Quelpr

CSEC Mathematics · May/June 2011 · Paper 2

61 questions and parts from this paper. Open one to see it in full, then practise it on Quelpr and get it marked against the mark scheme.

Practise this paper
  1. 1(a)(i)3 marksUsing a calculator, or otherwise, determine the EXACT value of: (2 1/4 + 1 1/8) / (4 1/2), expressing your answer as a fraction
  2. 1(a)(ii)3 marksUsing a calculator, or otherwise, determine the EXACT value of: 3.96 × 0.25 - √0.0256
  3. 1(b)5 marksCalculate the values of W, X, Y and Z.
  4. 2(a)3 marksWrite as a single fraction in its lowest terms (x-2)/3 + (x+1)/4.
  5. 2(b)2 marksCalculate the value of 3 * 4.
  6. 2(c)(i)2 marksFactorise completely xy³ + x²y.
  7. 2(c)(ii)2 marksFactorise completely 2mh - 2nh - 3mk + 3nk.
  8. 2(d)3 marksCalculate the values of a and b.
  9. 3(a)(i)1 markHow many students study neither Art nor Music?
  10. 3(a)(ii)3 marksCalculate the value of x.
  11. 3(a)(iii)1 markHence, state the number of students who study Music only.
  12. 3(b)(i)5 marksUsing a ruler, pencil, a pair of compasses and a protractor, draw accurately a quadrilateral EFGH using the following measurements: EF = 8 cm, ∠EFG = 125°, FG = 4 cm, ∠HEF = 70°, EH = 7 cm.
  13. 3(b)(ii)1 markMeasure and state in centimetres, the length of GH.
  14. 4(a)(i)2 marksSolve the inequality: 5 - 2x < 9.
  15. 4(a)(ii)1 markIf x is an integer, determine the SMALLEST value of x that satisfies the inequality in (a)(i) above.
  16. 4(b)(i)a)3 marksCalculate the length of each side of the square.
  17. 4(b)(i)b)3 marksCalculate the perimeter of the square.
  18. 4(b)(ii)a)4 marksCalculate the radius of the circle.
  19. 4(b)(ii)b)4 marksCalculate the area of the circle.
  20. 5(a)(i)1 markUsing the dimensions shown on the diagram, calculate the value of k, the scale factor of the enlargement.
  21. 5(a)(ii)1 markUsing the dimensions shown on the diagram, calculate the length of OM.
  22. 5(a)(iii)2 marksUsing the dimensions shown on the diagram, calculate the length of OM'.
  23. 5(b)(i)2 marksUsing the dimensions shown on the diagram, calculate, correct to 3 significant figures, the length of QS.
  24. 5(b)(ii)3 marksUsing the dimensions shown on the diagram, calculate, correct to 3 significant figures, the measure of ∠RQS.
  25. 5(b)(iii)3 marksUsing the dimensions shown on the diagram, calculate, correct to 3 significant figures, the area of ∆PQR.
  26. 6(a)(i)2 marksCalculate the value of g(1/2).
  27. 6(a)(ii)2 marksWrite an expression for gf(x) in its simplest form.
  28. 6(a)(iii)2 marksFind the inverse function f⁻¹(x).
  29. 6(b)(i)2 marksDetermine the coordinates of A and B.
  30. 6(b)(ii)2 marksDetermine the gradient of the line segment AB.
  31. 6(b)(iii)2 marksDetermine the equation of the line which passes through A and B.
  32. 7(a)2 marksCopy and complete the table to show the cumulative frequency for the distribution.
  33. 7(b)5 marksUsing a scale of 2 cm to represent 10 kg on the x-axis and 1 cm to represent 10 packages on the y-axis, draw the cumulative frequency curve for the data.
  34. 7(c)(i)2 marksEstimate from the graph the median mass of the packages.
  35. 7(c)(ii)3 marksEstimate from the graph the probability that a package, chosen at random, has a mass which is LESS than 35 kg.
  36. 8(a)2 marksDraw the FOURTH diagram in the sequence.
  37. 8(b)(i)1 markHow many sticks are in the SIXTH diagram?
  38. 8(b)(ii)1 markHow many thumb tacks are in the SEVENTH diagram?
  39. 8(c)(i)2 marksComplete the table by inserting the missing values at the rows marked (i) and (ii). (i) s=52, find t.
  40. 8(c)(ii)2 marksComplete the table by inserting the missing values at the rows marked (i) and (ii). (ii) t=55, find s.
  41. 8(d)2 marksWrite the rule, in terms of s and t, to show how t is related to s.
  42. 9(a)5 marksSolve the pair of simultaneous equations: y = x² - x + 3 and y = 6 - 3x.
  43. 9(b)(i)2 marksExpress the function f(x) = 4x² - 8x - 2 in the form a(x + h)² + k, where a, h and k are constants.
  44. 9(b)(ii)1 markState the minimum value of f(x).
  45. 9(b)(iii)1 markState the value of x for which f(x) is a minimum.
  46. 9(c)(i)2 marksCalculate the value of x.
  47. 9(c)(ii)2 marksWhat is the gradient of the graph during the SECOND stage? Explain, in one sentence, what the car is doing during this stage.
  48. 9(c)(iii)2 marksCalculate the distance travelled by the car on the THIRD stage of the journey.
  49. 10(a)(i)2 marksCalculate, giving reasons for your answer, the measure of angle XYZ.
  50. 10(a)(ii)2 marksCalculate, giving reasons for your answer, the measure of angle YXZ.
  51. 10(a)(iii)3 marksCalculate, giving reasons for your answer, the measure of angle OXZ.
  52. 10(b)(i)2 marksCalculate the value of x, as shown in the diagram.
  53. 10(b)(ii)3 marksCalculate the distance RP.
  54. 10(b)(iii)3 marksDetermine the bearing of R from P.
  55. 11(a)2 marksDetermine the inverse of the matrix [[3, 5], [2, 4]].
  56. 11(b)(i)2 marksDetermine the values of a and b.
  57. 11(b)(ii)3 marksDescribe fully the transformation, M.
  58. 11(c)(i)a)5 marksWrite in terms of a and b, an expression for WY.
  59. 11(c)(i)b)5 marksWrite in terms of a and b, an expression for WS.
  60. 11(c)(i)c)5 marksWrite in terms of a and b, an expression for SX.
  61. 11(c)(ii)3 marksR is the mid-point of VW. Prove that R, S and X are collinear.

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