ECZ 2023 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: Shade (A∪B)∩C' on the Venn diagram in the space below.
  2. Sets: The universal set E={0,1,2,3,4,5,6,7,8,9}, set A={ Prime numbers } and…
  3. Index Notation: Evaluate 3^2 + 3^(-1) × 2^0.
  4. Algebra: Simplify 2(x + 3y) - 3(4x - 2).
  5. Algebra: Factorise completely 3x^2 - 27.
  6. Coordinate Geometry: Find the gradient of a line which passes through the points (-3, -1) a…
  7. Vectors In Two Dimensions: The position vector of a point P is matrix(3; 4). Given that the point…
  8. Matrices: Given that P = matrix(4, -1, 0; 2, 0, 3) and Q = matrix(1; 2; 3), find…
  9. Matrices: Given that P = matrix(4, -1, 0; 2, 0, 3) and Q = matrix(1; 2; 3), find…
  10. Sequences and Series: An Arithmetic Progression is given as 1, 7, 13, ... Find the eighth te…
  11. Sequences and Series: An Arithmetic Progression is given as 1, 7, 13, ... Find the sum of th…
  12. Probability: In a bag there are 4 blue marbles, 3 red marbles and 2 white marbles. …
  13. Quadratic Equations: Solve the equation 2x^2 + x - 3 = 0.
  14. Symmetry: The following diagram shows a regular hexagonal right pyramid. Find th…
  15. Earth Geometry: Towns A and B are on longitudes 75°W and 45°E respectively. Find the t…
  16. Earth Geometry: The diagram shows towns P(45°S, 75°W) and Q(0°, 75°W). An aeroplane to…
  17. Index Notation: Solve 5^(-3x) = 125.
  18. Mensuration: The diagram shows a sector XOY. The angle subtended at the centre is 7…
  19. Approximations: The mass of a bag of mealie meal is 25.2kg. Calculate the (a) toleranc…
  20. Approximations: The mass of a bag of mealie meal is 25.2kg. Calculate the (b) relative…
  21. Bearings: In the diagram, three points A, B and C are on level ground. The beari…
  22. Bearings: In the diagram, three points A, B and C are on level ground. The beari…
  23. Relations and Functions: Given that f(x) = (3x - 5)/2 and g(x) = x + 2, find (a) f^(-1)(x).
  24. Relations and Functions: Given that f(x) = (3x - 5)/2 and g(x) = x + 2, find (b) f^(-1)(5).
  25. Relations and Functions: Given that f(x) = (3x - 5)/2 and g(x) = x + 2, find (c) f g(x).
  26. Circle Theorems: In the diagram, A, B, C and D are points on the circumference of a cir…
  27. Circle Theorems: In the diagram, A, B, C and D are points on the circumference of a cir…
  28. Circle Theorems: In the diagram, A, B, C and D are points on the circumference of a cir…
  29. Geometrical Transformations: The diagram shows triangles P and Q. Describe fully the single transfo…
  30. Computer and Calculator: In the answer space below is an incomplete flowchart for calculating t…
  31. Variation: Z varies inversely as the square of x and directly as y and z = 6 when…
  32. Variation: Z varies inversely as the square of x and directly as y and z = 6 when…
  33. Variation: Z varies inversely as the square of x and directly as y and z = 6 when…
  34. Social and Commercial Arithmetic: Paul invests K50 000.00 in a government bond at 9% simple interest per…
  35. Similarity and Congruency: Two cylindrical tins are geometrically similar. The radius of the base…
  36. Trigonometry: The diagram shows a right angled triangle ABC. BC is produced to D. AC…
  37. Coordinate Geometry: Find the equation of a straight line passing through the point (-2, 3)…
  38. Linear Programming: Write three inequalities that define the unshaded region R in the diag…
  39. Introduction To Calculus: Integrate 3x² − 5x + 9/x³ with respect to x.
  40. Quadratic Functions: The diagram shows the graph of the function y = x² + 2x − 15. The curv…
  41. Quadratic Functions: The diagram shows the graph of the function y = x² + 2x − 15. Find the…
  42. Travel Graphs: The diagram is a speed-time graph of a car. The car starts from rest a…
  43. Travel Graphs: The diagram is a speed-time graph of a car. The car starts from rest a…
  44. Travel Graphs: The diagram is a speed-time graph of a car. The car starts from rest a…

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