ECZ 2023 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: The Venn diagram shows three sets P,Q and R . Use set notation to desc…
  2. Sets: Set A={x:1<x≤15,x is a prime number } and set B={x:0≤x<10,x is an odd …
  3. Index Notation: Evaluate (8/27)^(1/3).
  4. Algebra: Factorise completely 3x^3 - 27x.
  5. Algebra: Simplify 2a^2 - 5b(a - b) + ab.
  6. Coordinate Geometry: The point A(-5, 3) and the point B have a midpoint (4, -2). Find the c…
  7. Vectors In Two Dimensions: Given that OP = matrix(4; 13) and the point Q is (16, 8), find |PQ|.
  8. Matrices: Given that A = matrix(1, 2, 4) and B = matrix(3; 0; 4), find (a) A^T,
  9. Matrices: Given that A = matrix(1, 2, 4) and B = matrix(3; 0; 4), find (b) AB.
  10. Sequences and Series: Given that 25 and 13 are the first and third terms of an arithmetic pr…
  11. Sequences and Series: Given that 25 and 13 are the first and third terms of an arithmetic pr…
  12. Probability: A letter is chosen at random from the letters of the word “EXCELLENT”.…
  13. Similarity and Congruency: The areas of two similar shapes are in the ratio 25 : 36. If the lengt…
  14. Index Notation: Solve the equation 2^(x + 3) = 1/16.
  15. Earth Geometry: The diagram shows two towns A and B on the equator. A is on longitude …
  16. Earth Geometry: A ship sailed due east from A to B at an average speed of 450 knots. F…
  17. Relations and Functions: The functions g and h are defined by g(x) = 3x + 1 and h(x) = (x - 1)/…
  18. Relations and Functions: The functions g and h are defined by g(x) = 3x + 1 and h(x) = (x - 1)/…
  19. Relations and Functions: The functions g and h are defined by g(x) = 3x + 1 and h(x) = (x - 1)/…
  20. Approximations: In a practical examination, Nellie recorded the volume, v, of water as…
  21. Approximations: The actual length of the longest side of a rectangular playing field i…
  22. Introduction To Calculus: Find ∫(x^3 + 2x + 3) dx.
  23. Geometrical Transformations: In the following diagram, triangle ABC is mapped onto triangle DEF by …
  24. Bearings: The diagram shows three points P, Q and R on level ground. The bearing…
  25. Bearings: The diagram shows three points P, Q and R on level ground. The bearing…
  26. Trigonometry: In the diagram, BCE is a right angled triangle in which BC = 4cm and C…
  27. Mensuration: The curved surface area of a cone with radius 4.2cm is 138.6cm^2. Find…
  28. Circle Theorems: In the following diagram, A, B, C, D and E lie on the circumference of…
  29. Circle Theorems: In the following diagram, A, B, C, D and E lie on the circumference of…
  30. Circle Theorems: In the following diagram, A, B, C, D and E lie on the circumference of…
  31. Social and Commercial Arithmetic: A sugar company paid K362 400.00 as dividend for 1 200 shares. A man h…
  32. Coordinate Geometry: Find the equation of a line parallel to the line 2x + y = 4 passing th…
  33. Variation: If a varies jointly as b and the square root of c and a = 21 when b = …
  34. Variation: If a varies jointly as b and the square root of c and a = 21 when b = …
  35. Variation: If a varies jointly as b and the square root of c and a = 21 when b = …
  36. Computer and Calculator: In the answer space below is an incomplete simple program in pseudocod…
  37. Symmetry: Shade two more sections of the diagram in the answer space so that it …
  38. Linear Programming: Write the three inequalities that define the unshaded region R.
  39. Quadratic Equations: Solve the equation x^2 = 4(x - 3)^2.
  40. Quadratic Functions: The diagram shows the sketch of the graph of y = -4x - x^2 cutting the…
  41. Quadratic Functions: The diagram shows the sketch of the graph of y = -4x - x^2 cutting the…
  42. Travel Graphs: The diagram shows the speed-time graph of a car during a period of t s…
  43. Travel Graphs: The diagram shows the speed-time graph of a car during a period of t s…
  44. Travel Graphs: The diagram shows the speed-time graph of a car during a period of t s…

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