Free Compass Math Test Practice Questions
with Answers - Sample 5

A set of algebra questions, with answers, similar to the questions in the compass math test are presented. The answers to the suggested questions are at the bottom of the page and the solutions with full explanations to these questions are also included.

  1. The solution of the equation \(-3x + 7 = 4x - 12\) falls between what 2 numbers?

    A) 3 and 3.5
    B) 1 and 2.5
    C) 2.1 and 3
    D) 4 and 4.5
    E) 19 and 7
  2. \(35x^2 - 11x - 6\) is the product of \(5x - 3\) and

    A) \(x - 2\)
    B) \(7x - 2\)
    C) \(7x - 6\)
    D) \(7x\)
    E) \(7x + 2\)
  3. For all real numbers \(x, y\) and \(z\), \(\sqrt[3]{64 x^3 y z^2} = \)

    A) \(8 x y^{1/3} z^{2/3}\)
    B) \(8 x y^{1/3} z\)
    C) \(4 x y^{1/3} z^{1/3}\)
    D) \(4 x y^{1/3} z^{2/3}\)
    E) \(4 x y^{1/3} z\)
  4. For all \(x\), \(45 x^4 - 115 x^3 - 60 x^2 = \)

    A) \(45 x^2(x + 4)(x - 3)\)
    B) \(5 x^2(9x + 4)(x - 3)\)
    C) \(5 x^2(9x - 4)(x + 3)\)
    D) \(5 x^2(9x - 4)(x - 3)\)
    E) \(45 x^2(x - 4)(x + 3)\)
  5. Which of the following is one of the factors of the polynomial \(-3x^2 - 7x + 26\)?

    A) \(x + 2\)
    B) \(x + 1\)
    C) \(-3x + 7\)
    D) \(x - 2\)
    E) \(3x - 2\)
  6. What is the product of the solutions of the equation \(2x^2 + x - 15 = 0\)?

    A) \(-\dfrac{15}{2}\)
    B) \(\dfrac{15}{2}\)
    C) \(15\)
    D) \(-15\)
    E) \(\dfrac{2}{15}\)
  7. If \(y = |x - 3|\), what is the value of \(y^2\) when \(x = -2\)?

    A) \(-5\)
    B) \(5\)
    C) \(25\)
    D) \(-25\)
    E) \(10\)
  8. The operation \(|||\) is defined by \(x \,|||\, y = x + y + xy\). If \(-5 \,|||\, y = -13\), then \(y = \)

    A) \(0\)
    B) \(2\)
    C) \(-2\)
    D) \(5\)
    E) \(0\)
  9. A car uses 15 gallons of gas to travel 300 miles. How many gallons are needed for this car to travel a distance of 430 miles?

    A) \(21.5\)
    B) \(22\)
    C) \(22.5\)
    D) \(23\)
    E) \(23.5\)
  10. David has 200 books in his library. 30% of these books are about science. Of these books about science, 20% are about mathematics. How many math books does David have?

    A) \(100\)
    B) \(60\)
    C) \(40\)
    D) \(50\)
    E) \(12\)
  11. \(\sqrt{32} \times \sqrt{2} = \)

    A) \(64\)
    B) \(16\)
    C) \(8\)
    D) \(32\)
    E) \(4\)
  12. If \(a = 3\) and \(b = -1\), then \(-3a^2 - 2ab + b^3 = \)

    A) \(-30\)
    B) \(32\)
    C) \(34\)
    D) \(-34\)
    E) \(-22\)
  13. \((-3x^2 - x - 10) - (- 3x + 8) = \)

    A) \(-3x^2 - 4x - 2\)
    B) \(-3x^2 + 2x - 18\)
    C) \(-6x^2 + 8x - 10\)
    D) \(-3x^2 - 4x - 18\)
    E) \(-3x^2 + 4x - 18\)
  14. \((4 - \sqrt{5})(4 + \sqrt{5}) = \)

    A) \(11\)
    B) \(1\)
    C) \(9\)
    D) \(-9\)
    E) \(20\)
  15. In a standard \((x,y)\) coordinate plane, the point \((-2 , -6)\) is located

    A) in quadrant I
    B) on the x axis
    C) in quadrant II
    D) in quadrant III
    E) in quadrant IV
  16. \(|-7 - 9| = \)

    A) \(-2\)
    B) \(-16\)
    C) \(2\)
    D) \(63\)
    E) \(16\)
  17. If the ratio of \(7\) to \(x\) is equal to \(\dfrac{42}{30}\), then \(x = \)

    A) \(5\)
    B) \(6\)
    C) \(7\)
    D) \(8\)
    E) \(9\)
  18. If \(x = \dfrac{1}{3}\), then \(4x^2 - 2x + 2 = \)

    A) \(\dfrac{8}{3}\)
    B) \(\dfrac{16}{9}\)
    C) \(\dfrac{4}{3}\)
    D) \(4\)
    E) \(\dfrac{17}{9}\)
  19. Which equation corresponds to a line that is perpendicular to the line \(2y + 3x = 6\)?

    A) \(y = -\dfrac{2}{3}x + 9\)
    B) \(y = \dfrac{3}{2}x + 4\)
    C) \(y = -\dfrac{3}{2}x - 5\)
    D) \(y = \dfrac{2}{3}\)
    E) \(y = \dfrac{2}{3}x + 3\)
  20. \(\dfrac{\sqrt{128}}{2} + \dfrac{5\sqrt{2}}{4} = \)

    A) \(\dfrac{\sqrt{130}}{2}\)
    B) \(\dfrac{21\sqrt{2}}{4}\)
    C) \(\dfrac{133\sqrt{2}}{4}\)
    D) \(\dfrac{138\sqrt{2}}{4}\)
    E) \(\dfrac{138\sqrt{2}}{6}\)

Answers to the Above Questions

  1. C
  2. E
  3. D
  4. B
  5. D
  6. A
  7. C
  8. B
  9. A
  10. E
  11. C
  12. E
  13. B
  14. A
  15. D
  16. E
  17. A
  18. B
  19. E
  20. B

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