CSEC Mathematics · January 2013 · Paper 2

66 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, calculate the exact value of (2.67 x 4.1) - 1.3^2.
2. 1(b)(i)3 marksCalculate the TOTAL cost of airfare and hotel accommodation for 3 nights using the rates offered by Petty's Travel Club.
3. 1(b)(ii)2 marksCalculate, in US dollars, the cost of the trip for 3 nights as advertised by Angie's travel club.
4. 1(b)(iii)1 markState, giving a reason for your answer, which travel club (Petty's or Angie's) has the better offer.
5. 1(b)(iv)2 marksCalculate the cost of the trip for three nights BEFORE the sales tax was added.
6. 2(a)2 marksSolve for p: 2(p + 5) - 7 = 4p.
7. 2(b)(i)2 marksFactorize completely: 25m^2 - 1.
8. 2(b)(ii)2 marksFactorize completely: 2n^2 - 3n - 20.
9. 2(c)(i)2 marksWrite two equations in x and y to represent the above information.
10. 2(c)(ii)a)4 marksCalculate the mass of ONE lollipop.
11. 2(c)(ii)b)4 marksCalculate the mass of ONE toffee.
12. 3(a)(i)4 marksCopy and complete the Venn Diagram to represent the information about the awards given, showing the number of students in EACH subset.
13. 3(a)(ii)2 marksCalculate the value of x.
14. 3(b)(i)a)4 marksCalculate, giving a reason for your answer, the measure of ∠ BAC.
15. 3(b)(i)b)4 marksCalculate, giving a reason for your answer, the measure of ∠ AED.
16. 3(b)(ii)2 marksExplain why triangles ABC and ADE are similar but not congruent.
17. 4(a)(i)2 marksMake r the subject of the formula: r - h = rh.
18. 4(a)(ii)2 marksMake r the subject of the formula: V = πr^2h.
19. 4(b)(i)2 marksEvaluate: f^-1(19).
20. 4(b)(ii)2 marksEvaluate: gf(3).
21. 4(c)(i)1 markDetermine the gradient of GH.
22. 4(c)(ii)3 marksDetermine the equation of the line JK.
23. 5(a)(i)1 markMeasure and state, in centimetres, the length of RT as drawn on the diagram.
24. 5(a)(ii)2 marksMeasure and state, in degrees, the size of the angle that shows the bearing of T from R.
25. 5(a)(iii)2 marksCalculate the actual distance, in metres, on the playground that RT represents.
26. 5(b)(i)2 marksCalculate, in centimetres, the length of RM that should be used on the scale drawing.
27. 5(b)(ii)4 marksUsing a ruler and a pair of compasses, draw the line RM on the scale drawing.
28. 5(b)(iii)1 markMark and name the angle in the scale drawing that measures 120°.
29. 6(a)(i)1 markCalculate for the cylinder: The radius.
30. 6(a)(ii)2 marksCalculate for the cylinder: The circumference of the cross section.
31. 6(b)(i)2 marksState the values of a and b.
32. 6(b)(ii)2 marksHence, calculate the area of the curved surface of the cylinder.
33. 6(c)4 marksCalculate, correct to one decimal place, the height of water in the cylinder.
34. 7(a)(i)1 markState the modal class interval.
35. 7(a)(ii)1 markState the class interval in which a score of 19.4 would lie.
36. 7(b)(i)a)2 marksCopy and complete the table to show the class mid-points.
37. 7(b)(i)b)2 marksCopy and complete the table to show the values of "f x x".
38. 7(b)(ii)3 marksCalculate the mean score for the sample.
39. 7(c)1 markExplain why the value of the mean obtained in (b)(ii) is only an estimate of the true value.
40. 7(d)2 marksWhat is the probability that a student selected at random qualifies for the next round?
41. 8(a)2 marksIn your answer booklet, draw the FOURTH diagram in the sequence.
42. 8(b)(i)5 marksDetermine the value of a.
43. 8(b)(ii)5 marksDetermine the value of b.
44. 8(b)(iii)5 marksDetermine the value of c.
45. 8(c)3 marksWrite down, in terms of n, the number of squares in the n^th diagram of the sequence.
46. 9(a)(i)2 marksCopy and complete the table for the function.
47. 9(a)(ii)5 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 from your table, drawing a smooth curve through all points.
48. 9(b)(i)2 marksWrite f(x) = 3x^2 – 5x + 1 in the form a(x – h)^2 + k where a, h and k are constants to be determined.
49. 9(b)(ii)2 marksHence, or otherwise, determine the minimum value of f(x) and the value of x for which f(x) is a minimum.
50. 9(b)(iii)4 marksSolve the equation 3x^2 – 5x + 1 = 0 expressing your answer correct to two decimal places.
51. 10(a)(i)2 marksCalculate, giving reasons for your answer, the measure of ∠ MRQ.
52. 10(a)(ii)2 marksCalculate, giving reasons for your answer, the measure of ∠ PMR.
53. 10(a)(iii)3 marksCalculate, giving reasons for your answer, the measure of ∠ PMN.
54. 10(b)(i)a)2 marksCalculate the measure of angle ABC.
55. 10(b)(i)b)2 marksCalculate the area of triangle ABC.
56. 10(b)(ii)a)2 marksIn your answer booklet, draw the triangle TAB showing the angle of elevation.
57. 10(b)(ii)b)2 marksCalculate the height, TA, of the lighthouse.
58. 11(a)(i)1 markExpress MK in terms of u and v.
59. 11(a)(ii)2 marksExpress SL in terms of u and v.
60. 11(a)(iii)2 marksExpress OS in terms of u and v.
61. 11(b)3 marksDetermine the coordinates of P.
62. 11(c)(i)1 markWrite down a matrix, H, of size 2 x 2 which represents an enlargement of scale factor 3 about the origin.
63. 11(c)(ii)2 marksDetermine the coordinates of the point (5, -7) under the combined transformation, H followed by J.
64. 11(d)(i)1 markWrite down a matrix of size 3 x 2 which represents the sales for the two weeks.
65. 11(d)(ii)1 markWrite down a matrix of size 1 x 3 which represents the cost of the different models of cell phones.
66. 11(d)(iii)2 marksWrite down the multiplication of the two matrices which represents the superstore's takings from the sale of cell phones for each of the two weeks.