ECZ 2019 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 (A∪C)'∩B in the Venn diagram in the answer space.
  2. Sets: Set A={ Prime numbers less than 12}. List set A .
  3. Index Notation: Evaluate (-1)^0 × 2^3.
  4. Quadratic Equations: Solve the equation (x - 1)(2x + 5) = 0.
  5. Algebra: Simplify 4x^2 + 2y^2 - xy - 6x^2 + 2xy.
  6. Algebra: Factorise completely 4ab + 6ac - 6bd - 9cd.
  7. Social and Commercial Arithmetic: A company declared a dividend of K1.50 per share. Musalala has 600 sha…
  8. Sequences and Series: Given that 17, m, 27, ... are consecutive terms of an Arithmetic Progr…
  9. Sequences and Series: For the sequence 11, 13, 15, ..., find the formula for the nth term.
  10. Matrices: The transpose of a matrix A is (-1 4 5). Find the matrix A.
  11. Matrices: Given that (1 2 3) matrix(1; x; 5) = (24), find the value of x.
  12. Probability: A number is chosen at random from the set {1, 2, 3, 4, 5, 6, 7, 8, 9, …
  13. Index Notation: Solve the equation 8^x = 128.
  14. Mensuration: The diagram below shows a sector AOB. Arc AB subtends an angle of 21° …
  15. Earth Geometry: The diagram below shows the positions of towns A, B and C on the earth…
  16. Earth Geometry: The diagram below shows the positions of towns A, B and C on the earth…
  17. Approximations: The length of a piece of wire is measured as 4.5 cm. Calculate (a) the…
  18. Approximations: The length of a piece of wire is measured as 4.5 cm. Calculate (b) the…
  19. Circle Theorems: In the diagram below, A, B, C and D are points on the circumference of…
  20. Circle Theorems: In the diagram below, A, B, C and D are points on the circumference of…
  21. Circle Theorems: In the diagram below, A, B, C and D are points on the circumference of…
  22. Trigonometry: In the diagram below, BCD is a straight line, AB = 12cm, AC = 20cm and…
  23. Coordinate Geometry: A and B are points with coordinates (-3, 3) and (5, 9) respectively. F…
  24. Variation: a varies directly as b and as the square of c and a = 30 when b = 2.5 …
  25. Variation: a varies directly as b and as the square of c and a = 30 when b = 2.5 …
  26. Variation: a varies directly as b and as the square of c and a = 30 when b = 2.5 …
  27. Introduction To Calculus: Find ∫(3x^2 + 8x - 5) dx.
  28. Geometrical Transformations: The diagram below shows two triangles A and B. Describe fully the sing…
  29. Bearings: In the diagram below, A, B and C are three points on level ground. The…
  30. Bearings: In the diagram below, A, B and C are three points on level ground. The…
  31. Symmetry: The diagram below shows a plane figure made up of congruent semi circl…
  32. Computer and Calculator: In the answer space below is an incomplete program written in pseudoco…
  33. Relations and Functions: The functions f and g are defined by f(x) = 2x - 3 and g(x) = 3x. Find…
  34. Relations and Functions: The functions f and g are defined by f(x) = 2x - 3 and g(x) = 3x. Find…
  35. Relations and Functions: The functions f and g are defined by f(x) = 2x - 3 and g(x) = 3x. Find…
  36. Coordinate Geometry: In the diagram below, A is the point (0, 4) and B is the point (2, 0) …
  37. Similarity and Congruency: The heights of two similar cylinders are 4 cm and 6 cm. If the volume …
  38. Linear Programming: Write down the three inequalities that define the unshaded region R, o…
  39. Vectors In Two Dimensions: M is the point (0, 5) and MN = matrix(-3; 4). Find ON.
  40. Quadratic Functions: The sketch shown below represents the graph of the curve y = x^2 - 4x …
  41. Quadratic Functions: The sketch shown below represents the graph of the curve y = x^2 - 4x …
  42. Travel Graphs: The diagram below is the speed time graph of a car. The car starts fro…
  43. Travel Graphs: The diagram below is the speed time graph of a car. The car starts fro…
  44. Travel Graphs: The diagram below is the speed time graph of a car. The car starts fro…

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