ECZ 2010 O-Level Paper 1 — Mathematics

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  1. Sets: Set A has 32 subsets. Find n(A).
  2. Sets: Use set notation to describe the shaded region in the Venn diagram.
  3. Matrices: Given that matrix(2, x; -4, 1) matrix(3; 4) = matrix(10; -8), find the…
  4. Symmetry: How many lines of symmetry does a regular heptagon have?
  5. Coordinate Geometry: The points A and B are (4, 0) and (0, 8) respectively. Find the equati…
  6. Relations and Functions: For the function g(x) = (4x - 3)/(2x - 5), find g(-1).
  7. Relations and Functions: For the function g(x) = (4x - 3)/(2x - 5), find g^-1(x).
  8. Circle Theorems: In the diagram, O is the centre of circle ABCD and ECT is a tangent at…
  9. Circle Theorems: In the diagram, BD = 9 cm and DT = 3 cm, with ECT a tangent at C. Calc…
  10. Sequences and Series: For the sequence 7, 9, 11, 13, ... write down the eleventh term.
  11. Sequences and Series: For the sequence 7, 9, 11, 13, ... write down the expression for the n…
  12. Bearings: The bearing of a point B from A is 129 degrees. What is the bearing of…
  13. Symmetry: Describe fully the rotational symmetry of a 72-sided regular polygon w…
  14. Earth Geometry: Two towns P and Q lie on latitude 43 degrees north. P is on longitude …
  15. Earth Geometry: A match is scheduled to kick off at exactly 15 00 hours local time at …
  16. Circle Theorems: In the diagram, PQR is parallel to STV, angle SQT = 90 degrees, angle …
  17. Circle Theorems: Using the same diagram, calculate angle PTS.
  18. Circle Theorems: Using the same diagram, calculate angle PUS.
  19. Similarity and Congruency: Two tins are geometrically similar and the ratio of their volumes is 6…
  20. Similarity and Congruency: Given that the height of the larger tin is 28 cm, calculate the height…
  21. Variation: It is given that x varies inversely as the square of y and directly as…
  22. Variation: x varies directly as z and inversely as the square of y, with constant…
  23. Probability: A pupil takes one bottle top at random from a bag. The probability tha…
  24. Probability: Find the probability that the bottle top is not a Sprite bottle top.
  25. Probability: Originally there were 16 Sprite bottle tops in the bag. Find the total…
  26. Geometrical Transformations: Triangle XYZ has vertices X(-5, 1), Y(-3, 1) and Z(-5, 5). Find the ve…
  27. Geometrical Transformations: Triangle X1Y1Z1 with vertices (5, 1), (3, 1), (5, 5) is mapped onto tr…
  28. Geometrical Transformations: Describe fully the single transformation which maps triangle XYZ with …
  29. Algebra: Factorize completely 4u^2/a^2 - 1/9.
  30. Variation: Mr Saukani takes three hours to drive from town A to town B at a speed…
  31. Linear Programming: Triangle PQR has vertices P(-1, 2), Q(2, 2) and R(-1, -1). Write down …
  32. Travel Graphs: Train A accelerates from rest to 50 m/s in 4 seconds, travels at that …
  33. Travel Graphs: Find the distance between the trains during the first 6 seconds.

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