Mathematics Knowledge · Practice test 6

25 questions · 24 minutes

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

Question 1Not answered

Factor out the greatest common factor from 12x + 18. What remains inside the parentheses after factoring out 6?
1. 2x + 18
2. 12x + 3
3. 2x + 3
4. 6x + 12
Correct answer: 2x + 3

Both 12x and 18 are divisible by 6, the greatest common factor. Dividing each term by 6 gives 2x + 3, so the expression factors as 6(2x + 3).

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Question 2Not answered

A right triangle has a hypotenuse of 13 and one leg of 5. How long is the other leg?
1. 8
2. 12
3. 14
4. 18
Correct answer: 12

Rearranging the theorem, the missing leg squared is 169 - 25 = 144, so the leg is 12. Subtracting the lengths directly gives 8, the usual error.

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Question 3Not answered

The area of a triangle is given by A = one half times b times h. If A = 24 and b = 6, what is h?
1. 8
2. 4
3. 2
4. 16
Correct answer: 8

Rearrange the formula before substituting: multiplying both sides by 2 and dividing by b gives h = 2A / b. Then h = 48 / 6 = 8. Forgetting the factor of 2 gives 4.

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Question 4Not answered

Written as a decimal, 15 percent equals
1. 1.5
2. 0.15
3. 0.015
4. 15.0
Correct answer: 0.15

Percent means per hundred, so divide by 100 and move the decimal point two places left. That turns 15 into 0.15.

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Question 5Not answered

A trapezoid has parallel sides of 10 and 16 and a height of 6. What is its area?
1. 156
2. 960
3. 78
4. 96
Correct answer: 78

Average the two parallel sides, then multiply by the height. The average is (10 + 16) / 2 = 13, and 13 x 6 = 78.

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Question 6Not answered

Two angles of a triangle are equal and the third measures 80 degrees. What does each equal angle measure?
1. 100 degrees
2. 40 degrees
3. 50 degrees
4. 80 degrees
Correct answer: 50 degrees

The two equal angles share whatever is left of 180 after the 80, which is 100 degrees, so each is 50. Halving 80 instead gives 40.

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Question 7Not answered

What is the value of 4 to the power of -3?
1. -64
2. 1/12
3. -12
4. 1/64
Correct answer: 1/64

A negative exponent means take the reciprocal of the positive power, so 4 to the -3 is 1 divided by 4 cubed, which is 1/64. A negative exponent never produces a negative result.

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Question 8Not answered

Solve for x: 3(x + 2) = 5x - 4
1. 1
2. -5
3. 2
4. 5
Correct answer: 5

Expand the left side to 3x + 6, then gather terms: 6 + 4 = 5x - 3x gives 10 = 2x, so x = 5.

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Question 9Not answered

Simplify 3(2x + 5) - 4. What is the constant term?
1. 1
2. 19
3. 11
4. -4
Correct answer: 11

Distribute the 3 across both terms inside the bracket: 3 x 2x = 6x and 3 x 5 = 15. Then 15 - 4 = 11, so the expression is 6x + 11.

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Question 10Not answered

Solve for x: x - 7 = -3
1. -10
2. 10
3. 4
4. -4
Correct answer: 4

Add 7 to both sides: -3 + 7 = 4. Subtracting instead gives -10, the usual sign error.

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Question 11Not answered

In an isosceles triangle the apex angle measures 40 degrees. What does each base angle measure?
1. 140 degrees
2. 40 degrees
3. 70 degrees
4. 80 degrees
Correct answer: 70 degrees

An isosceles triangle has two equal base angles. They share what is left after the apex, so together they make 180 - 40 = 140, and each is 70.

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Question 12Not answered

A circle has a radius of 7. Using 3.14 for pi, what is its circumference?
1. 43.96
2. 153.86
3. 21.98
4. 49
Correct answer: 43.96

Circumference is 2 times pi times the radius, so 2 x 3.14 x 7 = 43.96.

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Question 13Not answered

What is the next term in the sequence 6, 11, 16, 21, ...?
1. 26
2. 25
3. 27
4. 42
Correct answer: 26

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 21 + 5 = 26.

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Question 14Not answered

Simplify z to the 11th power divided by z to the 3rd power. The result is z to what power?
1. 14
2. 33
3. 3.67
4. 8
Correct answer: 8

Dividing powers of the same base means subtracting the exponents, so 11 - 3 = 8. Adding them gives 14, the usual error.

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Question 15Not answered

Two angles of a triangle measure 55 and 72 degrees. What is the third angle?
1. 53
2. 127
3. 63
4. 17
Correct answer: 53

The three angles of a triangle add to 180 degrees. The two given angles total 127, so the third is 180 - 127 = 53.

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Question 16Not answered

Solve for x: 4x - 5 = 27
1. 5.5
2. 88
3. 6
4. 8
Correct answer: 8

Add 5 to both sides to get 4x = 32, then divide by 4 to get x = 8.

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Question 17Not answered

The perimeter of a rectangle is P = 2L + 2W. If P = 40 and L = 12, what is W?
1. 16
2. 8
3. 28
4. 14
Correct answer: 8

Substitute and solve: 40 = 24 + 2W, so 2W = 16 and W = 8. Forgetting to halve at the end gives 16.

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Question 18Not answered

The expression x squared minus 49 factors as (x + a)(x - a). What is a?
1. 49
2. 14
3. 7
4. 24.5
Correct answer: 7

A difference of two squares factors into the sum and the difference of their roots. The root of 49 is 7, so the factors are (x + 7)(x - 7).

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Question 19Not answered

Simplify 5(x - 2) - 3(x + 1). What is the coefficient of x?
1. 8
2. -2
3. 2
4. 15
Correct answer: 2

Expanding gives 5x - 10 - 3x - 3, and the x terms combine to 2x. The whole expression simplifies to 2x - 13. Note the minus sign applies to both terms in the second bracket.

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Question 20Not answered

Solve for x: x divided by 6, minus 2, equals 3
1. 30
2. 6
3. 18
4. 0.83
Correct answer: 30

Add 2 to both sides to get x / 6 = 5, then multiply by 6 to get x = 30.

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Question 21Not answered

Simplify 4(2x - 3) + 5. What is the constant term?
1. -7
2. 2
3. -12
4. 8
Correct answer: -7

The 4 multiplies both terms inside the bracket, giving 8x - 12, and adding 5 leaves 8x - 7. Forgetting to multiply the -3 by 4 is the usual error.

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Question 22Not answered

Two angles are complementary. One measures twice the other. What does the smaller angle measure?
1. 30
2. 60
3. 45
4. 15
Correct answer: 30

If the smaller angle is x, the larger is 2x, and complementary angles add to 90: x + 2x = 90 gives 3x = 90, so x = 30.

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Question 23Not answered

What is the value of 3 to the power of -2?
1. 1/9
2. -9
3. -6
4. 1/6
Correct answer: 1/9

A negative exponent means take the reciprocal, so 3 to the -2 is 1 divided by 3 squared, which is 1/9. A negative exponent never makes the result negative.

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Question 24Not answered

Which of the following is a factor of x squared plus 7x plus 12?
1. (x + 2)
2. (x + 6)
3. (x + 5)
4. (x + 4)
Correct answer: (x + 4)

Look for two numbers that multiply to 12 and add to 7. The pairs multiplying to 12 are 1 and 12, 2 and 6, and 3 and 4, and only 3 and 4 add to 7. So the factors are (x + 3)(x + 4).

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Question 25Not answered

What is the next term in the sequence 3, 6, 12, 24, ...?
1. 36
2. 48
3. 30
4. 72
Correct answer: 48

Each term is double the one before it, so this is a geometric sequence with a common ratio of 2. The next term is 24 x 2 = 48. Adding the previous difference of 12 instead gives 36, which is the trap.

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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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