CSEC Mathematics · 2003 (Specimen) · Paper 2

88 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)1 markEvaluate 1.5^2 - 0.5^2.
2. 1(a)(ii)1 markEvaluate \frac{4.2 + 1.4}{0.02 \times 0.7}.
3. 1(a)(iii)2 marksEvaluate \sqrt{87.2}, writing your answer correct to 3 significant figures.
4. 1(b)(i)1 markCalculate how much, to the NEAREST cent, Mr Lee paid for EACH shirt.
5. 1(b)(ii)2 marksMr Lee sold the shirts at $19.99 EACH. Calculate the profit on EACH shirt.
6. 1(b)(iii)2 marksCalculate the profit in (ii) above as a percentage of the cost price of a shirt.
7. 1(b)(iv)2 marksCalculate for how much, to the NEAREST cent, Mr Lee should sell a shirt in order to obtain a profit of 45%.
8. 2(a)(i)2 marksFactorise completely: 2mg + 3g - 2mt - 3t
9. 2(a)(ii)2 marksFactorise completely: 3y^2 + 5y - 12
10. 2(a)(iii)2 marksFactorise completely: 2x^3 - 8x
11. 2(b)(i)1 markWrite an equation to represent: The admission cost for the Holder Family of 3 children and 2 adults is $48.00.
12. 2(b)(ii)1 markWrite an equation to represent: The admission cost for the Rodney Family of 5 children and 3 adults is $76.00.
13. 2(b)(iii) a)2 marksUsing the equations in (b)(i) and (ii), calculate the cost of admission to the cinema for a child.
14. 2(b)(iii) b)2 marksUsing the equations in (b)(i) and (ii), calculate the cost of admission to the cinema for an adult.
15. 3(a)(i)2 marksCopy and complete the Venn diagram to illustrate the given information: 18 have cell-phones, 15 drive cars, x have cell-phones and drive cars, 2x have no cell-phones and do not drive cars.
16. 3(a)(ii)3 marksWrite an equation in terms of x to represent that there are 40 students in Form 6, and solve the equation for x.
17. 3(a)(iii)2 marksDetermine n(C \cap D').
18. 3(b)(i)2 marksThe tank contains water to a depth of 6 m. Calculate, to the NEAREST \text{m}^3, the volume of water in the tank.
19. 3(b)(ii)3 marksWater is added to the tank so that the TOTAL volume of water is 650\text{ m}^3. Calculate, correct to 1 decimal place, the depth of the water in the tank.
20. 4(a)(i)1 markUsing a protractor, measure and state the size of angle a.
21. 4(a)(ii)1 markUsing a protractor, measure and state the size of angle b.
22. 4(b)(i)4 marksUsing only a ruler, a pencil and a pair of compasses, construct \Delta LMN such that MN = LM = 6.0\text{ cm} and \angle LMN = 60^\circ.
23. 4(c)(i)2 marksConstruct the circle which passes through the points L, M and N.
24. 4(c)(ii)2 marksMeasure and state the length of the radius of the circle drawn above.
25. 4(d)(i)1 markCalculate the size of angle g in the given figure.
26. 4(d)(ii)1 markCalculate the size of angle e in the given isosceles triangle figure.
27. 5(a)(i)1 markIn which year was the banana price GREATEST?
28. 5(a)(ii)1 markWhat was the price in that year?
29. 5(b)2 marksBetween which two consecutive years was the increase in the price of bananas GREATEST?
30. 5(c)(i)4 marksComplete the graph using the data from the table provided for the years 1977 to 1980.
31. 5(c)(ii)2 marksIs it possible to use the information given to predict the price of bananas in the year 1981? Give a reason for your answer.
32. 6(a)(i)1 markDraw the mirror line for this reflection on your answer sheet.
33. 6(a)(ii)1 markWrite the equation of the line you have drawn.
34. 6(b)3 marksTriangle A undergoes a single transformation, Q, such that its image is Triangle C. Describe COMPLETELY the transformation Q.
35. 6(c)(i)2 marksOn the answer sheet provided, draw the image of Triangle C after a reflection in the x-axis and label this triangle D.
36. 6(c)(ii)2 marksOn the answer sheet provided, draw the image of Triangle B under the translation T = \begin{pmatrix} -1 \\ -4 \end{pmatrix}, and label this triangle E.
37. 6(d)3 marksTriangle F is the image of Triangle C after an enlargement with centre at (0, 0) and scale factor 2. Determine the area of triangle F.
38. 7(a)1 markUse the graph to find an estimate for the number of strips in the sample.
39. 7(b)2 marksUse the graph to find an estimate for the number of strips of length 65 cm or longer.
40. 7(c)1 markUse the graph to find an estimate for the median length of the strips.
41. 7(d)2 marksUse the graph to find an estimate for the interquartile range.
42. 7(e)2 marksUse the graph to find an estimate for the minimum length of the longest 30 strips.
43. 7(f)2 marksUse the graph to find an estimate for the probability that a strip chosen at random is shorter than 45 cm.
44. 8(a)2 marksDraw the FOURTH triangle of the set on the grid provided on the answer sheet.
45. 8(b)4 marksCopy and complete the table for the 3rd, 4th, 5th, and 6th triangles.
46. 8(c)(i)1 markWrite a rule describing the sequence of numbers in Column 2 (Number of Dots on Perimeter).
47. 8(c)(ii)2 marksWrite a rule describing the sequence of numbers in Column 3 (Number of Dots Inside Triangle).
48. 8(d)2 marksCalculate the area of the 12th triangle.
49. 9(a)7 marksSolve the pair of simultaneous equations: 2x^2 + 4x + y = 0 and y - 3x = -15.
50. 9(b)3 marksBy simplifying, show that (2x + 3)^2 - (x + 4)(x - 4) = 3x^2 + 12x + 25.
51. 9(c)5 marksWrite 3x^2 + 12x + 25 in the form a(x + h)^2 + k where a, h and k are real numbers. Hence, or otherwise, solve the equation 3x^2 + 12x + 25 = 40.
52. 10(a)1 markMrs Cave wishes to buy x stereo sets and y television sets but the total number of sets must not exceed 20. Write an inequality in x and y to represent this information.
53. 10(b)2 marksEach stereo set costs 150.00 and each television set costs 300.00, and she can spend a maximum of 4,500.00 on the sets. Write an inequality in x and y$ to represent this information.
54. 10(c)2 marksShe must buy at least 5 of each set. Write TWO inequalities to represent this information.
55. 10(d)6 marksUsing a scale of 2 cm to represent 5 units on both axes, draw on your graph the FOUR inequalities from (a), (b) and (c) above. Identify, by shading, the region satisfying the FOUR inequalities.
56. 10(e)(i)1 markThe profit on each stereo is 80.00 and on each television is 100.00. Write an expression in x and y for P, the profit when all the sets are sold.
57. 10(e)(ii)2 marksHow many of EACH set should Mrs Cave buy in order to obtain MAXIMUM profit?
58. 10(e)(iii)1 markWhat is the MAXIMUM profit?
59. 11(a)(i)2 marksCalculate, giving a reason for your answer, the size of \angle OBD.
60. 11(a)(ii)2 marksCalculate, giving a reason for your answer, the size of \angle DBC.
61. 11(a)(iii)2 marksCalculate, giving a reason for your answer, the size of \angle DAB.
62. 11(b)(i)2 marksDraw a carefully labelled diagram to show the relative positions of A, B and C.
63. 11(b)(ii)2 marksShow that angle ABC = 120^\circ.
64. 11(b)(iii)3 marksCalculate the distance AC.
65. 11(b)(iv)2 marksCalculate, to the NEAREST degree, the bearing of C from A.
66. 12(a)(i)2 marksCalculate, correct to three significant figures, the height of the pole, CP.
67. 12(a)(ii)2 marksCalculate, correct to three significant figures, the length of AC, the diagonal of the rectangle ABCD.
68. 12(a)(iii)2 marksCalculate, correct to three significant figures, the angle of elevation of P from A.
69. 12(b)(i)2 marksCopy and complete the table of values for y = 1 + 2\sin x.
70. 12(b)(ii)4 marksDraw the graph of y = 1 + 2\sin x for 0^\circ \le x \le 180^\circ.
71. 12(b)(iii)3 marksUse your graph to find the approximate values of x for which 1 + 2\sin x = 2.3.
72. 13(a)(i)2 marksDetermine \vec{AC}.
73. 13(a)(ii)2 marksCalculate the magnitude of \vec{AC}.
74. 13(a)(iii)1 markWrite the unit vector that is in the same direction as \vec{AC}.
75. 13(b)(i) a)1 markExpress \vec{OR} in its simplest form in terms of \mathbf{u} and/or \mathbf{v}.
76. 13(b)(i) b)1 markExpress \vec{OS} in its simplest form in terms of \mathbf{u} and/or \mathbf{v}.
77. 13(b)(i) c)1 markExpress \vec{QP} in its simplest form in terms of \mathbf{u} and/or \mathbf{v}.
78. 13(b)(i) d)2 marksExpress \vec{SR} in its simplest form in terms of \mathbf{u} and/or \mathbf{v}.
79. 13(b)(i) e)2 marksExpress \vec{OT} in its simplest form in terms of \mathbf{u} and/or \mathbf{v}.
80. 13(b)(i) f)1 markExpress \vec{ST} in its simplest form in terms of \mathbf{u} and/or \mathbf{v}.
81. 13(b)(ii)2 marksUse the results of (d) and (f) above to prove that S, R and T lie in a straight line.
82. 14(a)5 marksUse a matrix method to solve the equations: 3x - y = 5 and 2x + 5y = 9.
83. 14(b)(i)1 markState the matrix S that represents the transformation, a reflection in the line y = x.
84. 14(b)(ii)1 markState the matrix T that represents the transformation, a reflection in the x-axis.
85. 14(c)(i)2 marksCalculate the single matrix TS.
86. 14(c)(ii)2 marksCalculate the single matrix ST.
87. 14(d)(i)2 marksDescribe COMPLETELY the single transformation represented by TS.
88. 14(d)(ii)2 marksDescribe COMPLETELY the single transformation represented by ST.