ECZ 2015 O-Level Paper 1 — Mathematics

All 48 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. Computer and Calculator: Find the exact value of 3 1/3 − 1/5.
  2. Computer and Calculator: Convert 0.375 to a common fraction in its lowest terms.
  3. Index Notation: A road construction company needed a sum of 0.04455 billion kwacha (1 …
  4. Computer and Calculator: Evaluate 12 + 3 × 6 − 36.
  5. Index Notation: Find the value of n, if 4ⁿ = 2² × 4².
  6. Social and Commercial Arithmetic: A furniture shop conducted a sale. In this sale, prices were reduced b…
  7. Sets: Describe the region shaded in the Venn diagram using set notation.
  8. Social and Commercial Arithmetic: Chanda changed $620 into Zambian Kwacha at an exchange rate of $1 = K6…
  9. Vectors In Two Dimensions: The position vectors of the points X and Y are matrix(3; -4) and matri…
  10. Probability: A fair six sided die numbered 1, 2, 3, 4, 5 and 6 is rolled. Find the …
  11. Algebra: Solve the simultaneous equations 5x − 8y = 4, 4x − 5y = 6.
  12. Sets: If E = {first eight natural numbers} and A = {1, 4, 7}, find the set A…
  13. Algebra: Factorise 2x² − x − 15.
  14. Sequences and Series: The patterns in the diagram were made using floor tiles. Find the numb…
  15. Sequences and Series: Given that m is the number of tiles in pattern number n of the floor-t…
  16. Trigonometry: The diagram shows a right angled triangle in which angle ACB = 90°, AB…
  17. Algebra: Given that t = √((n + 3)/n), express n in terms of t.
  18. Algebra: Simplify 7m − 2(3n − m) − 9n.
  19. Statistics: The table below shows the number of leave days taken by the employees …
  20. Statistics: The table below shows the number of leave days taken by the employees …
  21. Relations and Functions: Given that f(x) = (2x + 7)/8 and g(x) = (3x − 6)/6, find g(6).
  22. Relations and Functions: Given that f(x) = (2x + 7)/8 and g(x) = (3x − 6)/6, find f⁻¹(x).
  23. Relations and Functions: Given that f(x) = (2x + 7)/8 and g(x) = (3x − 6)/6, find the value of …
  24. Quadratic Equations: Solve the equation 2y² = 13y.
  25. Mensuration: A circular lawn has a radius of 14 metres. Mr Kakwempa is contracted t…
  26. Algebra: Solve the inequation 14x − 8 ≥ 20.
  27. Earth Geometry: An aeroplane leaves a town P(33°N, 32°E) and flies due south to a town…
  28. Similarity and Congruency: A map of a settlement area is drawn to a scale of 1 : 40 000. If the d…
  29. Similarity and Congruency: A map of a settlement area is drawn to a scale of 1 : 40 000. If the a…
  30. Symmetry: The diagram shows a regular hexagon inscribed in a circle with centre …
  31. Matrices: Given that P = matrix(3, -4; 1, 2), express P² as a single matrix.
  32. Variation: Given that y is proportional to x³ and that y = 250 when x = 10, find …
  33. Variation: y is proportional to x³ with constant of variation k = 1/4. Find y whe…
  34. Variation: y is proportional to x³ with constant of variation k = 1/4. Find x whe…
  35. Similarity and Congruency: In the triangle shown, PQ = QR, angle QPR = (3x + 31)° and angle QRP =…
  36. Geometrical Transformations: In the diagram, triangle ABC with A(1, 5), B(1, 2) and C(2, 2) is mapp…
  37. Quadratic Functions: Which sketch shows the graph of y + x² = 0?
  38. Circle Theorems: In the diagram, A, B, C and D are points on the circumference of a cir…
  39. Circle Theorems: In the diagram, A, B, C and D are points on the circumference of a cir…
  40. Circle Theorems: In the diagram, A, B, C and D are points on the circumference of a cir…
  41. Linear Programming: In the XOY plane shown, the unshaded region R is bounded by straight l…
  42. Social and Commercial Arithmetic: A sum of money is shared among Satala, Sichale and Sichambo in the rat…
  43. Social and Commercial Arithmetic: A sum of money is shared among Satala, Sichale and Sichambo in the rat…
  44. Similarity and Congruency: Two cylindrical mugs are geometrically similar. The smaller mug has di…
  45. Trigonometry: In the diagram, BCD is a straight line, AB = 12 cm, AC = 13 cm and ang…
  46. Travel Graphs: The figure shows the speed–time graphs of cars driven by Sulanji and L…
  47. Travel Graphs: From the speed–time graphs shown, calculate how far Lumbwa's car trave…
  48. Travel Graphs: From the speed–time graphs shown, what is Sulanji's acceleration betwe…

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