Mathematics Knowledge · Practice test 3

25 questions · 24 minutes

Answer every question, then tap Check results to see your score and the method behind each answer.

Question 1Not answered

A right triangle has a hypotenuse of 17 and one leg of 8. What is the length of the other leg?
1. 9
2. 15
3. 25
4. 19.7
Correct answer: 15

By the Pythagorean theorem, the missing leg squared equals 17 squared minus 8 squared, or 289 - 64 = 225, so the leg is 15.

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Question 2Not answered

What is the volume of a cube with an edge of 6?
1. 216
2. 36
3. 18
4. 24
Correct answer: 216

A cube's volume is the edge cubed, so 6 x 6 x 6 = 216.

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Question 3Not answered

Two parallel lines are cut by a transversal. If one interior angle measures 65 degrees, what does the interior angle on the same side of the transversal measure?
1. 65 degrees
2. 115 degrees
3. 25 degrees
4. 130 degrees
Correct answer: 115 degrees

Interior angles on the same side of the transversal are supplementary, so they add to 180 and the other is 115. Angles that are equal to 65 in this figure are the corresponding and alternate interior ones, which is why 65 is offered.

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Question 4Not answered

What is the next term in the sequence 4, 9, 14, 19, ...?
1. 24
2. 23
3. 25
4. 38
Correct answer: 24

Each term is 5 more than the one before it, so this is an arithmetic sequence with a common difference of 5. The next term is 19 + 5 = 24.

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Question 5Not answered

A rectangle measuring 12 by 8 has a rectangular piece measuring 4 by 3 cut out of it. What area remains?
1. 96
2. 108
3. 72
4. 84
Correct answer: 84

Work out both areas and subtract. The whole rectangle is 96 and the cut-out piece is 12, so 96 - 12 = 84 remains.

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Question 6Not answered

Evaluate 5 + 2 x (9 - 5) / 4
1. 9
2. 6
3. 7
4. 14
Correct answer: 7

Brackets first: 9 - 5 = 4. Multiply and divide left to right: 2 x 4 = 8, then 8 / 4 = 2. Finally add: 5 + 2 = 7.

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Question 7Not answered

Written in scientific notation, 0.00042 equals 4.2 x 10 to what power?
1. -3
2. 4
3. -5
4. -4
Correct answer: -4

Move the decimal point right until one non-zero digit stands before it: 0.00042 becomes 4.2 after four places. Moving right means a negative exponent, so the answer is 10 to the -4.

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Question 8Not answered

What is the value of |-9| + |-4|?
1. 13
2. -13
3. 5
4. -5
Correct answer: 13

Absolute value gives the distance from zero regardless of sign, so |-9| is 9 and |-4| is 4, and 9 + 4 = 13.

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Question 9Not answered

What is the measure of each interior angle of a regular hexagon?
1. 120 degrees
2. 60 degrees
3. 135 degrees
4. 720 degrees
Correct answer: 120 degrees

The interior angles of a hexagon total (6 - 2) x 180 = 720 degrees, and sharing that between six equal angles gives 120 each. The choice 720 is the total rather than each angle.

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Question 10Not answered

Written in scientific notation, 0.0058 equals 5.8 x 10 to what power?
1. -3
2. 3
3. -4
4. -2
Correct answer: -3

Move the decimal point right until one non-zero digit stands before it: 0.0058 becomes 5.8 after three places. Moving the decimal right means a negative exponent, so the answer is 10 to the -3.

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Question 11Not answered

A parallelogram measures 9 along its base and stands 6 high. What is its area?
1. 27
2. 30
3. 54
4. 15
Correct answer: 54

A parallelogram's area is base times height, with no halving, so 9 x 6 = 54. Halving as though it were a triangle gives 27.

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Question 12Not answered

What is the square root of 225?
1. 45
2. 15
3. 12.5
4. 112.5
Correct answer: 15

The square root asks which number multiplied by itself gives 225. Since 15 x 15 = 225, the answer is 15.

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Question 13Not answered

At what value of y does the line y = 2x + 7 cross the y-axis?
1. 2
2. -7
3. 0
4. 7
Correct answer: 7

The y-axis is where x = 0, so substituting gives y = 7. In slope-intercept form, the constant term is always the y-intercept.

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Question 14Not answered

If 2x + y = 11 and x - y = 1, what is the value of x?
1. 3
2. 7
3. 5
4. 4
Correct answer: 4

Adding the two equations cancels y: 2x + x = 11 + 1 gives 3x = 12, so x = 4.

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Question 15Not answered

If 2x + 3y = 18 and y = 2, what is the value of x?
1. 6
2. 9
3. 12
4. 3
Correct answer: 6

Substitute y = 2 to get 2x + 6 = 18, so 2x = 12 and x = 6. The choice 12 is the value of 2x rather than x.

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Question 16Not answered

A line passes through the points (2, 3) and (6, 11). What is its slope?
1. 0.5
2. 2
3. 4
4. 8
Correct answer: 2

Slope is the change in y over the change in x. Here y rises by 11 - 3 = 8 while x increases by 6 - 2 = 4, so the slope is 8 / 4 = 2. Dividing the other way round gives 0.5.

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Question 17Not answered

A circle has a circumference of 62.8. Using 3.14 for pi, what is its radius?
1. 20
2. 5
3. 31.4
4. 10
Correct answer: 10

Circumference equals 2 times pi times the radius, so the radius is circumference divided by 2 pi: 62.8 / 6.28 = 10.

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Question 18Not answered

Which of these values is the largest?
1. 3/8
2. 0.35
3. 0.4
4. 1/3
Correct answer: 0.4

Put everything in the same form before comparing. As decimals the four are 0.4, 0.375, 0.35, and about 0.333, so 0.4 is the largest. The fraction 3/8 is the closest rival.

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Question 19Not answered

Written out in full, 5.6 x 10 to the 3rd power equals
1. 56000
2. 560
3. 16.8
4. 5600
Correct answer: 5600

A positive exponent of 3 moves the decimal point three places right, turning 5.6 into 5600. The choice 16.8 comes from multiplying 5.6 by 3 instead.

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Question 20Not answered

The formula for simple interest is I = Prt. If I = 240, P = 2000, and t = 2, what is r?
1. 0.06
2. 0.6
3. 24
4. 0.006
Correct answer: 0.06

Divide both sides by Pt to isolate r: r = I / (Pt) = 240 / 4000 = 0.06.

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Question 21Not answered

What is the value of 9 to the power of 0?
1. 0
2. 9
3. 1
4. -9
Correct answer: 1

Any nonzero number raised to the power of zero equals 1, no matter how large the base is.

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Question 22Not answered

In an equilateral triangle, each angle measures
1. 45 degrees
2. 90 degrees
3. 120 degrees
4. 60 degrees
Correct answer: 60 degrees

All three sides are equal, so all three angles are equal, and they must share 180 degrees between them. That gives 60 degrees each.

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Question 23Not answered

Solve for x: 6x + 4 = 3x + 22
1. 9
2. 6
3. 3.67
4. 26
Correct answer: 6

Move the x terms to one side and the numbers to the other: 6x - 3x = 22 - 4 gives 3x = 18, so x = 6.

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Question 24Not answered

What is the cube root of 27?
1. 9
2. 27
3. 81
4. 3
Correct answer: 3

The cube root asks which number multiplied by itself three times gives 27. Since 3 x 3 x 3 = 27, the answer is 3. The choice 9 is the square root of 81, a common mix-up.

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Question 25Not answered

Two angles are complementary. If one measures 62 degrees, what does the other measure?
1. 28
2. 118
3. 62
4. 152
Correct answer: 28

Complementary angles add to 90 degrees, so the other is 90 - 62 = 28.

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/ 25 answered Check results

Your result

/ 25 correct

The ASVAB has no pass mark. Arithmetic Reasoning, Word Knowledge, Paragraph Comprehension and Mathematics Knowledge make up your AFQT percentile.

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