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ASVAB Practice Test · Mathematics Knowledge

ASVAB Practice Test: Numbers and Algebra Concepts

Importance ★★★★★ · 55% (estimate)

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Written by AI. Only units that passed a separate AI check (re-reading facts and numbers) are published. Tell us if you find a mistake.

Overview

This chapter covers the rules of numbers and basic algebra. You will review signed numbers, the order of operations, exponents and square roots, solving equations and inequalities, and factoring. Many questions can be solved quickly if you know the rules well.

When you multiply or divide two numbers with the same sign, the answer is positive. When the signs are different, the answer is negative. The order of operations is parentheses first, then exponents, then multiplication and division from left to right, then addition and subtraction from left to right.

An exponent tells how many times to multiply a number by itself, so 3 squared is 3 x 3 = 9. When you multiply powers with the same base, add the exponents. A square root is the number that, times itself, gives the original number, so the square root of 49 is 7.

To solve an equation, do the same thing to both sides until the variable is alone. Inequalities work the same way, except that multiplying or dividing both sides by a negative number flips the inequality sign. Factoring breaks an expression into parts that multiply together, such as x squared - 9 = (x + 3)(x - 3).

Key concepts

  • Signed numbers

    Multiplying or dividing two numbers with the same sign gives a positive answer. Different signs give a negative answer. Example: (-4) x (-2) = 8, and (-4) x 2 = -8.

    Memory tipSame signs positive, different signs negative.

  • Order of operations

    1) Parentheses. 2) Exponents. 3) Multiply and divide, left to right. 4) Add and subtract, left to right. Example: 2 + 3 x 4 = 14, not 20.

    Memory tipPEMDAS: Please Excuse My Dear Aunt Sally.

  • Exponent rules

    An exponent shows repeated multiplication. When multiplying the same base, add exponents: x^2 times x^3 = x^5. Any nonzero number to the zero power is 1.

    Memory tipSame base, multiply means add the exponents.

  • Solving an equation

    Do the same operation to both sides to get the variable alone. Example: 3x + 5 = 20, subtract 5 to get 3x = 15, divide by 3 to get x = 5.

    Memory tipPlug your answer back in to check.

  • Inequalities

    Solve like an equation, but if you multiply or divide both sides by a negative number, flip the sign. Example: -2x > 6 becomes x < -3.

    Memory tipNegative multiply or divide flips the sign.

  • Factoring

    Writing an expression as parts that multiply together. Difference of squares: a^2 - b^2 = (a + b)(a - b). Also x^2 + 5x + 6 = (x + 2)(x + 3).

    Memory tipFind two numbers that multiply to the last term and add to the middle.

Often tested

  • Do the same thing to both sides of an equation.
  • A negative number times a negative number is positive.
  • Multiply before you add unless parentheses say otherwise.
  • Flip the inequality sign when multiplying or dividing by a negative.
  • Any nonzero number to the zero power is 1.

3 sample questions

Verified practice questions from this unit.

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
▼ Show answer and explanation▲ Hide answer and explanation

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
▼ Show answer and explanation▲ Hide answer and explanation

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
▼ Show answer and explanation▲ Hide answer and explanation

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 5 questions from this unit →