ECZ 2026 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 (27/64)^(1/3).
  2. Algebra: Factorise completely pq - 3p - q^2 + 3q.
  3. Algebra: Simplify 8x + 4 - 3(2x - 3).
  4. Quadratic Equations: Solve the equation 2x^2 - 72 = 0.
  5. Sets: Shade (P∪Q)′∩R on the Venn diagram in the answer space below.
  6. Social and Commercial Arithmetic: The market value of a share is K25.00. How many shares can be bought f…
  7. Sequences and Series: The first and seventh terms of an arithmetic progression are -11 and 1…
  8. Sequences and Series: The first and seventh terms of an arithmetic progression are -11 and 1…
  9. Probability: The cards 1, 2, 3, 4, 5 and 6 are placed in a box. If a card is select…
  10. Vectors In Two Dimensions: If A is the point (1, 1) and vec(AB) = matrix(6; 5), find the coordina…
  11. Matrices: Given that matrix A = matrix(3, 4; -1, 0), find A^T.
  12. Matrices: Given that matrix A = matrix(3, 4; -1, 0) and matrix B = matrix(-1; 3)…
  13. Sets: Given that R = {x: 0 ≤ x < 10, x is an even number}, list the elements…
  14. Geometrical Transformations: A point F(-4, 1) is mapped onto a point G(5, -4) by a translation T. E…
  15. Earth Geometry: In the diagram, NS is the Prime Meridian. The positions of towns A and…
  16. Earth Geometry: In the diagram, NS is the Prime Meridian. The positions of towns A and…
  17. Approximations: The absolute error of a number n is 5 and the relative error for the s…
  18. Approximations: The absolute error of a number n is 5 and the relative error for the s…
  19. Trigonometry: Triangle ABC is right angled at B, BCD is a straight line and cos ACD …
  20. Introduction To Calculus: Find ∫(12/x^3 - 3x^2) dx.
  21. Circle Theorems: The points A, B, C and D are on the circumference of a circle centre O…
  22. Circle Theorems: The points A, B, C and D are on the circumference of a circle centre O…
  23. Circle Theorems: The points A, B, C and D are on the circumference of a circle centre O…
  24. Similarity and Congruency: Two buckets A and B are geometrically similar. The height of bucket A …
  25. Coordinate Geometry: The diagram shows a straight line AB passing through the points A(5, 0…
  26. Variation: P varies as q and inversely as the square of r, and when p = 6, q = 18…
  27. Variation: P varies as q and inversely as the square of r, and when p = 6, q = 18…
  28. Variation: P varies as q and inversely as the square of r, and when p = 6, q = 18…
  29. Symmetry: The following figure is made up of five identical cubes. State the num…
  30. Computer and Calculator: In the answer space is an incomplete program written in pseudocode for…
  31. Mensuration: The diagram shows a sector of a circle with centre O and radius 10.5 c…
  32. Coordinate Geometry: The points P and Q have coordinates (3, 6) and (-9, 4) respectively. F…
  33. Relations and Functions: Given that f(x) = 2/(x - 9) and g(x) = x + 5, find f^(-1)(x).
  34. Relations and Functions: Given that f(x) = 2/(x - 9) and g(x) = x + 5, find fg(x).
  35. Relations and Functions: Given that f(x) = 2/(x - 9) and g(x) = x + 5, find the value of x for …
  36. Bearings: In the diagram, angle POQ = 55°, OQ = QP and the bearing of Q from O i…
  37. Bearings: In the diagram, angle POQ = 55°, OQ = QP and the bearing of Q from O i…
  38. Linear Programming: Write the four inequalities that define the unshaded region R on the X…
  39. Index Notation: Solve the equation 4^(3x) = 8.
  40. Quadratic Functions: The diagram shows a sketch of the graph of y = (-2x + 4)(x + 5), which…
  41. Quadratic Functions: The diagram shows a sketch of the graph of y = (-2x + 4)(x + 5), which…
  42. Travel Graphs: The diagram shows the speed-time graph of a particle which starts from…
  43. Travel Graphs: The diagram shows the speed-time graph of a particle which starts from…
  44. Travel Graphs: The diagram shows the speed-time graph of a particle which starts from…

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