Free Compass Math Test Practice Questions
with Answers - Sample 3

A set of algebra and college 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. The solutions with full explanations to these questions are also included.

  1. If a number \(x\) is increased by one 1/4 of itself, which of the following expressions represents the new number?

    A) \(x + 1/4\)
    B) \(x + 0.25\)
    C) \(x + 0.25x\)
    D) \(4x - 0.25\)
    E) \(x/4\)
  2. \((5 + 1/5)x = 6\), find \(x\).

    A) \(1\frac{2}{13}\) (read as a mixed number)
    B) \(1\frac{1}{11}\) (read as a mixed number)
    C) \(0.8\)
    D) \(1\)
    E) \(2/13\)
  3. If \(f(x) = 3x + 2\), then \(f(2a + b) =\)

    A) \(6a + 2\)
    B) \(3a + 3b + 2\)
    C) \(3b + 2\)
    D) \(6a + 2\)
    E) \(6a + 3b + 2\)
  4. If \(f(x) = 3x + 2\) and \(g(x) = x^2 - 2\), then \(f(2) - g(3) =\)

    A) \(-1\)
    B) \(1\)
    C) \(2\)
    D) \(4\)
    E) \(-2\)
  5. For all \(x\), \((x + 3)(-x + 3) =\)

    A) \(x^2 - 9\)
    B) \(x^2 + 9\)
    C) \(-x^2 - 9\)
    D) \(9 - x^2\)
    E) \(9\)
  6. What is the tenth term of the geometric series if the first, second and third terms are \(0.5\), \(1.0\), \(2.0\), ... ?

    A) \(1024\)
    B) \(512\)
    C) \(256\)
    D) \(9\)
    E) \(10\)
  7. If \((2^x)(2^{-4x}) = 1/8\), then \(x = ?\)

    A) \(0\)
    B) \(-1\)
    C) \(1\)
    D) \(2\)
    E) \(-3\)
  8. The solution of the equation \(2x - 3 = 5x - 2\) falls between two consecutive integers

    A) \(0\) and \(1\)
    B) \(-1\) and \(0\)
    C) \(-2\) and \(-1\)
    D) \(1\) and \(2\)
    E) \(-3\) and \(-2\)
  9. What is the tenth term of the geometric sequence \(1, -\frac{1}{2}, \frac{1}{4}, -\frac{1}{8} \ldots\)

    A) \(1024\)
    B) \(-\frac{1}{1024}\)
    C) \(\frac{1}{1024}\)
    D) \(-512\)
    E) \(-\frac{1}{512}\)
  10. If \(f(x) = 3x^3 + 2x^2 + 3\) and \(g(x) = x^2 + 2\), then \(f(x)/g(x) = ?\)

    A) \(3x + 2\)
    B) \(-\frac{6x + 1}{x^2 + 2}\)
    C) \(3x + 2 - \frac{6x + 1}{x^2 + 2}\)
    D) \(\frac{3x + 2 - (6x + 1)}{x^2 + 2}\)
    E) \(\frac{6x + 1}{x^2 + 2}\)
  11. If \(i\) is the imaginary unit such that \(\sqrt{-1} = i\), then \((7i)^2 = ?\)
    A) \(-49\)
    B) \(49\)
    C) \(49i\)
    D) \(-49i\)
    E) \(-7\)
  12. Which of these is a complete factorization of \(f(x) = 3x^3 + x^2 + (3x + 1)(2x - 3)\)?

    A) \(x^2(3x + 1) + (3x + 1)(2x - 3)\)
    B) \((3x + 1)(x^2 + 2x - 3)\)
    C) \((3x + 1)(x + 1)(x - 3)\)
    D) \((3x + 1)(x - 1)(x + 3)\)
    E) \(3x^3 + 7x^2 - 7x - 3\)
  13. Find \(k\) if \(8! = 6! k\).

    A) \(\frac{4}{3}\)
    B) \(56\)
    C) \(1\)
    D) \(\frac{3}{4}\)
    E) \(48\)
  14. Find \(f(-2)\) if \(f(x) = 2x^2 + kx + 2\) and \(f(1) = 3\).

    A) \(-1\)
    B) \(0\)
    C) \(12\)
    D) \(8\)
    E) \(10\)
  15. In which interval does \(f(x) = -2x^2 - 3x - 4\) have a maximum value?
    A) \((0 , 1)\)
    B) \((-3 , -2)\)
    C) \((-0.5 , 0)\)
    D) \((-2 , -1)\)
    E) \((-1 , 0)\)
  16. Simplify \(x^{3/4} x^{1/3} x^{-2/3}\).
    A) \(x^{5/12}\)
    B) \(x^{1/2}\)
    C) \(x\)
    D) \(x^{3/4}\)
    E) \(x^{-1/3}\)
  17. Find \(x\) if \(\left(\frac{2}{7}\right)^{2x} = \left(\frac{7}{2}\right)^{3x + 5}\).
    A) \(-5\)
    B) \(5\)
    C) \(0\)
    D) \(-1\)
    E) \(1\)
  18. \(2x^2 + 3x - 5\) is the product of \((2x + 5)\) and another factor. What is the other factor?
    A) \(x + 3\)
    B) \(x - 1\)
    C) \(x + 1\)
    D) \(x - 5\)
    E) \(3\)
  19. If the operator ** is defined by \(x ** y = 2xy + x + y\). What is \(2 ** 3\)?
    A) \(6\)
    B) \(5\)
    C) \(8\)
    D) \(12\)
    E) \(17\)
  20. If \(i = \sqrt{-1}\), then \(i^2 + i^3 + i^4 + i^5 =\)
    A) \(i\)
    B) \(-i\)
    C) \(0\)
    D) \(4i\)
    E) \(-4i\)
  21. For all \(x\), \((2x - 4)^2 =\)
    A) \(4x^2 + 16\)
    B) \(4x^2 - 16\)
    C) \(x^2 - 16x + 16\)
    D) \(4x^2 - 16x + 16\)
    E) \(4x^2 + 16x + 16\)

Answers to the Above Questions

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

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