ECZ 2015 O-Level Paper 1 — Mathematics

All 36 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: Find the value of n, if 4^n = 2^2 × 4^2.
  2. Social and Commercial Arithmetic: A furniture shop conducted a sale. In this sale, prices were reduced b…
  3. Sets: Describe the region shaded in the Venn diagram using set notation.
  4. Vectors In Two Dimensions: The position vectors of the points X and Y are matrix(3; -4) and matri…
  5. Probability: A fair six sided die numbered 1, 2, 3, 4, 5 and 6 is rolled. Find the …
  6. Sets: If E = {first eight natural numbers} and A = {1, 4, 7}, find the set A…
  7. Algebra: Factorise 2x^2 − x − 15.
  8. Trigonometry: The diagram shows a right angled triangle in which angle ACB = 90°, AB…
  9. Algebra: Simplify 7m − 2(3n − m) − 9n.
  10. Relations and Functions: Given that f(x) = (2x + 7)/8 and g(x) = (3x − 6)/6, find g(6).
  11. Relations and Functions: Given that f(x) = (2x + 7)/8 and g(x) = (3x − 6)/6, find f^-1(x).
  12. Relations and Functions: Given that f(x) = (2x + 7)/8 and g(x) = (3x − 6)/6, find the value of …
  13. Quadratic Equations: Solve the equation 2y^2 = 13y.
  14. Mensuration: A circular lawn has a radius of 14 metres. Mr Kakwempa is contracted t…
  15. Earth Geometry: An aeroplane leaves a town P(33°N, 32°E) and flies due south to a town…
  16. Similarity and Congruency: A map of a settlement area is drawn to a scale of 1 : 40 000. If the d…
  17. Similarity and Congruency: A map of a settlement area is drawn to a scale of 1 : 40 000. If the a…
  18. Symmetry: The diagram shows a regular hexagon inscribed in a circle with centre …
  19. Matrices: Given that P = matrix(3, -4; 1, 2), express P^2 as a single matrix.
  20. Variation: Given that y is proportional to x^3 and that y = 250 when x = 10, find…
  21. Variation: y is proportional to x^3 with constant of variation k = 1/4, so y = (1…
  22. Variation: y is proportional to x^3 with constant of variation k = 1/4, so y = (1…
  23. Similarity and Congruency: In the triangle shown, PQ = QR, angle QPR = (3x + 31)° and angle QRP =…
  24. Geometrical Transformations: In the diagram, triangle ABC with A(1, 5), B(1, 2) and C(2, 2) is mapp…
  25. Quadratic Functions: Which sketch shows the graph of y + x^2 = 0?
  26. Circle Theorems: In the diagram, A, B, C and D are points on the circumference of a cir…
  27. Circle Theorems: In the diagram, A, B, C and D are points on the circumference of a cir…
  28. Circle Theorems: In the diagram, A, B, C and D are points on the circumference of a cir…
  29. Linear Programming: In the XOY plane shown, the unshaded region R is bounded by straight l…
  30. Social and Commercial Arithmetic: A sum of money is shared among Satala, Sichale and Sichambo in the rat…
  31. Social and Commercial Arithmetic: A sum of money is shared among Satala, Sichale and Sichambo in the rat…
  32. Similarity and Congruency: Two cylindrical mugs are geometrically similar. The smaller mug has di…
  33. Trigonometry: In the diagram, BCD is a straight line, AB = 12 cm, AC = 13 cm and ang…
  34. Travel Graphs: The figure shows the speed–time graphs of cars driven by Sulanji and L…
  35. Travel Graphs: From the speed–time graphs shown, calculate how far Lumbwa's car trave…
  36. Travel Graphs: From the speed–time graphs shown, what is Sulanji's acceleration betwe…

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