ECZ 2012 O-Level Paper 1 — Mathematics

All 32 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. Algebra: Simplify 3x - 7(2x - 5).
  2. Matrices: Given that A = matrix(1, -3; 4, 5) and B = matrix(9, 3; -12, 6), find …
  3. Algebra: Factorise completely 4 - 16x^2.
  4. Variation: Mr Hambwiimbwi planned to employ 20 men to build his house in 7 days. …
  5. Coordinate Geometry: Find the gradient of the straight line with equation 4x + 2y = 9.
  6. Symmetry: The diagram shows a squared floor tile with centre O. Describe fully t…
  7. Circle Theorems: In the diagram, A, B and C are points on the circumference of a circle…
  8. Circle Theorems: In the diagram, AT and TB are tangents to the circle at A and B, angle…
  9. Vectors In Two Dimensions: Given that vector a = matrix(-8; 6), find the magnitude of a.
  10. Similarity and Congruency: The diagram shows two circles with the same centre O. The radius of th…
  11. Sets: Given that E = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}, list the subse…
  12. Sets: Given that E = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}, list the subse…
  13. Trigonometry: In the diagram, BCD is a straight line, AB = 6 cm, BD = 13 cm, angle A…
  14. Trigonometry: Using the same diagram, calculate the area of triangle ACD.
  15. Probability: A pack of eleven identical cards is labelled 1 to 11. The cards are sh…
  16. Trigonometry: In the diagram, AC = 10 cm, BC = 5 cm and angle ACB = 60 degrees. Give…
  17. Relations and Functions: Given that f(x) = (3x - 5)/2, find f(-9).
  18. Relations and Functions: Given that f(x) = (3x - 5)/2, find f^-1(x).
  19. Relations and Functions: Given that f(x) = (3x - 5)/2 and g(x) = (x - 4)/6, find the value of x…
  20. Variation: Given that y varies directly as x and z, and that y = 9 when x = 6 and…
  21. Variation: Given that y = kxz with k = 3, find the value of y when x = 4 and z = …
  22. Variation: Given that y = kxz with k = 3, find the value of x when y = 4 1/2 and …
  23. Quadratic Equations: Solve the equation x^2 - 4x = 0.
  24. Circle Theorems: In the diagram, PQR is parallel to TS, QUT is a straight line, angle Q…
  25. Circle Theorems: Using the same diagram, calculate angle RUS.
  26. Geometrical Transformations: Triangle A has vertices (1, 3), (3, 3) and (3, 5). It is transformed b…
  27. Earth Geometry: A plane flew north from town A (28 S, 20 E) to town B (32 N, 20 E) in …
  28. Linear Programming: A region R is defined by y <= x, x + y <= 4 and y >= 0. Which of these…
  29. Index Notation: Evaluate 216^(1/3).
  30. Travel Graphs: The speed-time graph shows a van which starts from rest and accelerate…
  31. Travel Graphs: Using the same speed-time graph, find the distance travelled by the va…
  32. Travel Graphs: The car starts from the same place as the van but 4 seconds later, and…

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