Free Compass Math Practice: Substituting Values Into Algebraic Expressions

A set of questions, with answers, on substituting variables with values into algebraic expressions. These questions are similar to those in the compass math test. The answers to the questions are at the bottom of the page and the solutions with full explanations to these questions are also included.

  1. What is the value of \( 2(x^{3} - y^{2}) + 2(x^{3} + y^{2}) \) for \( x = 2 \) and \( y = -4 \)?

    A) -32
    B) 32
    C) 34
    D) -34
    E) 35


  2. If \( x = 3 \), what is the value of \( \frac{6}{x} + 4x - 20 \)?

    A) 6
    B) 2
    C) -6
    D) 14
    E) -34


  3. The surface area \( A \) of a cylindrical container is given by the formula:

    \[ A = 2\pi r^{2} + 2\pi r h \]

    where \( r \) is the radius, \( h \) is the height, and \( \pi \approx 3.14 \). Which value below is closest to the area of a container with radius \( 10 \) cm and height \( 5 \) cm?

    A) 628
    B) 1256
    C) 314
    D) 3140
    E) 942



  4. If \( x = -2 \) and \( y = 3 \), what is the value of \( -x^{-y} \)?

    A) \( \frac{1}{8} \)
    B) \( -\frac{1}{8} \)
    C) 8
    D) -8
    E) -6


  5. If \( y = -3 \), what is the value of \( \frac{y^{3} - 3}{-y + 3} \)?

    A) 5
    B) 10
    C) 6
    D) -5
    E) -6


  6. What is the value of \( 3x^{3} - 2x^{2} + 2 \) for \( x = -2 \)?

    A) 20
    B) -20
    C) 30
    D) -30
    E) 60


  7. If \( x = 2.7 \), what is the value of \( x + 0.75(x - 1.5) + 1.2 \)?

    A) 4.8
    B) 7.2
    C) 6.1
    D) 6.2
    E) 6.3


  8. If \( x = -0.07 \) and \( y = 1.2 \), what is the value of \( xy - 0.2(y - x) \)?

    A) 0.338
    B) -0.338
    C) 0.3
    D) -0.3
    E) 0.338


  9. At normal resting heart rates, the mean arterial pressure (MAP) can be approximated by:

    \[ \text{MAP} = DP + \frac{1}{3}(SP - DP) \]

    where \( DP \) is diastolic pressure and \( SP \) is systolic pressure. Find MAP, rounded to the nearest unit, for a person with \( SP = 101 \) mmHg and \( DP = 72 \) mmHg.

    A) 85
    B) 100
    C) 90
    D) 80
    E) 82


  10. What is the value of \( \frac{3}{x - 4y} + \frac{2}{0.5x + 8y} \) for \( x = -2 \) and \( y = -0.25 \)?

    A) \( \frac{11}{3} \)
    B) \( \frac{3}{11} \)
    C) \( -\frac{3}{11} \)
    D) \( -\frac{11}{3} \)
    E) 3


Answers to the Above Questions

  1. B
  2. C
  3. E
  4. A
  5. D
  6. D
  7. A
  8. B
  9. E
  10. D

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