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CSEC Mathematics · May/June 2006 · Paper 2

84 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 markswrite the answer exactly
  2. 1(a)(ii)1 markwrite the answer correct to two significant figures.
  3. 1(b)(i)6 marksCalculate the values of p and q
  4. 1(b)(ii)1 markCalculate the value of the Taxi after 2 years.
  5. 1(c)(i)2 marksCalculate the value of GUY 60 000 in US
  6. 1(c)(ii)2 marksCalculate the value of US 925 in EC .
  7. 2(a)3 marksSimplify (x-3)/3 - (x-2)/5
  8. 2(b)(i)a)1 markFactorise x²-5x
  9. 2(b)(i)b)1 markFactorise x²-81
  10. 2(b)(ii)3 marksSimplify (a²+4a)/(a²+3a-4)
  11. 2(c)(i)2 markswrite two equations in x and y to represent the information.
  12. 2(c)(ii)2 marksCalculate the cost of one cassette.
  13. 3(a)(i)2 marksGiving the reason for each step of your answer, calculate the size of ∠ LNK
  14. 3(a)(ii)2 marksGiving the reason for each step of your answer, calculate the size of ∠ NLM
  15. 3(a)(iii)2 marksGiving the reason for each step of your answer, calculate the size of ∠ KNM.
  16. 3(b)(i)1 markCopy and complete the Venn diagram to represent the information.
  17. 3(b)(ii)1 markWrite an expression in x for the number of students in the survey.
  18. 3(b)(iii)5 marksCalculate the value of x.
  19. 4(a)4 marksUsing a ruler, a pencil and a pair of compasses, construct the triangle ABC in which AB = 8 cm, ∠BAC = 60°, and AC = 5 cm (Credit will be given for a neat, clear diagram)
  20. 4(b)1 markMeasure and state the length of BC.
  21. 4(c)1 markFind the perimeter of ΔABC.
  22. 4(d)2 marksDraw on your diagram the line CD which is perpendicular to AB and meets AB at D.
  23. 4(e)2 marksDetermine the length of CD.
  24. 4(f)2 marksCalculate the area of ΔABC giving your answer to 1 decimal point.
  25. 5(a)2 marksvalues of a and b which define the domain of the graph
  26. 5(b)2 marksvalues of x for which x²-2x-3= 0
  27. 5(c)2 markscoordinates of the minimum point on the graph
  28. 5(d)2 markswhole number values of x for which x²-2x-3<1
  29. 5(e)3 marksgradient of f(x) = x²-2x-3 at x = 2.
  30. 6(a)2 marksCopy the diagram and show on the diagram, the distances x km, (x + 7) km and 13 km.
  31. 6(b)3 marksFrom the information on your diagram, write an equation in x which satisfies Pythagoras' Theorem. Show that the equation can be simplified to give x² + 7x - 60 = 0.
  32. 6(c)2 marksSolve the equation and find the distance GH.
  33. 6(d)4 marksDetermine the bearing of F from G.
  34. 7(a)1 markCopy and complete the mid-interval values column.
  35. 7(b)(i)3 marksCalculate an estimate of the mean gain in mass of the 100 cows. Hint: EACH of the 29 cows in the "10- 14" interval is assumed to have a mass of 12 kg.
  36. 7(b)(ii)5 marksOn your answer sheet, complete the drawing of the frequency polygon for the gain in mass of the cows.
  37. 7(c)2 marksCalculate the probability that a cow chosen at random from the experimental group gained 20 kg or more.
  38. 8(a)(i)2 marksOn the answer sheet provided, draw the next shape in the sequence
  39. 8(a)(ii)a)4 marksinsert appropriate values in columns 2 and 3 when n=4
  40. 8(a)(ii)b)1 markinsert appropriate values in columns 2 and 3 when n=7
  41. 8(b)(i)2 marksComplete the table by inserting appropriate values at r
  42. 8(b)(ii)2 marksComplete the table by inserting appropriate values at s
  43. 9(a)5 marksSolve the pair of simultaneous equations y = x + 2 and y = x².
  44. 9(b)(i)2 marksWrite an expression, in terms of l and x, for the length of the strip of wire.
  45. 9(b)(ii)2 marksShow that l = 13-2x.
  46. 9(b)(iii)2 marksShow that S = x² - 6x + 39.
  47. 9(b)(iv)4 marksCalculate the values of x for which S = 30.25.
  48. 10(i)2 marksWrite an inequality to represent this information.
  49. 10(ii)1 markWrite an inequality to represent this information.
  50. 10(iii)2 marksWrite an inequality to represent this information.
  51. 10(iv)a)5 marksUsing a scale of 2 cm to represent 10 vans on the x-axis and 2 cm to represent 10 cars on the y-axis, draw the graphs of the lines associated with the inequalities at (i), (ii) and (iii) above.
  52. 10(iv)b)1 markIdentify, by shading, the region which satisfies all three inequalities.
  53. 10(v)1 markWrite an expression in x and y for the total fees charged for parking x vans and y cars.
  54. 10(vi)1 markUsing your graph write down the coordinates of the vertices of the shaded region.
  55. 10(vii)2 marksCalculate the maximum fees charged.
  56. 11(a)(i)a)7 marksCopy and label the diagram clearly showing the distance 28 m
  57. 11(a)(i)b)1 markCopy and label the diagram clearly showing the angles of 40° and 54°
  58. 11(a)(i)c)1 markCopy and label the diagram clearly showing any right angles.
  59. 11(a)(ii)1 markCalculate the length of the antenna TW.
  60. 11(b)(i)8 marksCalculate, giving reasons for each step of your answer, ∠OCE
  61. 11(b)(ii)1 markCalculate, giving reasons for each step of your answer, ∠BAC
  62. 11(b)(iii)1 markCalculate, giving reasons for each step of your answer, ∠BOC
  63. 11(b)(iv)1 markCalculate, giving reasons for each step of your answer, ∠BDC.
  64. 12(a)(i)3 marksCalculate the length of the diagonal HF
  65. 12(a)(ii)2 marksCalculate the area of the parallelogram EFGH.
  66. 12(b)(i)a)2 marksCopy the sketch above, and draw and label two arcs to represent the Equator
  67. 12(b)(i)b)1 markCopy the sketch above, and draw and label two arcs to represent the Greenwich Meridian.
  68. 12(b)(ii)a)2 marksInsert the points Y and M on your diagram.
  69. 12(b)(ii)b)3 marksCalculate, correct to the nearest kilometre, the circumference of the circle of latitude 41°N.
  70. 12(b)(ii)c)3 marksCalculate the shortest distance between Y and M measured along the circle of latitude 41°N.
  71. 13(a)(i)1 markCopy and complete the diagram to show the point B such that OABC is a parallelogram
  72. 13(a)(ii)2 marksCopy and complete the diagram to show the vector u where u = OA + OC.
  73. 13(b)(i)1 markWrite as a column vector, in the form [x y], the vector OA
  74. 13(b)(ii)1 markWrite as a column vector, in the form [x y], the vector OC
  75. 13(b)(iii)2 marksWrite as a column vector, in the form [x y], the vector AC.
  76. 13(c)(i)3 marksdetermine the coordinates of G
  77. 13(c)(ii)5 marksprove, using a vector method, that A, G, and C lie on a straight line.
  78. 14(a)(i)3 marksCalculate the value of x.
  79. 14(a)(ii)2 marksfind M⁻¹.
  80. 14(a)(iii)2 marksShow that M⁻¹M = I.
  81. 14(b)(i)a)2 marksWrite in the form of a single 2 × 2 matrix, the coordinates of A and C
  82. 14(b)(i)b)2 marksWrite in the form of a single 2 × 2 matrix, the coordinates of A' and C'.
  83. 14(b)(ii)2 marksUsing matrices only, write an equation to represent the transformation of AC onto A'C'.
  84. 14(b)(iii)2 marksDetermine the values of p, q, r and s.

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