CSEC Mathematics · January 2011 · Paper 2

64 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)2 marksCalculate the exact value of (5.82 + 1.02) × 2.5.
2. 1(a)(ii)3 marksCalculate the exact value of (2 4/9) / (4 2/3 - 3/7).
3. 1(b)(i)1 markCalculate the basic weekly wage for ONE employee.
4. 1(b)(ii)2 marksCalculate the overtime wage for an employee who works 6 hours overtime in a certain week.
5. 1(b)(iii)2 marksCalculate the TOTAL paid in overtime wages for that week.
6. 1(b)(iv)1 markCalculate the TOTAL number of overtime hours worked by employees for that week.
7. 2(a)2 marksSimplify (2x/5 - x/3), expressing your answer as a single fraction.
8. 2(b)1 markFactorise completely a²b + 2ab.
9. 2(c)3 marksExpress p as the subject of the formula q = (p² - r) / t.
10. 2(d)(i)2 marksWrite an expression in terms of x to represent the TOTAL number of donuts sold.
11. 2(d)(ii)a)4 marksCalculate the number of donuts in a small box.
12. 2(d)(ii)b)1 markCalculate the number of donuts in a large box.
13. 3(a)2 marksSimplify the expression 7p³q³ × 2p²q.
14. 3(b)(i)2 marksCalculate, in cm³, the volume of milk in EACH carton.
15. 3(b)(ii)3 marksHow many cartons of milk should be bought to make the ice-cream?
16. 3(b)(iii)4 marksWhat is the height of milk in the cup? Give your answer to 3 significant figures.
17. 4(a)(i)1 markList the members of the set H.
18. 4(a)(ii)1 markList the members of the set J.
19. 4(a)(iii)3 marksDraw a Venn diagram to represent the sets U, H and J, showing ALL the elements in the subsets.
20. 4(b)(i)4 marksUsing a pencil, ruler and a pair of compasses only, construct a triangle LMN with angle LMN = 60°, MN = 9 cm and LM = 7 cm. ALL construction lines MUST be clearly shown.
21. 4(b)(ii)1 markMeasure and state the size of ∠MNL.
22. 4(b)(iii)2 marksOn the diagram, show the point, K, such that KLMN is a parallelogram.
23. 5(a)(i)2 marksDetermine the gradient of the line.
24. 5(a)(ii)3 marksDetermine the equation of the line which is perpendicular to 3y = 2x - 6, and passes through the point (4,7).
25. 5(b)(i)2 marksCalculate the value of k.
26. 5(b)(ii)2 marksCalculate the value of f(3).
27. 5(b)(iii)2 marksCalculate the value of x when f(x) = 95.
28. 6(i)3 marksCopy and complete the table to show the sales for EACH month. The table has rows for Month (Jan, Feb, Mar, Apr, May) and Sales in $Thousands, with 38 for Jan and 27 for Mar already filled.
29. 6(ii)1 markBetween which TWO consecutive months was there the GREATEST decrease in sales?
30. 6(iii)3 marksCalculate the mean monthly sales for the period January to May 2010.
31. 6(iv)2 marksCalculate the sales, in dollars, for the month of June.
32. 6(v)2 marksComment on how the sales in June compared with the sales in the previous five months.
33. 7(i)2 marksWrite down the coordinates of R and R'.
34. 7(ii)3 marksDescribe completely the transformation which maps triangle RST onto triangle R'S'T'.
35. 7(iii)a)7 marksOn your answer sheet, draw triangle R''S''T'', the image of triangle RST under the enlargement.
36. 7(iii)b)1 markCalculate the area of triangle R''S''T''.
37. 7(iii)c)1 markState TWO geometrical relationships between triangles RST and R''S''T''.
38. 8(a)(i)a)4 marksDraw and label rectangle B of area 27 square units and perimeter 24 units.
39. 8(a)(i)b)1 markDraw and label rectangle C of area 32 square units and perimeter 24 units.
40. 8(a)(ii)2 marksComplete the table to show the dimensions of rectangles B and C, drawn at (a)(i) above.
41. 8(b)2 marksDetermine the values of l and w. In the table, write the values of l, w and the area of rectangle D.
42. 8(c)2 marksDetermine the values of l and w. In the table, write the values of l, w and the area of rectangle E.
43. 9(a)(i)1 markEvaluate f(5).
44. 9(a)(ii)a)6 marksWrite an expression in x for f⁻¹(x).
45. 9(a)(ii)b)1 markWrite an expression in x for gf(x).
46. 9(b)(i)3 marksExpress the quadratic function 1 - 6x - x² in the form k - a(x + h)², where a, h and k are constants.
47. 9(b)(ii)a)2 marksHence state the maximum value of 1 - 6x - x².
48. 9(b)(ii)b)1 markHence state the equation of the axis of symmetry of the quadratic function.
49. 9(b)(iii)3 marksDetermine the roots of 1 - 6x - x² = 0, giving your answers to 2 decimal places.
50. 10(a)(i)2 marksCalculate, giving reasons for EACH step of your answer, the measure of ∠OGF.
51. 10(a)(ii)3 marksCalculate, giving reasons for EACH step of your answer, the measure of ∠DEF.
52. 10(b)(i)a)3 marksDraw a clearly labelled diagram to represent the above information. Show on the diagram the north/south direction.
53. 10(b)(i)b)1 markDraw a clearly labelled diagram to represent the above information. Show on the diagram the bearing 054°.
54. 10(b)(i)c)1 markDraw a clearly labelled diagram to represent the above information. Show on the diagram the distances 122 km and 60 km.
55. 10(b)(ii)a)7 marksCalculate the measure of angle JKL.
56. 10(b)(ii)b)1 markCalculate the distance JL.
57. 10(b)(ii)c)1 markCalculate the bearing of J from L.
58. 11(a)(i)3 marksDetermine the values of a, b, c and d.
59. 11(a)(ii)2 marksState the coordinates of Z such that Z(x,y) → Z'(5,1) under the transformation, M.
60. 11(a)(iii)2 marksDescribe FULLY the geometric transformation, M.
61. 11(b)(i)a)3 marksWrite in the form [[a], [b]] the vector OP.
62. 11(b)(i)b)1 markWrite in the form [[a], [b]] the vector OR.
63. 11(b)(ii)a)5 marksFind RS.
64. 11(b)(ii)b)1 markShow that P, R and S are collinear.