Intermediate Algebra Questions With Answers
Sample 1

Intermediate algebra questions on various topics are presented below, along with their answers. You can jump directly to the answers at the bottom of the page. For detailed step-by-step solutions and explanations, visit our full solution page.

  1. Write 230,000,000,000 in scientific notation.
  2. Evaluate: \[ 30 - \dfrac{12}{3} \times 2 \]
  3. Evaluate: \[ |4 - 8(3 - 12)| - |5 - 11| \]
  4. Evaluate: \[ -18 + 4 \left(\dfrac{6}{2}\right)^2 \]
  5. Evaluate: \[ 11 + \sqrt{-4 + \dfrac{6 \times 4}{3}} \]
  6. Simplify: \[ 12x^3 - 3(2x^3 + 4x - 1) - 5x + 7 \]
  7. Simplify: \[ \left(\dfrac{x^4}{x^3}\right)^3 \]
  8. Simplify: \[ \dfrac{(3x^2y^{-2})^3}{(9xy^3)^3} \]
  9. Simplify: \[ \dfrac{(2x^{-3}y^4)^3(x^3 + y)^0}{(4xy^{-2})^3} \]
  10. Write as a mathematical inequality: "9 is less than the product of M and N".
  11. Find the slope of the line perpendicular to the line with equation: \[ y = \dfrac{1}{3} x - 7 \]
  12. Write an equation of the line with slope \( -3 \) and y-intercept at \( (0 , -5) \).
  13. Solve the equation: \[ -5x + 20 = 25 \]
  14. Solve the inequality: \[ -3x + 4 \lt -8 \]
  15. Solve the equation: \[ 2x^2 - 32 = 0 \]
  16. Solve the equation: \[ -0.25x + 1.3 = -0.55x - 0.2 \]
  17. Solve the equation: \[ -0.25x^2 + 1.5 = -10.75 \]
  18. What is the slope of a line perpendicular to the line with equation \[ x = -3\]?
  19. What is the slope of a line parallel to the line with equation \[ x = 5 \]?
  20. What is the slope of a line perpendicular to the line with equation \[ y = 6 \] ?

Answers to the Above Questions
  1. \[ 2.3 \times 10^{11} \]
  2. \[ 22 \]
  3. \[ 70 \]
  4. \[ 18 \]
  5. \[ 13 \]
  6. \[ 6x^3 - 17x + 10 \]
  7. \[ x^3 \]
  8. \[ \dfrac{1}{27} \cdot \dfrac{x^6}{y^{15}} \]
  9. \[ \dfrac{1}{8} \cdot \dfrac{y^{18}}{x^{12}} \]
  10. \[ 9 \lt MN \]
  11. \[ -3 \]
  12. \[ y = -3x - 5 \]
  13. \[ x = -1 \]
  14. \[ x > 4 \]
  15. \[ x = -4, \quad x = 4 \]
  16. \[ x = -5 \]
  17. \[ x = -7, \quad x = 7 \]
  18. \[ 0 \]
  19. \[ \text{Undefined} \]
  20. \[ \text{Undefined} \]

More References and Links