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ASVAB Practice Test · Mathematics Knowledge

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ASVAB Practice Test Numbers and Algebra Summary

Importance
★★★★★ (5 / 5)
Weight
About 8 of 15 Mathematics Knowledge questions (55%)

Number properties, exponents, roots, equations, inequalities, and factoring.

📖 See Numbers and Algebra concepts →

Numbers and Algebra: must-know points

  • Do the same thing to both sides of an equation.
  • A negative number times a negative number is positive.

Numbers and Algebra: 9 sample questions

Practice questionReviewedMathematics Knowledge › Numbers and Algebra★★★★★

Question 1. Solve for x: 3x + 5 = 20

  1. ① x = 25/3
  2. ② x = 4
  3. ③ x = 15
  4. ④ x = 5
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Answer: ④ x = 5

Key point: Undo addition, then undo multiplication

  1. Subtract 5 from both sides: 3x = 15.
  2. Divide both sides by 3: x = 5.

Check: 3(5) + 5 = 15 + 5 = 20.

Wrong choices

  • (A) x = 25/3: 25/3 comes from adding 5 instead of subtracting it.
  • (B) x = 4: x = 4 gives 3(4) + 5 = 17, not 20.
  • (C) x = 15: 15 is the value of 3x, not x.
Practice questionReviewedMathematics Knowledge › Numbers and Algebra★★★★★

Question 2. What is (-4) x (-6)?

  1. ① 24
  2. ② 10
  3. ③ -10
  4. ④ -24
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Answer: ① 24

Key point: Negative x negative = positive

When two negative numbers are multiplied, the answer is positive. 4 x 6 = 24, so (-4) x (-6) = 24.

Check: (-4) x (-6) is the same as 4 x 6, which is 24.

Wrong choices

  • (B) 10: 10 adds 4 and 6 instead of multiplying.
  • (C) -10: -10 adds the numbers instead of multiplying.
  • (D) -24: -24 forgets that two negatives make a positive.
Practice questionReviewedMathematics Knowledge › Numbers and Algebra★★★★★

Question 3. What is the value of 2 to the 5th power (2^5)?

  1. ① 10
  2. ② 32
  3. ③ 16
  4. ④ 25
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Answer: ② 32

Key point: Exponent = repeated multiplication

  1. 2^5 means 2 multiplied by itself 5 times.
  2. 2 x 2 x 2 x 2 x 2 = 32.

Check: 2^4 = 16, and 16 x 2 = 32.

Wrong choices

  • (A) 10: 10 multiplies 2 by 5 instead of using 2 five times.
  • (C) 16: 16 is 2^4, one factor short.
  • (D) 25: 25 is 5^2, which reverses the base and exponent.
Practice questionReviewedMathematics Knowledge › Numbers and Algebra★★★★★

Question 4. Simplify: 4(2x - 3) - 2x

  1. ① 10x - 12
  2. ② 6x - 3
  3. ③ 6x + 12
  4. ④ 6x - 12
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Answer: ④ 6x - 12

Key point: Distribute, then combine like terms

  1. Distribute the 4: 4(2x) - 4(3) = 8x - 12.
  2. Subtract 2x: 8x - 2x - 12 = 6x - 12.

Check with x = 1: 4(2 - 3) - 2 = -4 - 2 = -6, and 6(1) - 12 = -6.

Wrong choices

  • (A) 10x - 12: 10x - 12 adds 2x instead of subtracting it.
  • (B) 6x - 3: 6x - 3 forgets to multiply the 3 by 4.
  • (C) 6x + 12: 6x + 12 gets the sign of the 12 wrong.
Practice questionReviewedMathematics Knowledge › Numbers and Algebra★★★★★

Question 5. What is √81 + √16?

  1. ① 5
  2. ② 97
  3. ③ 12
  4. ④ 13
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Answer: ④ 13

Key point: Find each square root first, then add

  1. √81 = 9, because 9 x 9 = 81.
  2. √16 = 4, because 4 x 4 = 16.
  3. 9 + 4 = 13.

Check: 9² = 81 and 4² = 16.

Wrong choices

  • (A) 5: 5 subtracts the roots (9 - 4) instead of adding them.
  • (B) 97: 97 adds 81 and 16 without taking any square roots.
  • (C) 12: 12 uses √81 = 8, but 8 x 8 = 64.
Practice questionReviewedMathematics Knowledge › Numbers and Algebra★★★★★

Question 6. Solve the inequality: -2x + 7 > 15

  1. ① x < -4
  2. ② x > 4
  3. ③ x < 4
  4. ④ x > -4
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Answer: ① x < -4

Key point: Dividing by a negative flips the sign

  1. Subtract 7 from both sides: -2x > 8.
  2. Divide both sides by -2. Dividing by a negative number flips the inequality sign: x < -4.

Check with x = -5: -2(-5) + 7 = 17, and 17 > 15 is true.

Wrong choices

  • (B) x > 4: x > 4 drops the negative and also forgets to flip the sign.
  • (C) x < 4: x < 4 drops the negative sign on the 4.
  • (D) x > -4: x > -4 forgets to flip the sign when dividing by a negative.
Practice questionReviewedMathematics Knowledge › Numbers and Algebra★★★★★

Question 7. If a = 2 and b = -1, what is the value of a² - 3ab?

  1. ① -10
  2. ② -2
  3. ③ 4
  4. ④ 10
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Answer: ④ 10

Key point: Substitute carefully with negatives

  1. a² = 2² = 4.
  2. 3ab = 3 x 2 x (-1) = -6.
  3. a² - 3ab = 4 - (-6) = 4 + 6 = 10.

Check: subtracting a negative is the same as adding, so 4 + 6 = 10.

Wrong choices

  • (A) -10: -10 gets the sign wrong; 4 - (-6) is 4 + 6, a positive number.
  • (B) -2: -2 treats 3ab as +6 and computes 4 - 6.
  • (C) 4: 4 is only the value of a², leaving out the second term.
Practice questionReviewedMathematics Knowledge › Numbers and Algebra★★★★★

Question 8. Factor completely: x² - 5x - 14

  1. ① (x - 7)(x + 2)
  2. ② (x + 7)(x - 2)
  3. ③ (x - 7)(x - 2)
  4. ④ (x - 14)(x + 1)
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Answer: ① (x - 7)(x + 2)

Key point: Find two numbers: product c, sum b

  1. Find two numbers that multiply to -14 and add to -5.
  2. -7 and +2 work: (-7)(2) = -14 and -7 + 2 = -5.
  3. So x² - 5x - 14 = (x - 7)(x + 2).

Check: (x - 7)(x + 2) = x² + 2x - 7x - 14 = x² - 5x - 14.

Wrong choices

  • (B) (x + 7)(x - 2): (x + 7)(x - 2) gives x² + 5x - 14; the middle sign is wrong.
  • (C) (x - 7)(x - 2): (x - 7)(x - 2) gives x² - 9x + 14.
  • (D) (x - 14)(x + 1): (x - 14)(x + 1) gives x² - 13x - 14.
Practice questionReviewedMathematics Knowledge › Numbers and Algebra★★★★★

Question 9. Solve the system: x + y = 10 and x - y = 4. What is the value of y?

  1. ① 4
  2. ② 7
  3. ③ 6
  4. ④ 3
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Answer: ④ 3

Key point: Add the equations to remove y

  1. Add the two equations: (x + y) + (x - y) = 10 + 4, so 2x = 14 and x = 7.
  2. Put x = 7 into x + y = 10: 7 + y = 10, so y = 3.

Check: 7 + 3 = 10 and 7 - 3 = 4.

Wrong choices

  • (A) 4: y = 4 gives x = 6, and 6 - 4 = 2, not 4.
  • (B) 7: 7 is the value of x, not y.
  • (C) 6: y = 6 gives x = 4, and 4 - 6 = -2, not 4.

Test yourself.

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