Intermediate Algebra Questions With Answers
Sample 3

Intermediate algebra questions on some of the most important topics and skills in algebra, with answers, are presented. The solutions are at the bottom of the page. Also included are the solutions with full explanations.


  1. Write 1.5 × 10-5 in standard form.

  2. Evaluate: 30 - |-x + 6| for x = 10

  3. Evaluate: 2xy3 + x - 2y for x = 2 and y = -2

  4. What is the slope of the line perpendicular to the line y = - 4

  5. Write an equation of the line with slope 2 and x-intercept (-4 , 0).

  6. Solve the equation: -3(-x + 5) + 20 = -10(x - 3) + 4

  7. Solve the inequality: 4(x - 6) + 4 < 8(x - 4)

  8. Solve the equation: 3(x - 2)2 - 12 = 0

  9. Solve the equation: x / 3 + 2 / 7 = x / 7 - 5

  10. Line L is defined as line through the point (2 , 7) and perpendicular to the line x + y = 0. What is the point of intersection of L and the line x + y = 0?

  11. What is the point of intersection of the lines: x + 2y = 4 and -x - 3y = -7?

  12. How many solutions do the system of equations 2x - 3y = 4 and 4x - 6y = -7 have?

  13. For what value(s) of A does the system of equation A x + 6y = 0 and 2x - 7y = 3 have no solutions?

  14. Solve |2x - 4| - 2 = 6.

  15. How many solutions does the equation 2x2 + 3x = 8 have?

  16. Solve the equation 3x2 + 6x - 1 = 8.

  17. Solve the system of equations: 2x + 5y = 18 and -3x - y = -1.

  18. What is the range of function f defined by: f = {(2,3),(1,4),(5,4),(0,3)}

  19. Factor the expression 2x2 + 3x + 1.

  20. Factor the expression 10x2 + 20x - 80.

Answers to the Above Questions
  1. 0.000015
  2. 26
  3. -26
  4. undefined (vertical line)
  5. y = 2x + 8
  6. 29/13
  7. x > 3
  8. {0 , 4}
  9. -111/4
  10. (-5/2 , 5/2)
  11. (-2 , 3)
  12. no solutions
  13. -12/7
  14. {-2 , 6}
  15. 2 real solutions
  16. {-3 , 1}
  17. (-1 , 4)
  18. {3 , 4}
  19. (2x + 1)(x + 1)
  20. 10(x - 2)(x + 4)

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