ECZ 2020 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. Algebra: Simplify 2(x + 3) - 3x(x - 2).
  2. Index Notation: Evaluate (∛27)².
  3. Algebra: Factorise completely 16x² - 100.
  4. Coordinate Geometry: The points A and B are (-5, 15) and (3w, w) respectively. Given that t…
  5. Vectors In Two Dimensions: The vector RS = matrix(-4; 3). Given that R is the point (-2, 1), find…
  6. Sets: On the Venn diagram in the answer space, shade the set A' ∩ (B ∪ C).
  7. Matrices: Given that M = matrix(-3, -1; 4, 2; 0, -2) and N = matrix(-2; 1), find…
  8. Matrices: Given that M = matrix(-3, -1; 4, 2; 0, -2) and N = matrix(-2; 1), find…
  9. Sequences and Series: For the sequence 7, 11, 15, 19, ..., find the 9th term.
  10. Sequences and Series: For the sequence 7, 11, 15, 19, ..., find the sum of the first 16 term…
  11. Probability: The probability that Masamba fails an examination is 3/10. What is the…
  12. Similarity and Congruency: A plan of a play boat is drawn to a scale of 1 : 20. If the actual are…
  13. Sets: Given that E = {3, 6, 9, 12, 15, 18}, A = {6, 9, 12} and B = {3, 6, 18…
  14. Index Notation: Solve the equation 3^(x + 3) = 27^5.
  15. Earth Geometry: The diagram shows two towns A and B on the equator. A is on longitude …
  16. Earth Geometry: A plane flies from A (35°W) to B (40°E) along the equator in 5 hours. …
  17. Relations and Functions: The functions f and g are defined by f(x) = 3x - 2 and g(x) = 4x + 1. …
  18. Relations and Functions: The functions f and g are defined by f(x) = 3x - 2 and g(x) = 4x + 1. …
  19. Relations and Functions: The functions f and g are defined by f(x) = 3x - 2 and g(x) = 4x + 1. …
  20. Approximations: Chiyalwa estimated the length of a string as 15 cm. If the true length…
  21. Approximations: Chiyalwa estimated the length of a string as 15 cm. If the true length…
  22. Geometrical Transformations: A point A(2, 4) is mapped onto A'(-3, 5) by a translation T. Find the …
  23. Introduction To Calculus: Integrate y = x⁻³ - 3x⁴ + 5.
  24. Bearings: In the diagram, the bearing of C from A is 160°. Angle ACB is 30° and …
  25. Bearings: In the diagram, the bearing of C from A is 160°. Angle ACB is 30° and …
  26. Trigonometry: The diagram shows triangle ABC in which angle ABC = 90°. BC is produce…
  27. Mensuration: Calculate the radius of a semicircle whose area is 77 cm². [Take π to …
  28. Circle Theorems: In the diagram, P, Q, R, S and T lie on a circle and TQ = TR. PR and T…
  29. Circle Theorems: In the diagram, P, Q, R, S and T lie on a circle, TQ = TR, PR is paral…
  30. Circle Theorems: In the diagram, P, Q, R, S and T lie on a circle, TQ = TR, PR is paral…
  31. Social and Commercial Arithmetic: A woman has 500 company shares with a nominal value of K70.00 each, wh…
  32. Coordinate Geometry: P is the point (3, 1) and Q is another point such that the gradient of…
  33. Computer and Calculator: An incomplete pseudocode for a program that calculates the curved surf…
  34. Symmetry: The diagram is a right triangular pyramid ABCD with AB = BC = CA. What…
  35. Variation: It is given that y varies directly as the cube root of x and inversely…
  36. Variation: y varies directly as the cube root of x and inversely as the square of…
  37. Variation: Given y = 16∛x / z², find (c) the values of z when y = 12 and x = 27.
  38. Linear Programming: Write the three inequalities that define the unshaded region R.
  39. Quadratic Equations: Solve the equation 5x² = x.
  40. Quadratic Functions: The diagram shows the sketch of the graph of y = -x² + 2x + 3 cutting …
  41. Quadratic Functions: For the graph y = -x² + 2x + 3, find (ii) the maximum value of the gra…
  42. Travel Graphs: The diagram is the speed-time graph of a moving object which decelerat…
  43. Travel Graphs: For the same journey (52 m/s decelerating to v = 4 m/s over 6 s, const…
  44. Travel Graphs: For the same journey (total distance 216 m over 6 s + 10 s + 4 s), cal…

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