Mathematics Knowledge · Practice test 7

25 questions · 24 minutes

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

Question 1Not answered

In the expansion of (2x - 3)(x + 5), what is the coefficient of x?
1. -13
2. 7
3. 2
4. -2
Correct answer: 7

Multiply out using FOIL: 2x times 5 gives 10x, and -3 times x gives -3x. Combining the middle terms, 10x - 3x = 7x, so the coefficient is 7.

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Question 2Not answered

What is the greatest common factor that can be pulled out of 15x squared + 25x?
1. 15
2. 25
3. 75
4. 5
Correct answer: 5

The coefficients 15 and 25 share a greatest common factor of 5, and both terms contain at least one x. So the largest term that factors out is 5x, and the numeric part is 5.

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Question 3Not answered

What is the volume of a rectangular solid measuring 7 by 4 by 5?
1. 16
2. 140
3. 70
4. 280
Correct answer: 140

Volume is length times width times height, so 7 x 4 x 5 = 140.

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Question 4Not answered

Using 3.14 for pi, what is the volume of a cone with a radius of 3 and a height of 8, rounded to the nearest tenth?
1. 75.4
2. 226.1
3. 150.7
4. 37.7
Correct answer: 75.4

A cone's volume is one third of pi times radius squared times height. That is 3.14 x 9 x 8 / 3, which is 75.4 rounded to the nearest tenth. Forgetting the one third gives 226.1.

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Question 5Not answered

Using 3.14 for pi, what is the volume of a cylinder with a radius of 3 and a height of 10?
1. 94.2
2. 188.4
3. 282.6
4. 90
Correct answer: 282.6

A cylinder's volume is the area of its circular base times its height. The base is 3.14 x 9 = 28.26, and multiplying by 10 gives 282.6. Using the radius instead of the radius squared gives 94.2.

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Question 6Not answered

The square root of 80 can be written as a times the square root of 5. What is a?
1. 16
2. 4
3. 8
4. 5
Correct answer: 4

Split 80 into 16 x 5. The root of 16 comes out of the radical as 4, leaving the root of 5 behind, so the answer is 4 root 5.

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Question 7Not answered

What is the volume of a cube with an edge of 4?
1. 64
2. 16
3. 12
4. 96
Correct answer: 64

A cube's volume is the edge cubed, so 4 x 4 x 4 = 64. The choice 96 is the surface area, 6 faces of 16 each.

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Question 8Not answered

The formula for perimeter of a rectangle is P = 2L + 2W. If P = 30 and W = 4, what is L?
1. 7.5
2. 22
3. 15
4. 11
Correct answer: 11

Substitute the known values: 30 = 2L + 8. Subtract 8 to get 2L = 22, then divide by 2 to get L = 11.

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Question 9Not answered

Solve for x: 4x = 36
1. 32
2. 9
3. 40
4. 144
Correct answer: 9

Divide both sides by 4 to undo the multiplication, giving x = 9.

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Question 10Not answered

A rectangle has a perimeter of 36 and a length of 11. What is its width?
1. 14
2. 25
3. 7
4. 18
Correct answer: 7

The two lengths use 22 of the perimeter, leaving 14 for the two widths, so each width is 7. Stopping at 14 forgets that it covers two sides.

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Question 11Not answered

Which of the following is a factor of x squared - 2x - 15?
1. (x - 5)
2. (x - 3)
3. (x + 3)
4. (x - 15)
Correct answer: (x - 5)

Look for two numbers that multiply to -15 and add to -2. Those numbers are -5 and 3, so the trinomial factors as (x - 5)(x + 3), making (x - 5) one of the factors.

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Question 12Not answered

In which quadrant does the point (-3, 5) lie?
1. Quadrant I
2. Quadrant II
3. Quadrant III
4. Quadrant IV
Correct answer: Quadrant II

Quadrants are numbered counterclockwise starting at the upper right. A negative x with a positive y puts the point up and to the left, which is Quadrant II.

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Question 13Not answered

Simplify a squared times a to the power of -5. The result is a to what power?
1. -3
2. 3
3. -10
4. 7
Correct answer: -3

Multiplying powers of the same base still means adding exponents, even when one is negative: 2 + (-5) = -3, so the result is a to the -3, or 1 over a cubed.

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Question 14Not answered

If x squared equals 81, what is the positive value of x?
1. 40.5
2. 162
3. 8
4. 9
Correct answer: 9

Take the square root of both sides. Since 9 x 9 = 81, the positive solution is 9. Note that -9 also satisfies the equation, which is why the question asks for the positive value.

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Question 15Not answered

What is the larger solution of x squared minus 5x plus 6 = 0?
1. 2
2. 6
3. 5
4. 3
Correct answer: 3

Find two numbers multiplying to 6 and adding to -5: those are -2 and -3, so the equation factors as (x - 2)(x - 3) = 0. The solutions are 2 and 3, and the larger is 3.

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Question 16Not answered

What is the sum of the interior angles of a pentagon?
1. 360
2. 720
3. 540
4. 180
Correct answer: 540

For a polygon with n sides, the interior angles sum to (n - 2) x 180. A pentagon has 5 sides, so the sum is 3 x 180 = 540 degrees.

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Question 17Not answered

What is the area of a triangle with a base of 18 and a height of 5?
1. 45
2. 90
3. 23
4. 13
Correct answer: 45

The area of a triangle is half the base times the height, so 18 x 5 = 90 and half of that is 45.

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Question 18Not answered

A circle has a diameter of 16. Using 3.14 for pi, what is its circumference?
1. 100.48
2. 50.24
3. 200.96
4. 25.12
Correct answer: 50.24

Circumference is pi times the diameter, so 3.14 x 16 = 50.24. Using the diameter where the formula wants the radius doubles the answer, giving 100.48.

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Question 19Not answered

In the expansion of (x + 4)(x + 6), what is the coefficient of x?
1. 10
2. 24
3. 2
4. -10
Correct answer: 10

Multiplying out gives x squared + 6x + 4x + 24, and the two middle terms combine to 10x, since 4 + 6 = 10.

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Question 20Not answered

What is the slope of the line y = -4x + 9?
1. 9
2. 4
3. -4
4. -9
Correct answer: -4

In slope-intercept form y = mx + b, the coefficient m is the slope, so here the slope is -4.

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Question 21Not answered

Simplify -2(4x - 7) + 3x. What is the coefficient of x?
1. 11
2. 5
3. -8
4. -5
Correct answer: -5

Distribute the -2: -2 x 4x = -8x and -2 x -7 = 14. Combine the x terms: -8x + 3x = -5x, so the coefficient of x is -5.

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Question 22Not answered

What is the value of 2 to the power of -3?
1. -8
2. 1/8
3. -6
4. 1/6
Correct answer: 1/8

A negative exponent means the reciprocal, so 2 to the -3 is 1 divided by 2 cubed, which is 1/8. The result stays positive.

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Question 23Not answered

A trapezoid has parallel sides of 8 and 12 and a height of 5. What is its area?
1. 50
2. 100
3. 480
4. 60
Correct answer: 50

Average the two parallel sides, then multiply by the height. The average is (8 + 12) / 2 = 10, and 10 x 5 = 50. Forgetting to average gives 100.

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Question 24Not answered

What is the volume of a rectangular solid measuring 5 by 3 by 8?
1. 16
2. 120
3. 158
4. 40
Correct answer: 120

Volume is length times width times height, so 5 x 3 x 8 = 120.

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Question 25Not answered

A right triangle has legs of 5 and 12. What is the length of the hypotenuse?
1. 13
2. 17
3. 8.5
4. 60
Correct answer: 13

By the Pythagorean theorem, the hypotenuse squared equals 25 + 144 = 169, so the hypotenuse is 13.

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

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