ECZ 2020 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 diagram below
  2. Algebra: Simplify 2a + (b - a) - 2b.
  3. Index Notation: Evaluate (64/125)^(-1/3).
  4. Coordinate Geometry: Given that the lines 3y = x + 6 and y = kx + 12 are perpendicular, fin…
  5. Algebra: Factorise completely 6ax - 4ay - 3bx + 2by.
  6. Vectors In Two Dimensions: Given that A is the point (-2, 1) and B is the point (1, 5), find |AB|…
  7. Matrices: Given that A = matrix(2, 3; 1, 0), B = matrix(-1, 0; x, 2) and C = mat…
  8. Matrices: Given that A = matrix(2, 3; 1, 0), B = matrix(-1, 0; x, 2) and C = mat…
  9. Sequences and Series: Given that the 11th term of an arithmetic progression is 43 and that t…
  10. Sequences and Series: Given that the 11th term of an arithmetic progression is 43 and that t…
  11. Earth Geometry: A plane flying at a speed of 900 knots takes 5 hours to fly from town …
  12. Earth Geometry: Point Q on longitude 85°E lies on the equator and is due east of P. Th…
  13. Probability: The probability of a girl not wearing a neck tie is 0.55. What is the …
  14. Index Notation: Given that 8^(x - 1) = 16, find the value of x.
  15. Sets: Given that S = {x: 1 < x ≤ 15, x is a prime number}, list the elements…
  16. Mensuration: The diagram below shows a right square pyramid ABCDE of base 6cm and E…
  17. Relations and Functions: A function f is defined by f(x) = 2x - 5. Find (a) f^(-1)(x),
  18. Relations and Functions: A function f is defined by f(x) = 2x - 5. Find (b) ff^(-1)(2),
  19. Relations and Functions: A function f is defined by f(x) = 2x - 5. Find (c) the value of x if f…
  20. Geometrical Transformations: The diagram below shows two figures P and Q on the XOY plane. Describe…
  21. Introduction To Calculus: Given that y = 2x^3 - 4/x^2, find dy/dx.
  22. Bearings: The diagram below shows three points O, A and B in which OB = AB. Give…
  23. Bearings: The diagram below shows three points O, A and B in which OB = AB. Give…
  24. Approximations: The values of x and y are given to 1 decimal place as x = 4.2 and y = …
  25. Approximations: The values of x and y are given to 1 decimal place as x = 4.2 and y = …
  26. Variation: It is given that y varies inversely as the square of x. The table belo…
  27. Variation: It is given that y varies inversely as the square of x. The table belo…
  28. Variation: It is given that y varies inversely as the square of x. The table belo…
  29. Circle Theorems: In the diagram below, A, B, C, and D lie on the circumference of the c…
  30. Circle Theorems: In the diagram below, A, B, C, and D lie on the circumference of the c…
  31. Circle Theorems: In the diagram below, A, B, C, and D lie on the circumference of the c…
  32. Trigonometry: The diagram below shows a right angled triangle PQR. Given that PQ = 1…
  33. Coordinate Geometry: A straight line L has equation 3y = 5x - 6. Find the y co-ordinate of …
  34. Similarity and Congruency: Rectangle ABCD and DAEF are geometrically similar. Given that AB = 10 …
  35. Social and Commercial Arithmetic: Mrs Kalomba bought 120 shares at a nominal value of K40.00 each which …
  36. Symmetry: On the diagram in the answer space, shade three more triangles to make…
  37. Computer and Calculator: Simple interest is given by the formula I = PTR/100. Complete the flow…
  38. Linear Programming: In the diagram below, point A is (1, 1), B is (0, 7), C is (14, 0), D …
  39. Quadratic Equations: Solve the equation x^2 - 7x = 8.
  40. Quadratic Functions: The diagram below is the graph of y = -4(x - 1/2)^2 + 9. Find the (i) …
  41. Quadratic Functions: The diagram below is the graph of y = -4(x - 1/2)^2 + 9. Find the (ii)…
  42. Travel Graphs: A sprinter runs a race of 200m. Her total time for running the race is…
  43. Travel Graphs: A sprinter runs a race of 200m. Her total time for running the race is…
  44. Travel Graphs: A sprinter runs a race of 200m. Her total time for running the race is…

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