ECZ 2024 O-Level Paper 1 — Mathematics

All 44 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 the region P∩R'∩Q on the Venn diagram in the answer space below.
  2. Sets: Given that E={ natural numbers less than 10},A={ even numbers } and B=…
  3. Algebra: Simplify 3(2x - 4) - 2(x - 1).
  4. Index Notation: Evaluate (-2)^0 * (-2)^(-3).
  5. Algebra: Factorise completely 27y^2 - 3x^2.
  6. Coordinate Geometry: A straight line L is represented by the equation 2x - y = 5. Find the …
  7. Vectors In Two Dimensions: The magnitude of PQ is 20 units. Given that OP = matrix(5; 0) and OQ =…
  8. Matrices: Given that A = matrix(4, 5; 1, 1), find A^T.
  9. Matrices: Given that A = matrix(4, 5; 1, 1) and B = matrix(x - 1, 1; 2, 0), find…
  10. Sequences and Series: Given that 99, 92 and 85 are the first three terms of an arithmetic pr…
  11. Sequences and Series: Given that 99, 92 and 85 are the first three terms of an arithmetic pr…
  12. Probability: A six-sided die is thrown once. Find the probability of getting a numb…
  13. Quadratic Equations: Solve the equation (1 - 2t)^2 = 25.
  14. Symmetry: In the following diagram, PQRSTU is a triangular prism such that PQ = …
  15. Earth Geometry: The diagram shows the position of towns A, B and C on the Earths surfa…
  16. Earth Geometry: A plane flies from A to B in 9 hours. Calculate its speed if the dista…
  17. Index Notation: Solve the equation 3^(1 - 2x) + 4 = 5.
  18. Mensuration: The diagram shows a sector AOB whose area is 231cm^2 and radius 14cm. …
  19. Relations and Functions: Given that f(x) = 3x + 5 and g(x) = (x + 4)/3, find (a) g^(-1)(x),
  20. Relations and Functions: Given that f(x) = 3x + 5 and g(x) = (x + 4)/3, find (b) gf(x),
  21. Relations and Functions: Given that f(x) = 3x + 5 and g(x) = (x + 4)/3, find (c) gf(4).
  22. Approximations: A container of cooking oil has a mass of 15.4kg. (a) Find the toleranc…
  23. Approximations: A container of cooking oil has a mass of 15.4kg. (b) Write down the re…
  24. Geometrical Transformations: The diagram in the answer space shows triangle ABC with vertices A(2, …
  25. Introduction To Calculus: The equation of a curve is y = x - 2x^2 + 1/x^3. Find dy/dx.
  26. Variation: It is given that a varies as b and inversely as the square of c and a …
  27. Variation: It is given that a varies as b and inversely as the square of c and a …
  28. Variation: It is given that a varies as b and inversely as the square of c and a …
  29. Circle Theorems: In the following diagram, P, Q and R are points on the circumference o…
  30. Circle Theorems: In the following diagram, P, Q and R are points on the circumference o…
  31. Circle Theorems: In the following diagram, P, Q and R are points on the circumference o…
  32. Social and Commercial Arithmetic: A company declares a dividend of 8%. Mary owns 1 300 shares of value K…
  33. Coordinate Geometry: The point (-1, -4) is the midpoint of the line PQ. Given that P is the…
  34. Bearings: In the following diagram, A, B and C are three points on level ground.…
  35. Bearings: In the following diagram, A, B and C are three points on level ground.…
  36. Similarity and Congruency: Two solid cylinders are geometrically similar. The ratio of their corr…
  37. Computer and Calculator: In the following diagram, ABCD is a trapezium. AB is parallel to CD an…
  38. Linear Programming: Write the three inequalities that define the unshaded region R on the …
  39. Coordinate Geometry: A straight line L is perpendicular to the line y = 3x + 4. Given that …
  40. Quadratic Functions: The diagram shows a sketch of the graph of a curve passing through A(-…
  41. Quadratic Functions: The diagram shows a sketch of the graph of a curve passing through A(-…
  42. Travel Graphs: The following diagram is a speed-time graph of a particle moving in a …
  43. Travel Graphs: The following diagram is a speed-time graph of a particle moving in a …
  44. Travel Graphs: The following diagram is a speed-time graph of a particle moving in a …

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