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 set notation to describe the shaded region in the Venn diagram bel…
  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 that the universal set E = {1, 2, 3, 4, 5, 6, 7, 8, 9}, P = {2, …
  12. Geometrical Transformations: The diagram below shows trapezium S and trapezium T. Describe fully a …
  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 tim…
  16. Earth Geometry: The diagram below shows positions of towns A, B and C. A plane flew fr…
  17. Mensuration: The diagram shows a sector AOB whose area is 34.65 cm^2. The angle sub…
  18. Similarity and Congruency: The ratio of the areas of two similar solids is 9:25. If the volume of…
  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: In the diagram, P, Q, R, S are points on the circle with centre O and …
  23. Circle Theorems: In the diagram, P, Q, R, S are points on the circle with centre O and …
  24. Circle Theorems: In the diagram, P, Q, R, S are points on the circle with centre O and …
  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: The diagram shows a triangular prism ABCDEF in which AE = AD = DE. Sta…
  33. Computer and Calculator: A program calculates the nth term Tn of an arithmetic progression from…
  34. Vectors In Two Dimensions: Given that vec(AB) = matrix(3; 1) and vec(BC) = matrix(1; -3), find ve…
  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 three points on level ground. The beari…
  37. Bearings: In the diagram, A, B and C are three points on level ground. The beari…
  38. Linear Programming: Use the diagram. Write the four inequalities that define the unshaded …
  39. Quadratic Functions: The diagram below shows a sketch of the graph of y = x^2 + 3x + 2, pas…
  40. Quadratic Functions: The diagram below shows a sketch of the graph of y = x^2 + 3x + 2, pas…
  41. Index Notation: Solve the equation 81 - 27^x = 0.
  42. Travel Graphs: The diagram below shows the speed-time graph of an object. The object …
  43. Travel Graphs: The diagram below shows the speed-time graph of an object. The object …
  44. Travel Graphs: The diagram below shows the speed-time graph of an object. The object …

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