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CSEC Mathematics · January 2007 · Paper 2

85 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)2 marksUsing a calculator, or otherwise, evaluate 5.24 (4-1.67)
  2. 1(a)(ii)3 marksUsing a calculator, or otherwise, evaluate 1.68 / (1.5^2 - 1.45)
  3. 1(b)3 marksHow much money was shared altogether?
  4. 1(c)(i)2 marksCalculate the cost of 5 litres of gasoline in St. Vincent, stating your answer correct to the nearest cent.
  5. 1(c)(ii)2 marksHow many litres of gasoline can be bought for EC $50.00 in St. Vincent? Give your answer correct to the nearest whole number.
  6. 2(a)(i)1 markEvaluate ab - bc
  7. 2(a)(ii)2 marksEvaluate b(a - c)^2
  8. 2(b)(i)3 marksSolve for x where x ∈ Z: x/2 + x/3 = 5
  9. 2(b)(ii)3 marksSolve for x where x ∈ Z: 4 - x ≤ 13
  10. 2(c)(i)a)1 markWrite an algebraic expression in m for the cost of FIVE muffins.
  11. 2(c)(i)b)1 markWrite an algebraic expression in m for the cost of SIX cupcakes.
  12. 2(c)(ii)1 markWrite an equation, in terms of m, to represent the following information: The TOTAL cost of 5 muffins and 6 cupcakes is $31.50.
  13. 3(a)3 marksDescribe, using set notation only, the shaded regions in each Venn diagram below. The first one is done for you. (i) U (A and B circles, intersection shaded) (ii) U (A and B circles, A shaded) (iii) U (A and B circles,…
  14. 3(b)3 marksDraw a Venn diagram to represent the information above.
  15. 3(c)(i)1 markDetermine how many elements are in EACH of the following sets: A ∪ B
  16. 3(c)(ii)1 markDetermine how many elements are in EACH of the following sets: A ∩ B
  17. 3(c)(iii)1 markDetermine how many elements are in EACH of the following sets: (A ∩ B)'
  18. 3(c)(iv)1 markDetermine how many elements are in EACH of the following sets: U
  19. 4(a)(i)3 marksUsing a pencil, ruler and a pair of compasses only, construct Δ ABC with BC = 6 cm and AB = AC = 8 cm. All construction lines must be clearly shown.
  20. 4(a)(ii)2 marksDraw a line segment AD such that AD meets BC at D and is perpendicular to BC.
  21. 4(a)(iii)a)1 markMeasure and state the length of the line segment AD.
  22. 4(a)(iii)b)1 markMeasure and state the size of angle ABC.
  23. 4(b)(i)2 marksCalculate the gradient of PQ.
  24. 4(b)(ii)2 marksCalculate the midpoint of PQ.
  25. 5(a)(i)1 markCalculate g(3).
  26. 5(a)(ii)2 marksCalculate f(-2).
  27. 5(a)(iii)2 marksCalculate f⁻¹(11).
  28. 5(b)(i)1 markWrite down the equation of the mirror line.
  29. 5(b)(ii)3 marksDetermine the coordinates of the vertices of Δ A''B''C''.
  30. 5(b)(iii)2 marksState the transformation that maps Δ ABC onto Δ A''B''C''.
  31. 6(i)2 marksCopy and complete the table above to show the cumulative frequency for the distribution.
  32. 6(ii)6 marksUsing a scale of 2 cm to represent a score of 5 on the horizontal axis and a scale of 2 cm to represent 10 students on the vertical axis, draw a cumulative frequency curve of the scores. Start your horizontal scale at…
  33. 6(iii)2 marksUsing the cumulative frequency curve, determine the median score for the distribution.
  34. 6(iv)2 marksWhat is the probability that a student chosen at random has a score greater than 40?
  35. 7(a)(i)2 marksCalculate the volume, in cm³, of the prism.
  36. 7(a)(ii)4 marksCalculate the total surface area, in cm², of the prism.
  37. 7(b)(i)2 marksCalculate, giving your answer correct to 2 decimal places, the length of the minor arc MN.
  38. 7(b)(ii)2 marksCalculate, giving your answer correct to 2 decimal places, the perimeter of the figure MON.
  39. 7(b)(iii)2 marksCalculate, giving your answer correct to 2 decimal places, the area of the figure MON.
  40. 8(i)2 marksCalculate the number of triangles formed when n = 3.
  41. 8(ii)2 marksDetermine the number of triangles formed when n = 6.
  42. 8(iii)3 marksCalculate the value of n.
  43. 8(iv)3 marksDetermine the number of small triangles in a shape after carrying out the procedure m times.
  44. 9(a)(i)1 markFactorise completely 2p^2 - 7p + 3.
  45. 9(a)(ii)2 marksFactorise completely 5p + 5q + p^2 - q^2.
  46. 9(b)3 marksExpand (x + 3)^2 (x - 4), writing your answer in descending powers of x.
  47. 9(c)(i)3 marksWrite f(x) in the form f(x) = a(x + b)^2 + c where a, b, c ∈ R.
  48. 9(c)(ii)1 markState the equation of the axis of symmetry.
  49. 9(c)(iii)1 markState the coordinates of the minimum point.
  50. 9(c)(iv)2 marksSketch the graph of f(x).
  51. 9(c)(v)a)1 markOn the graph of f(x) show clearly the minimum point.
  52. 9(c)(v)b)1 markOn the graph of f(x) show clearly the axis of symmetry.
  53. 10(a)(i)1 markWrite an inequality to represent this information.
  54. 10(a)(ii)2 marksWrite an inequality to represent this information.
  55. 10(a)(iii)2 marksWrite the information represented by this inequality as a sentence in your own words.
  56. 10(b)(i)3 marksOn the answer sheet provided, draw the graph of the TWO inequalities obtained in (a)(i) and (a)(ii) above.
  57. 10(b)(ii)2 marksWrite the coordinates of the vertices of the region that satisfies the four inequalities (including y ≥ 0).
  58. 10(c)(i)1 markWrite an expression in x and y to represent the profit Pam makes.
  59. 10(c)(ii)2 marksCalculate the maximum profit Pam makes.
  60. 10(c)(iii)2 marksIf Pam buys 4 pens, show on your graph the maximum number of pencils she can buy.
  61. 11(a)(i)a)2 marksState, with a reason, why PTQ is a straight line.
  62. 11(a)(i)b)2 marksState, with a reason, the length PQ.
  63. 11(a)(i)c)2 marksState, with a reason, why PS is parallel to QR.
  64. 11(a)(ii)a)2 marksCalculate the length PN.
  65. 11(a)(ii)b)2 marksCalculate the length RS.
  66. 11(b)(i)2 marksCalculate, giving reasons for your answers, the size of EACH of the following angles: ∠MNL.
  67. 11(b)(ii)3 marksCalculate, giving reasons for your answers, the size of EACH of the following angles: ∠LMO.
  68. 12(a)2 marksIllustrate the above information in a clearly labelled diagram.
  69. 12(a)(i)1 markThe diagram should show the north direction.
  70. 12(a)(ii)2 marksThe diagram should show bearings 135° and 060°.
  71. 12(a)(iii)2 marksThe diagram should show distances 8 km and 15 km.
  72. 12(b)(i)3 marksCalculate the distance AC.
  73. 12(b)(ii)3 marksCalculate ∠BCA.
  74. 12(b)(iii)2 marksCalculate the bearing of A from C.
  75. 13(a)(i)1 markSketch the diagram above in your answer booklet and insert the point X on OM such that OX = (1/3) OM.
  76. 13(a)(ii)1 markProduce PX to Q such that PX = 4 XQ.
  77. 13(b)(i)2 marksWrite OM in terms of r and s.
  78. 13(b)(ii)3 marksWrite PX in terms of r and s.
  79. 13(b)(iii)4 marksWrite QM in terms of r and s.
  80. 13(c)4 marksShow that PN = 2PM + OP.
  81. 14(a)4 marksDetermine the value(s) of p.
  82. 14(b)(i)2 marksWrite the equations in the form AX = B where A, X and B are matrices.
  83. 14(b)(ii)a)2 marksCalculate the determinant of the matrix A.
  84. 14(b)(ii)b)2 marksShow that A⁻¹ = [[-4/7, 5/7], [3/7, -2/7]].
  85. 14(b)(ii)c)5 marksUse the matrix A⁻¹ to solve for x and y.

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