CSEC Mathematics · January 2015 · Paper 2

62 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)3 marksUsing a calculator, or otherwise, calculate the EXACT value of (12.8)² - (30 ÷ 0.375).
2. 1(b)(i)2 marksCalculate the fraction of his monthly income spent on food.
3. 1(b)(ii)2 marksCalculate the fraction of his monthly income that he saved.
4. 1(c)(i)2 marksAt Bank A, US 1.00 = BD 1.96. Calculate the value of US 700 in BD. US means United States dollars and BD means Barbados dollars.
5. 1(c)(ii)2 marksAt Bank B, the value of US 700 is BD 1 386. Calculate the value of US $1.00 in BDS at this bank.
6. 2(a)2 marksSimplify p³q² × pq³.
7. 2(b)2 marksExpress as a single fraction in its simplest form a/5 + 3a/2.
8. 2(c)(i)2 marksFactorize completely: x² - 5x + 4
9. 2(c)(ii)2 marksFactorize completely: m² - 4n²
10. 2(d)(i)1 markSolve for x: 2x - 7 ≤ 3.
11. 2(d)(ii)1 markIf x is a positive integer, list the possible values of x.
12. 2(e)2 marksFind the value of 2π√(l/g) where π = 3.14, l = 0.625 and g = 10.
13. 3(a)(i)4 marksUse the given information to complete the Venn diagram below.
14. 3(a)(ii)1 markWrite an expression, in x, which represents the TOTAL number of families in the survey.
15. 3(a)(iii)1 markWrite an equation which may be used to solve for x.
16. 3(b)6 marksUsing a ruler, a pencil and a pair of compasses only, construct parallelogram ABCD with AB = 8 cm, AD = 6 cm and ∠DAB = 60°. Marks will be awarded for construction lines clearly shown.
17. 4(a)2 marksComplete the table of values for the equation y = 40x + 75.
18. 4(b)5 marksOn the grid on page 13, using a scale of 2 cm to represent one hour on the x-axis and 2 cm to represent 50 dollars on the y-axis, plot the 7 pairs of values shown in your completed table. Draw a straight line through…
19. 4(c)(i)2 marksUsing your graph, determine the total charges when the job took 4.5 hours. Draw lines on your graph to show how the values for (c)(i) and (c)(ii) were obtained.
20. 4(c)(ii)2 marksUsing your graph, determine the time, in hours, spent on a job if the total charges were $300. Draw lines on your graph to show how the values for (c)(i) and (c)(ii) were obtained.
21. 4(c)(iii)1 markUsing your graph, determine the fixed charge for a visit.
22. 5(i)1 markWrite down the coordinates of N.
23. 5(ii)4 marksOn the grid above, draw ΔFGH, the reflection of ΔLMN in the y-axis.
24. 5(iii)2 marksUsing vector notation, describe the transformation which maps ΔLMN onto ΔPQR.
25. 5(iv)3 marksComplete the following statement: ΔPQR is mapped onto ΔFGH by a combination of two transformations. First, ΔPQR is mapped onto ΔLMN by a ___________, parallel to the ___________; then ΔLMN is mapped onto ΔFGH by a…
26. 5(v)2 marksΔPQR and ΔFGH are congruent. State TWO reasons why they are congruent.
27. 6(a)(i)1 markMeasure and state the length of PQ on the drawing. PQ = ___________
28. 6(a)(ii)2 marksDetermine the scale of the drawing. The scale is 1: ___________
29. 6(a)(iii)4 marksCalculate the actual area of the face LMNPK on the building.
30. 6(b)(i)1 markState the length of the diameter of the semicircle, AFE.
31. 6(b)(ii)3 marksCalculate the perimeter of the swimming pool.
32. 7(a)(i)2 marksComplete the table below to show the information given in the histogram.
33. 7(a)(ii)1 markComplete the column headed "Cumulative Frequency".
34. 7(b)5 marksOn the grid provided on page 19, using a scale of 2 cm to represent 5 kg on the x-axis and 2 cm to represent 10 parcels on the y-axis, draw the cumulative frequency curve for the data.
35. 7(c)2 marksUse the graph drawn at (b) to estimate the median mass of the parcels. Draw lines on your graph to show how this estimate was obtained.
36. 8(a)2 marksDraw the fourth figure in the sequence.
37. 8(b)(i)1 markComplete the table by inserting the missing value for Figure (n) = 4.
38. 8(b)(ii)2 marksComplete the table by inserting the missing value for Figure (n) = 10.
39. 8(b)(iii)2 marksComplete the table by inserting the missing value for No. of Squares = 50.
40. 8(b)(iv)3 marksComplete the table by inserting the missing value for Figure (n) = n.
41. 9(a)(i)1 markEvaluate f(7).
42. 9(a)(ii)2 marksWrite an expression, in terms of x, for f⁻¹(x).
43. 9(a)(iii)2 marksWrite an expression, in terms of x, for fg(x).
44. 9(b)(i)3 marksExpress the quadratic function f(x) = 3x² + 6x - 2, in the form a(x + h)² + k, where a, h and k are constants.
45. 9(b)(ii)1 markHence, or otherwise, state the minimum value of f(x) = 3x² + 6x - 2.
46. 9(b)(iii)2 marksState the equation of the axis of symmetry of the function f(x) = 3x² + 6x - 2.
47. 9(b)(iv)4 marksSketch the graph of y = 3x² + 6x - 2, showing on your sketch a) the intercept on the y-axis b) the coordinates of the minimum point.
48. 10(a)(i)2 marksCalculate, correct to 1 decimal place, the length QS.
49. 10(a)(ii)2 marksCalculate, correct to 1 decimal place, the measure of ∠QTS.
50. 10(a)(iii)2 marksCalculate, correct to 1 decimal place, the area of triangle QRS.
51. 10(a)(iv)1 markCalculate, correct to 1 decimal place, the perpendicular distance from Q to RS.
52. 10(b)(i)2 marksCalculate, giving the reason for each step of your answer, the measure of: ∠OJH
53. 10(b)(ii)2 marksCalculate, giving the reason for each step of your answer, the measure of: ∠JOG
54. 10(b)(iii)2 marksCalculate, giving the reason for each step of your answer, the measure of: ∠JKG
55. 10(b)(iv)2 marksCalculate, giving the reason for each step of your answer, the measure of: ∠JLG
56. 11(a)(i)2 marksWrite the following simultaneous equations 3x + 2y = -1 and 5x + 4y = 6 in the form AX = B, where A, X and B are matrices.
57. 11(a)(ii)4 marksUse a matrix method to solve for x and y.
58. 11(b)(i)1 markWrite as a column vector in the form (x y): OR
59. 11(b)(ii)1 markWrite as a column vector in the form (x y): OS
60. 11(b)(iii)2 marksWrite as a column vector in the form (x y): SR
61. 11(b)(iv)1 markFind |OS|.
62. 11(b)(v)4 marksGiven that OT = (2 5), prove that OSTR is a parallelogram.