ECZ 2019 GCE 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: The Venn diagram below shows three sets A,B and C . Use set notation t…
  2. Sets: Given that E={0,1,2,3,4,5,6,7,8,9},A={2,3,6,8} and B={3,6,7,9}, list (…
  3. Algebra: Simplify 4 − 2(b − a) − 1.
  4. Index Notation: Evaluate (⁴√81)³.
  5. Algebra: Factorise completely 32x² − 50.
  6. Coordinate Geometry: Find the gradient of a line which passes through (−5, 3) and (−4, 1).
  7. Vectors In Two Dimensions: The vector PQ = [−3; 2]. Given that the point P is (1, 4), find the co…
  8. Matrices: Given that S = [1 0 −4; −2 1 1] (a 2×3 matrix with rows separated by s…
  9. Matrices: Given that R = [2 −1; 1 3] and S = [1 0 −4; −2 1 1] (rows separated by…
  10. Sequences and Series: For the sequence −10, −7, −4, −1, …, find the 17th term.
  11. Sequences and Series: For the sequence −10, −7, −4, −1, …, find the sum of the first 20 term…
  12. Probability: There are 4 blue and 5 white marbles in a bag. What is the probability…
  13. Quadratic Equations: Solve the equation 2x² + 5x − 3 = 0.
  14. Symmetry: The diagram shows a prism with a base that is a regular hexagon. How m…
  15. Earth Geometry: The diagram shows the points A(60°N, 30°W), B(30°S, 30°W) and C(30°S, …
  16. Earth Geometry: The points A(60°N, 30°W) and B(30°S, 30°W) lie on the same meridian. I…
  17. Index Notation: Evaluate 3⁰ × 3³ + 3¹.
  18. Mensuration: The diagram shows a sector of a circle with centre O and radius 4.2 cm…
  19. Approximations: The mass, m, of a block of wood is 876.4 g, correct to 1 decimal place…
  20. Approximations: The length of a piece of wire is 15.2 cm, correct to 1 decimal place. …
  21. Bearings: Mr Moenda travels on a bearing of 141° from A to B. He then continues …
  22. Bearings: Mr Moenda travels on a bearing of 141° from A to B, then from B on a b…
  23. Relations and Functions: The functions f and g are defined as f(x) = 2x + 1 and g(x) = (3x − 5)…
  24. Relations and Functions: The functions f and g are defined as f(x) = 2x + 1 and g(x) = (3x − 5)…
  25. Relations and Functions: The functions f and g are defined as f(x) = 2x + 1 and g(x) = (3x − 5)…
  26. Circle Theorems: In the diagram, A, B, C, D and E are points on the circumference of a …
  27. Circle Theorems: In the diagram, A, B, C, D and E are points on the circumference of a …
  28. Circle Theorems: In the diagram, A, B, C, D and E are points on the circumference of a …
  29. Geometrical Transformations: A point R(−3, 1) is mapped onto a point S(2, −1) by a translation T. E…
  30. Computer and Calculator: An incomplete program in pseudocode reads: Start; Enter ……; m = ……; Ou…
  31. Variation: y varies directly as x and inversely as the square of z. Given that y …
  32. Variation: y varies directly as x and inversely as the square of z, with constant…
  33. Variation: y varies directly as x and inversely as the square of z, with constant…
  34. Social and Commercial Arithmetic: A company's working capital consists of 450 10% preference shares of K…
  35. Similarity and Congruency: The ratio of the volumes of two similar solids is 64 : 27. The surface…
  36. Trigonometry: The diagram shows triangle KLM in which KL = 16 cm, angle KLM = 150° a…
  37. Coordinate Geometry: The equation of line A is 3x + 2y = 10. Line B is parallel to line A a…
  38. Linear Programming: The diagram shows an unshaded region R bounded by four lines: the dash…
  39. Introduction To Calculus: Find the integral of 3x³/2 − 5x + 1/x² with respect to x.
  40. Quadratic Functions: A function y = (1 + x)(x − 2). Which description matches the sketch of…
  41. Quadratic Functions: A function y = (1 + x)(x − 2), i.e. y = x² − x − 2. Find the minimum v…
  42. Travel Graphs: The speed-time graph shows an object which starts from rest and accele…
  43. Travel Graphs: In the same journey (rest → 10 m/s in 2 s; constant for 6 s; accelerat…
  44. Travel Graphs: In the same journey (rest → 10 m/s in 2 s; constant 10 m/s for 6 s; sp…

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