CSEC Mathematics · January 2009 · 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)3 marksCalculate the EXACT value of 3 3/4 / (2 1/5 - 1 2/3), giving your answer as a fraction.
2. 1(b)(i)2 marksKaren exchanged BDS2 000.00 and received EC2 700.00. Calculate the value of one BDS in EC.
3. 1(b)(ii)2 marksIf Karen exchanged EC432.00 for BDS, calculate the amount of BDS$ which Karen would receive.
4. 1(c)4 marksCalculate the TOTAL amount of money in the account at the end of two years.
5. 2(a)3 marksSimplify, expressing your answer as a single fraction: 2m/n - 5m/(3n).
6. 2(b)1 markIf a * b = a² - b, evaluate 5 * 2.
7. 2(c)2 marksFactorize completely 3x - 6y + x² - 2xy.
8. 2(d)(i)2 marksState, in terms of x, the length of EACH of the pieces.
9. 2(d)(ii)1 markWrite an expression, in terms of x, to represent the sum of the lengths of the three pieces of drinking straw.
10. 2(d)(iii)3 marksHence, calculate the value of x.
11. 3(a)(i)1 markCopy the Venn diagram shown below.
12. 3(a)(ii)2 marksShow on your Venn diagram the information relating to the students in Form 5.
13. 3(a)(iii)3 marksCalculate the number of students who study BOTH Physical Education and Music.
14. 3(b)(i)3 marksCalculate, in metres, the length of MK.
15. 3(b)(ii)3 marksCalculate, in metres, the length of JK.
16. 4(a)2 marksState the coordinates of P and Q.
17. 4(b)(i)2 marksDetermine the gradient of the line segment PQ.
18. 4(b)(ii)2 marksDetermine the equation of the line segment PQ.
19. 4(c)2 marksThe point (-8, t) lies on the line segment PQ. Determine the value of t.
20. 4(d)3 marksDetermine the equation of AB in the form y = mx + c.
21. 5(a)2 marksCalculate the volume in cubic centimetres, of ONE large cereal box.
22. 5(b)4 marksCalculate the total surface area of ONE large cereal box.
23. 5(c)(i)2 marksCalculate the volume of ONE small cereal box.
24. 5(c)(ii)2 marksIf the height of a small box is 20 cm, list TWO different pairs of values which the company can use for the length and width of a small box.
25. 6(a)6 marksUsing a ruler, a pencil and a pair of compasses only, construct the rectangle.
26. 6(b)(i)2 marksState, in the form (x y), the vector which represents the translation.
27. 6(b)(ii)a)4 marksFind and label on your answer sheet the point G, the centre of the enlargement. Show your method clearly.
28. 6(b)(ii)b)1 markState the coordinates of G.
29. 6(b)(ii)c)1 markState the scale factor of the enlargement.
30. 7(a)2 marksCopy and complete the table to show the cumulative frequency for the distribution.
31. 7(b)(i)5 marksUsing a scale of 1 cm to represent 5 marks on the horizontal axis and 1 cm to represent 5 students on the vertical axis, draw the cumulative frequency curve for the scores.
32. 7(b)(ii)1 markWhat assumption have you made in drawing your curve through the point (0,0)?
33. 7(c)2 marksUse your graph to determine the number of students who passed the test.
34. 7(d)2 marksWhat is the probability that a student chosen at random had a mark less than or equal to 30?
35. 8(a)2 marksDraw the fourth diagram in the sequence.
36. 8(b)4 marksComplete the table by inserting the missing values at the rows marked (i) and (ii).
37. 8(c)(i)1 markHow many dots are in the sixth diagram of the sequence?
38. 8(c)(ii)1 markHow many line segments are in the seventh diagram of the sequence?
39. 8(c)(iii)2 marksWrite the rule which shows how l is related to d.
40. 9(a)3 marksMake t the subject of the formula P/2 = sqrt((t+r)/g).
41. 9(b)(i)3 marksExpress the function f(x) = 2x² - 4x - 13 in the form f(x) = a(x + h)² + k.
42. 9(b)(ii)4 marksHence, or otherwise, determine the values of x at which the graph cuts the x-axis.
43. 9(b)(iii)2 marksHence, or otherwise, determine the interval for which f(x) ≤ 0.
44. 9(b)(iv)1 markHence, or otherwise, determine the minimum value of f(x).
45. 9(b)(v)2 marksHence, or otherwise, determine the value of x at which f(x) is a minimum.
46. 10(a)(i)1 markCalculate f(6).
47. 10(a)(ii)1 markFind f⁻¹(x).
48. 10(a)(iii)3 marksShow that fg(2) = fg(-2) = 0.
49. 10(b)(i)1 markFor how many minutes was the train at rest at B?
50. 10(b)(ii)3 marksDetermine the average speed of the train, in km/h, on its journey from A to B.
51. 10(b)(iii)3 marksCalculate the time, in minutes, taken for the train to travel from B to C.
52. 10(b)(iv)3 marksOn your answer sheet, draw the line segment which describes the journey of the train from B to C.
53. 11(a)(i)1 markCopy and complete the table for the graph of y = (1/2)tan x, for 10° ≤ x ≤ 60°.
54. 11(a)(ii)4 marksUsing a scale of 2 cm to represent 10° (10 degrees) on the horizontal axis and 10 cm to represent 1 unit on the vertical axis, plot the values from the table and draw a smooth curve through your points.
55. 11(a)(iii)1 markUse your graph to estimate the value of x when y = 0.7.
56. 11(b)(i)2 marksCalculate, giving reasons for your answer, the size of angle OAE.
57. 11(b)(ii)3 marksCalculate, giving reasons for your answer, the size of angle AOB.
58. 11(b)(iii)2 marksCalculate, giving reasons for your answer, the size of angle ACB.
59. 11(b)(iv)2 marksCalculate, giving reasons for your answer, the size of angle ADB.
60. 12(a)(i)2 marksCalculate the length of UW.
61. 12(a)(ii)2 marksCalculate the size of the angle UVW.
62. 12(a)(iii)2 marksCalculate the area of triangle TUW.
63. 13(a)(i)1 markWrite as a column vector, in the form (x y), OP.
64. 13(a)(ii)1 markWrite as a column vector, in the form (x y), OQ.
65. 13(b)(i)2 marksExpress QR as a vector in the form (x y).
66. 13(b)(ii)1 markUsing a vector method, show that OP is parallel to QR.
67. 13(b)(iii)2 marksDetermine the magnitude of the vector PR.
68. 13(c)(i)2 marksWrite QS as a column vector, in terms of a and b.
69. 13(c)(ii)3 marksGiven that QS = OP, calculate the value of a and the value of b.
70. 13(c)(iii)3 marksUsing a vector method, show that OPSQ is a parallelogram.
71. 14(a)3 marksCalculate the matrix product 3AB.
72. 14(b)(i)2 marksState the effect of V on triangle ABC.
73. 14(b)(ii)3 marksDetermine the 2 x 2 matrix that represents the combined transformation of V followed by W.
74. 14(b)(iii)3 marksUsing your matrix in (b)(ii), determine the coordinates of the image of triangle ABC under this combined transformation.
75. 14(c)(i)2 marksWrite the following simultaneous equations in the form AX = B where A, X and B are matrices: 11x + 6y = 6 and 9x + 5y = 7.
76. 14(c)(ii)2 marksHence, write the solution for x and y as a product of two matrices.