ECZ 2016 GCE Paper 1 — Mathematics

All 34 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: A set has three elements. How many subsets does it have?
  2. Sets: Using the Venn diagram in the answer space, shade the region represent…
  3. Algebra: Simplify 2m − 4n − 3(3n − m).
  4. Index Notation: Evaluate 3² + 2³ × 2⁰.
  5. Index Notation: It is given that 10ˣ = 3 and 10ʸ = 9. What is the value of 10^(y−x)?
  6. Earth Geometry: A plane flew from town A(67°S, 40°E) to a town B(23°N, 40°E). Calculat…
  7. Social and Commercial Arithmetic: Bronze is made up of zinc, tin and copper in the ratio 1 : 4 : 25 resp…
  8. Trigonometry: In the diagram, MP = 13 km, QR = 6 km and MR = 24 km. MR is parallel a…
  9. Trigonometry: In the diagram, MP = 13 km, QR = 6 km and MR = 24 km. MR is parallel a…
  10. Sequences and Series: What is the position of 999 in the sequence represented by the nth ter…
  11. Vectors In Two Dimensions: Given that AB = [−3; 4] (a column vector), find |AB|.
  12. Matrices: If A = [1 −2; −1 4] (rows separated by semicolons) and C = [−1; 3] (a …
  13. Trigonometry: DEFG is a rectangular piece of land in which GE = 12.5 m (a diagonal) …
  14. Social and Commercial Arithmetic: The cost of advertising in a local newspaper for one week is K15.40 pe…
  15. Quadratic Equations: The diagram shows an isosceles triangle ABC where AB = BC = (x − 3) cm…
  16. Statistics: The pie chart shows how members of a club voted for the position of ch…
  17. Statistics: In the same pie chart (Emelia 105°, Inonge 120°, Mercy 135°), 20 membe…
  18. Relations and Functions: A function h is defined as h(x) = (3x + 2)/4. Find h(−2).
  19. Relations and Functions: A function h is defined as h(x) = (3x + 2)/4. Find the value of x for …
  20. Relations and Functions: A function h is defined as h(x) = (3x + 2)/4. Find h⁻¹(x).
  21. Probability: A target is a square piece of wood ABCD of side 50 cm. M and N are mid…
  22. Circle Theorems: In the diagram, TR is a diameter of the circle with centre O, and QR a…
  23. Circle Theorems: In the same diagram (TR a diameter, QR ∥ PS, TÔS = 80°, TR̂P = 10°), f…
  24. Circle Theorems: In the same diagram (TR a diameter, QR ∥ PS, TÔS = 80°, TR̂P = 10°), f…
  25. Bearings: The diagram shows three towns Kime (K), Teswa (T) and Luwaya (L). Angl…
  26. Bearings: In the same diagram (angle KTL = 110°, bearing of L from T = 123°), fi…
  27. Travel Graphs: At 07 30 hours, an old Mini Bus starts off from Luwaya to Teswa at an …
  28. Linear Programming: The boundary of the shaded region R is formed by the lines y = 2, L₁ (…
  29. Geometrical Transformations: A is the point (3, −4). Find the coordinates of the image of A under a…
  30. Geometrical Transformations: A is the point (3, −4). Find the coordinates of the image of A under a…
  31. Quadratic Equations: Solve the equation 3x² = 5x.
  32. Travel Graphs: The speed-time graph shows a car which accelerates uniformly from rest…
  33. Travel Graphs: In the same journey (30 m/s constant speed until t = 80 s, rest at 100…
  34. Travel Graphs: In the same journey (constant 30 m/s until 80 s, then uniform decelera…

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