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CSEC Mathematics · January 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)(i)4 marksCalculate the EXACT value of: 1 - 3/7 / (1/2 * 4/5)
  2. 1(a)(ii)2 marksCalculate the EXACT value of: 2 - 0.24 / 0.15
  3. 1(b)(i)2 marksWhat is the TOTAL hire purchase price of the bicycle?
  4. 1(b)(ii)1 markCalculate the difference between the total hire purchase price and the cash price.
  5. 1(b)(iii)2 marksExpress your answer in (ii) above as a percentage of the cash price.
  6. 2(a)(i)2 marksSolve the inequality: 3 - 2x < 7
  7. 2(a)(ii)1 markIf x is a whole number, determine the SMALLEST value that satisfies the inequality in (a) (i) above.
  8. 2(b)(i)1 markFactorize completely x^2 - xy
  9. 2(b)(ii)1 markFactorize completely a^2 - 1
  10. 2(b)(iii)2 marksFactorize completely 2p - 2q - p^2 + pq
  11. 2(c)(i)1 markWrite an expression, in terms of k, for the amount of money collected from the sale of sponge cakes for the day.
  12. 2(c)(ii)2 marksWrite an expression, in terms of k, for the TOTAL amount of money collected.
  13. 2(c)(iii)2 marksDetermine the value of k.
  14. 3(a)(i)3 marksDraw a Venn diagram to represent this information.
  15. 3(a)(ii)a)1 markList, using set notation, the members of the set S U T
  16. 3(a)(ii)b)2 marksList, using set notation, the members of the set S'
  17. 3(b)(i)6 marksCalculate, giving reasons for your answers, the size of angle ABC.
  18. 3(b)(ii)6 marksCalculate, giving reasons for your answers, the size of angle ABD.
  19. 3(b)(iii)6 marksCalculate, giving reasons for your answers, the size of angle BAD.
  20. 4(a)(i)1 markHow long did the journey take?
  21. 4(a)(ii)2 marksCalculate his average speed in km h^-1.
  22. 4(b)(i)2 marksCalculate the area of the circle.
  23. 4(b)(ii)2 marksCalculate the area of the square OPQR.
  24. 4(b)(iii)3 marksCalculate the area of the shaded region.
  25. 5(a)3 marksDraw a frequency table to represent the data shown in the bar graph.
  26. 5(b)2 marksHow many boys are there in the Book Club?
  27. 5(c)1 markWhat is the modal number of books read?
  28. 5(d)2 marksHow many books did the boys read during the Easter holiday?
  29. 5(e)2 marksCalculate the mean number of books read.
  30. 5(f)2 marksWhat is the probability that a boy chosen at random read THREE OR MORE books?
  31. 6(a)(i)3 marksDescribe FULLY the single transformation that will map triangle BCL onto triangle FHL.
  32. 6(a)(ii)3 marksDescribe FULLY the single transformation that will map triangle BCL onto triangle HFG.
  33. 6(b)(i)5 marksUsing a ruler, a pencil and a pair of compasses, construct parallelogram WXYZ in which WX = 7.0 cm, WZ = 5.5 cm and angle XWZ = 60°.
  34. 6(b)(ii)1 markMeasure and state the length of the diagonal WY.
  35. 7(a)3 marksGiven that y = x^2 - 4x, copy and complete the table below.
  36. 7(b)4 marksUsing a scale of 2 cm to represent 1 unit on both axes, draw the graph of the function y = x^2 - 4x for -1 ≤ x ≤ 5.
  37. 7(c)(i)1 markOn the same axes used in (b) above, draw the line y = 2.
  38. 7(c)(ii)2 marksState the x-coordinates of the two points at which the curve meets the line.
  39. 7(c)(iii)1 markHence, write the equation whose roots are the x-coordinates stated in (c) (ii).
  40. 8(a)(i)3 marksComplete the row for n=6 in the table.
  41. 8(a)(ii)2 marksComplete the row for n in the table.
  42. 8(b)(i)1 markUsing the pattern observed in these two statements, determine the sum of the series: 1^3 + 2^3 + 3^3 + 4^3 + 5^3 + 6^3 + 7^3 + 8^3
  43. 8(b)(ii)2 marksUsing the pattern observed in these two statements, determine the sum of the series: 1^3 + 2^3 + 3^3 + ... + n^3.
  44. 8(c)2 marksHence, or otherwise, determine the EXACT value of the sum of the series: 1^3 + 2^3 + 3^3 + 4^3 + ... + 12^3
  45. 9(a)(i)2 marksWrite an equation relating V and P.
  46. 9(a)(ii)2 marksIf V = 12.8 when P = 500, determine the constant of variation.
  47. 9(a)(iii)2 marksCalculate the value of V when P = 480.
  48. 9(b)(i)2 marksUsing Pythagoras theorem, write an equation in terms of a to represent the relationship among the three sides.
  49. 9(b)(ii)4 marksSolve the equation for a.
  50. 9(b)(iii)3 marksHence, state the lengths of the THREE sides of the triangle.
  51. 10(a)(i)2 marksWrite an inequality to represent this information.
  52. 10(a)(ii)2 marksWrite an inequality to represent this information.
  53. 10(b)(i)5 marksUsing a scale of 2 cm on the x-axis to represent 10 balls and 2 cm on the y-axis to represent 5 bats, draw the graphs of the lines associated with the inequalities at (a) (i) and (ii) above.
  54. 10(b)(ii)1 markShade the region which satisfies the two inequalities at (a) (i) and (ii) and the inequalities x ≥ 0 and y ≥ 0.
  55. 10(b)(iii)2 marksUse your graph to write the coordinates of the vertices of the shaded region.
  56. 10(c)(i)2 marksUse the coordinates of the vertices given at (b) (iii) above to determine the profit for each of those combinations.
  57. 10(c)(ii)1 markHence, state the maximum profit that may be made.
  58. 11(a)(i)2 marksCalculate, giving a reason for EACH step of your answer, angle WOY.
  59. 11(a)(ii)2 marksCalculate, giving a reason for EACH step of your answer, angle OWY.
  60. 11(b)(i)5 marksSketch a diagram to represent the information given below. Show clearly all measurements and any north-south lines that may be required.
  61. 11(b)(ii)3 marksCalculate, to one decimal place, the distance AC.
  62. 11(b)(iii)3 marksCalculate, to the nearest degree, the bearing of C from A.
  63. 12(a)(i)2 marksCalculate, to one decimal place, the horizontal distance AB.
  64. 12(a)(ii)4 marksCalculate, to one decimal place, the height of the tower, BC.
  65. 13(a)(i)1 markMake a sketch of the diagram and show the points P and Q.
  66. 13(a)(ii)a)1 markWrite, in terms of x and y, an expression for vector AC.
  67. 13(a)(ii)b)2 marksWrite, in terms of x and y, an expression for vector PQ.
  68. 13(a)(iii)2 marksHence show that vector PQ = 1/2 vector AC.
  69. 13(b)(i)a)4 marksExpress in the form (a, b) the vector RT.
  70. 13(b)(i)b)4 marksExpress in the form (a, b) the vector SR.
  71. 13(b)(ii)a)5 marksUse a vector method to determine the position vector of F.
  72. 13(b)(ii)b)5 marksHence, state the coordinates of F.
  73. 14(a)5 marksCalculate the values of x and y.
  74. 14(b)(i)2 marksShow that R is non-singular.
  75. 14(b)(ii)2 marksFind R^-1, the inverse of R.
  76. 14(b)(iii)2 marksShow that R R^-1 = I.
  77. 14(b)(iv)4 marksUsing a matrix method, solve the pair of simultaneous equations: 2x - y = 0 and x + 3y = 7.

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