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CSEC Mathematics · January 2010 · Paper 2

82 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)3 marksUsing a calculator, or otherwise, calculate the exact value of 2.76/0.8 + 8.7^2.
  2. 1(b)(i)1 markCalculate his fixed salary for the year.
  3. 1(b)(ii)1 markCalculate the amount he received in commission for the year.
  4. 1(b)(iii)1 markCalculate his TOTAL income for the year.
  5. 1(c)(i)2 marksCalculate the number of cups of pancake mix he must use.
  6. 1(c)(ii)3 marksHow many pancakes did she make?
  7. 2(a)3 marksGiven that a = 6, b = -4 and c = 8, calculate the value of (a^2 + b) / (c - b).
  8. 2(b)(i)2 marksSimplify the expression: 3(x - y) + 4(x + 2y).
  9. 2(b)(ii)3 marksSimplify the expression: (4x^2 * 3x^4) / (6x^3).
  10. 2(c)(i)3 marksSolve the inequality x - 3 < 3x - 7.
  11. 2(c)(ii)1 markDetermine the SMALLEST value of x that satisfies the inequality in (c)(i) above.
  12. 3(a)(i)4 marksDraw a Venn diagram to represent this information.
  13. 3(a)(ii)a)1 markList the members of the set T ∩ E.
  14. 3(a)(ii)b)1 markList the members of the set (T ∪ E)'.
  15. 3(b)(i)3 marksConstruct, accurately, the triangle ABC shown below, where AC = 6 cm, ∠ACB = 60°, ∠CAB = 60°.
  16. 3(b)(ii)2 marksComplete the diagram to show the kite, ABCD, in which AD = 5 cm.
  17. 3(b)(iii)1 markMeasure and state the size of ∠DAC.
  18. 4(a)(i)2 marksCalculate the value of x.
  19. 4(a)(ii)3 marksCalculate the value of θ.
  20. 4(b)(i)1 markMeasure and state, in centimetres, the distance from S to F on the map.
  21. 4(b)(ii)2 marksCalculate the distance, in metres, from S to F on the ACTUAL playing field.
  22. 4(b)(iii)a)3 marksCalculate his average speed in m/s, giving your answer correct to 3 significant figures.
  23. 4(b)(iii)b)3 marksCalculate his average speed in km/h, giving your answer correct to 3 significant figures.
  24. 5(a)3 marksA straight line passes through the point T(4,1) and has a gradient of 3/5. Determine the equation of this line.
  25. 5(b)(i)3 marksUsing a scale of 1 cm to represent 1 unit on both axes, draw the triangle ABC with vertices A(2,3), B(5,3) and C(3,6).
  26. 5(b)(ii)1 markOn the same axes used in (b)(i), draw and label the line y = 2.
  27. 5(b)(iii)2 marksDraw the image of triangle ABC under a reflection in the line y = 2. Label the image A'B'C'.
  28. 5(b)(iv)1 markDraw a new triangle A''B''C'' with vertices A''(-7,4), B''(-4,4) and C''(-6,7).
  29. 5(b)(v)2 marksName and describe the single transformation that maps triangle ABC onto triangle A''B''C''.
  30. 6(a)2 marksCopy and complete the frequency table to represent this data.
  31. 6(b)5 marksUsing a scale of 2 cm to represent 5 km on the horizontal axis and a scale of 1 cm to represent 1 student on the vertical axis, draw a histogram to represent the data.
  32. 6(c)2 marksCalculate the probability that a student chosen at random from this class recorded the distance travelled to school as 26 km or more.
  33. 6(d)2 marksWhich average, mean, mode or median, is MOST appropriate for estimating the cost of the service? Give a reason for your answer.
  34. 7(i)1 markUsing the graph above, determine the value of f(x) when x = 0.
  35. 7(ii)2 marksUsing the graph above, determine the values of x when f(x) = 0.
  36. 7(iii)2 marksUsing the graph above, determine the coordinates of the maximum point.
  37. 7(iv)2 marksUsing the graph above, determine the equation of the axis of symmetry.
  38. 7(v)2 marksUsing the graph above, determine the values of x when f(x) = 5.
  39. 7(vi)2 marksUsing the graph above, determine the interval within which x lies when f(x) > 5. Write your answer in the form a < x < b.
  40. 8(a)(i)2 marksDetermine the value of x.
  41. 8(a)(ii)2 marksDetermine the value of y.
  42. 8(a)(iii)2 marksDetermine the value of z.
  43. 8(b)2 marksWrite down an expression for S in terms of n, where S represents the number of sticks used to make a pattern of n hexagons.
  44. 8(c)2 marksDetermine the value of h.
  45. 9(a)(i)3 marksExpress v in terms of E and m.
  46. 9(a)(ii)2 marksDetermine the value of v when E = 45 and m = 13.
  47. 9(b)(i)3 marksWrite g(x) in the form a(x + b)^2 + c, where a, b and c ∈ R.
  48. 9(b)(ii)4 marksSolve the equation g(x) = 0, writing your answer(s) correct to 2 decimal places.
  49. 9(b)(iii)a)3 marksCopy the sketch and state the y-coordinate of A.
  50. 9(b)(iii)b)3 marksCopy the sketch and state the x-coordinate of C.
  51. 9(b)(iii)c)3 marksCopy the sketch and state the x and y-coordinates of B.
  52. 10(a)(i)2 marksWrite an inequality to represent the given condition.
  53. 10(a)(ii)2 marksWrite an inequality to represent this condition.
  54. 10(b)(i)4 marksUsing a scale of 2 cm on the x-axis to represent 5 small pizzas and 2 cm on the y-axis to represent 5 large pizzas, draw the graphs of the lines associated with the inequalities at (a)(i) and (a)(ii) above.
  55. 10(b)(ii)1 markShade the region which is defined by ALL of the following combined: the inequalities written at (a)(i) and (a)(ii), the inequalities x ≥ 0 and y ≥ 0.
  56. 10(b)(iii)2 marksUsing your graph, state the coordinates of the vertices of the shaded region.
  57. 10(c)(i)1 markWrite an expression in x and y for the TOTAL profit made on the sale of the pizzas.
  58. 10(c)(ii)3 marksUse the coordinates of the vertices given at (b)(iii) to determine the MAXIMUM profit.
  59. 11(a)(i)2 marksShow that angle PRQ = 126°.
  60. 11(a)(ii)3 marksCalculate the distance PQ, giving your answer to the nearest metre.
  61. 11(b)(i)4 marksCopy and complete the diagram to show the pole SK and the angles of elevation of S from L and M.
  62. 11(b)(ii)a)6 marksCalculate, correct to ONE decimal place, the length of KL.
  63. 11(b)(ii)b)6 marksCalculate, correct to ONE decimal place, the length of LM.
  64. 12(a)(i)2 marksCalculate, giving reasons for your answer, the measure of angle GFH.
  65. 12(a)(ii)3 marksCalculate, giving reasons for your answer, the measure of angle GDE.
  66. 12(a)(iii)2 marksCalculate, giving reasons for your answer, the measure of angle DEF.
  67. 12(b)(i)3 marksCalculate the area of triangle GCH.
  68. 12(b)(ii)3 marksCalculate the area of the minor sector bounded by arc GH and radii GC and HC.
  69. 12(b)(iii)2 marksCalculate the area of the shaded segment.
  70. 13(a)(i)a)3 marksExpress the vector OB in the form [a b].
  71. 13(a)(i)b)3 marksExpress the vector OA + OB in the form [a b].
  72. 13(a)(ii)2 marksDetermine the values of x and y.
  73. 13(b)(i)a)1 markWrite an expression for vector HF in terms of u and/or v.
  74. 13(b)(i)b)2 marksWrite an expression for vector MF in terms of u and/or v.
  75. 13(b)(i)c)2 marksWrite an expression for vector OH in terms of u and/or v.
  76. 13(b)(ii)2 marksShow that vector OG = (3/5)(2v + u).
  77. 13(b)(iii)3 marksHence, prove that O, G, and H lie on a straight line.
  78. 14(a)3 marksEvaluate L - N^2.
  79. 14(b)2 marksCalculate the values of x for which M is singular.
  80. 14(c)3 marksCalculate the values of p and q.
  81. 14(d)3 marksDetermine the values of r and s.
  82. 14(e)4 marksDetermine the coordinates of the image of (8,5) under the combined transformation, R followed by T.

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