CSEC Mathematics · May/June 2005 · Paper 2

76 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)3 marksCalculate the exact value of [2\frac{1}{2}]^2 - 5\frac{1}{3}, expressing your answer as a common fraction.
2. 1(a)(ii)2 marksCalculate the exact value of \sqrt{0.16} + 0.26.
3. 1(b)(i)3 marksHow much was Kim charged?
4. 1(b)(ii)2 marksCalculate the number of hours for which he was billed.
5. 1(b)(iii)2 marksWhat is Chris' total bill?
6. 2(a)3 marksExpress \frac{2-b}{b} + \frac{2+b}{4b} as a single fraction in its simplest form.
7. 2(b)(i)2 marksFactorise completely 2m^2 - 18.
8. 2(b)(ii)2 marksFactorise completely 3pq^2 - pq + 3rq - r.
9. 2(c)(i)2 marksWrite an expression in x for the total mass of the jar and the marbles.
10. 2(c)(ii)3 marksCalculate the value of x if the total mass of the jar and the marbles is 1100 grams.
11. 3(a)(i)2 marksList the members of the set A.
12. 3(a)(ii)3 marksDescribe the set B using set builder notation.
13. 3(b)4 marksDraw a Venn diagram to represent U, A and B, showing the elements of each set.
14. 3(c)(i)3 marksList the members of A \cap B.
15. 3(c)(ii)3 marksList the members of (A \cup B)'.
16. 3(c)(iii)3 marksList the members of A' \cap B.
17. 4(a)(i)1 markShow that QV = 20 cm.
18. 4(a)(ii)3 marksState the values in centimetres, of a, b and c.
19. 4(a)(iii)4 marksCalculate the total surface area of the wedge.
20. 4(b)(i)2 marksPerform a reflection of the quadrilateral EFGH in the line y = x. Label the images of E, F, G, H as E', F', G', H' respectively.
21. 4(b)(ii)2 marksOn the same diagram, on your answer sheet, draw E''F''G''H'', the image of EFGH after a translation by the vector \begin{pmatrix} -6 \\ 1 \end{pmatrix}.
22. 5(a)(i)4 marksUsing a scale of 1 cm to represent 10 metres, draw the triangle KLM.
23. 5(a)(ii)a)4 marksMeasure the angle MKL.
24. 5(a)(ii)b)4 marksState the bearing of L from K.
25. 5(a)(ii)c)4 marksDetermine the distance ML, in metres.
26. 5(b)(i)2 marksWrite this equation in the form y = mx + c.
27. 5(b)(ii)2 marksDetermine the equation of the straight line that is parallel to the line 3y - 2x = 6 and passes through (0, 0).
28. 6(i)2 marksCopy and complete the frequency table to represent the data shown in the bar graph.
29. 6(ii)2 marksHow many students were there in the class?
30. 6(iii)2 marksHow many students studied less than five subjects?
31. 6(iv)2 marksHow many students studied at least five subjects?
32. 6(v)1 markWhich of these measures (mean, median, mode) is the most suitable average to describe the number of subjects studied by Form 5 students? Give ONE reason for your choice.
33. 7(a)(i)3 marksCalculate the exact value of 16^{1/2}.
34. 7(a)(ii)3 marksCalculate the exact value of 25^{3/2}.
35. 7(a)(iii)3 marksCalculate the exact value of 2^{-3}.
36. 7(b)(i)4 marksEvaluate h(0), g(-3) and hg(-3).
37. 7(b)(ii)3 marksObtain an expression for g^{-1}(x).
38. 8(a)2 marksHow many points must Adam exchange for these items?
39. 8(b)(i)2 marksList TWO of the three sets of gifts she can choose.
40. 8(b)(ii)2 marksShow why it is NOT possible for her to select a yoyo as one of her gifts.
41. 8(b)(iii)4 marksWhat combination of items will give her the maximum profit?
42. 9(a)(i)2 marksCopy and complete the table of values for the function.
43. 9(a)(ii)2 marksState the range of f(x) in the form a \le y \le b, where a and b are constants and y = f(x).
44. 9(b)5 marksUsing a scale of 4 cm to represent 1 unit on the x-axis and 1 cm to represent 1 unit on the y-axis, draw the graph of the function, f(x) = \frac{12}{x^2}.
45. 9(c)(i)2 marksEstimate the value of x for which f(x) = 7. Draw lines on your graph to show how you obtained your estimated value.
46. 9(c)(ii)4 marksOn your graph, draw a tangent to the curve at the point where x = 2. Extend the tangent to intersect the x and y axes. Using your tangent, estimate the gradient of f(x) at x = 2.
47. 10(a)6 marksFind the values of (x, y) for which y = 2x + 5 and xy - 3y = 21.
48. 10(b)(i)1 markState the interval of time when the velocity was constant.
49. 10(b)(ii)a)4 marksCalculate the acceleration of the aircraft during the first 10 seconds.
50. 10(b)(ii)b)4 marksCalculate the acceleration of the aircraft when t = 50 seconds.
51. 10(b)(iii)4 marksCalculate the total distance travelled over the period of 60 seconds.
52. 11(a)2 marksCopy the diagram, showing clearly the given bearings.
53. 11(b)(i)1 markCalculate the size of angle RTW.
54. 11(b)(ii)3 marksCalculate the distance RW, to the nearest metre.
55. 11(b)(iii)3 marksCalculate the size of angle TRW.
56. 11(b)(iv)3 marksCalculate the area of triangle RTW.
57. 11(c)3 marksCalculate the area of the sector TRS.
58. 12(a)(i)a)1 markUsing the graph, find the value of f(x) when x = 22.5°.
59. 12(a)(i)b)2 marksUsing the graph, find the values of x for which f(x) = 0.
60. 12(a)(i)c)1 markUsing the graph, draw the line f(x) = 2.
61. 12(a)(ii)3 marksUsing the two graphs, solve the equation 2 cos x = 1.
62. 12(b)(i)2 marksState why LMNS is a rectangle.
63. 12(b)(ii)a)6 marksCalculate the size of angle LNS.
64. 12(b)(ii)b)6 marksCalculate the size of angle LKS.
65. 12(b)(ii)c)6 marksCalculate the size of angle LOS.
66. 13(i)3 marksFind \vec{OA} and \vec{BC}.
67. 13(ii)a)3 marksFind \vec{AD}.
68. 13(ii)b)3 marksFind the coordinates of E.
69. 13(iii)3 marksShow that BC is parallel to DE and is twice the length of DE.
70. 13(iv)3 marksFind the position vector \vec{OF}.
71. 14(a)(i)2 marksWrite down a 2 x 3 matrix, A, to represent this information.
72. 14(a)(ii)1 markWrite down a 1 x 2 matrix, B, to represent this information.
73. 14(a)(iii)3 marksCalculate the matrix product BA. What does the product BA represent?
74. 14(a)(iv)a)2 marksWrite the total profit made as a product of two matrices.
75. 14(a)(iv)b)2 marksCalculate the total profit made on the transaction.
76. 14(b)5 marksDetermine the values p, q, r and s.