CSEC Mathematics · May/June 2004 · 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.

1. 1(a)(i)6 marksDetermine the exact value of 2.3² + 4.1².
2. 1(a)(ii)6 marksDetermine the exact value of 0.18 / 0.6 - 0.003.
3. 1(a)(iii)6 marksDetermine the exact value of (3 1/5 - 2 2/3) / (2/5).
4. 1(b)(i)2 marksWrite your answer in Part (a)(i) correct to one significant figure.
5. 1(b)(ii)2 marksWrite your answer in Part (a)(ii) in standard form.
6. 1(c)(i)4 marksCalculate the amount Mr Mitchell will receive at the end of the two-year period.
7. 1(c)(ii)4 marksCalculate the value of Mr Williams' land after a period of two years.
8. 2(a)(i)4 marksSimplify (x² - 1) / (x - 1).
9. 2(a)(ii)4 marksSimplify (4ab² + 2a²b) / (ab).
10. 2(b)2 marksExpress as a single fraction: 3p/2 + q/p.
11. 2(c)4 marksSolve for x, given 3x² - 7x + 2 = 0.
12. 3(a)(i)5 marksDraw a Venn diagram to represent this information.
13. 3(a)(ii)5 marksHow many members play both tennis and cricket?
14. 3(b)(i)a)6 marksUsing the eight scores, determine the mean.
15. 3(b)(i)b)6 marksUsing the eight scores, determine the median.
16. 3(b)(i)c)6 marksUsing the eight scores, determine the mode.
17. 3(b)(ii)6 marksOnly six scores are to be used. Which two scores may be omitted to leave the value of the median the same?
18. 4(a)(i)5 marksCalculate the value of t when m = 20 and n = 48.
19. 4(a)(ii)5 marksExpress m as subject of the formula t = (5m) / (12n).
20. 4(b)(i)7 marksCalculate correct to one decimal place the length of GF.
21. 4(b)(ii)7 marksCalculate correct to one decimal place the length of HD.
22. 4(b)(iii)7 marksCalculate correct to one decimal place the size of the angle HDE.
23. 5(a)(i)3 marksWrite down the coordinates of the point P.
24. 5(a)(ii)3 marksDraw a line segment PQ through the point, P, such that the gradient of PQ is -3/2.
25. 5(b)(i)4 marksDraw the reflection of quadrilateral A in the mirror line, labelled M₁. Label its image B.
26. 5(b)(ii)4 marksDraw the reflection of quadrilateral B in the mirror line, labelled M₂. Label its image C.
27. 5(c)3 marksComplete the sentence in part (c) on your answer sheet, describing FULLY the single geometric transformation which maps quadrilateral A onto quadrilateral C.
28. 6(a)1 markWhat was the charge for a plumbing job which took 20 minutes?
29. 6(b)(i)2 marksHow many minutes were spent completing repairs that cost $38.00?
30. 6(b)(ii)2 marksHow many minutes were spent completing repairs that cost $20.00?
31. 6(c)1 markWhat is the amount of the fixed charge?
32. 6(d)2 marksCalculate the gradient of the line.
33. 6(e)2 marksWrite down the equation of the line in terms of d and t.
34. 6(f)3 marksDetermine the length of time taken to complete a job for which the charge was $78.00.
35. 7(a)(i)a)6 marksCalculate the radius of the circle.
36. 7(a)(i)b)6 marksCalculate the circumference of the circle.
37. 7(a)(ii)6 marksCalculate the area enclosed by the square.
38. 7(b)(i)6 marksFind to the nearest km, the shortest distance between Rose Hall and South Port.
39. 7(b)(ii)6 marksDetermine the bearing of South Port from Spring Hall.
40. 8(a)2 marksWhat percent of the mixture using Recipe A is chocolate?
41. 8(b)2 marksBy showing suitable calculations, determine which of the two recipes, A or B, is richer in chocolate.
42. 8(c)2 marksIf the mixtures from Recipe A and Recipe B are combined, what is the percent of chocolate in the new mixture?
43. 8(d)(i)6 marksWhat is the cost of making 150 bottles of chocolate drink?
44. 8(d)(ii)6 marksWhat should be the selling price of each bottle of chocolate drink to make an overall profit of 20%?
45. 9(a)6 marksCalculate the values of m and n.
46. 9(b)(i)9 marksObtain an expression, in terms of x, for the area of rectangle AKLM.
47. 9(b)(ii)9 marksGiven that the area of rectangle AKLM is 60 cm², show that 2x² + 7x - 15 = 0.
48. 9(b)(iii)9 marksHence, calculate the value of x and state the length of AK and AM.
49. 10(a)(i)5 marksWrite TWO inequalities which satisfy these conditions.
50. 10(a)(ii)5 marksWrite TWO inequalities which satisfy these conditions.
51. 10(b)6 marksUsing a scale of 2 cm to represent 10 kg on each axis, draw the graph of the FOUR inequalities in (a)(i) and (a)(ii). On your graph, shade ONLY the region which satisfies all four inequalities.
52. 10(c)(i)4 marksUsing your graph, determine the number of kilograms of each type of nut the vendor must sell in order to make the maximum profit.
53. 10(c)(ii)4 marksCalculate the maximum profit.
54. 11(a)(i)a)4 marksCalculate the size of angle VZW, giving reasons for your answer.
55. 11(a)(i)b)4 marksCalculate the size of angle XYZ, giving reasons for your answer.
56. 11(b)(i)11 marksDraw a diagram to represent the information given below. Show clearly the north line in your diagram.
57. 11(b)(ii)11 marksCalculate, to the nearest kilometre, the actual distance GH.
58. 11(b)(iii)11 marksCalculate, to the nearest degree, the bearing of H from G.
59. 12(a)(i)7 marksExpress in fractional or surd form the value of cos θ.
60. 12(a)(ii)7 marksShow that the area of triangle CDE is 150√3 square units, where CD = 30 units and DE = 20 units.
61. 12(a)(iii)7 marksCalculate the length of the side EC.
62. 12(b)(i)8 marksCopy the sketch above of the earth and insert the points A and B on your diagram.
63. 12(b)(ii)a)8 marksCalculate, correct to the nearest kilometre, the radius of the circle of latitude 24° N.
64. 12(b)(ii)b)8 marksCalculate, correct to the nearest kilometre, the shortest distance between A and B, measured along the circle of latitude 24° N.
65. 13(a)(i)3 marksWrite as a column vector, in the form (x y), the vector OA.
66. 13(a)(ii)3 marksWrite as a column vector, in the form (x y), the vector CB.
67. 13(b)1 markCalculate |OA|, the magnitude of OA.
68. 13(c)(i)4 marksState two geometrical relationships between the line segments OA and CB.
69. 13(c)(ii)4 marksExplain why OABC is a parallelogram.
70. 13(d)(i)7 marksDetermine the position vector OM.
71. 13(d)(ii)7 marksDetermine the position vector ON. Hence, state one conclusion which can be made about the diagonals of the parallelogram OABC.
72. 14(a)(i)5 marksReflect triangle P in the y-axis. Label its image Q.
73. 14(a)(ii)5 marksDraw the line y = x and reflect triangle Q in this line. Label its image R.
74. 14(a)(iii)3 marksDescribe, in words, the single geometric transformation which maps triangle P onto triangle R.
75. 14(a)(iv)3 marksReflect triangle Q in the x-axis. Label its image S.
76. 14(a)(v)3 marksWrite down the 2 x 2 matrix for the transformation which maps triangle P onto triangle S.
77. 14(b)(i)a)4 marksWrite down the 2 x 2 matrix for a reflection in the y-axis.
78. 14(b)(i)b)4 marksWrite down the 2 x 2 matrix for a reflection in the line y = x.
79. 14(b)(ii)4 marksUsing the two matrices in b(i) above, obtain a SINGLE matrix for a reflection in the y-axis followed by a reflection in the line y = x.