Quelpr

CSEC Mathematics · May/June 2015 · Paper 2

78 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)1 mark2 2/5 - 1 1/3 + 3 1/2
  2. 1(a)(ii)2 marks(4.14 ÷ 5.75) + (1.62)²
  3. 1(a)(iii)1 mark2 × 3.142 × 1.25
  4. 1(a)(iv)2 marks√2.89 × tan 45°
  5. 1(b)(i)1 markCalculate the value of X, the cost of 1 kg of sugar.
  6. 1(b)(ii)2 marksIf the cost price of 1 kg of rice is 80 cents MORE than for 1 kg of flour, calculate the values of Y and Z.
  7. 1(b)(iii)3 marksA tax of 10% of the total cost price of the three items is added to Mrs Rowe's bill. What is Mrs Rowe's TOTAL bill including the tax?
  8. 2(a)(i)1 marka - b + c
  9. 2(a)(ii)1 mark2ab
  10. 2(b)(i)1 markp ml
  11. 2(b)(ii)1 markq glasses each containing r ml.
  12. 2(c)2 marksWrite as a single fraction, as simply as possible 2k/3 + (2-k)/5
  13. 2(d)(i)2 marksWrite a pair of simultaneous equations in x and y to represent the information given above.
  14. 2(d)(ii)1 markState clearly what x and y represent. x represents ____________ y represents ____________
  15. 2(e)(i)1 marka³ - 12a
  16. 2(e)(ii)2 marks2x² - 5x + 3
  17. 3(a)(i)1 markHow many students play neither the guitar nor the violin?
  18. 3(a)(ii)1 markWrite an expression, in terms of x, which represents the TOTAL number of students in the class.
  19. 3(a)(iii)1 markWrite an equation which may be used to determine the total number of students in the class.
  20. 3(a)(iv)2 marksHow many students play the guitar?
  21. 3(b)(i)4 marksUsing a ruler, a pencil and a pair of compasses, construct triangle ABC with AB = 9 cm, angle ABC = 90° and BC = 6 cm.
  22. 3(b)(ii)1 markMeasure and state the size of angle BAC.
  23. 3(b)(iii)2 marksOn the diagram, show the point D such that ABCD is a parallelogram.
  24. 4(a)2 marksComplete the table for the function y = x² – 2x – 3.
  25. 4(b)4 marksOn the graph on page 13, plot the graph of y = x²-2x-3 using a scale of 2 cm to represent 1 unit on the x-axis and 1 cm to represent 1 unit on the y-axis.
  26. 4(c)1 markOn the graph on page 13, draw a smooth curve passing through the points on your graph.
  27. 4(d)(i)1 markThe values of x for which x²-2x-3 = 0 are ____________ and ____________
  28. 4(d)(ii)1 markThe minimum value of x² - 2x - 3 is ____________
  29. 4(d)(iii)1 markThe equation of the line of symmetry of the graph of y = x²-2x-3 is ____________
  30. 5(a)(i)1 markCalculate the distance it travels in 2 1/4 hours.
  31. 5(a)(ii)2 marksCalculate the time, in seconds, it takes to travel 315 metres, given that 1 km/h = 5/18 m/s.
  32. 5(b)(i)1 mark1 millimetre = 1 metre
  33. 5(b)(ii)1 mark2 cm = 6 m
  34. 5(c)(i)1 markDetermine, in centimetres, the distance from Q to R on the map. QR = ____________ cm
  35. 5(c)(ii)2 marksDetermine, by counting, the area in square centimetres of the plane PQRS on the map.
  36. 5(c)(iii)2 marksCalculate the ACTUAL distance, in kilometres, between Q and R.
  37. 5(c)(iv)2 marksCalculate the ACTUAL area, in square metres, of the plane PQRS.
  38. 6(a)(i)2 marksCalculate the volume of water in Tank B.
  39. 6(a)(ii)1 markIf the area of the base of A is 314 m², calculate the length of the radius of Tank A.
  40. 6(a)(iii)2 marksTank A holds 8 times as much water as Tank B. Calculate the height, h, of Tank A.
  41. 6(b)(i)1 markThe size of the scale factor is ____________
  42. 6(b)(ii)1 markThe scale factor is negative because ____________
  43. 6(b)(iii)1 markThe length of PQ is √13 units, therefore, the length of P'Q' is ____________ units.
  44. 6(b)(iv)1 markThe area of triangle PQR is ____________ square units.
  45. 6(b)(v)2 marksThe area of P'Q'R' is ____________ times the area of triangle PQR which is ____________ square units.
  46. 7(a)2 marksComplete the table below to show the sales for EACH month.
  47. 7(b)(i)1 markBetween which TWO consecutive months was there the GREATEST increase in sales? ____________ and ____________
  48. 7(b)(ii)1 markBetween which TWO consecutive months was there the SMALLEST increase in sales? ____________ and ____________
  49. 7(b)(iii)2 marksWhat feature of the line graph enables you to infer that the increase in sales between two consecutive months was the greatest or the smallest?
  50. 7(c)2 marksCalculate the mean monthly sales for the period July to November 2014.
  51. 7(d)(i)1 markCalculate the sales, in dollars, for the month of December.
  52. 7(d)(ii)2 marksComplete the line graph to show the sales for December.
  53. 8(a)2 marksDraw Figure 4 of the sequence.
  54. 8(b)(i)2 marksComplete the row for Figure 4 in the table.
  55. 8(b)(ii)2 marksComplete the row for Number of Unit Triangles = 144 in the table.
  56. 8(b)(iii)2 marksComplete the row for Figure 25 in the table.
  57. 8(b)(iv)2 marksComplete the row for Figure n in the table.
  58. 9(a)(i)2 marksCalculate the percentage for a student who scores 60 marks
  59. 9(a)(ii)2 marksOn the graph sheet on page 27, plot a graph to show the information in (i).
  60. 9(a)(iii)1 markA candidate is awarded 95 marks on the examination. Use the graph drawn at (ii) to determine the candidate's percentage. Draw lines on your graph to show how the percentage was obtained. Percentage: ____________
  61. 9(a)(iv)2 marksA candidate is awarded a Grade A if her percentage is 85% or more. Use the graph drawn at (ii) to determine the minimum mark the candidate needs to be awarded a Grade A. Draw lines on your graph to show how the…
  62. 9(b)(i)2 marksEvaluate g(5).
  63. 9(b)(ii)2 marksWrite an expression in terms of x for f⁻¹(x).
  64. 9(b)(iii)4 marksWrite an expression for gf(x), in the form (x + a) (x + b), where a and b ∈ R.
  65. 10(a)(i)3 marksLabel the diagram to show • the distance 60 m • the angles of 35° and 42° • any right angle(s).
  66. 10(a)(ii)4 marksCalculate the length of the flagpole, giving your answer to the nearest metre.
  67. 10(b)(i)1 markOn the diagram show the bearing of 040°.
  68. 10(b)(ii)1 markCalculate the measure of ∠KLM.
  69. 10(b)(iii)3 marksCalculate the length, to the nearest kilometre, of KM.
  70. 10(b)(iv)2 marksCalculate the measure of ∠LKM to the nearest degree.
  71. 10(b)(v)1 markCalculate the bearing of M from K.
  72. 11(a)(i)2 marksCalculate the matrix product AB where A = [[1, 1], [2, 3]] and B = [[1, 2], [0, 1]]
  73. 11(a)(ii)2 marksShow that the matrix product of A and B is NOT commutative, that is, AB ≠ BA.
  74. 11(a)(iii)2 marksFind A⁻¹, the inverse of A.
  75. 11(a)(iv)2 marksGiven that M = [[2x, 2], [9, 3]], calculate the value(s) of x for which |M| = 0.
  76. 11(b)(i)1 markCalculate the value of |OR|.
  77. 11(b)(ii)2 marksExpress in the form [x, y], the vectors RS and ST. RS = ____________ ST = ____________
  78. 11(b)(iii)2 marksUsing the results of combining the vectors in (b) (ii) on page 33, justify that RS is parallel to ST and that RST is a straight line.

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