CSEC Mathematics · January 2006 · Paper 2

83 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)4 marksUsing a calculator, or otherwise, calculate the exact value of (2 1/4 × 4/5) / (3/5 - 1/2).
2. 1(a)(ii)3 marksCalculate correct to 3 significant figures, the value of 18.75 - (2.11)^2.
3. 1(b)(i)2 marksCalculate the interest on the loan at the end of the first year.
4. 1(b)(ii)1 markCalculate the total amount owing at the end of the first year.
5. 1(b)(iii)1 markCalculate the amount still outstanding at the start of the second year.
6. 1(b)(iv)1 markCalculate the interest on the outstanding amount at the end of the second year.
7. 2(a)2 marksGiven that m = -2 and n = 4, calculate the value of (2m + n)(2m - n).
8. 2(b)4 marksSolve the simultaneous equations: 5x + 6y = 37 and 2x - 3y = 4.
9. 2(c)(i)2 marksFactorise completely 4x^2 - 25.
10. 2(c)(ii)2 marksFactorise completely 6p - 9ps + 4q - 6qs.
11. 2(c)(iii)2 marksFactorise completely 3x^2 + 4x - 4.
12. 3(a)3 marksGiven the formula s = 1/2(u + v)t, express u in terms of v, s, and t.
13. 3(b)(i)3 marksCopy and complete the Venn diagram to illustrate the information.
14. 3(b)(ii)2 marksWrite an expression in x to represent the TOTAL number of customers who visited the bakery on that day.
15. 3(b)(iii)3 marksCalculate the number of customers who bought bread ONLY.
16. 4(a)(i)1 markState the gradient of any line that is parallel to l.
17. 4(a)(ii)3 marksDetermine the equation of the line parallel to l that passes through the point (2, -6).
18. 4(b)(i)2 marksMeasure and state, in centimetres, the length of the line segment, BC.
19. 4(b)(ii)2 marksHence, calculate in kilometres, the actual shortest distance from City B to City C.
20. 4(b)(iii)4 marksUsing a protractor, determine the bearing of B from A.
21. 5(a)(i)2 marksCalculate the curved surface area of the cylinder.
22. 5(a)(ii)2 marksCalculate the surface area of the hemisphere.
23. 5(a)(iii)2 marksCalculate the TOTAL surface area of the solid paperweight.
24. 5(b)5 marksUsing a ruler, a pencil, and a pair of compasses, construct the parallelogram KLMN, in which KL = 8 cm, KN = 6 cm, and ∠LKN = 60°.
25. 6(a)2 marksState the coordinates of the points R' and S'.
26. 6(b)3 marksDescribe the rotation completely.
27. 6(c)3 marksOn the answer sheet provided, draw and label quadrilateral P''Q''R''S'' which is the image of P'Q'R'S' after it has been reflected in the x-axis.
28. 6(d)2 marksDescribe completely, the single transformation that maps quadrilateral PQRS onto P''Q''R''S''.
29. 7(a)2 marksCopy and complete the following grouped frequency table for the data above. Length of Right Foot (cm): 14-16 (Frequency 4), 17-19, 20-22 (Frequency 8), 23-25 (Frequency 5), 26-28 (Frequency 2).
30. 7(b)1 markState the lower boundary of the class interval 14-16.
31. 7(c)1 markState the width of the class interval 20-22.
32. 7(d)1 markA student's right foot measured 16.8 cm. State the class interval in which this length would lie.
33. 7(e)2 marksA student was chosen at random from the group, and the length of his right foot was measured. Calculate the probability that the length was GREATER THAN or EQUAL to 20 cm.
34. 7(f)1 markState the modal length of a student's right foot.
35. 7(g)3 marksCalculate an estimate of the mean length of a student's right foot using the midpoints of the class intervals in (a) above.
36. 8(a)2 marksCopy and complete the table of values: t (0, 0.5, 1, 1.5, 2, 2.5, 3, 3.5, 4) and h (0.0, 8.8, 15, 18.8, __, 18.8, __, 8.8, 0.0).
37. 8(b)(i)1 markDraw the graph of h = 20t - 5t^2 for 0 ≤ t ≤ 4. You may proceed as follows: Using a scale of 2 cm to represent 0.5 seconds, draw the horizontal t-axis for 0 ≤ t ≤ 4.
38. 8(b)(ii)1 markUsing a scale of 1 cm to represent 1 metre, draw the vertical h-axis for 0.0 ≤ h ≤ 21.0.
39. 8(b)(iii)2 marksPlot the points from your table of values on the axes drawn.
40. 8(b)(iv)1 markJoin the points with a smooth curve.
41. 8(c)(i)1 markUsing your graph, calculate estimates of the GREATEST height above the ground reached by the ball.
42. 8(c)(ii)2 marksUsing your graph, calculate estimates of the number of seconds for which the ball was MORE than 12 metres above the ground.
43. 8(c)(iii)1 markUsing your graph, calculate estimates of the interval of time during which the ball was moving upwards.
44. 9(a)6 marksSolve the pair of simultaneous equations: 2x + y = 7 and x^2 - xy = 6.
45. 9(b)3 marksExpress 4x^2 - 12x - 3 in the form a(x + h)^2 + k, where a, h and k are real numbers.
46. 9(c)(i)1 markUsing your answer from (b) above, or otherwise, calculate the minimum value of 4x^2 - 12x - 3.
47. 9(c)(ii)1 markUsing your answer from (b) above, or otherwise, calculate the value of x for which the minimum occurs.
48. 9(c)(iii)4 marksUsing your answer from (b) above, or otherwise, calculate the values of x for which 4x^2 - 12x - 3 = 0 expressing your answers to 3 significant figures.
49. 10(a)(i)1 markWrite an inequality to represent this information.
50. 10(a)(ii)1 markWrite an inequality to represent this information.
51. 10(a)(iii)2 marksWrite TWO inequalities to represent this information.
52. 10(b)(i)1 markUsing a scale of 2 cm to represent 5 Sonix radios and 2 cm to represent 5 Zent radios, draw the horizontal axis for 0 ≤ x ≤ 30 and the vertical axis for 0 ≤ y ≤ 25.
53. 10(b)(ii)4 marksOn these axes, draw the four boundary lines for the four inequalities written in (a) (i), (ii) and (iii) above.
54. 10(b)(iii)1 markShade the region on your graph that satisfies ALL four of the inequalities written in (a) (i), (ii) and (iii) above.
55. 10(b)(iv)2 marksState the coordinates of the vertices of the shaded region.
56. 10(c)(i)1 markExpress the TOTAL profit in terms of x and y.
57. 10(c)(ii)2 marksCalculate the MAXIMUM profit.
58. 11(a)(i)2 marksCalculate the size of EACH of the following angles, giving reasons for EACH step of your answers: ∠ACB.
59. 11(a)(ii)2 marksCalculate the size of EACH of the following angles, giving reasons for EACH step of your answers: ∠CBD.
60. 11(a)(iii)2 marksCalculate the size of EACH of the following angles, giving reasons for EACH step of your answers: ∠AED.
61. 11(b)3 marksShow that ΔBCE and ΔADE are similar.
62. 11(c)(i)3 marksCalculate the length of EB.
63. 11(c)(ii)3 marksCalculate correct to 1 decimal place the area of ΔAED.
64. 12(a)(i)6 marksSketch the diagram and label the equator.
65. 12(a)(ii)6 marksSketch the diagram and label the Greenwich Meridian.
66. 12(a)(iii)6 marksSketch the diagram and label latitude 52°N.
67. 12(a)(iv)6 marksSketch the diagram and label latitude 6°N.
68. 12(b)(i)2 marksShow on your diagram the position, L, of London and A, of Accra.
69. 12(b)(ii)4 marksCalculate, to the NEAREST kilometre, the shortest distance between London and Accra along their common circle of longitude. Use π = 3.14.
70. 12(c)(i)1 markShow on your diagram a possible point of location of Kyle, K.
71. 12(c)(ii)2 marksCalculate the radius of the circle of latitude on which K lies.
72. 13(a)(i)2 marksExpress in the form (x, y) the position vectors OA, OB, OC, and OD where O is the origin (0, 0).
73. 13(a)(ii)2 marksExpress in the form (x, y) the vectors AB and DC.
74. 13(b)2 marksCalculate |AB| and hence determine the unit vector in the direction of AB.
75. 13(c)(i)2 marksUsing the answers in (a) (ii), state TWO geometrical relationships between the line segments AB and DC.
76. 13(c)(ii)2 marksExplain why ABCD is a parallelogram.
77. 13(d)5 marksUsing a vector method, determine the position vector of G, the midpoint of the line AC. Hence, state the coordinates of the point of intersection of the diagonals AC and BD of parallelogram ABCD.
78. 14(a)(i)3 marksCalculate, in terms of x, the determinant of L.
79. 14(a)(ii)3 marksCalculate the values of x given that L is singular.
80. 14(b)(i)6 marksFind M^-1, the inverse of M.
81. 14(b)(ii)6 marksHence, calculate the value of x and of y for which M(x; y) = (12; -8).
82. 14(c)(i)3 marksCalculate the image, (x', y'), of (3, -1) under N.
83. 14(c)(ii)3 marksCalculate the coordinates of the point, (x, y), which is mapped by N onto (7, 4).