CSEC Mathematics · May/June 2007 · Paper 2

74 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 marksUsing a calculator, or otherwise, determine the exact value of (3.7)² – (6.24 + 1.3).
2. 1(b)2 marksHow many teachers are there at the school?
3. 1(b)(ii)2 marksHow many students do NOT own personal computers?
4. 1(b)(iii)4 marksWhat fraction of the students in the school own play stations? Express your answer in its lowest terms.
5. 2(a)4 marksEvaluate 4 * 8.
6. 2(a)(ii)1 markEvaluate 2 * (4 * 8).
7. 2(b)2 marksSimplify, expressing your answer in its simplest form: (5p / 3q) ÷ (4p² / 9).
8. 2(c)5 marksWrite two equations in a and b to represent the information above.
9. 2(c)(ii)1 markCalculate the values of a and b.
10. 3(a)5 marksState what game(s) is/are played by Leo.
11. 3(a)(i)b)1 markState what game(s) is/are played by Mia.
12. 3(a)(i)c)1 markState what game(s) is/are played by Neil.
13. 3(a)(ii)1 markDescribe in words the members of the set H' ∩ S.
14. 3(b)(i)a)7 marksUsing a pencil, a ruler and a pair of compasses only, construct a triangle PQR in which QR = 8.5 cm, PQ = 6 cm and PR = 7.5 cm.
15. 3(b)(i)b)1 markConstruct a line PT such that PT is perpendicular to QR and meets QR at T.
16. 3(b)(ii)a)1 markMeasure and state the size of angle PQR.
17. 3(b)(ii)b)1 markMeasure and state the length of PT.
18. 4(a)(i)6 marksUsing the map of the golf course, find the distance, to the nearest m, from South Gate to East Gate.
19. 4(a)(ii)1 markUsing the map of the golf course, find the distance, to the nearest m, from North Gate to South Gate.
20. 4(a)(iii)1 markUsing the map of the golf course, find the area on the ground represented by 1 cm² on the map.
21. 4(a)(iv)1 markUsing the map of the golf course, find the actual area of the golf course, giving the answer in square metres.
22. 4(b)(i)5 marksCalculate the length of the edge AB, in cm.
23. 4(b)(ii)1 markCalculate the total surface area of the prism, in cm².
24. 5(a)2 marksWrite an equation in x, y and k to describe the inverse variation, where k is the constant of variation.
25. 5(b)(i)6 marksUsing the information in the table above, calculate the value of k, the constant of variation.
26. 5(b)(ii)1 markUsing the information in the table above, calculate the value of r.
27. 5(b)(iii)1 markUsing the information in the table above, calculate the value of f.
28. 5(c)4 marksDetermine the equation of the line which is parallel to the line y = 2x + 3 and passes through the coordinate (4,7).
29. 6(a)(i)a)5 marksWrite on your answer sheet the scale factor for the enlargement.
30. 6(a)(i)b)1 markWrite on your answer sheet the coordinates of the centre of the enlargement.
31. 6(a)(ii)1 markDraw and label the triangle L''M''N'' on your answer sheet.
32. 6(b)(i)6 marksCalculate, correct to one decimal place, the distance PR.
33. 6(b)(ii)1 markGiven that ∠QPR = 142°, state the bearing of R from P.
34. 7(a)2 marksCopy and complete the frequency table to represent this data.
35. 7(b)2 marksUsing the raw scores, determine the range for the data.
36. 7(c)6 marksUsing a scale of 2 cm to represent 5 seconds on the horizontal axis and a scale of 1 cm to represent 1 student on the vertical axis, draw a frequency polygon to represent the data. NOTE: An empty interval must be shown…
37. 7(d)2 marksTo qualify for the finals, a student must complete the race in less than 60 seconds. What is the probability that a student from this class will qualify for the finals?
38. 8(a)5 marksCopy and complete the following table, stating what fraction of the rectangle each part represents.
39. 8(b)2 marksWrite the parts in order of the size of their perimeters.
40. 8(c)(i)3 marksWhat is the area of the trapezium in square units?
41. 8(c)(ii)1 markSketch the trapezium clearly showing the outline of each of the three parts.
42. 9(a)(i)7 marksCalculate the value of g (-2).
43. 9(a)(ii)1 markWrite an expression for gf(x) in its simplest form.
44. 9(a)(iii)1 markFind the inverse function g⁻¹(x).
45. 9(b)(i)8 marksWrite an expression in the form ax² + bx + c for the area of the rectangle.
46. 9(b)(ii)1 markGiven that the area of the rectangle is 294 cm², determine the value of x.
47. 9(b)(iii)1 markHence, state the dimensions of the rectangle, in centimetres.
48. 10(a)2 marksWrite down the inequalities to represent conditions (2) and (3).
49. 10(b)2 marksDescribe, in words, the condition represented by the inequality x < 2y.
50. 10(c)7 marksUsing a scale of 2 cm to represent 10 units on both axes, draw the graphs of ALL FOUR inequalities represented in the table above.
51. 10(d)4 marksPlot the points A, B and C on your graph. Hence determine which of the three packets satisfy ALL the conditions.
52. 12(a)(i)6 marksCalculate the size of angle YXZ.
53. 12(a)(ii)1 markCalculate the area of the triangle YXZ, expressing your answer correct to one decimal place.
54. 12(a)(iii)1 markCalculate the area of the octagon.
55. 12(b)a)9 marksCalculate the size of angle TPQ, giving reasons for your answer.
56. 12(b)b)1 markCalculate the size of angle MTQ, giving reasons for your answer.
57. 12(b)c)1 markCalculate the size of angle TQS, giving reasons for your answer.
58. 12(b)d)1 markCalculate the size of angle SRQ, giving reasons for your answer.
59. 13(a)2 marksSketch the diagram above. Show the approximate positions of points R and S such that R is the mid-point of OK and S is a point on OM such that OS = (1/3)OM.
60. 13(b)(i)8 marksWrite down, in terms of k and m, the vector MK.
61. 13(b)(ii)1 markWrite down, in terms of k and m, the vector RM.
62. 13(b)(iii)1 markWrite down, in terms of k and m, the vector KS.
63. 13(b)(iv)1 markWrite down, in terms of k and m, the vector RS.
64. 13(c)5 marksL is the mid-point of RM. Using a vector method, prove that RS is parallel to KL.
65. 14(a)(i)7 marksFind 3A.
66. 14(a)(ii)1 markFind B⁻¹.
67. 14(a)(iii)1 markFind 3A + B⁻¹.
68. 14(a)(iv)1 markFind the value of a, b, c and d given that 3A + B⁻¹ = C.
69. 14(b)(i)a)8 marksDescribe in words, the geometric transformation J which maps EFGH onto E'F'G'H'.
70. 14(b)(i)b)1 markDescribe in words, the geometric transformation K which maps E'F'G'H' onto E''F''G''H''.
71. 14(b)(ii)a)1 markWrite the matrix which represents the transformation described above as J.
72. 14(b)(ii)b)1 markWrite the matrix which represents the transformation described above as K.
73. 14(b)(iii)1 markThe point P (6, 2) is mapped onto P' by the transformation J. State the co-ordinates of P'.
74. 14(b)(iv)1 markThe point Q (5, -4) is mapped onto Q' by the transformation K. State the co-ordinates of Q'.