Basic Education Certificate Examination · Mathematics

Numbers, Sets and Algebra

35 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 35 questions

  1. If set P = {factors of 12} and set Q = {factors of 18}, what is P ∩ Q?
  2. Convert the binary number 11011_two to a base ten (denary) number.
  3. Find the highest common factor (HCF) of 36, 54, and 90.
  4. Find the least common multiple (LCM) of 12, 18, and 24.
  5. Simplify the algebraic expression: 3(2x - 4) - 2(x - 5).
  6. Solve for x in the linear equation: 5x - 7 = 2x + 8.
  7. Solve the inequality: 3x - 4 < 5x + 6.
  8. Express the number 0.000458 in standard form (scientific notation).
  9. Round the number 84,763 to three significant figures.
  10. If a = 3 and b = -2, evaluate the expression: 2a^2 - 3ab + b^3.
  11. Factorize completely the quadratic expression: x^2 - 7x + 12.
  12. Factorize completely the difference of two squares: 9x^2 - 25y^2.
  13. Make 'r' the subject of the formula: V = πr^2h.
  14. If 3^(2x - 1) = 27, find the value of x.
  15. Evaluate: (2/3 + 1/4) ÷ (5/6 - 1/2).
  16. Solve the simultaneous equations: 2x + y = 7 and 3x - y = 8.
  17. Express 75% as a fraction in its simplest form.
  18. If universal set U = {integers from 1 to 10} and A = {prime numbers}, what is the complement A'?
  19. Simplify: (4x^3y^2) * (3x^2y^4).
  20. Solve for y: (y + 3) / 4 - (y - 1) / 3 = 1.
  21. If 15 men can weed a school farm in 6 days, how many days will 10 men take working at the same rate?
  22. Find the value of x if log_10(x) = 3.
  23. Simplify the fraction to lowest terms: (x^2 - 9) / (x^2 + 5x + 6).
  24. If 25% of a number is 40, what is 60% of that same number?
  25. Solve for m: 2m/3 + 5 = 11.
  26. What is the square root of 0.0064?
  27. If n(A) = 15, n(B) = 20, and n(A ∪ B) = 28, find n(A ∩ B).
  28. Evaluate: 101_two + 110_two in binary notation.
  29. If 4 pencils cost GH₵ 18.00, how much will 7 pencils cost at the same rate?
  30. Find the truth set of 2x - 3 <= 7 for integers x.
  31. The sum of three consecutive odd numbers is 57. Find the largest of the three numbers.
  32. Express 0.375 as a common fraction in its lowest terms.
  33. What is the value of 5^0 + 5^(-1)?
  34. Factorize completely: 6ax - 9ay + 4bx - 6by.
  35. If x/2 = y/3 = z/5 and x + y + z = 50, find the value of z.

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