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CSEC Mathematics · May/June 2009 · Paper 2

79 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, calculate the EXACT value of 2 2/3 + 1 1/5 divided by 6 2/5, giving your answer as a common fraction.
  2. 1(a)(ii)3 marksCalculate the EXACT value of the square root of 0.0256 divided by 25, giving your answer in standard form.
  3. 1(b)(i)1 markCalculate his hourly rate.
  4. 1(b)(ii)2 marksCalculate his overtime wage for 10 hours of overtime.
  5. 1(b)(iii)3 marksCalculate the TOTAL wages earned by the truck driver for a 55-hour week.
  6. 2(a)(i)2 marksFactorise completely: 2ax + 3ay - 2bx - 3by
  7. 2(a)(ii)2 marksFactorise completely: 5x² - 20
  8. 2(a)(iii)2 marksFactorise completely: 3x² + 4x - 15
  9. 2(b)(i)2 marksWrite a pair of simultaneous equations in x and y to represent the given information above.
  10. 2(b)(ii)4 marksSolve the equations obtained in (b)(i) above to find the cost of one packet of biscuits and the cost of one cup of ice cream.
  11. 3(a)(i)2 marksCopy and complete the Venn diagram below to represent the information obtained from the survey.
  12. 3(a)(ii)1 markWrite an expression in x for the TOTAL number of students in the survey.
  13. 3(a)(iii)2 marksCalculate the value of x.
  14. 3(b)(i)4 marksUsing a ruler, a pencil, and a pair of compasses, construct the rhombus PQRS accurately.
  15. 3(b)(ii)2 marksJoin QS. Measure and state, in centimetres, the length of QS.
  16. 4(a)(i)1 markFor the period of time between the two readings, calculate the distance travelled in kilometres.
  17. 4(a)(ii)3 marksFor the period of time between the two readings, calculate the average speed of the aircraft in km/h.
  18. 4(b)(i)2 marksMeasure and state, in centimetres, the distance on the map from L to M along a straight line.
  19. 4(b)(ii)2 marksCalculate the actual distance, in kilometres, from L to M.
  20. 4(b)(iii)3 marksThe actual distance between two points is 4.5 km. Calculate the number of centimetres that should be used to represent this distance on the map.
  21. 5(a)(i)1 markCalculate the value of f(-2).
  22. 5(a)(ii)2 marksCalculate the value of gf(1).
  23. 5(a)(iii)2 marksCalculate the value of f⁻¹(3).
  24. 5(b)(i)2 marksCopy and complete the table below.
  25. 5(b)(ii)5 marksUsing a scale of 2 cm to represent 1 unit on the x-axis and 1 cm to represent 1 unit on the y-axis, draw the graph of y = x² + 2x - 3 for -4 ≤ x ≤ 2.
  26. 6(a)(i)3 marksDescribe, FULLY, the single transformation which maps triangle A onto triangle D.
  27. 6(a)(ii)3 marksDescribe, FULLY, the single transformation which maps triangle A onto triangle B.
  28. 6(b)4 marksState the coordinates of the vertices of triangle C, the image of triangle A after a reflection in the line y = x.
  29. 7(a)2 marksCopy and complete the table, showing the cumulative frequency.
  30. 7(b)4 marksOn the answer sheet provided, use the values from your table to complete the cumulative frequency curve.
  31. 7(c)(i)2 marksUse your graph from (b) above to estimate the median for the data.
  32. 7(c)(ii)2 marksUse your graph from (b) above to estimate the number of students who waited for no more than 29 minutes.
  33. 7(c)(iii)2 marksUse your graph from (b) above to estimate the probability that a student, chosen at random from the group, waited for no more than 17 minutes.
  34. 8(a)2 marksDraw Diagram 4 in the sequence.
  35. 8(b)8 marksComplete the table by inserting the appropriate values at the rows marked (i), (ii) and (iii).
  36. 9(a)4 marksSolve the pair of simultaneous equations: y = 4 - 2x and y = 2x² - 3x + 1.
  37. 9(b)3 marksExpress 2x² - 3x + 1 in the form a(x + h)² + k, where a, h and k are real numbers.
  38. 9(c)(i)1 markUsing your answer from (b) above, or otherwise, calculate the minimum value of 2x² - 3x + 1.
  39. 9(c)(ii)1 markUsing your answer from (b) above, or otherwise, calculate the value of x for which the minimum occurs.
  40. 9(d)4 marksSketch the graph of y = 2x² - 3x + 1, clearly showing the coordinates of the minimum point, the value of the y-intercept, and the values of x where the graph cuts the x-axis.
  41. 9(e)2 marksSketch on your graph of y = 2x² - 3x + 1, the line which intersects the curve at the values of x and y calculated in (a) above.
  42. 10(a)(i)1 markWrite an inequality to represent the information that the number of violins must be less than or equal to the number of guitars.
  43. 10(a)(ii)2 marksWrite an inequality to represent the information about the total cost of guitars and violins given the budget of $4500.
  44. 10(a)(iii)1 markWrite an inequality to represent the information that the owner must buy at least 5 violins.
  45. 10(b)(i)4 marksUsing a scale of 2 cm on the horizontal axis to represent 5 guitars, and 2 cm on the vertical axis to represent 5 violins, draw the graphs of the lines associated with the THREE inequalities written in (a) (i), (ii) and…
  46. 10(b)(ii)1 markShade the region on your graph that satisfies all THREE inequalities.
  47. 10(b)(iii)2 marksState the coordinates of the vertices of the shaded region.
  48. 10(c)(i)1 markExpress the TOTAL profit in terms of x and y.
  49. 10(c)(ii)3 marksCalculate the maximum profit.
  50. 11(a)(i)1 markCalculate angle ABC.
  51. 11(a)(ii)1 markCalculate angle AOC.
  52. 11(a)(iii)1 markCalculate angle BCD.
  53. 11(a)(iv)1 markCalculate angle BAC.
  54. 11(a)(v)1 markCalculate angle OAC.
  55. 11(a)(vi)1 markCalculate angle OAB.
  56. 11(b)(i)2 marksCopy the diagram above. On your diagram label the angles that show the bearings of 025° and 080°.
  57. 11(b)(ii)a)7 marksCalculate angle OPQ.
  58. 11(b)(ii)b)7 marksCalculate the length, to the nearest kilometre, of OQ.
  59. 11(b)(ii)c)7 marksCalculate the bearing of Q from O.
  60. 12(a)(i)a)2 marksCopy the sketch and label the arc which represents 60°N.
  61. 12(a)(i)b)2 marksCopy the sketch and label the arc which represents 35°E.
  62. 12(a)(ii)a)2 marksCopy the sketch and insert the point J (60°N, 35°E).
  63. 12(a)(ii)b)2 marksCopy the sketch and insert the point K (60°N, 15°W).
  64. 12(b)(i)3 marksCalculate, to the nearest kilometre, the SHORTEST distance from J to the North Pole measured along the common circle of longitude.
  65. 12(b)(ii)4 marksCalculate, to the nearest kilometre, the SHORTEST distance from J to K measured along the common circle of latitude.
  66. 12(c)4 marksCalculate the latitude of H.
  67. 13(a)(i)4 marksExpress in the form (x, y) the vectors AB and AG.
  68. 13(a)(ii)2 marksExpress in the form (x, y) the position vector OG.
  69. 13(b)(i)a)6 marksWrite in terms of a and b the vector AB.
  70. 13(b)(i)b)6 marksWrite in terms of a and b the vector AC.
  71. 13(b)(i)c)6 marksWrite in terms of a and b the vector DC.
  72. 13(b)(i)d)6 marksWrite in terms of a and b the vector DX.
  73. 13(b)(ii)2 marksState TWO geometrical relationships between DX and DC.
  74. 13(b)(iii)1 markState ONE geometrical relationship between the points D, C, and X.
  75. 14(a)4 marksCalculate the values of x.
  76. 14(b)(i)2 marksWrite a single matrix, in the form ((a, b), (c, d)), to represent the combined transformation S followed by R.
  77. 14(b)(ii)3 marksCalculate the image of the point (5, -2) under the combined transformation in (b)(i) above.
  78. 14(c)(i)2 marksDetermine the inverse matrix of N.
  79. 14(c)(ii)4 marksHence, calculate the value of x and the value of y for which 3x - y = 5 and 2x + 5y = 9.

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