ASVAB Study Guide
MK · Practice test 5 of 12

Mathematics Knowledge Practice Test 5

Tap an answer to check it instantly and read the explanation. 10 questions: 3 easy, 4 medium and 3 hard.

AFQT subtest 10 questions No time limit
0 / 10 answered · 0 correct
  1. Question 1 easy

    Solve for y: $$4y - 7 = 2y + 9$$

    Show answer & explanation

    Correct answer: A — 8

    To solve for y, get all the y terms on one side and the constant numbers on the other. First, subtract $$2y$$ from both sides: $$2y - 7 = 9$$. Then, add 7 to both sides: $$2y = 16$$. Finally, divide by 2: $$y = 8$$

  2. Question 2 easy

    Combine the following like terms: $$5x^2 + 3x - 2x^2 + 4xy - x$$

    Show answer & explanation

    Correct answer: A — $$3x^2 + 2x + 4xy$$

    Combine only the terms with the exact same variables and exponents. Combine the x² terms: $$5x^2 - 2x^2 = 3x^2$$. Combine the x terms: $$3x - x = 2x$$. The $$4xy$$ term has no other like terms to combine with. The final expression is $$3x^2 + 2x + 4xy$$

  3. Question 3 easy

    Solve for x: $$3(2x - 4) = 5x + 7(x - 2)$$

    Show answer & explanation

    Correct answer: C — $$\frac{1}{3}$$

    First, distribute the numbers outside the parentheses: $$6x - 12 = 5x + 7x - 14$$. Combine like terms on the right side: $$6x - 12 = 12x - 14$$. Next, isolate x by subtracting $$6x$$ from both sides: $$-12 = 6x - 14$$. Add 14 to both sides: $$2 = 6x$$. Finally, divide by 6: $$x = \frac{2}{6}$$, which simplifies to $$\frac{1}{3}$$

  4. Question 4 medium

    If $$4a + 3b = 24$$ and $$b = 2a$$, what is the value of a?

    Show answer & explanation

    Correct answer: A — 2.4

    Substitute the value of b (which is $$2a$$) into the first equation: $$4a + 3(2a) = 24$$. Multiply: $$4a + 6a = 24$$. Combine like terms: $$10a = 24$$. Divide by 10 to isolate a: $$a = 2.4$$

  5. Question 5 medium

    Solve for z: $$\frac{(z + 5)}{3} = 2z - 5$$

    Show answer & explanation

    Correct answer: A — 4

    First, eliminate the denominator by multiplying both sides of the equation by 3: $$z + 5 = 3(2z - 5)$$. Distribute the 3 on the right side: $$z + 5 = 6z - 15$$. Subtract z from both sides: $$5 = 5z - 15$$. Add 15 to both sides: $$20 = 5z$$. Finally, divide by 5 to find z: $$z = 4$$

  6. Question 6 medium

    What is the value of $$6x - 4$$ when $$x = -3$$?

    Show answer & explanation

    Correct answer: C — -22

    Substitute -3 for x into the expression: $$6(-3) - 4$$. First, multiply: $$6 \times (-3) = -18$$. Then, subtract 4: $$-18 - 4 = -22$$

  7. Question 7 medium

    What is the value of $$4p - 3q$$ when $$p = 5$$ and $$q = 2$$?

    Show answer & explanation

    Correct answer: A — 14

    Substitute $$p = 5$$ and $$q = 2$$ into the expression: $$4(5) - 3(2)$$. Calculate the products: $$20 - 6$$. Subtract the values: $$20 - 6 = 14$$

  8. Question 8 hard

    Choose the equation that best represents the statement: "Five times a number decreased by 8 is 27."

    Show answer & explanation

    Correct answer: A — $$5x - 8 = 27$$

    Five times a number translates to $$5x$$. "Decreased by 8" means subtracting $$8 (5x - 8)$$. "Is 27" means equals $$27 (= 27)$$. Putting it together gives $$5x - 8 = 27$$

  9. Question 9 hard

    Choose the expression that best represents the statement: "The product of seven and a number, increased by four."

    Show answer & explanation

    Correct answer: C — $$7x + 4$$

    The product of seven and a number translates to multiplication, $$7x$$. "Increased by four" means adding 4. Combining them yields $$7x + 4$$

  10. Question 10 hard

    Solve for k: $$3(k - 2) + 4 = 2(k + 5) - 3$$

    Show answer & explanation

    Correct answer: A — 9

    First, distribute the numbers outside the parentheses: $$3k - 6 + 4 = 2k + 10 - 3$$. Simplify both sides by combining like terms: $$3k - 2 = 2k + 7$$. Next, subtract $$2k$$ from both sides: $$k - 2 = 7$$. Finally, add 2 to both sides: $$k = 9$$