ECZ 2025 O-Level Paper 1 — Mathematics

All 40 questions from this paper, each with a verified worked solution. Open any question to see it with the first step of the working free.

  1. Sets: Shade A'∩(B∩C) on the diagram in the answer space below.
  2. Sets: If P={1,3,5,7},P∪Q={1,2,3,4,5,6,7} and P∩Q={5,7}, list Q.
  3. Algebra: Simplify 3(x + 3) - 2x(x - 1).
  4. Algebra: Factorise completely 3a - c - 3ab + bc.
  5. Quadratic Equations: Solve the equation (x − 1)² − 25 = 0.
  6. Social and Commercial Arithmetic: A village banking cooperative for women declared a dividend at the end…
  7. Index Notation: Evaluate 4^(1/2) × 4.
  8. Sequences and Series: Given that 7, 11, 15, 19, … is an arithmetic progression, find: (a) th…
  9. Probability: The probability that a learner will not miss the school bus on any par…
  10. Similarity and Congruency: Two similar solids X and Y have surface areas 5 cm² and 20 cm² respect…
  11. Approximations: A bottle of mineral water has a capacity of 500 ± 0.5 millilitres. Fin…
  12. Trigonometry: Given that tan ∠BAC = 3/4, find the value of sin ∠BAC.
  13. Relations and Functions: The functions f and g are defined as f(x) = 2x + 1 and g(x) = 3/(x - 2…
  14. Introduction To Calculus: Find ∫(6x^2 - x + 3) dx.
  15. Index Notation: Solve the equation x^(3/2) = 8.
  16. Coordinate Geometry: In the following diagram, P is the point (0, 4), Q is the point (-4, 0…
  17. Matrices: Given that A = matrix(1, -5; 2, 4; 3, 7), find the transpose of A.
  18. Matrices: Given that B = matrix(-2, 4) and C = matrix(3; 1), find matrix BC.
  19. Earth Geometry: A plane flies from P to R at a speed of 650 knots for 6 hours. Find th…
  20. Earth Geometry: When it is 08 00 hours at P, the local time at Q is 11 00 hours. P is …
  21. Symmetry: The diagram shows a circle with centre O and six identical triangles. …
  22. Bearings: In the following diagram L, K, and M are points on level ground. The b…
  23. Bearings: In the following diagram L, K, and M are points on level ground. The b…
  24. Computer and Calculator: The following diagram shows a flowchart for a program to calculate the…
  25. Circle Theorems: A, B, C and D are points on the circumference of a circle with centre …
  26. Circle Theorems: A, B, C and D are points on the circumference of a circle with centre …
  27. Circle Theorems: A, B, C and D are points on the circumference of a circle with centre …
  28. Variation: Three variables p, q and r are such that p varies as q and inversely a…
  29. Variation: Three variables p, q and r are such that p varies as q and inversely a…
  30. Variation: Three variables p, q and r are such that p varies as q and inversely a…
  31. Geometrical Transformations: Triangle M has vertices (2, 1), (5, 1) and (5, 3). Triangle N is the i…
  32. Vectors In Two Dimensions: The vectors a = matrix(7; 2), b = matrix(m; -3) and c = matrix(5; n), …
  33. Mensuration: In the following diagram, the sector OAB of a circle has radius r and …
  34. Linear Programming: Write the three inequalities that define the unshaded region R on the …
  35. Quadratic Functions: The graph of y = -x^2 + 12x - 11 cuts the x-axis at points A and B. Fi…
  36. Quadratic Functions: The graph of y = -x^2 + 12x - 11 is shown. Find the maximum value of y…
  37. Travel Graphs: The diagram shows the speed-time graph of a moving object. Find the ac…
  38. Travel Graphs: The diagram shows the speed-time graph of a moving object. Given that …
  39. Travel Graphs: Calculate the average speed of the object in the first 14 seconds.
  40. Coordinate Geometry: Find the length of the straight line joining the points A(−13, 2) and …

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