ECZ 2016 O-Level 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: Given that E={a,b,c,d,e,f,g,h},A={a,b,c,d} and B={b,c,d,e,f}, list (A∪…
  2. Sets: Use set notation to describe the shaded region in the diagram below.
  3. Index Notation: Evaluate 8^(2/3).
  4. Algebra: Simplify 3(a + 5) − a(a − 2).
  5. Symmetry: The diagram shows a right pyramid with a square base ABCD and apex P. …
  6. Matrices: Express (−1 2 −3)(5 −2 ; 4 2 ; 3 1) as a single matrix.
  7. Vectors In Two Dimensions: On the diagram, OP = p and OQ = q. Express the resultant OR = p + q as…
  8. Sequences and Series: The first and second terms of an arithmetic progression are 100 and 95…
  9. Sequences and Series: For the same progression (first term 100, common difference −5), find …
  10. Probability: There are 45 green and red marbles in a bag. The probability of choosi…
  11. Similarity and Congruency: Two geometrically similar containers have base areas 80 cm² and 180 cm…
  12. Earth Geometry: Mogadishu and Kinshasa are on longitudes 45°E and 15°E respectively. I…
  13. Earth Geometry: What is the shortest distance over the Earth’s surface between A(32°N,…
  14. Approximations: The length of a wire is 5.2 cm, correct to 1 decimal place. What is it…
  15. Social and Commercial Arithmetic: The dividend due on 1 000 shares at the end of a financial year is K2 …
  16. Coordinate Geometry: Find the gradient of the straight line whose equation is 3y + x = 5.
  17. Geometrical Transformations: Triangle P has vertices (−4, 0), (−4, 1) and (−2, 1). It is mapped ont…
  18. Algebra: Factorise completely km − 6ln + 3kn − 2lm.
  19. Mensuration: MN is an arc of a circle with centre O and radius 21 cm. Given that ∠M…
  20. Matrices: Find the transpose of the matrix B = (4 −1 ; 2 5).
  21. Approximations: Find the percentage error of the mass of a bag of sugar that weighs 10…
  22. Coordinate Geometry: Find the equation of the straight line passing through (−4, 4) and per…
  23. Bearings: ABC is an equilateral triangle. A is due North of B and CN is parallel…
  24. Bearings: For the same equilateral triangle (A due North of B), find the bearing…
  25. Relations and Functions: Given that f(x) = (5x + 4)⁄5, find f⁻¹(x).
  26. Relations and Functions: Using f(x) = (5x + 4)⁄5, find f⁻¹(−2).
  27. Relations and Functions: Given f(x) = (5x + 4)⁄5 and g(x) = x − 1, find fg(x) in its simplest f…
  28. Index Notation: Evaluate 5⁰ + 5¹.
  29. Computer and Calculator: An incomplete pseudocode calculates and outputs the volume V of a cyli…
  30. Introduction To Calculus: Find ∫(6x² − 5) dx.
  31. Trigonometry: In triangle PQR, PQ = 12 cm, QR = 10 cm and ∠PQR = 150°. Calculate the…
  32. Circle Theorems: PR is a diameter of a circle with centre O; Q and S are on the circumf…
  33. Circle Theorems: For the same circle (PR a diameter, ∠QPR = 42°), calculate PRQ.
  34. Circle Theorems: For the same circle (tangent at P meets QS produced at T, ∠PQS = 26°, …
  35. Variation: It is given that w varies directly as the square of x and inversely as…
  36. Variation: It is given that w = kx²⁄y. If x = −6, y = 12 and w = 15, find k.
  37. Variation: Using w = 5x²⁄y, find the value of y when x = 8 and w = 20.
  38. Linear Programming: On the XOY plane, region R is unshaded. Write the four inequalities th…
  39. Quadratic Equations: Solve the equation x² = 3x.
  40. Quadratic Functions: The sketch shows the graph of y = 3 − 2x − x², passing through P, Q an…
  41. Quadratic Functions: For the graph y = 3 − 2x − x², find the coordinates of the turning poi…
  42. Travel Graphs: A particle accelerates uniformly from a speed of v m/s to a speed of 5…
  43. Travel Graphs: The distance travelled by the particle from 0 to 20 seconds is 80 m. F…
  44. Travel Graphs: For the same motion (start speed v = 4⁄3 m/s, acceleration v⁄5), find …

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