ECZ 2021 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: Using set notation, describe the shaded region.
  2. Sets: Given that A = {x: x<6, x is a natural number}, list set A.
  3. Algebra: Simplify 2ab − ab² − 7ab + a²b + 5ab².
  4. Index Notation: Evaluate 9^(1/2) + 1.
  5. Quadratic Equations: Solve the equation x² − 2x = 0.
  6. Algebra: Factorise completely 2x² − x − 6.
  7. Social and Commercial Arithmetic: At the end of the financial year, a public limited company declared a …
  8. Sequences and Series: Given that 9, 15, 21, 27 ... is an Arithmetic Progression, find the tw…
  9. Sequences and Series: Given that 9, 15, 21, 27 ... is an Arithmetic Progression, find the fo…
  10. Matrices: Given that A = (1 −3 5 / 2 1 0) is a 2 × 3 matrix, find the transpose …
  11. Matrices: Given that P = (2 −1 / 3 4) and Q = (−2 / 3), find PQ.
  12. Probability: A letter is chosen at random from the letters of the word HELLO. What …
  13. Index Notation: Solve the equation 125^x = 1/25.
  14. Mensuration: The diagram shows a sector XOY. The arc XY subtends an angle of θ at t…
  15. Earth Geometry: The diagram shows the positions of towns A, B and C on the earth's sur…
  16. Earth Geometry: The diagram shows towns A, B and C on the earth's surface, where NACS …
  17. Approximations: The mass (m) of a bag of maize is 62kg to the nearest kilogram. Comple…
  18. Approximations: A woman estimates the weight of her dog to be 13.15kg. The actual weig…
  19. Circle Theorems: In the diagram, A, B, C and D are points on the circumference of a cir…
  20. Circle Theorems: In the diagram, A, B, C and D are points on the circumference of a cir…
  21. Circle Theorems: In the diagram, A, B, C and D are points on the circumference of a cir…
  22. Coordinate Geometry: The diagram shows two lines l and n that are perpendicular to each oth…
  23. Trigonometry: The diagram shows triangle ABC in which AB = 5cm and AC = 13cm. Angle …
  24. Variation: Given that z varies as x and inversely as the square of y, and that z …
  25. Variation: Given that z varies as x and inversely as the square of y, with consta…
  26. Variation: Given that z varies as x and inversely as the square of y, with consta…
  27. Introduction To Calculus: Find ∫(10x⁴ − 4x + 3/x²) dx.
  28. Computer and Calculator: The diagram in the answer space shows an incomplete flowchart to calcu…
  29. Geometrical Transformations: Triangle ABC is mapped onto triangle A₁B₁C₁ by a translation represent…
  30. Bearings: In the diagram, A, B and C are points on level ground. The bearing of …
  31. Bearings: In the diagram, A, B and C are points on level ground. The bearing of …
  32. Relations and Functions: The functions f and g are defined by f(x) = (x − 3)/4 and g(x) = 2x + …
  33. Relations and Functions: The functions f and g are defined by f(x) = (x − 3)/4 and g(x) = 2x + …
  34. Relations and Functions: The functions f and g are defined by f(x) = (x − 3)/4 and g(x) = 2x + …
  35. Coordinate Geometry: The points P and Q have coordinates (2, 6) and (−3, −6) respectively. …
  36. Similarity and Congruency: The areas of the faces of cubes A and B are 9cm² and 25cm² respectivel…
  37. Linear Programming: Write the four inequalities that define the unshaded region R on the d…
  38. Vectors In Two Dimensions: The components of the vectors OA and OB are (2 / 3) and (4 / 2) respec…
  39. Quadratic Functions: The diagram shows a sketch of the graph of y = 5 − 4x − x², cutting th…
  40. Quadratic Functions: The diagram shows a sketch of the graph of y = 5 − 4x − x². Find the m…
  41. Travel Graphs: The diagram is a speed-time graph of a moving car. The car decelerates…
  42. Travel Graphs: From the speed-time graph, the car decelerates from 24m/s to 18m/s in …
  43. Travel Graphs: From the speed-time graph, the car travels at 18m/s until the 13th sec…
  44. Symmetry: Describe fully the symmetry of the diagram below, given that OA and OB…

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