ECZ 2022 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∪B' )∩C on the diagram in the answer space below.
  2. Sets: Given that the universal set E={1,3,5,7,9,11},X={1,5,9} and Y={3,9,11}…
  3. Index Notation: Evaluate (3/2)^(-2).
  4. Algebra: Factorise completely 2ax + 4ay - 3bx - 6by.
  5. Algebra: Simplify 3(4x - 5) + 2.
  6. Quadratic Equations: Solve the equation 4y^2 - 8y = 0.
  7. Social and Commercial Arithmetic: A company declared a dividend of K2.75 per share. A businessman invest…
  8. Sequences and Series: Given that 2, -1, -4 ... are consecutive terms of an Arithmetic progre…
  9. Sequences and Series: Given that 2, -1, -4 ... are consecutive terms of an Arithmetic progre…
  10. Probability: The probability that a boy will be late for school on any particular d…
  11. Vectors In Two Dimensions: The vector RS = matrix(-4; 5). Given that the coordinates of the point…
  12. Matrices: The matrix M = matrix(1, 5; 2, 7) and the matrix N = matrix(0, 1; 2, 0…
  13. Matrices: The matrix M = matrix(1, 5; 2, 7) and the matrix N = matrix(0, 1; 2, 0…
  14. Geometrical Transformations: The diagram shows two triangles A and B. Describe fully the single tra…
  15. Earth Geometry: In the following diagram, points A and B lie on latitude 60°S while po…
  16. Earth Geometry: In the following diagram, points A and B lie on latitude 60°S while po…
  17. Coordinate Geometry: Find the gradient of the line passing through the points A(4, -6) and …
  18. Index Notation: Solve the equation 2x^3 = 16.
  19. Circle Theorems: In the following diagram, AB and AC are tangents to the circle, centre…
  20. Circle Theorems: In the following diagram, AB and AC are tangents to the circle, centre…
  21. Circle Theorems: In the following diagram, AB and AC are tangents to the circle, centre…
  22. Approximations: The mass of a loaf of bread is 702.1g correct to 1 decimal place. Find…
  23. Approximations: The mass of a loaf of bread is 702.1g correct to 1 decimal place. Find…
  24. Similarity and Congruency: Two similar solids P and Q have volumes 80cm^3 and 270cm^3 respectivel…
  25. Trigonometry: In the diagram, FGH is a straight line, FG = 8cm, EG = 10cm and angle …
  26. Variation: y varies directly as the square of x and inversely as z and y = 2 when…
  27. Variation: y varies directly as the square of x and inversely as z and y = 2 when…
  28. Variation: y varies directly as the square of x and inversely as z and y = 2 when…
  29. Symmetry: The diagram below shows a regular triangular prism. Describe the symme…
  30. Computer and Calculator: In the answer space below is an incomplete program written in pseudoco…
  31. Coordinate Geometry: ABC is a straight line. The coordinates of the points A and B are (2, …
  32. Mensuration: In the diagram, AOB is a sector of a circle, centre O. Angle AOB = 72°…
  33. Relations and Functions: Given that f(x) = 3x + 1 and g(x) = 4x - 1, find (a) f^(-1)(x),
  34. Relations and Functions: Given that f(x) = 3x + 1 and g(x) = 4x - 1, find (b) f^(-1)(-5),
  35. Relations and Functions: Given that f(x) = 3x + 1 and g(x) = 4x - 1, find (c) fg(x).
  36. Bearings: In the following diagram, angle BAC is 46° and AC = BC. B is due east …
  37. Bearings: In the following diagram, angle BAC is 46° and AC = BC. B is due east …
  38. Linear Programming: Write the four inequalities that define the unshaded region R in the d…
  39. Introduction To Calculus: Given that y = 2x^2 - 4x + 3, find dy/dx.
  40. Quadratic Functions: The sketch shows the graph of y = x^2 - 2x - 8. Find the coordinates o…
  41. Quadratic Functions: The sketch shows the graph of y = x^2 - 2x - 8. Find the coordinates o…
  42. Travel Graphs: The diagram below is the speed-time graph of an object. The object sta…
  43. Travel Graphs: The diagram below is the speed-time graph of an object. The object sta…
  44. Travel Graphs: The diagram below is the speed-time graph of an object. The object sta…

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