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CSEC Mathematics · January 2005 · Paper 2

75 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)3 marksUsing a calculator, or otherwise, evaluate √(13.2 / 0.33), writing your answer correct to 3 decimal places.
  2. 1(b)(i)8 marksIn one month, calls were made lasting for a total of 1 hour and 5 minutes. Show by calculations, that the cost for using the land line telephone was less than the cost for using the cellular telephone.
  3. 1(b)(ii)8 marksFor the month of March, the land line telephone was used, and the bill was $54.60. Calculate the total time, in minutes, for which the calls lasted.
  4. 2(a)(i)4 marksCalculate the value of r when p = 6 and q = 12.
  5. 2(a)(ii)4 marksRearrange the formula to make q the subject.
  6. 2(b)(i)6 marksFactorize completely 3g - 3t + 2mg - 2mt.
  7. 2(b)(ii)6 marksFactorize completely 3x² + 2x - 8.
  8. 2(b)(iii)6 marksFactorize completely 3x² - 27.
  9. 2(c)2 marksGiven that y varies inversely as x, use the values of x and y from the table to calculate the value of a.
  10. 3(a)(i)6 marksCopy and complete the following Venn diagram to represent the information.
  11. 3(a)(ii)6 marksWrite an equation in x for the number of candidates in the universal set.
  12. 3(a)(iii)6 marksCalculate the value of x.
  13. 3(a)(iv)6 marksShade the region F' ∩ S.
  14. 4(a)6 marksUsing a ruler, a pencil and a pair of compasses only, construct the rectangle PQRS in which PQ = 8 cm and PS = 6 cm. Measure and state the length of the diagonal, in centimetres.
  15. 4(b)(i)4 marksWrite an expression in terms of y for the area of the figure shown.
  16. 4(b)(i)6 marksCalculate ∠ZXV.
  17. 4(b)(ii)4 marksCalculate the value of y if the area of the figure is 28 m².
  18. 4(b)(ii)6 marksCalculate ∠ZVX.
  19. 4(b)(iii)6 marksCalculate the length of VZ.
  20. 4(b)(iv)6 marksCalculate the bearing of V from X.
  21. 5(a)(i)5 marksCalculate the value of g(4).
  22. 5(a)(ii)5 marksCalculate the value of fg(2).
  23. 5(a)(iii)5 marksCalculate the value of g⁻¹(7).
  24. 5(b)3 marksWrite as a single fraction in its simplest form 3/x + 4/(x + 1).
  25. 5(c)3 marksCalculate the value of 9^(1/2) × 8^(2/3) × 4⁻¹.
  26. 6(a)(i)5 marksCalculate the gradient of the line AB.
  27. 6(a)(ii)5 marksWrite down the gradient of any line that is perpendicular to AB.
  28. 6(a)(iii)5 marksDetermine the equation of the line which passes through D (3,2) and is perpendicular to AB. Write your answer in the form: y = mx + c.
  29. 6(b)(i)7 marksDraw a triangle with coordinates (2, 1), (3, 3) and (4, 3). Label it A.
  30. 6(b)(ii)7 marksDraw the image of triangle A after a reflection in the line y = -1. Label it B.
  31. 6(b)(iii)7 marksDraw the image of triangle A after a translation by the vector (2, -4). Label it C.
  32. 7(i)2 marksEstimate the number of students who scored less than 23 marks.
  33. 7(ii)2 marksEstimate the number of students who scored more than 17 marks.
  34. 7(iii)3 marksEstimate the interquartile range of the marks scored.
  35. 7(iv)3 marksEstimate the probability that a randomly chosen student from the class scored between 17 marks and 23 marks.
  36. 7(v)2 marksEstimate the value of x if only 30 students from the class scored more than x marks.
  37. 8(a)4 marksTaking π = 3.14, calculate the volume of metal in a single link of chain, writing your answer correct to 3 significant figures.
  38. 8(b)2 marksShow that the length of the chain is 16 mm + 14 mm.
  39. 8(c)4 marksCopy and complete the table below which shows the length of the chain formed when rings are linked in a straight line.
  40. 9(a)5 marksSolve the pair of simultaneous equations x² = 4 - y and x = y + 2.
  41. 9(b)2 marksBy simplifying, show that (2x - 3)(2x + 3) - (x - 4)² = 3x² + 8x - 25.
  42. 9(c)(i)5 marksWrite 3x² + 8x - 25 in the form a(x + h)² + k where a, h and k are real numbers.
  43. 9(c)(ii)5 marksHence, or otherwise, determine the minimum value of 3x² + 8x - 25.
  44. 9(d)3 marksSolve the equation 3x² + 8x - 25 = 0 giving your answers correct to one decimal place.
  45. 10(i)1 markWrite an inequality to represent this information.
  46. 10(ii)2 marksWrite an inequality to represent this information.
  47. 10(iii)2 marksWrite an inequality to represent this information.
  48. 10(iv)(a)6 marksUsing a scale of 2 cm to represent 5 calculators on the x-axis and 2 cm to represent 10 folders on the y-axis, draw the graphs of the lines associated with the inequalities at (i), (ii) and (iii) above.
  49. 10(iv)(b)6 marksIdentify, by shading, the region which satisfies all three inequalities.
  50. 10(v)1 markWrite an expression in x and y for the total profit, P.
  51. 10(vi)1 markWrite down the coordinates of the vertices of the shaded region.
  52. 10(vii)2 marksCalculate the maximum profit.
  53. 11(a)(i)7 marksCalculate the angle of elevation of U from S.
  54. 11(a)(ii)7 marksCalculate the length of UT.
  55. 11(a)(iii)7 marksCalculate the length of RU.
  56. 11(b)(i)8 marksCalculate ∠SON.
  57. 11(b)(ii)8 marksCalculate ∠NMQ.
  58. 11(b)(iii)8 marksCalculate ∠PLN.
  59. 11(b)(iv)8 marksCalculate ∠SNM.
  60. 12(a)(i)4 marksDraw a diagram to represent the earth showing the equator, the line of 0° longitude, and points A and B.
  61. 12(a)(ii)4 marksCalculate the shortest distance between A and B measured along their common circle of latitude.
  62. 12(b)(i)7 marksGiven that y = 2 - cos x, copy and complete the table below.
  63. 12(b)(ii)7 marksUsing a scale of 2 cm to represent 30° on the x-axis, and 1 cm to represent 0.2 on the y-axis, draw the graph of y = 2 - cos x for 0° ≤ x ≤ 180°.
  64. 12(b)(iii)7 marksUsing the graph, or otherwise, determine the value of x for which 2 - cos x = 1.8.
  65. 13(a)(i)3 marksCalculate PQ, writing your answer in the form [x, y].
  66. 13(a)(ii)3 marksCalculate |PQ|.
  67. 13(b)(i)2 marksExpress CF in terms of a and b in simplified form.
  68. 13(b)(ii)2 marksExpress CE in terms of a and b in simplified form.
  69. 13(b)(iii)2 marksExpress CM in terms of a and b in simplified form.
  70. 13(b)(iv)3 marksExpress MG in terms of a, b, and k.
  71. 13(b)(v)3 marksDetermine the value of k for which MG = CO.
  72. 14(a)(i)2 marksFind the inverse of the matrix M = [[2, 1], [-1, 3]].
  73. 14(a)(ii)4 marksCalculate the values of x and y for which M * [[x], [y]] = [[12], [1]].
  74. 14(b)(i)6 marksDetermine the values of p, q, r and s.
  75. 14(b)(ii)3 marksCalculate the coordinates of the point C' which is the image of C (-2, 2) under T.

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