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…
  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 ax^2y − 4ay^3.
  7. Vectors In Two Dimensions: The points P and Q have coordinates (2, 4) and (−3, 1) respectively. E…
  8. Matrices: Given that A = matrix(3, 2, 1; 4, 3, 0) and B = matrix(1, 2, 3; 3, 2, …
  9. Matrices: Given that A = matrix(3, 2, 1; 4, 3, 0) and B = matrix(1, 2, 3; 3, 2, …
  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 di…
  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: The diagram below is a sector with centre O and radius 7cm. Angle at O…
  17. Relations and Functions: The functions f and g are defined by f(x) = 2x + 1 and g(x) = 5x − 1. …
  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: The functions f and g are defined by f(x) = 2x + 1 and g(x) = 5x − 1. …
  20. Geometrical Transformations: The kite in the diagram in the answer space has coordinates (0, 0), (2…
  21. Introduction To Calculus: Differentiate y = ⅓x^3 − 5x^2 − 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 at the same time. X travels on a bearin…
  24. Approximations: Misozi and Filamba estimated the length of a line to be 9cm and 10cm r…
  25. Approximations: Misozi and Filamba estimated the length of a line to be 9cm and 10cm r…
  26. Variation: It is given that t = kv^2, where k is the constant of variation. table…
  27. Variation: It is given that t = kv^2, where k is the constant of variation. table…
  28. Variation: It is given that t = kv^2, where k is the constant of variation. table…
  29. Circle Theorems: In the diagram below, A, B, C, D, E and F are points on the circumfere…
  30. Circle Theorems: In the diagram below, A, B, C, D, E and F are points on the circumfere…
  31. Circle Theorems: In the diagram below, A, B, C, D, E and F are points on the circumfere…
  32. Trigonometry: It is given that triangle PQR below is right angled at R. QR = 4cm and…
  33. Similarity and Congruency: The ratio of the surface areas of two cubes is 16:25. What is the volu…
  34. Social and Commercial Arithmetic: A businessman bought 300 company shares at K60.00. The nominal price w…
  35. Coordinate Geometry: The equation of a straight line L is given by 2y = 4x − 5. Find the eq…
  36. Symmetry: The diagram below shows a cone with apex V and radius r. How many plan…
  37. Computer and Calculator: The diagram below is an incomplete program flow chart to calculate the…
  38. Linear Programming: Write down the four inequalities that define the unshaded region R, on…
  39. Quadratic Equations: If y = (1 − 2x)(1 + x) − 2, find the values of x for which y = −2.
  40. Quadratic Functions: The sketch shown below represents a section of the curve y = x(x − 2).…
  41. Quadratic Functions: The sketch shown below represents a section of the curve y = x(x − 2).…
  42. Travel Graphs: The diagram below shows a speed-time graph of a car journey. Find the …
  43. Travel Graphs: The diagram below shows a speed-time graph of a car journey. If the to…
  44. Travel Graphs: The diagram below shows a speed-time graph of a car journey. If the to…

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