Alberta Diploma Exams · Mathematics 30-1

Exponents, Logarithms and Polynomials

39 practice questions, each with the answer and an explanation.

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Random questions from this topic, one at a time. You see the answer and the explanation straight after each one.

All 39 questions

  1. What is the vertex of the parabola y = (x - 2)² - 2?
  2. What is the vertex of the parabola y = (x + 4)² + 1?
  3. Simplify (x² - 4) / (x - 2), x ≠ 2.
  4. What is the vertex of the parabola y = (x - 5)² + 6?
  5. Which single logarithm equals log 4 + log 3?
  6. Which single logarithm equals log 3 + log 4?
  7. What is the vertex of the parabola y = (x - 3)² + 6?
  8. How many real roots does 3x^2 - 2x = 0 have?
  9. If f(x) = 3x + 5 and g(x) = 2x - 1, what is f(g(3))?
  10. What is the remainder when 3x^3 + x^2 + 2x - 2 is divided by (x + 2)?
  11. How many real roots does x^2 - 7x - 3 = 0 have?
  12. What is the remainder when 2x^3 - 3x^2 - 2x - 7 is divided by (x - 3)?
  13. A sample of 320 g of a radioactive isotope has a half-life of 8 days. How much remains after 32 days?
  14. A population of 500 bacteria doubles every 4 hours. Which expression gives the population after t hours?
  15. If f(x) = 3x - 3 and g(x) = 2x + 1, what is f(g(1))?
  16. How many real roots does x^2 + 2x - 1 = 0 have?
  17. A population of 200 bacteria doubles every 3 hours. Which expression gives the population after t hours?
  18. Solve for x: log base 5 of x = 4.
  19. If f(x) = 4x + 2 and g(x) = 3x - 3, what is f(g(2))?
  20. How many real roots does 3x^2 - 2x - 4 = 0 have?
  21. If f(x) = 1x + 3 and g(x) = 1x + 4, what is f(g(1))?
  22. For what value of c is (x + 2) a factor of x² + c?
  23. For what value of c is (x - 1) a factor of x² + 1x + c?
  24. Simplify (x² - 16) / (x - 4), x ≠ 4.
  25. Simplify (x² - 25) / (x - 5), x ≠ 5.
  26. Which single logarithm equals log 5 + log 2?
  27. Which single logarithm equals log 2 + log 5?
  28. If f(x) = 2x - 3 and g(x) = 2x + 3, what is f(g(2))?
  29. A sample of 320 g of a radioactive isotope has a half-life of 5 days. How much remains after 15 days?
  30. A population of 100 bacteria doubles every 3 hours. Which expression gives the population after t hours?
  31. Solve for x: log base 3 of x = 2.
  32. If f(x) = 4x - 3 and g(x) = 2x - 3, what is f(g(1))?
  33. Solve for x: log base 3 of x = 4.
  34. What is the remainder when 2x^3 + 5x^2 - 5x + 5 is divided by (x - 2)?
  35. What is the remainder when 2x^3 + 4x^2 - 6x - 2 is divided by (x + 2)?
  36. A sample of 80 g of a radioactive isotope has a half-life of 8 days. How much remains after 32 days?
  37. A sample of 320 g of a radioactive isotope has a half-life of 12 days. How much remains after 48 days?
  38. How many real roots does x^2 - 6x + 1 = 0 have?
  39. For what value of c is (x + 2) a factor of x² + 4x + c?

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