ECZ 2018 GCE 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 Venn diagram bel…
  2. Sets: Given that E={1,2,3,4,5,6,7,8},A={1,2,3,4} and B={2,3,4,5,6}, list (A∪…
  3. Algebra: Simplify 4(x + 2y) − (3x − 8y).
  4. Index Notation: Evaluate 27^(2/3).
  5. Coordinate Geometry: A straight line passing through A(3, 2) and B(5, y) has gradient −2. F…
  6. Algebra: Factorise completely 5x² − 5.
  7. Matrices: Given that C = [5 −1; 2 1] (a 2×2 matrix with rows separated by semico…
  8. Sequences and Series: The first three terms of an arithmetic progression are 5, 7 and 9. Fin…
  9. Sequences and Series: The first three terms of an arithmetic progression are 5, 7 and 9. Fin…
  10. Probability: In a game, the probability of a player losing is 0.3. What is the prob…
  11. Vectors In Two Dimensions: The coordinates of B and C are (2, 5) and (4, −3) respectively. If M i…
  12. Similarity and Congruency: The scale of a map is 1 : 20 000. The actual area of residential plots…
  13. Earth Geometry: The difference in longitude between town A and town B is 105°. B is we…
  14. Earth Geometry: The distance between P and Q is 3 600 nautical miles. If an aeroplane …
  15. Matrices: The transpose of a matrix P is [1 3 4; 2 5 1; 3 0 1] (rows separated b…
  16. Index Notation: Solve the equation 2^(2x − 1) = 16^(−2x).
  17. Mensuration: A sector AOB of a circle with centre O has radius 7 cm. The area of th…
  18. Social and Commercial Arithmetic: Ngiwezi invested K14 500.00 in a business firm. The condition was that…
  19. Circle Theorems: In the diagram, RWS is a tangent to the circle at W. The points V, W, …
  20. Circle Theorems: In the diagram, RWS is a tangent to the circle at W. The points V, W, …
  21. Circle Theorems: In the diagram, RWS is a tangent to the circle at W. The points V, W, …
  22. Similarity and Congruency: The ratio of the heights of two geometrically similar containers is 2 …
  23. Geometrical Transformations: In the diagram, triangle ABC has vertices A(1, 3), B(1, 1) and C(4, 1)…
  24. Variation: Two variables x and y have corresponding values shown in the table: wh…
  25. Variation: Two variables x and y are such that y varies directly as (x² + 1), and…
  26. Variation: Two variables x and y are such that y = 4(x² + 1). Given that y = 104 …
  27. Relations and Functions: Given that f(x) = 8x, find f⁻¹(x).
  28. Relations and Functions: Given that f(x) = 8x and g(x) = (3x − 2)/4, find an expression for fg(…
  29. Relations and Functions: Given that f(x) = 8x and g(x) = (3x − 2)/4, find the value of x for wh…
  30. Bearings: A cyclist starts from town W and cycles on a bearing of 216° to town P…
  31. Bearings: A cyclist starts from town W and cycles on a bearing of 216° to town P…
  32. Symmetry: The diagram shows a regular hexagonal prism. State the number of plane…
  33. Approximations: A piece of timber measures 5.25 cm long. Calculate the relative error …
  34. Introduction To Calculus: Integrate 3x⁴ − 4x⁻³ with respect to x.
  35. Quadratic Equations: Solve the equation (2x − 1)² = 25.
  36. Coordinate Geometry: Find the equation of the line which is parallel to 2x + y = 3 and pass…
  37. Computer and Calculator: In triangle XYZ, the side opposite angle X is x = YZ, the side opposit…
  38. Linear Programming: In the diagram, R is the unshaded region bounded by three lines: the l…
  39. Trigonometry: Given a right-angled triangle XYZ where ∠Z is 90° and sin X = 4/5, fin…
  40. Quadratic Functions: The diagram shows a sketch of a parabola which opens upwards and meets…
  41. Quadratic Functions: The diagram shows a sketch of the parabola y = x² + 2x − 8, which meet…
  42. Travel Graphs: The speed-time graph shows a particle which started from rest and acce…
  43. Travel Graphs: The speed-time graph shows a particle which accelerated uniformly from…
  44. Travel Graphs: The speed-time graph shows a particle which accelerated uniformly from…

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