ASVAB Mathematics Knowledge Practice Test

25 practice questions

Choose an answer, then check it under Show answer.

1. Question 1 of 25Medium

   Which expression is equivalent to 5(3x - 2y) - 3(2x - 4y)?

   1. AA. 9x - 2y
   2. BB. 9x + 2y
   3. CC. 21x + 2y
   4. DD. 9x - 22y
   Show answer to question 1

   Answer: B. 9x + 2y

   Distributing across both sets of parentheses yields 15x - 10y - 6x + 12y. Combining like terms gives (15x - 6x) + (-10y + 12y), which simplifies to 9x + 2y. The expression 9x - 22y results from failing to distribute the negative sign to the second term, wrongly calculating -3(-4y) as -12y.

2. Question 2 of 25Hard

   Which of the following expressions is equivalent to (16x^8)^(-3/4) for all positive values of x?

   1. AA. 8 / x^6
   2. BB. 1 / (12x^6)
   3. CC. 1 / (8x^6)
   4. DD. 1 / (8x^2)
   Show answer to question 2

   Answer: C. 1 / (8x^6)

   Applying the rational exponent to the coefficient gives the fourth root of 16 raised to the power of negative 3, which equals 1/8. Multiplying the variable exponent by -3/4 gives -6, placing x^6 in the denominator alongside 8 to yield 1 / (8x^6). A common error is multiplying 16 by 3/4 to get 12 instead of taking the fourth root and cubing it.

3. Question 3 of 25Hard

   What is the greatest common factor of 48, 72, and 120?

   1. AA. 16
   2. BB. 12
   3. CC. 8
   4. DD. 24
   Show answer to question 3

   Answer: D. 24

   Breaking each number into prime factors gives 48 = 2^4 * 3, 72 = 2^3 * 3^2, and 120 = 2^3 * 3 * 5. Taking the lowest power of the shared factors 2 and 3 yields 2^3 * 3 = 24. While 12 is a common factor of all three numbers, it is not the largest possible common factor.

4. Question 4 of 25Easy

   What is the total surface area of a cube with an edge length of 4 centimeters?

   1. AA. 16 square centimeters
   2. BB. 96 square centimeters
   3. CC. 64 square centimeters
   4. DD. 32 square centimeters
   Show answer to question 4

   Answer: B. 96 square centimeters

   The cube has six square faces, and each face has area 4 × 4 = 16 square centimeters, so the total is 6 × 16 = 96 square centimeters. The value 64 square centimeters comes from cubing the edge length, which relates to volume, not surface area.

5. Question 5 of 25Hard

   Solve for x: (2x + 1)/5 - (x - 2)/3 = 1

   1. AA. 22
   2. BB. -12
   3. CC. 2
   4. DD. 8
   Show answer to question 5

   Answer: C. 2

   Multiplying all terms by the common denominator 15 yields 3(2x + 1) - 5(x - 2) = 15. Distributing carefully gives 6x + 3 - 5x + 10 = 15, which simplifies to x + 13 = 15, so x = 2. Failing to distribute the negative sign to both terms in -(x - 2) leads to -5x - 10, resulting in the incorrect answer 22.

6. Question 6 of 25Medium

   What is 62.5% expressed as a fraction in simplest form?

   1. AA. 3/5
   2. BB. 7/8
   3. CC. 5/6
   4. DD. 5/8
   Show answer to question 6

   Answer: D. 5/8

   Writing 62.5% as 625/1000 and dividing both the numerator and denominator by their greatest common factor, 125, gives 5/8. The option 3/5 is equivalent to 60%, which ignores the extra 2.5%, while 7/8 represents 87.5%.

7. Question 7 of 25Hard

   What is the slope of the line that passes through the points (4, -3) and (4, 5)?

   1. AA. Undefined
   2. BB. 8
   3. CC. -8
   4. DD. 0
   Show answer to question 7

   Answer: A. Undefined

   Applying the slope formula produces (5 - (-3)) / (4 - 4) = 8 / 0. Because division by zero is impossible in mathematics, any vertical line has an undefined slope. A slope of 0 is incorrect because that applies strictly to horizontal lines where the vertical change in the numerator is zero.

8. Question 8 of 25Easy

   Which of the following shows 14x^3 - 21x^2 factored completely?

   1. AA. 7x^2(2x - 3)
   2. BB. 7x(2x^2 - 3x)
   3. CC. 7x^2(2x + 3)
   4. DD. x^2(14x - 21)
   Show answer to question 8

   Answer: A. 7x^2(2x - 3)

   Factoring out the greatest common factor of 7x^2 leaves the binomial (2x - 3). The option 7x(2x^2 - 3x) is not completely factored because the terms inside the parentheses still share a common factor of x.

9. Question 9 of 25Hard

   Triangle ABC is similar to triangle DEF. The length of side AB is x + 3 and the length of corresponding side DE is 5. The length of side BC is 3x - 1 and the length of corresponding side EF is 10. What is the length of side BC?

   1. AA. 7
   2. BB. 10
   3. CC. 20
   4. DD. 14
   Show answer to question 9

   Answer: C. 20

   Setting up the proportion (x + 3) / 5 = (3x - 1) / 10 leads to 2(x + 3) = 3x - 1, which solves to x = 7. Substituting 7 back into the expression for BC gives 3(7) - 1 = 20. The option 7 is incorrect because it represents the variable x rather than the requested side length.

10. Question 10 of 25Hard

    What is the product of (3 * sqrt(2) - 1) and (2 * sqrt(2) + 5)?

    1. AA. 17 + 13 * sqrt(2)
    2. BB. 7 + 17 * sqrt(2)
    3. CC. 7 + 13 * sqrt(2)
    4. DD. 1 + 13 * sqrt(2)
    Show answer to question 10

    Answer: C. 7 + 13 * sqrt(2)

    Multiplying using the distributive property gives 12 from the first terms, 15 * sqrt(2) from the outer terms, -2 * sqrt(2) from the inner terms, and -5 from the last terms. Combining the constant integers gives 12 - 5 = 7, and combining the radical terms gives 13 * sqrt(2), resulting in 7 + 13 * sqrt(2). The value 7 + 17 * sqrt(2) is incorrect because it adds the absolute values of the middle terms instead of subtracting 2 * sqrt(2) from 15 * sqrt(2).

11. Question 11 of 25Medium

    What is the value of x in the system of equations below? 2x + 3y = 13 x - 2y = -4

    1. AA. -1
    2. BB. 2
    3. CC. 3
    4. DD. 5
    Show answer to question 11

    Answer: B. 2

    Multiplying the second equation by 2 gives 2x - 4y = -8, and subtracting this from the first equation yields 7y = 21, so y = 3. Substituting y = 3 into x - 2y = -4 gives x - 6 = -4, which simplifies to x = 2. The value 3 is the correct result for y, a common error when candidates stop before solving for x.

12. Question 12 of 25Easy

    Which equation represents a straight line with a slope of -3 and a y-intercept of 4?

    1. AA. y = 3x - 4
    2. BB. y = -4x + 3
    3. CC. y = -3x + 4
    4. DD. y = 4x - 3
    Show answer to question 12

    Answer: C. y = -3x + 4

    In slope-intercept form, y = mx + b, m is the slope and b is the y-intercept. Substituting -3 for m and 4 for b yields y = -3x + 4. The equation y = 4x - 3 incorrectly swaps the slope and the y-intercept.

13. Question 13 of 25Easy

    What is the value of -7 + 12?

    1. AA. 19
    2. BB. -5
    3. CC. 5
    4. DD. -19
    Show answer to question 13

    Answer: C. 5

    Adding numbers with different signs gives the sign of the number with the larger absolute value, so 12 - 7 = 5. The result -5 would come from incorrectly keeping the negative sign of -7.

14. Question 14 of 25Easy

    An angle measures 38 degrees. What is the measure of its supplement?

    1. AA. 62 degrees
    2. BB. 52 degrees
    3. CC. 152 degrees
    4. DD. 142 degrees
    Show answer to question 14

    Answer: D. 142 degrees

    Two angles are supplementary if their measures sum to 180 degrees, so subtracting 38 from 180 gives 142 degrees. The value 52 degrees results from finding the complement instead of the supplement by subtracting from 90 degrees.

15. Question 15 of 25Hard

    The four-digit number 5,2d6 is divisible by both 4 and 9. What digit is d?

    1. AA. 7
    2. BB. 3
    3. CC. 9
    4. DD. 5
    Show answer to question 15

    Answer: D. 5

    The digit sum is 13 + d, which must be a multiple of 9; only d = 5 gives 18. With d = 5, the last two digits are 56, and 56 is divisible by 4. The digit 3 gives last two digits 36, which is divisible by 4, but its digit sum 16 is not divisible by 9.

16. Question 16 of 25Medium

    Simplify the expression: 3(2x - 4) - 2(x - 5)

    1. AA. 4x - 9
    2. BB. 4x - 2
    3. CC. 4x - 22
    4. DD. 4x + 2
    Show answer to question 16

    Answer: B. 4x - 2

    Distributing 3 gives 6x - 12, and distributing -2 gives -2x + 10. Combining like terms results in (6x - 2x) + (-12 + 10) = 4x - 2. The distractor 4x - 22 occurs if the negative sign is not properly distributed to the -5, mistakenly calculating -12 - 10 instead of -12 + 10.

17. Question 17 of 25Easy

    What is the value of 2/5 + 1/3?

    1. AA. 13/15
    2. BB. 3/8
    3. CC. 7/15
    4. DD. 11/15
    Show answer to question 17

    Answer: D. 11/15

    The correct answer is 11/15 because finding a common denominator of 15 converts the expression to 6/15 + 5/15, which sums to 11/15. The value 3/8 is incorrect and results from improperly adding both numerators and denominators together.

18. Question 18 of 25Easy

    If x = -4 and y = 3, what is the value of 2x - 5y + 7?

    1. AA. 0
    2. BB. -30
    3. CC. 14
    4. DD. -16
    Show answer to question 18

    Answer: D. -16

    Substituting the values gives 2(-4) - 5(3) + 7, which simplifies to -8 - 15 + 7 = -16. A result of 0 is a common mistake that occurs when the negative sign on x is omitted, leading to 8 - 15 + 7.

19. Question 19 of 25Medium

    What is the product of (3x - 4y) and (2x + 5y)?

    1. AA. 6x^2 - 20y^2
    2. BB. 6x^2 + 7xy - 20y^2
    3. CC. 6x^2 - 7xy - 20y^2
    4. DD. 6x^2 + 23xy - 20y^2
    Show answer to question 19

    Answer: B. 6x^2 + 7xy - 20y^2

    Multiplying the terms using the FOIL method gives 6x^2 + 15xy - 8xy - 20y^2, which combines to 6x^2 + 7xy - 20y^2. The expression 6x^2 - 7xy - 20y^2 is incorrect because the positive cross-term (15xy) has a greater absolute value than the negative cross-term (-8xy), resulting in a positive middle coefficient.

20. Question 20 of 25Medium

    What is the distance between the points (-3, 5) and (2, -7)?

    1. AA. 13
    2. BB. 17
    3. CC. 11
    4. DD. 169
    Show answer to question 20

    Answer: A. 13

    Subtracting the coordinates gives a horizontal change of 5 and a vertical change of negative 12. Squaring both yields 25 and 144, and the square root of their sum, 169, is 13. The value 17 results from simply adding the absolute horizontal and vertical distances (5 plus 12) without applying the square root to the sum of the squares.

21. Question 21 of 25Medium

    What is the value of 48 / 4 * 2 - 3^2 + 5?

    1. AA. 2
    2. BB. 20
    3. CC. 10
    4. DD. 23
    Show answer to question 21

    Answer: B. 20

    Exponents are calculated first (3 squared is 9), followed by division and multiplication from left to right (48 divided by 4 is 12, and 12 times 2 is 24). Finally, addition and subtraction are performed from left to right (24 - 9 + 5 = 20). The distractor 2 occurs if multiplication is incorrectly performed before division, giving 48 divided by 8.

22. Question 22 of 25Medium

    In triangle ABC, the measure of angle A is 48 degrees and the measure of angle B is 84 degrees. Which term best describes triangle ABC?

    1. AA. Acute isosceles
    2. BB. Obtuse isosceles
    3. CC. Acute scalene
    4. DD. Right isosceles
    Show answer to question 22

    Answer: A. Acute isosceles

    The sum of angles in a triangle is 180 degrees, which means the third angle measures 180 - (48 + 84) = 48 degrees. Because all three angles are under 90 degrees, the triangle is acute; having two equal angles means two opposite sides are also equal, making it isosceles. Acute scalene is incorrect because having two identical angle measures prevents all three sides from being different.

23. Question 23 of 25Medium

    Which of the following is equivalent to √75 + √27?

    1. AA. 8√3
    2. BB. √102
    3. CC. 15√3
    4. DD. 8√6
    Show answer to question 23

    Answer: A. 8√3

    Factoring out the largest perfect square from each term yields √75 = 5√3 and √27 = 3√3. Adding these like radical terms produces 8√3. The expression √102 is incorrect because radicals cannot be combined by simply adding the numbers underneath them.

24. Question 24 of 25Medium

    The interior angles of a triangle are in a ratio of 2:3:4. What is the measure of the largest angle?

    1. AA. 60 degrees
    2. BB. 40 degrees
    3. CC. 20 degrees
    4. DD. 80 degrees
    Show answer to question 24

    Answer: D. 80 degrees

    Because the angles sum to 180 degrees, the ratio parts add to 9, making each part equal to 20 degrees. Multiplying 20 degrees by 4 gives the largest angle of 80 degrees. An answer of 60 degrees corresponds to the middle angle rather than the largest.

25. Question 25 of 25Medium

    A point located at (-3, 2) is translated 5 units to the right and 4 units down. What are the coordinates of the resulting point?

    1. AA. (2, -2)
    2. BB. (2, 6)
    3. CC. (-8, 6)
    4. DD. (-8, -2)
    Show answer to question 25

    Answer: A. (2, -2)

    Moving 5 units right increases the x-coordinate by 5 (-3 + 5 = 2), and moving 4 units down decreases the y-coordinate by 4 (2 - 4 = -2), giving (2, -2). The option (2, 6) incorrectly adds 4 to the y-coordinate instead of subtracting it.

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