CSEC Mathematics · May/June 2013 · Paper 2

67 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 marksUsing a calculator, or otherwise, calculate the EXACT value of 1 4/5 - 1/3 / 2 2/5.
2. 1(a)(ii)2 marksUsing a calculator, or otherwise, calculate the EXACT value of √1.5625 + (0.32)².
3. 1(b)3 marksWhich size carton of orange juice is the BETTER buy? Justify your answer.
4. 1(c)(i)1 markCalculate the interest on the loan for the first year.
5. 1(c)(ii)2 marksHow much did she still owe at the beginning of the second year?
6. 1(c)(iii)1 markCalculate the interest on the remaining balance for the second year.
7. 2(a)(i)2 marksFactorize completely: 2x² - 8x.
8. 2(a)(ii)2 marksFactorize completely: 3x² - 5x - 2.
9. 2(b)(i)2 marksMake C the subject of the formula F = 9/5 C + 32.
10. 2(b)(ii)1 markGiven that F = 113, calculate the value of C.
11. 2(c)(i)a)1 markWrite an expression, in terms of x, for the number of tickets sold at $10 each.
12. 2(c)(i)b)1 markWrite an expression, in terms of x, for the TOTAL amount of money collected for the sale of the 500 tickets.
13. 2(c)(ii)3 marksCalculate the number of tickets sold at $6 each.
14. 3(a)(i)3 marksCopy the Venn diagram below and complete it to show, in terms of x, the number of students in each region.
15. 3(a)(ii)1 markWrite an expression, in terms of x, which represents the TOTAL number of students in the survey.
16. 3(a)(iii)2 marksDetermine the number of students in Form 5 who used ONLY cameras.
17. 3(b)(i)2 marksCalculate the length of BC.
18. 3(b)(ii)1 markExplain why triangles ABC and ADE are similar.
19. 3(b)(iii)3 marksDetermine the length of DE.
20. 4(a)(i)1 markMeasure and state, in centimetres, the length of DE.
21. 4(a)(ii)1 markMeasure and state, in degrees, the size of <ECD.
22. 4(a)(iii)2 marksDetermine the perimeter of the triangle CDE.
23. 4(a)(iv)1 markCalculate the area of the triangle CDE.
24. 4(b)(i)2 marksDetermine the gradient of AB.
25. 4(b)(ii)2 marksDetermine the coordinates of the midpoint of AB.
26. 4(b)(iii)3 marksDetermine the equation of the perpendicular bisector of AB.
27. 5(a)(i)1 markExpress A in terms of R and a constant k.
28. 5(a)(ii)2 marksCalculate the value of the constant k.
29. 5(a)(iii)2 marksCopy and complete the table.
30. 5(b)(i)3 marksDetermine the value of fg(2).
31. 5(b)(ii)3 marksDetermine the value of f⁻¹(3).
32. 6(a)(i)2 marksCalculate the speed of the car in m/s.
33. 6(a)(ii)2 marksCalculate the distance, in metres, between the two sign posts.
34. 6(b)(i)2 marksDescribe fully the transformation that maps ΔLMN onto ΔL'M'N'.
35. 6(b)(ii)2 marksOn the answer sheet provided, draw triangle L''M''N'' the image of triangle LMN, after a translation by the vector (0, -3).
36. 6(b)(iii)3 marksName and describe a combination of TWO transformations which may be used to map ΔL''M''N'' onto ΔL'M'N'.
37. 7(a)2 marksCopy and complete the table to show the cumulative frequency.
38. 7(b)5 marksUsing a scale of 1 cm to represent $5 on the horizontal axis and 1 cm to represent 5 students on the vertical axis, draw the cumulative frequency graph for the data.
39. 7(c)(i)2 marksUse your graph to estimate the median amount of money spent.
40. 7(c)(ii)2 marksUse your graph to estimate the probability that a student chosen at random spent less than $23 during the week.
41. 8(a)2 marksDraw a sketch of Diagram 4, the fourth diagram in the sequence.
42. 8(b)(i)2 marksComplete the table by inserting the missing values at the rows marked (i) for N=4.
43. 8(b)(ii)4 marksComplete the table by inserting the missing values at the rows marked (ii) for N=20.
44. 8(c)(i)1 markWrite the rule which may be used to find the value of W where N is known.
45. 8(c)(ii)1 markWrite the rule which may be used to find the value of B where N is known.
46. 9(a)(i)1 markWrite an inequality to represent the information that her bag has space for only 6 fruits.
47. 9(a)(ii)1 markWrite an inequality to represent the information that she must buy AT LEAST 2 mangoes.
48. 9(a)(iii)2 marksWrite the information represented by the inequality y ≤ 2x as a sentence in your own words.
49. 9(a)(iv)3 marksOn the answer sheet provided, draw the lines associated with the two inequalities obtained in (i) and (ii) above.
50. 9(a)(v)1 markShade on your graph the region which represents the solution set for the three inequalities.
51. 9(b)(i)3 marksWrite 3x² - 12x + 8 in the form a(x + h)² + k where a, h and k are constants.
52. 9(b)(ii)a)4 marksSketch the graph of y = 3x² - 12x + 8, showing on your sketch the intercept on the y-axis.
53. 9(b)(ii)b)4 marksSketch the graph of y = 3x² - 12x + 8, showing on your sketch the coordinates of the minimum point.
54. 10(a)(i)1 markCalculate, giving reasons for your answer, the measure of <EBF.
55. 10(a)(ii)2 marksCalculate, giving reasons for your answer, the measure of <BOA.
56. 10(a)(iii)2 marksCalculate, giving reasons for your answer, the measure of <AFB.
57. 10(a)(iv)2 marksCalculate, giving reasons for your answer, the measure of <OAF.
58. 10(b)(i)3 marksSketch separate diagrams of the triangles RFT, TFS and SFR. Mark on EACH diagram the given measures of sides and angles.
59. 10(b)(ii)2 marksShow, by calculation, that RF = 49.1 m.
60. 10(b)(iii)1 markCalculate the length of SR correct to 1 decimal place.
61. 10(b)(iv)2 marksCalculate the angle of elevation of the top of the tower, T, from S.
62. 11(a)(i)a)2 marksExpress in terms of a and b the vector AB.
63. 11(a)(i)b)2 marksExpress in terms of a and b the vector PQ.
64. 11(a)(ii)2 marksState TWO geometrical relationships that exist between OB and PQ. Give reasons for your answers.
65. 11(b)(i)2 marksEvaluate M⁻¹, the inverse of M.
66. 11(b)(ii)2 marksShow that M⁻¹M = I.
67. 11(b)(iii)5 marksUse a matrix method to solve for r, s, t and u in the equation [[2, 1], [4, 3]] * [[r, s], [t, u]] = [[2, 1], [4, -1]].