Quelpr

CSEC Mathematics · May/June 2008 · Paper 2

77 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)4 marksUsing a calculator or otherwise, calculate the exact value of 2 1/5 - 1 1/3 / 1 5/8, giving your answer as a fraction in its lowest terms.
  2. 1(b)(i)1 markCalculate his annual salary.
  3. 1(b)(ii)2 marksCalculate Mr. Allen's TOTAL allowances for 2007.
  4. 1(b)(iii)3 marksCalculate Mr. Allen's income tax for 2007.
  5. 1(b)(iv)2 marksWhat percentage of Mr. Allen's annual salary was paid in income tax?
  6. 2(a)2 marksSimplify completely: (3a - 1)^2.
  7. 2(b)3 marksMake p the subject of the formula q = 5 / (3 + p).
  8. 2(c)(i)1 markFactorize completely 3mn - 6n^2.
  9. 2(c)(ii)2 marksFactorize completely 25p^2 - q^2.
  10. 2(d)4 marksSolve the following simultaneous equations: 3x - 2y = 19 and 2x + 3y = 4.
  11. 3(a)(i)2 marksList the members of the set a) G ∩ H b) G ∪ H'.
  12. 3(a)(ii)1 markDetermine the value of n(G ∪ H).
  13. 3(a)(iii)3 marksDescribe in words a) the Universal set U b) the set H.
  14. 4(a)2 marksCalculate the area of triangle ABC.
  15. 4(b)3 marksCalculate the length of the edge CD.
  16. 4(b)(i)5 marksUse a ruler and a protractor to draw accurately the quadrilateral PQRS shown below. PQ = 8 cm, QR = 4 cm, PS = 6.5 cm, angle PQR = 125° and angle QPS = 70°.
  17. 4(b)(ii)1 markMeasure and state the length of RS.
  18. 4(c)2 marksCalculate, to one decimal place, the length of the edge AC.
  19. 4(d)3 marksState the number of faces, edges, and vertices of the prism.
  20. 5(a)1 markDraw the line x = 4.
  21. 5(b)3 marksDraw the image of triangle LMN after a reflection in the line x = 4 and label the image L'M'N'.
  22. 5(c)(i)2 marksDraw the triangle L''M''N''.
  23. 5(c)(ii)4 marksDescribe completely the transformation which maps triangle LMN onto triangle L''M''N''.
  24. 5(d)2 marksCalculate the value of Area of triangle L''M''N'' / Area of triangle LMN.
  25. 6(a)6 marksUsing a scale of 4 cm to represent one million persons on the vertical axis and 2 cm to represent five years on the horizontal axis, draw a line-graph to represent the population from 1980 to 2005. Start your horizontal…
  26. 6(b)2 marksOn your graph, show how to estimate the population of the country in 1998. Write your estimated value.
  27. 6(c)(i)1 markDuring which five-year period was there the greatest increase in population?
  28. 6(c)(ii)1 markDuring which five-year period was there the smallest increase in population?
  29. 6(d)1 markExplain how the two facts about the population, (c) (i) and (c) (ii), are shown on your graph.
  30. 7(a)4 marksA line segment connects the points A (1,8) and B (j, k). If the mid-point of AB is (4, 5), calculate the values of j and k.
  31. 7(b)(i)1 markCalculate f(0).
  32. 7(b)(ii)1 markCalculate g(2).
  33. 7(b)(iii)2 marksCalculate f^(-1)(x).
  34. 7(b)(iv)3 marksCalculate the value of x if fg(x) = 1.
  35. 8(a)2 marksSketch the geometrical pattern whose side is 5 cm long.
  36. 8(b)(i)3 marksComplete the table for the geometrical pattern whose side is 6 cm long.
  37. 8(b)(ii)2 marksComplete the table for the geometrical pattern whose side is 20 cm long.
  38. 8(c)3 marksHence, complete the table for the geometrical pattern whose side is n cm long.
  39. 9(a)4 marksSolve the pair of simultaneous equations y = x^2 - 3x - 12 and y = 2x - 16.
  40. 9(b)(i)3 marksExpress y = x^2 - 3x - 12 in the form y = (x - h)^2 + k, where h and k are constants.
  41. 9(b)(ii)2 marksHence determine the minimum value of the function y = x^2 - 3x - 12.
  42. 9(b)(iii)3 marksCalculate, correct to one decimal place, the roots of the equation x^2 - 3x - 12 = 0.
  43. 9(c)(i)1 markSketch the graph of y = x^2 - 3x - 12, showing clearly: the value of x where the function is a minimum.
  44. 9(c)(ii)2 marksSketch the graph of y = x^2 - 3x - 12, showing clearly: the x-intercepts.
  45. 10(a)3 marksCopy and complete the table below for the function y = 20 / x^2 for 2 ≤ x ≤ 7.
  46. 10(b)(i)4 marksUsing a scale of 2 cm to represent 1 unit on both axes, plot the points whose x and y values are given in the table at (a).
  47. 10(b)(ii)1 markDraw a smooth curve through the points.
  48. 10(c)(i)1 markUse your graph to estimate the value of y when x = 4.5.
  49. 10(c)(ii)2 marksUse your graph to estimate the value of x when y = 3.5.
  50. 10(d)4 marksDraw the tangent to the curve at the point (3, 2.2) as accurately as possible. Hence, estimate the gradient of the curve at the point (3, 2.2). [Show clearly on your graph how the estimates at (c) (i), (ii) and (d) were…
  51. 11(a)1 markCopy and label the diagram.
  52. 11(b)4 marksOn your diagram, show the point, Q, such that the bearing of Q from R is 033° and the bearing of S from Q is 118°. (Clearly show both bearings on your diagram.)
  53. 11(c)(i)1 markState the size of ∠QRS.
  54. 11(c)(ii)1 markState the size of ∠RQS.
  55. 11(c)(iii)1 markState the size of ∠QST.
  56. 11(d)(i)2 marksCalculate, correct to the nearest kilometre, the distance QS.
  57. 11(d)(ii)2 marksCalculate, correct to the nearest kilometre, the distance QT.
  58. 11(e)3 marksCalculate the bearing of Q from S.
  59. 12(a)(i)2 marksCalculate, stating reasons for your answers, the size of the following angles: KLN.
  60. 12(a)(ii)3 marksCalculate, stating reasons for your answers, the size of the following angles: NKL.
  61. 12(a)(iii)2 marksCalculate, stating reasons for your answers, the size of the following angles: LMN.
  62. 12(b)(i)3 marksCopy the diagram and a) label the arc which represents 25°W b) draw an arc to represent the circle of latitude 60°N.
  63. 12(b)(ii)2 marksOn your diagram, show the points a) R (60°N, 25°W) b) T (60°N, 40°E).
  64. 12(b)(iii)3 marksCalculate to the nearest kilometre, the distance from R to T measured along the circle of latitude 60°N.
  65. 13(a)(i)1 markWrite the following position vectors in the form (x y): OA.
  66. 13(a)(ii)1 markWrite the following position vectors in the form (x y): OB.
  67. 13(a)(iii)1 markWrite the following position vectors in the form (x y): OC.
  68. 13(b)(i)2 marksWrite as a column vector, in the form (x y): BA.
  69. 13(b)(ii)2 marksWrite as a column vector, in the form (x y): AC in terms of p.
  70. 13(c)3 marksCalculate the values of p for which |AC| = 10.
  71. 13(d)5 marksUsing a vector method, prove that the points A, B and D are collinear.
  72. 14(a)2 marksShow that M is a singular matrix.
  73. 14(b)3 marksCalculate the values of a and b such that: (2 1 / a 4) (5 / b) = (8 / 7).
  74. 14(c)(i)3 marksGiven that S = (0 x / y 0), calculate the values of x and y.
  75. 14(c)(ii)(a)3 marksCalculate the coordinates of G'.
  76. 14(c)(ii)(b)3 marksUnder the same transformation, H(p, q) is mapped onto H'(2, 6). Calculate the values of p and q.
  77. 14(c)(iii)4 marksObtain the coordinates of the image of P(10, 12), under the combined transformation, S followed by T.

More CSEC Mathematics papers