ECZ 2022 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 diagram in the answer space below.
  2. Sets: Given that E={1,2,3,4,5,6,7,8,9,10},A={ Prime numbers }, B={ Multiples…
  3. Index Notation: Evaluate 5^3 × 1/(5^2).
  4. Algebra: Expand and simplify (2a + 3)(3a – 4).
  5. Quadratic Equations: Solve the equation 4x^2 = 9x.
  6. Algebra: Factorise completely 2ab + xy – 2ay – bx.
  7. Social and Commercial Arithmetic: A company declares an annual dividend of 6%. The value of each share i…
  8. Sequences and Series: For the sequence 5, 12, 19, ..., find the (a) sixth term.
  9. Sequences and Series: For the sequence 5, 12, 19, ..., find the (b) nth term.
  10. Earth Geometry: The distance between town F and town G is 8 100 nautical miles. If a p…
  11. Earth Geometry: Town B is east of town A. When it is 11 00 hours at B, it is 07 00 hou…
  12. Matrices: Given that the matrix C = matrix(7, 3; 1, 4; 2, 5), find C^T.
  13. Matrices: Express as a single matrix matrix(1, 8) matrix(0, -1; 2, 5).
  14. Probability: The probability of Kasukulu waking up late is 0.3. What is the probabi…
  15. Mensuration: The following diagram shows a sector POQ of radius 6cm. Angle POQ = θ …
  16. Geometrical Transformations: On the diagram in the answer space, draw triangle Q, the image of tria…
  17. Approximations: A piece of wood measures 25cm long. Find the (a) upper and lower limit…
  18. Approximations: A piece of wood measures 25cm long. Find the (b) percentage error.
  19. Relations and Functions: Given that f(x) = x - 4 and h(x) = 2x + 3, find (a) h^(-1)(x),
  20. Relations and Functions: Given that f(x) = x - 4 and h(x) = 2x + 3, find (b) h^(-1)(5),
  21. Relations and Functions: Given that f(x) = x - 4 and h(x) = 2x + 3, find (c) hf(x).
  22. Bearings: In the following diagram, P, Q and R are three points on level ground.…
  23. Bearings: In the following diagram, P, Q and R are three points on level ground.…
  24. Coordinate Geometry: A line passes through the points A(-2, 5) and B(0, y). Given that the …
  25. Similarity and Congruency: Two cylinders A and B are geometrically similar and the ratio of their…
  26. Symmetry: The diagram below shows a square based right pyramid with an axis AB. …
  27. Circle Theorems: In the following diagram, A, B, C and D are points on the circumferenc…
  28. Circle Theorems: In the following diagram, A, B, C and D are points on the circumferenc…
  29. Circle Theorems: In the following diagram, A, B, C and D are points on the circumferenc…
  30. Variation: y varies directly as x and inversely as the square of z and y = 8 when…
  31. Variation: y varies directly as x and inversely as the square of z and y = 8 when…
  32. Variation: y varies directly as x and inversely as the square of z and y = 8 when…
  33. Index Notation: Solve the equation x^(1/3) = 9.
  34. Computer and Calculator: In the answer space below is an incomplete flowchart for calculating t…
  35. Coordinate Geometry: Points A and B have coordinates (2, -3) and (7, 9) respectively. Find …
  36. Introduction To Calculus: Given that y = 4x^3 – 3x^2 + 5x, find dy/dx.
  37. Linear Programming: Write down the three inequalities that define the unshaded region R on…
  38. Vectors In Two Dimensions: The components of the vectors OA and OB are matrix(2; 3) and matrix(4;…
  39. Quadratic Functions: The diagram shows the sketch of the graph of y = 3 - 2x - x^2 passing …
  40. Quadratic Functions: The diagram shows the sketch of the graph of y = 3 - 2x - x^2 passing …
  41. Travel Graphs: The following diagram is the speed time graph of a car. (a) Calculate …
  42. Travel Graphs: The following diagram is the speed time graph of a car. (b) Find the v…
  43. Travel Graphs: The following diagram is the speed time graph of a car. (c) Calculate …
  44. Trigonometry: In the diagram, ABC is a straight line, angle BCD = 90° and tan AB̂D =…

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