ECZ 2018 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 region in the diagram below.
  2. Sets: The Venn diagram below shows sets A and B . List A'∩B.
  3. Index Notation: Find the value of x^0 × 2^3.
  4. Algebra: Factorise completely 18 - 2x^2.
  5. Vectors In Two Dimensions: Z is a point (-1, 8) and M is a point (2, 12). Find the magnitude of Z…
  6. Social and Commercial Arithmetic: Floyd had 125 shares in a company. At the end of a financial year, the…
  7. Similarity and Congruency: A cylinder with diameter 2 cm has a volume of 5 cm^3. Find the volume …
  8. Matrices: Express matrix(1, 4, 0; 2, 1, 1; 3, 2, 4) matrix(-1, 4, 5; 2, 2, 3; 0,…
  9. Sequences and Series: For an arithmetic progression 16, 25, 34, 43, 52, ........, write down…
  10. Sequences and Series: For an arithmetic progression 16, 25, 34, 43, 52, ........, write down…
  11. Earth Geometry: A plane leaves a town P(0°, 30°W) and flies due East to a town Q(0°, 5…
  12. Earth Geometry: A plane leaves a town P(0°, 30°W) and flies due East to a town Q(0°, 5…
  13. Matrices: Given that matrix M = matrix(3, -1, 0; -2, 1, 3; 0, -1, 2), find M^T.
  14. Algebra: Expand and simplify (c + 3)^2.
  15. Probability: A box contains 5 green, 3 yellow and 6 red beads of the same type. Fin…
  16. Coordinate Geometry: Find the equation of a straight line passing through (1, 5) and (2, 10…
  17. Variation: y varies directly as the square of x and y = 96 when x = 4. Find the (…
  18. Variation: y varies directly as the square of x and y = 96 when x = 4. Find the (…
  19. Variation: y varies directly as the square of x and y = 96 when x = 4. Find the (…
  20. Quadratic Equations: Solve the equation 2x^2 = 8.
  21. Approximations: The mass (m) of a bag of mealie meal is 25 kg. Complete the statement …
  22. Bearings: In the diagram below, F is due east of E, angle GEF = 60° and angle EF…
  23. Bearings: In the diagram below, F is due east of E, angle GEF = 60° and angle EF…
  24. Coordinate Geometry: The point (5, 2) is the midpoint of a straight line joining A(x, 9) an…
  25. Approximations: The length of a line is 8 cm. If this is recorded as 8.2 cm, calculate…
  26. Relations and Functions: Given that f(x) = 2x - 5 and g(x) = x + 3, Find (a) f^(-1)(x).
  27. Relations and Functions: Given that f(x) = 2x - 5 and g(x) = x + 3, Find (b) f^(-1)(-10).
  28. Relations and Functions: Given that f(x) = 2x - 5 and g(x) = x + 3, Find (c) gf(3).
  29. Introduction To Calculus: Given that y = 2x^3 - 5x^2 + 4x + 2, find dy/dx.
  30. Trigonometry: In the diagram below, AC = 10 cm, angle ABC = 90° and angle BAC = 30°.…
  31. Circle Theorems: In the diagram below, O is the centre of the circle. A, B, C and D are…
  32. Circle Theorems: In the diagram below, O is the centre of the circle. A, B, C and D are…
  33. Circle Theorems: In the diagram below, O is the centre of the circle. A, B, C and D are…
  34. Quadratic Functions: The diagram below shows a sketch of the graph of y = 2 + x - x^2 passi…
  35. Quadratic Functions: The diagram below shows a sketch of the graph of y = 2 + x - x^2 passi…
  36. Symmetry: The diagram below shows a triangular prism with AB = BC = AC = DE = EF…
  37. Computer and Calculator: In the answer space below is an incomplete program in pseudo code to c…
  38. Linear Programming: On the XOY plane below, region R is unshaded. Write the three inequali…
  39. Index Notation: Solve the equation x^(1/3) = 4.
  40. Mensuration: In the diagram below, OPQ is a sector of a circle whose centre is O, r…
  41. Geometrical Transformations: The diagram below shows ΔA. If ΔA is mapped onto ΔB by a translation T…
  42. Travel Graphs: The diagram below is a speed-time graph of a particle which accelerate…
  43. Travel Graphs: The diagram below is a speed-time graph of a particle which accelerate…
  44. Travel Graphs: The diagram below is a speed-time graph of a particle which accelerate…

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