ECZ 2025 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 P={x:10≤x≤20,x is a prime number }, list set P .
  3. Algebra: Simplify 2(y - 3) - 3(2 - y).
  4. Index Notation: Evaluate (⁴√(16/81))^3.
  5. Algebra: Factorise completely 2ab - 3b + 10a - 15.
  6. Quadratic Equations: Solve the equation (1/2)x^2 - 8 = 0.
  7. Social and Commercial Arithmetic: A company with 6 000 shares declared a dividend of K56 000.00. What am…
  8. Probability: The probability that Gift will not be late for a job interview is 0.05…
  9. Index Notation: Solve the equation 2^(x - 1) - 4 = 0.
  10. Mensuration: The diagram shows a sector POQ. Arc PQ subtends an angle of 45° at the…
  11. Earth Geometry: The diagram shows the positions of three towns A, B and C on the earth…
  12. Earth Geometry: The diagram shows the positions of three towns A, B and C on the earth…
  13. Approximations: If a machine that loads mealie meal into 25 kg bags has a tolerance of…
  14. Approximations: If 12.5 litres of water was poured out of a container containing 20 li…
  15. Circle Theorems: In the following diagram A, B, C, D and E are points on the circumfere…
  16. Circle Theorems: In the following diagram A, B, C, D and E are points on the circumfere…
  17. Circle Theorems: In the following diagram A, B, C, D and E are points on the circumfere…
  18. Trigonometry: In the diagram, AB = 8 cm, AD = 10 cm, DC = 12 cm and angle ABC = 90°.…
  19. Coordinate Geometry: Use the diagram. C = (0, 4) and D = (6, 0). Line AB is perpendicular t…
  20. Variation: It is given that x = kz/(y^2), where k is the constant of variation. T…
  21. Variation: It is given that x = kz/y^2, where k is a constant of variation. table…
  22. Variation: It is given that x = kz/y^2, where k is a constant of variation. table…
  23. Introduction To Calculus: Find ∫(3x^3 + 4x) dx.
  24. Geometrical Transformations: In the diagram, quadrilateral P is mapped onto Q by a single transform…
  25. Bearings: The diagram shows three points O, P and Q on level ground. OPQ is an e…
  26. Bearings: The diagram shows three points O, P and Q on level ground. OPQ is an e…
  27. Symmetry: The diagram shows a cuboid with a rectangular base and square ends. PQ…
  28. Computer and Calculator: An incomplete flowchart calculates the area A of a triangle with base …
  29. Relations and Functions: The functions f and g are defined by f(x) = (x + 3)/2 and g(x) = 1 - 2…
  30. Relations and Functions: The functions f and g are defined by f(x) = (x + 3)/2 and g(x) = 1 - 2…
  31. Relations and Functions: The functions f and g are defined by f(x) = (x + 3)/2 and g(x) = 1 - 2…
  32. Coordinate Geometry: The points A and B are (−7, 1) and (−4, 5) respectively. Find the leng…
  33. Similarity and Congruency: Two similar pyramids A and B have surface areas 180 cm^2 and 80 cm^2 r…
  34. Linear Programming: Write three inequalities that define the unshaded region R in the diag…
  35. Vectors In Two Dimensions: Given that vec(PQ) = matrix(2; 3) and vec(OQ) = matrix(4; -1), find th…
  36. Quadratic Functions: The sketch represents the graph of the curve y = x^2 − 6x + 5 passing …
  37. Quadratic Functions: The sketch represents the graph of the curve y = x^2 − 6x + 5 passing …
  38. Sequences and Series: The formula for the nth term of an arithmetic progression is 2n − 3. F…
  39. Sequences and Series: The formula for the nth term of an arithmetic progression is 2n − 3. F…
  40. Matrices: Given that A = matrix(−1, 2; 3, 0; 1, 4), find A^T.
  41. Matrices: Given that matrix(−2, 1; x, −2) matrix(3; 1) = matrix(−5; 7), find the…
  42. Travel Graphs: The diagram below shows the speed graph of a particle. The particle st…
  43. Travel Graphs: The diagram below shows the speed graph of a particle. The particle st…
  44. Travel Graphs: The diagram below shows the speed graph of a particle. The particle st…

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