Free Compass Math Test Practice Questions
with Answers - Sample 4

A set of college algebra and trigonometry 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. If \(f(x) = 2x - 3\), \(g(x) = -2x^{3} + 2\) and \(h(x) = 3x\), then \(h(2) + f(g(-1)) =\)

    A) 10
    B) -14
    C) 11
    D) 5
    E) 1
  2. If \(\frac{3^{x^{2}}}{3^{4x}} = \frac{1}{81}\), then \(x =\)

    A) -1
    B) 0
    C) 1
    D) 2
    E) 3
  3. What are the solutions of \(x(x - 2) = 5\)?

    A) 2 and 7
    B) 5 and 2
    C) -5 and 7
    D) \(-1 + \sqrt{6}\) and \(-1 - \sqrt{6}\)
    E) \(1 - \sqrt{6}\) and \(1 + \sqrt{6}\)
  4. The formula for the \(n\)th term, \(a_n\), of an arithmetic progression is given by \(a_n = a_1 + (n - 1)d\), where \(a_1\) represents the first term of the progression and \(d\) represents its common difference. What is the value of the 20th term of the arithmetic progression 4, 7, 10,...?

    A) 61
    B) 64
    C) 58
    D) 67
    E) 20
  5. In a 16-by-12 rectangle, what is the perimeter of the triangle formed by two sides of the rectangle and the diagonal?

    A) 56
    B) 48
    C) 192
    D) 28
    E) 40
  6. If \(\sqrt{-1} = i\), then \((-2 + 2i)^{5} =\)

    A) \(-32 + 32i\)
    B) \(32 - 32i\)
    C) \(-32 - 32i\)
    D) \(128 - 128i\)
    E) \(-128 + 128i\)
  7. For all values of \(x > 0\), \(\log\left(x^{2} \sqrt[3]{7}\right) =\)

    A) \(\log\left(x^{2} + \sqrt[3]{7}\right)\)
    B) \(2\log(x) + \frac{1}{3}\log(7)\)
    C) \(\log(x) + \log(7)\)
    D) \(x^{2} + \sqrt[3]{7}\)
    E) \(\frac{7}{3}\log(x)\)
  8. Which of these interval represents all the real values that are the range of \(y = \frac{1}{4 - x^{2}}\)?

    A) \((-\infty, 0) \cup [\frac{1}{4}, +\infty)\)
    B) \((\frac{1}{4}, +\infty)\)
    C) \((-\infty, 0) \cup (\frac{1}{4}, +\infty)\)
    D) \([\frac{1}{4}, +\infty)\)
    E) \((-\infty, +\infty)\)
  9. Which of these intervals represents all values of \(x\) that makes \(\sqrt{x^{2} + 2x}\) a real number?

    A) \((-\infty, -2) \cup [0, +\infty)\)
    B) \((-\infty, -2] \cup [0, +\infty)\)
    C) \((-\infty, -2] \cup (0, +\infty)\)
    D) \((-\infty, -2) \cup (0, +\infty)\)
    E) \((-\infty, +\infty)\)
  10. \(\log 32 + \log 16 =\)

    A) \(\log 48\)
    B) \(3\log 16\)
    C) \(9 \log 2\)
    D) \(12 \log 2\)
    E) \(8 \log 2\)
  11. If \(9^{(x + 1)} = 3 \cdot 9^{y}\), then

    A) \(x = y + 1\)
    B) \(x + 1 = y\)
    C) \(x = y\)
    D) \(2x = 2y - 1\)
    E) \(x = y + 1\)
  12. If A is a matrix given by \[ \begin{bmatrix} a & 0 \\ c & d \end{bmatrix} \] then the determinant of A is \[ \det(A) = a d \]

    A) \(a(a + ed)\)
    B) \(-a(a - ed)\)
    C) \(a + ed\)
    D) \(-a(-a + ed)\)
    E) \(-a(a + ed)\)
  13. If \(\cos(80^{\circ}) = a\) and \(\cos(60^{\circ})\cos(20^{\circ}) = b\), then \(\sin(60^{\circ})\sin(20^{\circ}) =\)

    A) \(a + b\)
    B) \(a - b\)
    C) \(a b\)
    D) \(\frac{a}{b}\)
    E) \(b - a\)
  14. Which pair of functions have the same graph?

    A) \(\sin(x)\) and \(\cos(x + \frac{3\pi}{2})\)
    B) \(\sin(x)\) and \(\cos(x + \frac{\pi}{2})\)
    C) \(\sin(x)\) and \(\cos(x + \pi)\)
    D) \(\sin(x)\) and \(\cos(x - \frac{3\pi}{2})\)
    E) \(\sin(x)\) and \(\cos(x + \frac{5\pi}{2})\)
  15. Which of these functions have the highest period?

    A) \(\cos(x + \frac{3\pi}{2})\)
    B) \(\sin(2x - \pi)\)
    C) \(\cos(0.2x)\)
    D) \(10 \sin(x)\)
    E) \(\cos(200x)\)
  16. What is the measure of \(x\), \(0 < x < \frac{5\pi}{2}\), if \(|-\sin(x) + 1| = 2\)?

    A) \(2\pi\)
    B) \(\frac{3\pi}{2}\)
    C) \(\frac{\pi}{2}\)
    D) \(\pi\)
    E) \(\frac{2\pi}{3}\)
  17. If \(\pi < x < 2\pi\) and \(\cos(x) = -\frac{1}{2}\), then \(x =\)

    A) \(\frac{\pi}{3}\)
    B) \(\frac{3\pi}{2}\)
    C) \(\frac{5\pi}{3}\)
    D) \(\frac{4\pi}{3}\)
    E) \(\frac{5\pi}{4}\)
  18. \(\left[\frac{\cos(t)}{\cot(t)}\right] \csc^{2}(t) =\)

    A) \(\sin(t)\)
    B) \(\csc(t)\)
    C) \(\cos(t)\)
    D) \(\tan(t)\)
    E) \(\cot(t)\)
  19. If \(f(u) = 2\cos(u) + 5\) and \(g(v) = 0.5\sin(2v)\), what is \(f(g(\frac{\pi}{2}))\)?

    A) 7
    B) 0
    C) 5
    D) 3
    E) -3
  20. If \(\pi < x < 2\pi\) and \(\tan(x) = \frac{1}{4}\), then \(\sin(x) =\)

    A) 1
    B) \(\frac{1}{\sqrt{17}}\)
    C) \(\frac{1}{\sqrt{15}}\)
    D) \(-\frac{1}{\sqrt{17}}\)
    E) \(-\frac{1}{\sqrt{15}}\)

Answers to the Above Questions

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

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