Intermediate Algebra Practice Questions and Answers - Sample 5

A set of multiple choice intermediate algebra questions, with answers, are presented. The answers are at the bottom of the page. Also included are the solutions with full explanations.

  1. If \( f(x) = 4x^3 - 4x^2 + 10 \), then \( f(-2) = \)
    1. 26
    2. -38
    3. 10
    4. 38

  2. Which of these values of \( x \) satisfies the inequality \( -7x + 6 \leq -8 \)
    1. -2
    2. 0
    3. -7
    4. 2

  3. The domain of the function \( f(x) = \sqrt{6 - 2x} \) is given by
    1. \( x > 0 \)
    2. \( x \geq 6 \)
    3. \( x \leq 3 \)
    4. \( x \leq 6 \)

  4. The lines \( y = 2x \) and \( 2y = -x \) are
    1. parallel
    2. perpendicular
    3. horizontal
    4. vertical

  5. The equation \( |-2x - 5| - 3 = k \) has no solution if \( k = \)
    1. -5
    2. -3
    3. 7
    4. 0

  6. The inequality corresponding to the statement: "the price is no less than 100 Dollars" is
    1. \( x < 100 \)
    2. \( x \geq 100 \)
    3. \( x \leq 100 \)
    4. \( x > 100 \)

  7. Which of these relations DOES NOT represent a function?
    1. {(2,3), (-4,3), (7,3)}
    2. {(0,0), (-1,-1), (2,2)}
    3. {(2,3), (-5,3), (2,7)}
    4. {(-1,3), (-5,3), (-9,0)}

  8. Which of these points DOES NOT lie on the graph of \( y = -x + 3 \)?
    1. (9,6)
    2. (3,0)
    3. (-2,5)
    4. (2,2)

  9. What is the slope of the line perpendicular to the line \( y = -5x + 9 \)?
    1. 5
    2. -5
    3. \( \dfrac{1}{5} \)
    4. \( -\dfrac{1}{5} \)

  10. Which property is used to write: \( 3(xy) = (3x)y \)?
    1. Commutative property of multiplication
    2. Multiplicative inverse property
    3. Distributive property
    4. Associative property of multiplication

  11. In which quadrant do the lines \( x = 3 \) and \( y = -4 \) intersect?
    1. I
    2. II
    3. III
    4. IV

  12. The value of \( 2^{-| -2 |} \) is
    1. 4
    2. 0.25
    3. -4
    4. -0.25

  13. If \( a \) and \( b \) are positive real numbers, then \( (a^0 - 3b^0)^5 \) =
    1. 0
    2. 1
    3. -32
    4. 32

  14. Which inequality describes the situation: "length \( L \) is at most 45 cm".
    1. \( L = 45 \text{ cm} \)
    2. \( L > 45 \text{ cm} \)
    3. \( L \geq 45 \text{ cm} \)
    4. \( L \leq 45 \text{ cm} \)

  15. The equation \( mx - 8 = 6 - 7(x + 3) \) DOES NOT have any solution if \( m = \)
    1. 3
    2. 7
    3. -7
    4. 0

  16. The equation \( -mx + 1 = 13 - 4(x + 3) \) is an identity if \( m = \)
    1. 4
    2. -4
    3. 1
    4. -1

  17. Which of the following is ALWAYS true?
    1. A function is not a relation
    2. Every function is a relation
    3. Every relation is a function
    4. A relation is not a function

  18. Which of these inequalities has NO solutions?
    1. \( 7x + 4 > 3 \)
    2. \( |x - 1| > -10 \)
    3. \( |x + 3| < -2 \)
    4. \( -100x + 5 \geq 8 \)

  19. The lines \( y = (a - 5)x + 5 \) and \( y = -2x + 7 \) are parallel if \( a = \)
    1. -2
    2. 3
    3. 5
    4. -5

  20. The lines \( y = (a - 5)x + 5 \) and \( y = -2x + 7 \) are perpendicular if \( a = \)
    1. \( \dfrac{11}{2} \)
    2. 5
    3. \( -\dfrac{2}{9} \)
    4. \( \dfrac{9}{2} \)

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

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