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 16x^2 - 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 vec(RS) = matrix(-4; 3). Given that R is a point (-2, 1), f…
  6. Sets: On the Venn diagram in the answer space below, shade the set A' ∩ (B ∪…
  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 of Masamushi failing an examination is 3/10. What is t…
  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 below shows two towns A and B on the equator. A is on long…
  16. Earth Geometry: The diagram below shows two towns A and B on the equator. A is on long…
  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. The true length of…
  21. Approximations: Chiyalwa estimated the length of a string as 15 cm. The true length of…
  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 - 3x^4 + 5.
  24. Bearings: In the diagram below, the bearing of C from A is 160°. Angle ACB is 30…
  25. Bearings: In the diagram below, the bearing of C from A is 160°. Angle ACB is 30…
  26. Trigonometry: The diagram below shows triangle ABC in which angle ABC = 90°. BC is p…
  27. Mensuration: Calculate the radius of a semicircle whose area is 77 cm^2. [Take π to…
  28. Circle Theorems: In the diagram below, P, Q, R, S and T lie on a circle and TQ = TR. PR…
  29. Circle Theorems: In the diagram below, P, Q, R, S and T lie on a circle and TQ = TR. PR…
  30. Circle Theorems: In the diagram below, P, Q, R, S and T lie on a circle and TQ = TR. PR…
  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 below is a right triangular pyramid ABCD with AB = BC = CA…
  35. Variation: It is given that y varies directly as the cube root of x and inversely…
  36. Variation: It is given that y varies directly as the cube root of x and inversely…
  37. Variation: It is given that y varies directly as the cube root of x and inversely…
  38. Linear Programming: Write three inequalities that define the unshaded region R.
  39. Quadratic Equations: Solve the equation 5x^2 = x.
  40. Quadratic Functions: The diagram below shows the sketch of the graph of y = -x^2 + 2x + 3 c…
  41. Quadratic Functions: The diagram below shows the sketch of the graph of y = -x^2 + 2x + 3 c…
  42. Travel Graphs: The diagram below is a graph of a moving object which decelerates unif…
  43. Travel Graphs: The diagram below is a graph of a moving object which decelerates unif…
  44. Travel Graphs: The diagram below is a graph of a moving object which decelerates unif…

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