72 times the length of the sidewalk path.
B
The path down the sidewalk is 20 feet shorter in length than that of the path across the vacant lot.
C
The path down the sidewalk is about 0.72 times the length of the path across the vacant lot.
D
The path across the vacant lot is about 1.39 times the length of the sidewalk path.
 

 16 

If the radius of a cone is multiplied by 4, and the height is multiplied by 6, by what amount will the volume be multiplied?
A
4
C
96
B
24
D
6
 

 17 

Elaine plans to make her special Apple-Granola Jumble to take to a party. The recipe calls for an 11-inch diameter round pan. Elaine only has a 10-inch square pan, an 11-inch square pan, a 12-inch square pan, and a 12-inch diameter round pan. Which pan comes closest in area to the one that the recipe calls for?
A
11-inch square pan
C
10-inch square pan
B
12-inch diameter round pan
D
12-inch square pan
 

 18 

A manufacturing assembly line can produce 21 items per minute. How many items can the assembly line produce in 6 hours?
A
4
C
126
B
7,560
D
210
 

 19 

An architect uses the Pythagorean theorem to determine that the length of a beam is mc019-1.jpg feet long. Between which two consecutive integers does mc019-2.jpg lie on a number line?
A
9 and 10
C
6 and 7
B
5 and 6
D
7 and 8
 

 20 

Betty is building a wooden frame for a painting that she drew in art class. For added stability the frame will have two diagonal braces in the back. She determines that the length of one of the braces is mc020-1.jpg inches. What is the length of the brace rounded to the nearest tenth of an inch?
mc020-2.jpg
A
24.6 inches
C
31.2 inches
B
22.4 inches
D
29.7 inches
 

 21 

Jaime used a pair of similar triangles to calculate the distance across a river. He found that the river is mc021-1.jpg meters wide. What is this distance written as a decimal to the nearest hundredth?
A
25.19 meters
C
18.41 meters
B
24.04 meters
D
22.35 meters
 

 22 

A biologist finds the mass of an insect to be mc022-1.jpg grams. Express this number as a fraction in simplified form.
A
mc022-4.jpg
C
mc022-6.jpg
B
mc022-5.jpg
D
mc022-7.jpg
 

 23 

Of the students in Mr. Clayton’s geometry class, 9.4% play only basketball, 12.6% play volleyball exclusively, 11.6% play football only, and 12.4% are only on the swimming team. Use mental math to find the percent of students in the class who only play one sport.
A
46%
C
50.9%
B
34%
D
42.7%
 

 24 

Koto needs to cut pipes for her plumbing business. She needs pipes that are mc024-1.jpg feet, mc024-2.jpg feet, and mc024-3.jpg feet long. If the piece of pipe originally measured 16 feet, how much of the pipe will be left after she is done cutting the pieces off?
A
2 feet
C
30 feet
B
4.2 feet
D
18.2 feet
 

 25 

The absolute value of a number is the distance that it is located from zero on the number line. How far is mc025-1.jpg from zero on the number line?
A
18
C
mc025-2.jpg
B
–27
D
mc025-3.jpg
 
 
nar002-1.jpg
 

 26 

A, B, C, D, and E are five points on the number line. Which one represents a number that, when squared, will change its sign?
A
A
C
C
B
D
D
B
 

 27 

A, B, C, D, and E are five points on the number line. Which one represents a number that, when squared, will not change value?
A
D
C
A
B
E
D
C
 

 28 

A, B, C, D, and E are five points on the number line. Consider the pairs C and D, D and E, A and D, and B and A. Of those pairs, which pair of points can be multiplied together to get a negative number?
A
C and D
C
B and A
B
A and D
D
D and E
 

 29 

If you were to take the number represented by Point C and cube it, would the result be less than –1, between –1 and 0, between 0 and 1, or greater than 1?
A
greater than 1
C
between 0 and 1
B
between -1 and 0
D
less than -1
 

 30 

Gerri wants to evaluate the following expression:
mc030-1.jpg
What value is equivalent to the expression?
A
–296.296
C
–216,000
B
–18.519
D
–0.741
 



 
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