Intermediate Algebra Practice
True or False Algebra Questions With Solutions

Test your understanding of intermediate algebra with these true or false questions. Answers are provided below, along with detailed solutions and explanations to help you learn from your mistakes and reinforce key algebra concepts.

Questions

  1. (True or False)   \( x^2 \) and \( 2x \) are like terms.

  2. (True or False)   \( x^{-3} \) and \( -3x \) are unlike terms.

  3. (True or False)   \( \frac{1}{x - 9} = 0 \) for \( x = 9 \).

  4. (True or False)   The set of ordered pairs \( \{(0,0),(2,0),(3,0),(10,0)\} \) represents a function.

  5. (True or False)   \( |a - b| = b - a \) if \( b - a \lt 0 \).

  6. (True or False)   \( |x^2 + 1| = x^2 + 1 \).

  7. (True or False)   \( \sqrt{(x - 5)^2} = x - 5 \).

  8. (True or False)   \( (x - 2)(x + 2) = x^2 - 4x - 4 \).

  9. (True or False)   \( \sqrt{x + 9} = \sqrt{x} + \sqrt{9} \), for all \( x \in \mathbb{R} \).

  10. (True or False)   \( |x - 3| = |x| + |3| \), for all \( x \in \mathbb{R} \) and negative.

  11. (True or False)   \( (x + 2)^3 = x^3 + 2^3 \), for all \( x \in \mathbb{R} \).

  12. (True or False)   If \( k = 4 \), then the equation \( x^2 - kx = -4 \) has one solution only.

  13. (True or False)   The discriminant of the equation: \( 2x^2 - 4x + 9 = 0 \) is negative.

  14. (True or False)   The degree of the polynomial \( P(x) = (x - 2)(-x + 3)(x - 4) \) is equal to -3.

  15. (True or False)   The distance between the points \( (0 , 0) \) and \( (1 , 1) \) in a rectangular system of axes is equal to 1.

  16. (True or False)   The slope of the line \( 2x + 3y = -2 \) is negative.

  17. (True or False)   The relation \( 2y + x^2 = 2 \) represents \( y \) as a function of \( x \).

  18. (True or False)   The relation \( 2y + x^2 = 2 \) represents \( x \) as a function of \( y \).

  19. (True or False)   The relation \( |x| = |y| \) DOES NOT represent \( x \) as a function of \( y \).

  20. (True or False)   The relation \( |x| = |y| \) DOES NOT represent \( y \) as a function of \( x \).

Answers to the Above Questions

  1. FALSE (different power)
  2. TRUE
  3. FALSE (\( \frac{1}{9-9} = \frac{1}{0} \), undefined)
  4. TRUE
  5. FALSE (\( |a - b| = a - b \) if \( b - a \lt 0 \))
  6. TRUE
  7. FALSE \( \sqrt{(x - 5)^2} = |x - 5| \)
  8. FALSE
  9. FALSE (try \( x = 16 \))
  10. TRUE
  11. FALSE (try \( x = 2 \))
  12. TRUE
  13. TRUE
  14. FALSE (degree = 3)
  15. FALSE (\( \sqrt{2} \))
  16. TRUE
  17. TRUE
  18. FALSE (solve for \( y \) and you get 2 solutions)
  19. TRUE
  20. TRUE

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