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CSEC Mathematics · January 2014 · Paper 2

69 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.

Practise this paper
  1. 1(a)3 marksCalculate the EXACT value of (3/4 + 1/8) ÷ (5/6 - 2/3).
  2. 1(b)3 marksUsing a calculator or otherwise, calculate √2.891 + 1.2/(1.31)² giving your answer correct to 2 decimal places.
  3. 1(c)1 markCalculate the TOTAL cost of the 165 bracelets inclusive of duty.
  4. 1(c)(ii)a)2 marksCalculate the TOTAL profit he made on the sale of the 165 bracelets.
  5. 1(c)(ii)b)2 marksCalculate the profit as a percentage of the cost price, giving your answer to the nearest whole number.
  6. 2(a)(i)3 marksSolve for x, where x is a real number: 2(x-6) + 3x ≤ 8.
  7. 2(a)(ii)1 markUsing a number line, show your solution to Part (a)(i).
  8. 2(b)(i)2 marksFactorize completely: 3x - 6y + ax - 2ay.
  9. 2(b)(ii)1 markFactorize completely: p² - 1.
  10. 2(c)2 marksExpand and simplify (2k - 3)(k - 2).
  11. 2(d)3 marksShow that the point of intersection is (1, -1).
  12. 3(a)(i)2 marksRepresent this information on a Venn diagram.
  13. 3(a)(ii)1 markCalculate the number of students who study Spanish (S) but NOT French (F).
  14. 3(a)(iii)1 markWrite, using set notation, the relationship between F and S.
  15. 3(b)(i)1 markState, in terms of x, the length l of the floor.
  16. 3(b)(ii)a)3 marksDetermine the value of x.
  17. 3(b)(ii)b)2 marksCalculate the area of the floor.
  18. 4(a)(i)1 markState the correct equation for Line 1.
  19. 4(a)(ii)1 markState the correct equation for Line 2.
  20. 4(a)(iii)1 markState the correct equation for Line 3.
  21. 4(b)1 markShow that the gradient of Line 2 is 1.
  22. 4(c)2 marksShade the region which is described as y ≥ x + 2.
  23. 4(d)3 marksWrite THREE inequalities that define the shaded region, S, shown in the diagram.
  24. 4(e)2 marksWrite the equation of the straight line which is perpendicular to Line 1 and passes through the origin.
  25. 5(a)(i)3 marksUsing a ruler, a pencil and a pair of compasses, construct triangle ABC with BC = 10 cm, AB = 6 cm and AC = 8 cm.
  26. 5(a)(ii)1 markMeasure and state the size of angle ABC.
  27. 5(a)(iii)2 marksComplete the diagram to show a quadrilateral, CABD, such that CD = CA and BD = BA.
  28. 5(b)(i)2 marksCalculate the area of the trapezium PQRS.
  29. 5(b)(ii)1 markCalculate the volume of the block of metal.
  30. 5(b)(iii)3 marksCalculate, in grams, the mass of ONE cubic centimetre of metal.
  31. 6(a)(i)2 marksCalculate, giving reasons for your answer, the value of x.
  32. 6(a)(ii)2 marksCalculate, giving reasons for your answer, the value of y.
  33. 6(a)(iii)2 marksCalculate, giving reasons for your answer, the value of z.
  34. 6(b)(i)1 markState the coordinates of the vertex, J, of triangle JKL.
  35. 6(b)(ii)1 markState the length of the side K'L' of triangle J'K'L'.
  36. 6(b)(iii)2 marksDescribe FULLY a single transformation that maps triangle JKL onto triangle J'K'L'.
  37. 6(b)(iv)2 marksState the coordinates of triangle J''K''L'', the image of triangle JKL, under the translation by the vector [5, -3].
  38. 7(a)1 markHow many seedlings were in the sample?
  39. 7(b)(i)1 markWrite down the lower class limit.
  40. 7(b)(ii)1 markWrite down the upper class boundary.
  41. 7(b)(iii)1 markWrite down the class width.
  42. 7(c)(i)2 marksCopy and complete the table by inserting the midpoints of EACH class interval.
  43. 7(c)(ii)1 markCopy and complete the table by inserting the missing values for the class interval after the interval "33-37".
  44. 7(d)5 marksUsing a scale of 2 cm to represent 5 cm on the horizontal axis and 2 cm to represent 5 seedlings on the vertical axis, draw a frequency polygon to represent the data as shown in your table at (c).
  45. 8(a)2 marksOn the answer sheet provided, draw Figure 4, the FOURTH figure in the sequence.
  46. 8(b)(i)2 marksComplete the row for No. of Trapezia (n) = 4.
  47. 8(b)(ii)2 marksComplete the row for No. of Trapezia (n) = 10.
  48. 8(b)(iii)2 marksComplete the row where No. of Triangles = 64.
  49. 8(b)(iv)2 marksComplete the row for No. of Trapezia (n) = n.
  50. 9(a)(i)a)1 markEvaluate g(4).
  51. 9(a)(i)b)2 marksEvaluate hg(4).
  52. 9(a)(ii)a)4 marksWrite an expression in x for h⁻¹(x).
  53. 9(a)(ii)b)4 marksWrite an expression in x for gg(x).
  54. 9(b)(i)2 marksState the roots of the equation x² + bx + c = 0.
  55. 9(b)(ii)a)2 marksDetermine the value of c.
  56. 9(b)(ii)b)2 marksShow that b = -4.
  57. 9(b)(iii)2 marksState the coordinates of the MINIMUM point on the graph of the function y = x² + bx + c.
  58. 10(a)(i)2 marksCalculate, giving reasons for your answer, the measure of ∠FAW.
  59. 10(a)(ii)2 marksCalculate, giving reasons for your answer, the measure of ∠SKF.
  60. 10(a)(iii)2 marksCalculate, giving reasons for your answer, the measure of ∠ASW.
  61. 10(b)(i)a)3 marksCalculate, correct to one decimal place, the distance QR.
  62. 10(b)(i)b)2 marksCalculate, correct to one decimal place, the area of triangle PQR.
  63. 10(b)(ii)4 marksCalculate the bearing of R from P.
  64. 11(a)(i)3 marksDetermine, T⁻¹, the inverse of T.
  65. 11(a)(ii)4 marksThe matrix T maps the point (a, b) onto the point (4, 9). Determine the values of a and b.
  66. 11(b)(i)2 marksDraw a sketch of the triangle OMN and label the points O, M, N and L.
  67. 11(b)(ii)a)3 marksWrite in terms of m and n an expression for MN.
  68. 11(b)(ii)b)3 marksWrite in terms of m and n an expression for ML.
  69. 11(b)(iii)3 marksDetermine the position vector of L.

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