ECZ 2024 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. Index Notation: Evaluate (8/27)^(2/3).
  2. Algebra: Simplify 4(x − 2) + 3(2x − 3).
  3. Quadratic Equations: Solve the equation (3x - 5)(x + 2) = 0.
  4. Algebra: Factorise completely 7x^2 - 7.
  5. Sets: Use the diagram. Write the set notation for the shaded region.
  6. Social and Commercial Arithmetic: A businessman got 800 shares worth K7 200.00. What was the cost of eac…
  7. Sequences and Series: The sequence 20, 17, 14, ... is an arithmetic progression. Find the 9t…
  8. Sequences and Series: The sequence 20, 17, 14, ... is an arithmetic progression. Find the su…
  9. Probability: A fair die is rolled once. Find the probability of a 4 showing up.
  10. Trigonometry: In the diagram below, ABC is a straight line, AD = 5 cm, BD = 13 cm an…
  11. Sets: Given E = {1,2,3,4,5,6,7,8,9}, P = {2,4,6,8} and Q = {2,3,5,7}, list P…
  12. Geometrical Transformations: Use the diagram. Describe fully the single transformation that maps tr…
  13. Matrices: Given that A = matrix(2, -1, 3), find A^T.
  14. Matrices: Given that A = matrix(3; 2) and B = matrix(1, −2), find AB.
  15. Earth Geometry: The diagram below shows positions of towns A,B and C. What is the time…
  16. Earth Geometry: A plane flew from town A to town C in 5 hours. What was the speed of t…
  17. Mensuration: A sector has angle 81° and area 34.65 cm^2. Calculate its radius. [π =…
  18. Similarity and Congruency: The ratio of the surface areas of two similar solids is 9:25. The volu…
  19. Variation: Given that y varies directly as x and inversely as the square of z, an…
  20. Variation: Given that y varies directly as x and inversely as the square of z, an…
  21. Variation: Given that y varies directly as x and inversely as the square of z, an…
  22. Circle Theorems: Use the diagram. P, Q, R and S lie on a circle with centre O, angle PQ…
  23. Circle Theorems: Use the diagram. P, Q, R and S lie on a circle with centre O, angle PQ…
  24. Circle Theorems: Use the diagram. P, Q, R and S lie on a circle with centre O, angle PQ…
  25. Coordinate Geometry: Two points A and B have coordinates (-5, -3) and (-1, a) respectively.…
  26. Introduction To Calculus: Given that y = 4x^3 - 2x^2 + 1, find dy/dx.
  27. Approximations: The length of a sugarcane is measured as 2.6 m. Its true length is 2.5…
  28. Approximations: The length of a sugarcane is measured as 2.6 m. Its true length is 2.5…
  29. Relations and Functions: The functions f and g are defined by f(x) = 3x - 4 and g(x) = (x + 1)/…
  30. Relations and Functions: The functions f and g are defined by f(x) = 3x - 4 and g(x) = (x + 1)/…
  31. Relations and Functions: The functions f and g are defined by f(x) = 3x - 4 and g(x) = (x + 1)/…
  32. Symmetry: A triangular prism has equilateral triangular ends. State the number o…
  33. Computer and Calculator: A program calculates the nth term Tn of an arithmetic progression from…
  34. Vectors In Two Dimensions: Given that AB = matrix(3; 1) and BC = matrix(1; -3), find AC.
  35. Coordinate Geometry: The straight line y = (1/2)x + p passes through (-2, 2). Find the coor…
  36. Bearings: In the diagram, A, B and C are points on level ground. The bearing of …
  37. Bearings: In the diagram, A, B and C are points on level ground. The bearing of …
  38. Linear Programming: Use the diagram. Write the four inequalities that define the unshaded …
  39. Graphs of Functions: The diagram below shows a sketch of a graph of y = x^2 + 3x + 2 passin…
  40. Graphs of Functions: The diagram below shows a sketch of a graph of y = x^2 + 3x + 2 passin…
  41. Index Notation: Solve the equation 81 - 27^x = 0.
  42. Travel Graphs: An object accelerates uniformly from 0 m/s to 20 m/s in 4 seconds, mov…
  43. Travel Graphs: An object accelerates uniformly from 0 m/s to 20 m/s in 4 seconds, mov…
  44. Travel Graphs: An object accelerates uniformly from 0 m/s to 20 m/s in 4 seconds, mov…

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