CSEC Mathematics · January 2016 · Paper 2

63 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)2 marksUsing a calculator, or otherwise, calculate the EXACT value of (3.6 + √51.84) ÷ 3.75
2. 1(b)3 marksWhich of the jars shown above is the BETTER buy? Show ALL working to support your answer.
3. 1(c)2 marksCalculate: The interest, in dollars, earned after six months
4. 1(c)(ii)2 marksThe TOTAL amount of money in his account after 3 years
5. 1(c)(iii)2 marksHow long it will be before his investment earns $449.40
6. 2(a)(i)3 marksSolve for x, where x is a real number. 8 - x ≤ 5x + 2
7. 2(a)(ii)1 markShow your solution to (a)(i) on the number line below.
8. 2(b)2 marksExpand and simplify 2x(x + 5) - 3(x - 4).
9. 2(c)2 marksSimplify (3x² × 4x³) / 2x
10. 2(d)2 marksWrite as a single fraction, in its lowest terms, (x+1)/2 + (5-x)/5
11. 2(e)2 marksFactorize completely 4x² - 4
12. 3(a)(i)1 markHow many students have visited Dominica ONLY?
13. 3(a)(ii)1 markWrite an expression, in terms of x, to represent the TOTAL number of students who have visited Canada.
14. 3(a)(iii)2 marksGiven that there are 25 students in Form 5A, calculate the value of x.
15. 3(a)(iv)3 marksHence, write down the number of students in each of the following subsets: C ∪ D, C ∩ D, (C ∪ D)'
16. 3(b)(i)4 marksUsing a ruler, a pencil and a pair of compasses, construct accurately, the square EFGH where EF = 6 cm. (Show ALL construction lines and curves.)
17. 3(b)(ii)1 markMeasure, and state in centimetres, the length of the diagonal FH.
18. 4(a)(i)1 markState, in cm, the length of LM as shown in the diagram.
19. 4(a)(ii)1 markEstimate, by counting squares, the area of the map shown in the diagram.
20. 4(a)(iii)1 markComplete the following statement: On the map, 1 cm represents ______ km.
21. 4(a)(iv)1 markWrite the scale of the map in the form 1 : x.
22. 4(a)(v)1 markWhat distance on the island will be 3 cm on the map?
23. 4(a)(vi)2 marksWhat area on the island will be represented by 3 cm² on the map?
24. 4(b)(i)2 marksCalculate the area of the cross section PQRST.
25. 4(b)(ii)2 marksAn engineer needs a similar prism whose volume is NOT more than 900 cm³. Estimate, in cm, the length of the longest prism he can use.
26. 5(a)(i)2 marksCalculate, giving your answer to 1 decimal place, the length RS.
27. 5(a)(ii)2 marksthe measure of angle RTW.
28. 5(b)(i)1 markWrite down the coordinates of the vertices of ΔABC.
29. 5(b)(ii)1 markWrite down the coordinates of the vertices of ΔA'B'C'.
30. 5(b)(iii)2 marksDescribe FULLY the transformation that maps triangle ABC onto triangle A'B'C'.
31. 5(b)(iv)3 marksOn the graph on page 16, draw the line x = 1 AND the triangle A''B''C'', the image of triangle ABC after a reflection in the line x = 1.
32. 5(b)(v)1 markState ONE geometrical relationship among ΔABC, ΔA'B'C' and ΔA''B''C''.
33. 6(a)(i)1 markComplete the line graph on page 18 to represent the given information.
34. 6(a)(ii)1 markBetween which two consecutive years was there the GREATEST increase in cars sold?
35. 6(a)(iii)2 marksWhat was the TOTAL number of cars sold in the five year period 2010 to 2014?
36. 6(a)(iv)2 marksThe mean number of cars sold from 2010 to 2015 was 22.5 hundred. How many cars were sold in 2015?
37. 7(a)2 marksComplete the cumulative frequency column in the table.
38. 7(b)5 marksOn the grid on page 23, using a scale of 2 cm to represent 5 minutes on the x-axis and 2 cm to represent 5 students on the y-axis, draw a cumulative frequency curve to represent the information in the table.
39. 7(c)(i)2 marksUsing the graph, estimate the median time taken to complete the experiment.
40. 7(c)(ii)2 marksthe probability that a student, chosen at random, took 30 minutes or less to complete the experiment.
41. 8(a)2 marksDraw the fourth figure in the sequence.
42. 8(b)(i)2 marksThe table below shows the number of dots and lines in each figure. Study the pattern in the table and complete the table by inserting the missing values in the rows numbered (i), (ii), (iii) and (iv). (i) Figure 4
43. 8(b)(ii)2 marksThe table below shows the number of dots and lines in each figure. Study the pattern in the table and complete the table by inserting the missing values in the rows numbered (i), (ii), (iii) and (iv). (ii) Figure 10
44. 8(b)(iii)2 marksThe table below shows the number of dots and lines in each figure. Study the pattern in the table and complete the table by inserting the missing values in the rows numbered (i), (ii), (iii) and (iv). (iii) Figure with…
45. 8(b)(iv)2 marksThe table below shows the number of dots and lines in each figure. Study the pattern in the table and complete the table by inserting the missing values in the rows numbered (i), (ii), (iii) and (iv). (iv) Figure N
46. 9(a)(i)2 marksState the other TWO inequalities which define the shaded region.
47. 9(a)(ii)2 marksIdentify the three pairs of (x, y) values for which P has a maximum or a minimum value.
48. 9(a)(iii)3 marksWhich pair of (x, y) values makes P a maximum? Justify your answer.
49. 9(b)(i)4 marksEvaluate EACH of the following: g(-1/2), fg(-1/2)
50. 9(b)(ii)4 marksWrite an expression in x for f⁻¹(x).
51. 10(a)(i)2 marksDetermine the area of the minor sector HOK.
52. 10(a)(ii)3 marksthe area of triangle HOK.
53. 10(a)(iii)2 marksthe area of the shaded segment.
54. 10(b)(i)2 marksCalculate, giving the reason for each step of your answer, the measure of: ∠ADC
55. 10(b)(ii)2 marks∠ACD
56. 10(b)(iii)2 marks∠CAD
57. 10(b)(iv)2 marks∠OEA
58. 11(a)(i)5 marksExpress EACH of the following in the form (x y): OB, AB, OM
59. 11(a)(ii)2 marksUsing a vector method, show that AC and OB are parallel.
60. 11(b)2 marksDetermine the value of p for which the matrix M is singular.
61. 11(c)(i)2 marksCalculate 2A + B.
62. 11(c)(ii)2 marksDetermine B⁻¹, the inverse of B.
63. 11(c)(iii)2 marksGiven that (5 -1; 0 3)(x y) = (6 9), calculate the values of x and y.