ECZ 2014 O-Level Paper 1 — Mathematics

All 48 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. Computer and Calculator: Find the exact value of 2 2/3 − 7/12.
  2. Computer and Calculator: Find the exact value of 0.002 × 0.6.
  3. Algebra: Simplify 7a + 2b − 4(3a − b).
  4. Index Notation: Asia has an area of 44 579 000 square kilometres. Write 44 579 000 in …
  5. Matrices: Given that P = matrix(3, -1; -2, 0) and Q = matrix(3, 4; -4, x), find …
  6. Algebra: Factorise completely 5x² − x − 4.
  7. Social and Commercial Arithmetic: When a car was sold at K12 000.00, a profit of 20% was made. What was …
  8. Statistics: A sweet manufacturing company intends to start manufacturing lolly pop…
  9. Statistics: The letters in the brand names IYALOWA, YONZUNA, YATOWALA, YEMUNATI, Y…
  10. Probability: The brand names IYALOWA, YONZUNA, YATOWALA, YEMUNATI, YATOBALA, ILWEEL…
  11. Algebra: Solve the simultaneous equations 3x = 4y + 1, 7x + y = 23.
  12. Sets: The Venn diagram shows the number of pupils who take Mathematics (M), …
  13. Sets: In the Venn diagram shown, 22 pupils take Physics and 20 pupils take M…
  14. Computer and Calculator: Evaluate 14 + 3(7 − 2) − 2 × 5.
  15. Quadratic Equations: Solve the equation 2(x − 2)² = 18.
  16. Sequences and Series: The first three figures of a sequence are shown. Figure 1 is a square …
  17. Sequences and Series: For the sequence of figures shown, write an expression, in terms of n,…
  18. Algebra: Find the largest integer, x, which satisfies the inequality −5 < x + 3…
  19. Algebra: Given that a = (d − b)/(cd − 1), make d the subject of the formula.
  20. Index Notation: Evaluate −4² + 4³.
  21. Similarity and Congruency: In the figure, ABCDE is part of a regular polygon. AC and BD meet at X…
  22. Travel Graphs: Convert a speed of 144 km/h to m/s.
  23. Symmetry: The regular hexagon shown is divided into 12 congruent triangles, two …
  24. Earth Geometry: Two places A and B lie on the equator and are 2 820 nautical miles apa…
  25. Relations and Functions: A function is defined by f(x) = 10x + 9. Find f(−2).
  26. Relations and Functions: A function is defined by f(x) = 10x + 9. Find k, if f(k) = k.
  27. Relations and Functions: A function is defined by f(x) = 10x + 9. Find f⁻¹(x).
  28. Similarity and Congruency: A square park has its map drawn to a scale of 1 : n. Four beacons P, Q…
  29. Similarity and Congruency: A square park has beacons at its four corners; two adjacent beacons ar…
  30. Quadratic Functions: Given that y = kx² − 1, where k is a constant, and that y = 17 when x …
  31. Quadratic Functions: Given that y = 2x² − 1, find the value of y when x = −5.
  32. Quadratic Functions: Given that y = 2x² − 1, find the values of x when y = 7.
  33. Trigonometry: The diagram shows an isosceles triangle ABC in which AB = AC = 41 cm, …
  34. Circle Theorems: In the diagram, O is the centre of the circle ABCD. AC is a diameter, …
  35. Circle Theorems: In the diagram, O is the centre of the circle ABCD. AC is a diameter, …
  36. Circle Theorems: In the diagram, O is the centre of the circle ABCD. AC is a diameter, …
  37. Social and Commercial Arithmetic: Given that 3x = 2y, find the ratio x : y.
  38. Trigonometry: A kite (K) being flown is such that its vertical height HK is 6 m and …
  39. Mensuration: The diagram shows a sector AOB in which OA = 4 cm and angle AOB = 45°.…
  40. Graphs of Functions: Part of the graph of y = x³ is sketched for x ≤ 0. Which sketch shows …
  41. Similarity and Congruency: The ratio of the surface areas of two similar solids is 1 : 64. Calcul…
  42. Geometrical Transformations: The diagram shows two shapes ABCD and PQRS on an XOY plane. Describe f…
  43. Social and Commercial Arithmetic: An outing expedition centre charges K300.00 per person for a full day,…
  44. Linear Programming: A region R is defined by the inequalities x > 1, x ≤ 2, y ≤ 1 and y ≥ …
  45. Vectors In Two Dimensions: Given that A is a point (3, 2) and B is a point (−1, 5), find AB as a …
  46. Travel Graphs: The diagram is the speed–time graph of a bus which leaves a bus stop a…
  47. Travel Graphs: For the bus journey shown, the bus reaches 20 m/s after 10 seconds. Fi…
  48. Travel Graphs: For the bus journey shown, V = 20 m/s and the two bus stops are 1 kilo…

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