ECZ 2017 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: Shade B'∩(A∩C) in the Venn diagram in the answer space.
  2. Sets: Given that E={2,4,6,8,10;12},A={4,8,12} and B={2,10,12}, list A'nB.
  3. Algebra: Simplify 3x − (y − 2x) − 3y.
  4. Index Notation: Evaluate (81/16)^(−1/4) + (81/16)^0.
  5. Coordinate Geometry: The gradient of the line joining the points (−2, k) and (k, −14) is 2.…
  6. Algebra: Factorise completely ax²y − 4ay³.
  7. Vectors In Two Dimensions: The points P and Q have coordinates (2, 4) and (−3, 1) respectively. E…
  8. Matrices: Given the matrix A = (3 2 1 ; 4 3 0), find Aᵀ (the transpose of A).
  9. Matrices: Given A = (3 2 1 ; 4 3 0) and B = (1 2 3 ; 3 2 1 ; 0 1 0), find AB as …
  10. Sequences and Series: For the sequence 25, 22, 19, 16, …, find the formula for the nth term.
  11. Sequences and Series: For the sequence 25, 22, 19, 16, …, find the sum of the first 20 terms…
  12. Earth Geometry: Town L is on (0°, 30°W) and town K is on (0°, 60°E), as shown in the d…
  13. Earth Geometry: Town L is on (0°, 30°W) and town K is on (0°, 60°E). What is the dista…
  14. Probability: The probability that Chakupaleza will go for remedial lessons on a par…
  15. Index Notation: Solve the equation 10ˣ = 0.0001.
  16. Mensuration: A sector of a circle has radius 7 cm and an angle of 270° at the centr…
  17. Relations and Functions: Given g(x) = 5x − 1, find g⁻¹(x).
  18. Relations and Functions: The functions f and g are defined by f(x) = 2x + 1 and g(x) = 5x − 1. …
  19. Relations and Functions: Given f(x) = 2x + 1 and g(x) = 5x − 1, find fg(−3).
  20. Geometrical Transformations: A kite has vertices (0, 0), (2, 1), (5, 0) and (2, −1). Find the coord…
  21. Introduction To Calculus: Differentiate y = ⅓x³ − 5x² − 2x with respect to x.
  22. Bearings: Two boats X and Y leave port P at the same time. X travels on a bearin…
  23. Bearings: Two boats X and Y leave port P; X on a bearing of 159° and Y on a bear…
  24. Approximations: Misozi and Filamba estimated the length of a line as 9 cm and 10 cm re…
  25. Approximations: Misozi and Filamba estimated the length of a line as 9 cm and 10 cm re…
  26. Variation: It is given that t = kv², where k is the constant of variation. Given …
  27. Variation: It is given that t = kv². Using k = 4, find the value of t when v = 5.
  28. Variation: It is given that t = kv² with k = 4. Find the value of v when t = 36.
  29. Circle Theorems: In the diagram, A, B, C, D, E and F lie on the circumference of a circ…
  30. Circle Theorems: In the diagram (A–F on a circle, angle FBD = 70°, angle AEF = 20°), fi…
  31. Circle Theorems: In the diagram (A–F on a circle, angle FBD = 70°, angle AEF = 20°, AD …
  32. Trigonometry: Triangle PQR is right-angled at R, with QR = 4 cm and tan(angle QPR) =…
  33. Similarity and Congruency: The ratio of the surface areas of two cubes is 16 : 25. If the volume …
  34. Social and Commercial Arithmetic: A businessman bought 300 company shares at K60.00 each. The nominal pr…
  35. Coordinate Geometry: The equation of a straight line L is 2y = 4x − 5. Find the equation of…
  36. Symmetry: The diagram shows a cone with apex V and base radius r. How many plane…
  37. Computer and Calculator: An incomplete program flow chart calculates the curved surface area S …
  38. Linear Programming: The diagram shows an unshaded region R bounded by straight lines. Writ…
  39. Quadratic Equations: If y = (1 − 2x)(1 + x) − 2, find the values of x for which y = −2.
  40. Quadratic Functions: The sketch represents a section of the curve y = x(x − 2). Find the co…
  41. Quadratic Functions: For the curve y = x(x − 2), what is the minimum value of the function?
  42. Travel Graphs: The diagram is a speed-time graph of a car journey. The speed rises fr…
  43. Travel Graphs: The speed-time graph shows a car accelerating to 30 m/s in 5 s, travel…
  44. Travel Graphs: For the same journey (total distance 825 m, total time T = 45 s), find…

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