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CSEC Mathematics · May/June 2014 · Paper 2

71 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 mark5.25 ÷ 0.015
  2. 1(a)(ii)1 mark√6.5025
  3. 1(a)(iii)2 marks3.142 × 2.236² (correct to 3 significant figures)
  4. 1(b)(i)2 marksHow many buckets of gravel are needed for 4 buckets of cement?
  5. 1(b)(ii)a)3 marksIf 20 buckets of sand are used, how many buckets of Cement will be needed?
  6. 1(b)(ii)b)3 marksIf 20 buckets of sand are used, how many buckets of Gravel will be needed?
  7. 1(c)(i)2 marksWhat is the TOTAL hire purchase price of the laptop?
  8. 1(c)(ii)1 markHow much is saved by buying the laptop for cash?
  9. 2(a)3 marksx - 2 / 3 + x + 1 / 4
  10. 2(b)(i)1 markWhen 4 is added to a certain number the result is the same as halving the number and adding 10.
  11. 2(b)(ii)1 markSquaring a number and subtracting 6 gives the same result as doubling the number and adding 9.
  12. 2(c)(i)1 markUse information from the diagram to write a formula for y in terms of x.
  13. 2(c)(ii)1 markIf the number 4 is the input, what number would be the output?
  14. 2(c)(iii)1 markIf the number 8 was the output, what number was the input?
  15. 2(c)(iv)1 markReverse the formula written at (c) (i) above to write x in terms of y.
  16. 2(d)3 marks2x + 3y = 9; 3x - y = 8
  17. 3(a)(i)1 markHow many members are in the universal set, U?
  18. 3(a)(ii)1 markList the members of the subset A.
  19. 3(a)(iii)1 markList the members of the subset B.
  20. 3(a)(iv)3 marksDraw a Venn diagram to represent the relationships among A, B and U.
  21. 3(b)(i)a)3 marksa triangle PQR in which PQ = 8 cm, PR = 6 cm and angle P = 60°
  22. 3(b)(i)b)2 marksthe line segment RX which is perpendicular to PQ and meets PQ at X. [Note: Credit will be given for clearly drawn construction lines.]
  23. 3(b)(ii)1 markMeasure and state the size of angle QRX.
  24. 4(a)(i)1 markCopy and complete: 1 cm on the map represents ______ cm on the island.
  25. 4(a)(ii)1 markCopy and complete: An area of 1 cm² on the map represents an area of ______ cm² on the island.
  26. 4(a)(iii)1 markCopy and complete: Given that 1 km = 100 000 cm, a distance of 1 cm on the map represents a distance of ______ km on the island.
  27. 4(b)(i)1 markL and M are two tracking stations. State, in centimetres, the distance LM on the map.
  28. 4(b)(ii)2 marksCalculate the ACTUAL distance, in kilometres, from L to M on the island.
  29. 4(c)(i)2 marksThe area shaded on the map is a forest reserve. By counting squares estimate, in cm², the area of the forest reserve as shown on the map.
  30. 4(c)(ii)2 marksCalculate, in km², the ACTUAL area of the forest reserve.
  31. 5(a)(i)3 marksOn the answer sheet provided, draw triangle A'B'C', the image of triangle ABC, under an enlargement, centre O and scale factor 2.
  32. 5(a)(ii)3 marksTriangle A"B"C" is the image of triangle ABC, under a transformation, M. Describe completely the transformation, M.
  33. 5(b)(i)1 markDetermine the angle of elevation of T from P
  34. 5(b)(ii)2 marksDetermine the length of FP
  35. 5(b)(iii)3 marksDetermine the angle of elevation of T from Q.
  36. 6(a)(i)1 markDetermine the value of x.
  37. 6(a)(ii)1 markDetermine the value of y.
  38. 6(b)(i)1 markDetermine the gradient of the line MN
  39. 6(b)(ii)2 marksDetermine the equation of the line MN
  40. 6(b)(iii)2 marksDetermine the equation of the line parallel to MN, and passing through the origin.
  41. 6(c)2 marksOn the answer sheet provided, carefully draw the tangent line to the graph y = x² at the point (2, 4).
  42. 6(d)2 marksEstimate the gradient of the tangent to the curve at (2, 4).
  43. 7(a)4 marksCopy and complete the frequency table for the data shown above.
  44. 7(b)1 markState the modal number of books in the bags of the sample of students.
  45. 7(c)(i)2 marksthe TOTAL number of books
  46. 7(c)(ii)2 marksthe mean number of books per bag.
  47. 7(d)2 marksDetermine the probability that a student chosen at random has LESS THAN 4 books in his/her bag.
  48. 8(a)2 marksDraw Figure 4, the next figure in the sequence above.
  49. 8(b)4 marksComplete the table below by inserting the missing information at the rows numbered (i) and (ii).
  50. 8(c)2 marksWrite an expression in f for the number (n) of dots used in drawing the fth figure.
  51. 8(d)2 marksWhich figure in the sequence contains 145 dots?
  52. 9(a)(i)1 markState the value of x for which f(x) is undefined.
  53. 9(a)(ii)3 marksCalculate the value of gf(5).
  54. 9(a)(iii)3 marksFind f⁻¹(x).
  55. 9(b)(i)4 marksUsing 2 cm to represent 1 second on the x-axis and 1 cm to represent 10 metres on the y-axis, plot a graph to show the height of the ball during the first 6 seconds.
  56. 9(b)(ii)a)2 marksthe average speed of the ball during the first 2 seconds
  57. 9(b)(ii)b)2 marksthe speed of the ball when t = 3 seconds.
  58. 10(a)(i)2 marksCalculate, giving a reason for EACH step of your answer, the measure of: <BOE
  59. 10(a)(ii)2 marksCalculate, giving a reason for EACH step of your answer, the measure of: <OED
  60. 10(a)(iii)3 marksCalculate, giving a reason for EACH step of your answer, the measure of: <BFE
  61. 10(b)(i)2 marksCalculate the bearing of P from Q
  62. 10(b)(ii)3 marksCalculate the distance PR correct to 2 decimal places
  63. 10(b)(iii)3 marksCalculate the measure of <QPR to the nearest degree.
  64. 11(a)2 marksDetermine the value of p for which the matrix M does NOT have an inverse.
  65. 11(b)2 marksExpress the equations 4x - 2y = 0 and 2x + 3y = 4 in the form AX = B, where A, X and B are matrices.
  66. 11(c)(i)2 marksWhat term is used to describe OP?
  67. 11(c)(ii)a)1 markWrite OP in the form [a, b].
  68. 11(c)(ii)b)1 markWrite OQ in the form [a, b].
  69. 11(c)(ii)c)2 marksWrite PQ in the form [a, b].
  70. 11(c)(iii)3 marksGiven that OP = RQ, determine the coordinates of the point, R.
  71. 11(c)(iv)2 marksState the type of quadrilateral formed by PQRO. Justify your answer.

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