ECZ 2017 GCE Paper 1 — Mathematics

All 43 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: On the Venn diagram in the answer space below, shade the region define…
  2. Sets: Given that E={1,2,3,4,5,6,7,8},A={1,8} and B={2,3,4,5,6,7}, list (A∪B)…
  3. Algebra: Simplify 2a − 7b − 2(a − 3b).
  4. Algebra: Factorise completely x²/4y² − 1/9.
  5. Matrices: Given that [2 x; −5 1] [4; 3] = [14; −17] (rows separated by semicolon…
  6. Similarity and Congruency: Two tins are geometrically similar. If the ratio of their volumes is 2…
  7. Vectors In Two Dimensions: Given that a = [3; −4] (a column vector), find |a|.
  8. Sequences and Series: For the sequence 11, 13, 15, 17, …, find the 13th term.
  9. Sequences and Series: If the arithmetic mean of 5 and c is 11, what is the value of c?
  10. Matrices: If Aᵀ = (1 −2 3 −4 5), a row matrix, write the matrix A.
  11. Introduction To Calculus: Find the derivative of y = 2x³ − 2x² − 3x + 1, with respect to x.
  12. Index Notation: Solve the equation 25ˣ = 5.
  13. Earth Geometry: A soccer match kicked off at 14 00 hours at A(20°N, 30°E). What would …
  14. Earth Geometry: Two towns P and Q are on the same longitude. Given that P is (40°N, 15…
  15. Probability: A die and a coin are rolled and tossed, respectively. What is the prob…
  16. Index Notation: Given that x = 3.2 × 3⁴ and y = 4 × 3², evaluate x/y.
  17. Circle Theorems: In the diagram, points A, B, C and D are on a circle. BD is a diameter…
  18. Circle Theorems: In the same diagram (BD a diameter, AĈB = 42°, CÂD = 33°), find AĈD.
  19. Circle Theorems: In the same diagram (BD a diameter, AĈB = 42°, CÂD = 33°, AC and BD in…
  20. Relations and Functions: The functions g and f are defined as g : x → (x − 1)/2 and f : x → 3x …
  21. Relations and Functions: With g : x → (x − 1)/2 and f : x → 3x − 5, find x if f(x) = g(x).
  22. Relations and Functions: With g : x → (x − 1)/2 and f : x → 3x − 5, find g⁻¹f(x).
  23. Variation: y varies inversely as the square root of x, where x is positive. Write…
  24. Variation: y varies inversely as the square root of x (y = k/√x). Given that y = …
  25. Variation: y varies inversely as the square root of x, with y = 8/√x. Find the va…
  26. Social and Commercial Arithmetic: Maphone Manufacturing Company paid a total dividend of K12 600.00 at t…
  27. Trigonometry: The diagram shows triangle ABC in which AC = 18 cm, CÂB = 30° and AB̂C…
  28. Mensuration: The curved surface area of a cone is 88 cm². Given that the base radiu…
  29. Computer and Calculator: A flow chart computes tax on an income: Enter Income → Is Income < 3 0…
  30. Approximations: A bag of potatoes has mass (15.4 ± 0.05) kg. Find the tolerance of thi…
  31. Approximations: A bag of potatoes has mass (15.4 ± 0.05) kg. Write down the relative e…
  32. Bearings: A, B and C are three points on level ground. B is on a bearing of 070°…
  33. Bearings: A, B and C are three points on level ground. B is on a bearing of 070°…
  34. Symmetry: The diagram shows a regular hexagonal prism with an axis drawn through…
  35. Geometrical Transformations: The diagram shows two triangles ABC and A′B′C′ on the XOY plane: A(−4½…
  36. Coordinate Geometry: The diagram shows a Cartesian plane with points A(6, 6), B(0, −2), C(0…
  37. Coordinate Geometry: The diagram shows a Cartesian plane with points A(6, 6), B(0, −2), C(0…
  38. Linear Programming: Write the four inequalities that define the unshaded region R on the X…
  39. Quadratic Functions: The diagram shows a sketch of the graph of y = x² − 6x + 8, cutting th…
  40. Quadratic Functions: The diagram shows a sketch of the graph of y = x² − 6x + 8, cutting th…
  41. Travel Graphs: The speed-time graph shows a 100 m sprinter who accelerates uniformly …
  42. Travel Graphs: In the same race (12 m/s maintained until the 10th second, then unifor…
  43. Travel Graphs: In the same race (0 to 12 m/s over 3 s, constant 12 m/s from the 3rd t…

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