CSEC Mathematics · January 2012 · Paper 2

71 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 marksUsing a calculator, or otherwise, calculate the EXACT value of (3 1/4)^2 ÷ 3 1/2, expressing your answer as a fraction.
2. 1(a)(ii)3 marksCalculate √0.0529 + 0.216, expressing your answer in standard form.
3. 1(b)(i)1 markCalculate the typist's basic weekly wage.
4. 1(b)(ii)1 markCalculate the overtime wage for ONE hour of overtime work.
5. 1(b)(iii)2 marksCalculate the wage she would earn for overtime if she worked for a TOTAL of 52 hours during a given week.
6. 1(b)(iv)2 marksCalculate the number of overtime hours she must work during a given week to earn a TOTAL wage of $1440.
7. 2(a)3 marksSolve the pair of simultaneous equations: 3x + 2y = 13 and x - 2y = -1.
8. 2(b)(i)1 markFactorise completely x² - 16.
9. 2(b)(ii)2 marksFactorise completely 2x² - 3x + 8x - 12.
10. 2(c)(i)a)1 markWrite in terms of x, the number of tickets for children.
11. 2(c)(i)b)1 markWrite in terms of x, the amount spent on tickets for adults.
12. 2(c)(i)c)1 markWrite in terms of x, the amount spent on tickets for children.
13. 2(c)(ii)1 markShow that the TOTAL amount spent on the 28 tickets is $(15x + 420).
14. 2(c)(iii)2 marksGiven that the cost of the 28 tickets was $660, calculate the number of adult tickets bought by the company.
15. 3(a)(i)1 markList the members of the set A.
16. 3(a)(ii)1 markList the members of the set B.
17. 3(a)(iii)3 marksDraw a Venn diagram to represent the sets A, B and U.
18. 3(b)(i)a)4 marksUsing a pair of compasses, a ruler and a pencil, construct a triangle CDE in which DE = 10 cm, DC = 8 cm and ∠CDE = 45°.
19. 3(b)(i)b)2 marksUsing a pair of compasses, a ruler and a pencil, construct a line, CF, perpendicular to DE such that F lies on DE.
20. 3(b)(ii)1 markUsing a protractor, measure and state the size of ∠ DCE.
21. 4(a)(i)1 markHow long did the bus spend at Chagville?
22. 4(a)(ii)1 markHow long did the bus take to travel from Belleview to Chagville?
23. 4(a)(iii)2 marksCalculate, in kilometres, the distance from Belleview to Chagville.
24. 4(b)3 marksWhat is the height of the water in the bucket?
25. 4(c)(i)1 markState, in terms of h, the area of the shaded face of the cuboid.
26. 4(c)(ii)1 markWrite an expression, in terms of h, for the volume of the cuboid.
27. 4(c)(iii)2 marksIf the volume of the cuboid is 286 cm³ calculate the height, h, of the cuboid.
28. 5(a)(i)4 marksCalculate, giving reasons for your answers, the measure of ∠ MLP.
29. 5(a)(ii)4 marksCalculate, giving reasons for your answers, the measure of ∠ LJK.
30. 5(a)(iii)4 marksCalculate, giving reasons for your answers, the measure of ∠ JKL.
31. 5(a)(iv)4 marksCalculate, giving reasons for your answers, the measure of ∠ KLJ.
32. 5(b)(i)2 marksState the coordinates of P and Q.
33. 5(b)(ii)2 marksDescribe fully the transformation that maps triangle PQR onto triangle P'Q'R'.
34. 5(b)(iii)2 marksWrite down the coordinates of the images of P and Q under the translation (3, -6).
35. 6(a)2 marksCopy and complete the table.
36. 6(b)4 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, plot the points whose x and y values are recorded in your table, and draw a smooth curve through your points.
37. 6(c)2 marksUsing your graph, estimate the value of y when x = 3.5. Show on your graph how the value was obtained.
38. 6(d)(i)1 markWrite the equation of the axis of symmetry of the graph.
39. 6(d)(ii)1 markEstimate the minimum value of the function y.
40. 6(d)(iii)1 markState the values of the solutions of the equation: x² – 2x – 3 = 0.
41. 7(a)3 marksCopy and complete the frequency table for the data in the sample.
42. 7(b)(i)1 markDetermine the modal class interval.
43. 7(b)(ii)2 marksDetermine the number of seedlings in the sample.
44. 7(b)(iii)4 marksDetermine the mean height of the seedlings.
45. 7(b)(iv)2 marksDetermine the probability that a seedling chosen at random has a height that is GREATER than 30 cm.
46. 8(a)2 marksOn your answer sheet, draw Figure 4, the FOURTH shape in the pattern.
47. 8(b)(i)4 marksComplete the table for Figure 4.
48. 8(b)(ii)4 marksComplete the table for Figure 10.
49. 8(c)2 marksWhich figure in the sequence uses 106 straws?
50. 8(d)2 marksObtain an expression in n, for the total number of straws used in the nth pattern.
51. 9(a)(i)2 marksMake x the subject of the formula y = (2x+3)/(x-4).
52. 9(a)(ii)2 marksHence, determine the inverse of f(x) = (2x+3)/(x-4), where x ≠ 4.
53. 9(a)(iii)2 marksFind the value of x for which f(x) = 0.
54. 9(b)(i)2 marksState the other TWO inequalities which define the shaded region.
55. 9(b)(ii)3 marksIdentify the three pairs of (x, y) values for which p has a maximum or a minimum value.
56. 9(b)(iii)4 marksWhich pair of (x, y) values makes p a maximum? Justify your answer.
57. 10(a)(i)2 marksDetermine the size of angle AOB.
58. 10(a)(ii)3 marksCalculate, to the nearest whole number, the area of the hexagon.
59. 10(b)(i)2 marksCopy the diagram. Show the angle of elevation, 28° and ONE right angle.
60. 10(b)(ii)a)2 marksCalculate, giving your answer to 2 significant figures, the measure of PL.
61. 10(b)(ii)b)3 marksCalculate, giving your answer to 2 significant figures, the measure of KM.
62. 10(b)(ii)c)3 marksCalculate, giving your answer to 2 significant figures, the angle of elevation of P from M.
63. 11(a)(i)a)1 markWrite as a column vector, in the form (x, y), OA.
64. 11(a)(i)b)1 markWrite as a column vector, in the form (x, y), OB.
65. 11(a)(i)c)2 marksWrite as a column vector, in the form (x, y), BA.
66. 11(a)(ii)a)1 markWrite as a column vector in the form (x, y), BG.
67. 11(a)(ii)b)1 markWrite as a column vector in the form (x, y), OG.
68. 11(b)(i)2 marksEvaluate L + 2M.
69. 11(b)(ii)2 marksEvaluate LM.
70. 11(c)(i)2 marksFind Q⁻¹.
71. 11(c)(ii)3 marksUsing a matrix method, find the values of x and y in the equation (4 2; 1 1) (x; y) = (8; 3).