ECZ 2021 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: Use set notation to describe the shaded part in the Venn diagram below…
  2. Sets: It is given that the universal set E={ first 8 whole numbers } and A={…
  3. Algebra: Simplify 2y - 3(x - 4) - y.
  4. Index Notation: Evaluate -3^2 + 3^2.
  5. Quadratic Equations: Solve the equation (2x - 5)(x + 3) = 0
  6. Coordinate Geometry: Find the equation of a straight line passing through the points (3, 4)…
  7. Algebra: Factorise completely 3x^3 - 12xy^2.
  8. Matrices: Matrix M = matrix(-2, 3; 4, -2). Find the transpose of M.
  9. Matrices: Matrix P = matrix(2, -1; 0, 3) and Q = matrix(-1; 3). Find PQ.
  10. Social and Commercial Arithmetic: A certain company sells shares at K1.30 per share. A businesswoman had…
  11. Sequences and Series: The third and fourth terms of an Arithmetic progression are 6 and 3 re…
  12. Sequences and Series: The third and fourth terms of an Arithmetic progression are 6 and 3 re…
  13. Probability: The probability of getting a black button from a box is 2/9. Find the …
  14. Mensuration: The diagram below shows a sector AOB with centre O and radius 21cm. Th…
  15. Earth Geometry: The positions of three towns A, B and C on the earth’s surface are sho…
  16. Earth Geometry: The positions of three towns A, B and C on the earth’s surface are sho…
  17. Approximations: A learner measured the length of a line to be 2.2cm. If the actual len…
  18. Approximations: A learner measured the length of a line to be 2.2cm. If the actual len…
  19. Circle Theorems: The points A, B, C and D are on the circumference of a circle centre O…
  20. Circle Theorems: The points A, B, C and D are on the circumference of a circle centre O…
  21. Circle Theorems: The points A, B, C and D are on the circumference of a circle centre O…
  22. Bearings: The diagram below shows three points J, K and L on level ground. K is …
  23. Bearings: The diagram below shows three points J, K and L on level ground. K is …
  24. Coordinate Geometry: Find the equation of a straight line which is perpendicular to the lin…
  25. Computer and Calculator: In the answer space below is an incomplete flowchart for calculating t…
  26. Symmetry: The figure below shows a parallelogram with centre O. Describe fully t…
  27. Geometrical Transformations: The diagram below shows triangle A which is mapped onto triangle B by …
  28. Variation: It is given that y varies directly as 2x and inversely as z^2 and y = …
  29. Variation: It is given that y varies directly as 2x and inversely as z^2 and y = …
  30. Variation: It is given that y varies directly as 2x and inversely as z^2 and y = …
  31. Introduction To Calculus: Find ∫(6x^2 - 2x + 7) dx.
  32. Similarity and Congruency: The areas of two similar cylinders are 64cm^2 and 36cm^2 respectively.…
  33. Trigonometry: In the diagram below, AB = 3cm, BC = 4cm, AD = 13cm and ABC = ACD = 90…
  34. Vectors In Two Dimensions: A is the point (1, 2) and B is the point (-2, 5). Find AB as a column …
  35. Linear Programming: Write three inequalities that define the unshaded region R, on the dia…
  36. Index Notation: Given that √2 = 2^x, find the value of x.
  37. Quadratic Functions: The diagram below shows the graph of y = (-x + 2)(x - 5). The graph cu…
  38. Quadratic Functions: The diagram below shows the graph of y = (-x + 2)(x - 5). The graph cu…
  39. Travel Graphs: The diagram below shows the speed-time graph of a moving object. (a) F…
  40. Travel Graphs: The diagram below shows the speed-time graph of a moving object. (b) G…
  41. Travel Graphs: The diagram below shows the speed-time graph of a moving object. (c) C…
  42. Relations and Functions: The functions f and g are defined by f(x) = (x + 9)/2 and g(x) = x − 2…
  43. Relations and Functions: The functions f and g are defined by f(x) = (x + 9)/2 and g(x) = x − 2…
  44. Relations and Functions: The functions f and g are defined by f(x) = (x + 9)/2 and g(x) = x − 2…

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