CSEC Mathematics · January 2004 · 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.

1. 1(a)3 marksFind the exact value of 2 1/3 - 1 2/5 / 4/7, giving the answer as a fraction in its LOWEST terms.
2. 1(b)2 marksIf the price of the table is $250, what is the price of EACH chair?
3. 1(c)(i)5 marksCalculate the total hire purchase price of the suite.
4. 1(c)(ii)5 marksCalculate the extra cost of buying on hire purchase as a percentage of the cash price.
5. 2(a)(i)3 marksCalculate the value of 4p - qr.
6. 2(a)(ii)3 marksCalculate the value of 2r².
7. 2(b)(i)5 marksMake F the subject of the formula.
8. 2(b)(ii)5 marksThe temperature in London is 15°C. Use the formula derived in (i) above to convert this temperature to degrees Fahrenheit.
9. 2(c)4 marksSolve the following pair of simultaneous equations: 2x + 3y = 18; x + 5y = 23.
10. 3(a)(i)6 marksDraw a Venn diagram to represent the information above.
11. 3(a)(ii)a)6 marksList, using set notation, the members of the set P ∩ Q.
12. 3(a)(ii)b)6 marksList, using set notation, the members of the set (P ∪ Q)'.
13. 3(b)(i)4 marksCalculate the scale factor of the enlargement which maps triangle ABE onto triangle ACD.
14. 3(b)(ii)4 marksCalculate the area of triangle ACD, in cm², given that the area of triangle ABE is 18 cm².
15. 4(a)(i)6 marksHow long did it take the bus to travel from South Point to Bird Park?
16. 4(a)(ii)6 marksSouth Point is 80 km away from Bird Park. Calculate the speed of the bus, in km/h, along this section of the route.
17. 4(b)(i)5 marksCalculate, giving your answer correct to 3 significant figures, the area, in cm², of the cross section.
18. 4(b)(ii)5 marksCalculate, giving your answer correct to 3 significant figures, the volume, in cm³, of the prism.
19. 5(a)(i)3 marksCalculate g(25).
20. 5(a)(ii)3 marksCalculate gf(15).
21. 5(b)(i)10 marksCopy and complete the table below.
22. 5(b)(ii)10 marksUsing a scale of 2 cm to represent 1 unit on the x-axis and 1 cm to represent 1 unit on the y-axis, draw the graph of y = x² - 3x for -2 ≤ x ≤ 5.
23. 5(b)(iii)10 marksOn the same axes as (ii) above, draw the line y = x for -2 ≤ x ≤ 5.
24. 5(b)(iv)10 marksUse your graphs to determine the solution of the equation x² - 3x = x.
25. 6(a)(i)6 marksCalculate, giving your answer correct to 3 significant figures, the distance KL.
26. 6(a)(ii)6 marksCalculate, giving your answer correct to 3 significant figures, the bearing of Port L from Port K.
27. 6(b)(i)6 marksDraw the mirror line and label it M.
28. 6(b)(ii)6 marksWrite down the y intercept of the mirror line M.
29. 6(b)(iii)6 marksDetermine the equation of the mirror line M.
30. 7(a)4 marksCalculate the mean of the frequency distribution assuming that each mark within each interval has a value equal to the midpoint of the interval.
31. 7(b)2 marksCopy and complete the cumulative frequency table.
32. 7(c)(i)6 marksUsing the cumulative frequency curve on the answer sheet provided, find the median mark scored.
33. 7(c)(ii)6 marksUsing the cumulative frequency curve on the answer sheet provided, find the number of students who scored no more than 12 marks.
34. 7(c)(iii)6 marksUsing the cumulative frequency curve on the answer sheet provided, find the number of students who scored more than 8 but less than 18 marks.
35. 7(c)(iv)6 marksUsing the cumulative frequency curve on the answer sheet provided, find the probability that a student chosen at random would score no more than 24 marks.
36. 8(a)3 marksUsing ruler and compasses only, construct triangle PVY where each side is of length 6 cm.
37. 8(b)2 marksDraw lines on your diagram to sub-divide triangle PVY into nine identical equilateral triangles.
38. 8(c)2 marksThe table below shows how the number of unit lengths in each side of a figure is related to the number of basic triangles in that figure. Copy and complete the table.
39. 8(d)3 marksCalculate the area of the basic triangle in cm².
40. 9(a)(i)5 marksUsing the graph, determine the time at which the athlete left the training camp.
41. 9(a)(ii)5 marksUsing the graph, determine the distance from the camp to the park.
42. 9(a)(iii)5 marksUsing the graph, determine the length of time he spent at the park.
43. 9(a)(iv)5 marksUsing the graph, determine the speed of the athlete on his way to the park, in km/h.
44. 9(b)(i)3 marksDetermine the time at which the cyclist meets the athlete.
45. 9(b)(ii)3 marksDetermine the distance from the park to where the cyclist and the athlete meet.
46. 10(a)(i)4 marksWrite TWO inequalities to represent this information.
47. 10(a)(ii)4 marksWrite an inequality to represent this information.
48. 10(b)7 marksUsing a scale of 1 cm to represent 5 units on each axis, draw a graph of the THREE inequalities and label the region, R, which satisfies ALL of the inequalities.
49. 10(c)(i)7 marksWrite f(x) = 4x² - 7x + 3 in the form f(x) = a(x + b)² + c, where a, b and c are constants.
50. 10(c)(i)4 marksWrite an expression for the profit, P.
51. 10(c)(ii)4 marksDetermine the number of dresses and shirts that Mrs Singh should buy to make the maximum profit.
52. 10(c)(ii)a)7 marksState the minimum value of f(x).
53. 10(c)(ii)b)7 marksState the value of x for which the minimum occurs.
54. 10(c)(iii)4 marksCalculate the maximum profit.
55. 11(a)4 marksCalculate, to the nearest km, the SHORTEST distance between S and T, along the parallel of latitude.
56. 11(b)(i)11 marksCalculate, giving your answer correct to 2 decimal places, the radius of the circle.
57. 11(b)(ii)11 marksCalculate, giving your answer correct to 2 decimal places, the area of the minor sector AOB.
58. 11(b)(iii)11 marksCalculate, giving your answer correct to 2 decimal places, the area of the shaded region.
59. 12(a)(i)8 marksCalculate, giving reasons for your answers, the size of angle BEO.
60. 12(a)(ii)8 marksCalculate, giving reasons for your answers, the size of angle BCE.
61. 12(a)(iii)8 marksCalculate, giving reasons for your answers, the size of angle BAE.
62. 12(a)(iv)8 marksCalculate, giving reasons for your answers, the size of angle BOE.
63. 12(b)(i)7 marksUsing triangle MNT, show that the length of MT to the nearest metre, is 26 m.
64. 12(b)(ii)7 marksHence, calculate the height of the tower, TL.
65. 13(a)2 marksWrite in the form [x y] the position vectors of A, B and C.
66. 13(b)(i)4 marksWrite in the form [x y] the vector AB.
67. 13(b)(ii)4 marksWrite in the form [x y] the vector AC.
68. 13(b)(iii)4 marksWrite in the form [x y] the vector BC.
69. 13(c)5 marksShow by a vector method that triangle ABC is an isosceles triangle.
70. 13(d)4 marksDetermine the position vector of the point D, such that BD is parallel to AC and ABDC forms a parallelogram.
71. 14(a)2 marksCalculate the value of p.
72. 14(b)(i)5 marksExpress the pair of equations in the form AX = B, where A, X and B are matrices.
73. 14(b)(ii)5 marksDetermine the inverse of matrix A.
74. 14(b)(iii)5 marksEvaluate: A⁻¹B.
75. 14(c)(i)8 marksDescribe FULLY the transformation, V.
76. 14(c)(ii)8 marksDescribe FULLY the transformation, W.
77. 14(c)(iii)8 marksWrite the single matrix [[p, r], [q, p]], which represents the combined transformation, V followed by W.
78. 14(c)(iv)8 marksCalculate the image of the point (6,-4) under the combined transformation in (c) (iii) above.