Quelpr

CSEC Mathematics · May/June 2005 · Paper 2

71 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 4 1/5 - (1 1/3 x 3)
  2. 1(b)5 marksThe table below shows Amanda's shopping bill. Some numbers were removed and replaced with letters. Calculate the values of A, B, C and D.
  3. 1(b)(ii)3 marksAmanda sold 6 of the 12 stickers which she had bought at 75 cents each, and the remaining stickers at 40 cents each. Show, using calculations, whether Amanda made a profit or loss on buying and selling stickers.
  4. 2(a)(i)2 marksFactorise 5a²b + ab²
  5. 2(a)(ii)2 marksFactorise 9k² - 1
  6. 2(a)(iii)2 marksFactorise 2y² - 5y + 2
  7. 2(b)2 marksExpand and simplify (2x + 5) (3x - 4)
  8. 2(c)(i)2 marksWrite down, in terms of x, an expression for the number of points scored by Shakeel.
  9. 2(c)(ii)2 marksWrite an equation which may be used to find the value of x.
  10. 3(a)(i)4 marksCalculate the number of students who take BOTH Music and Drama.
  11. 3(a)(ii)1 markCalculate the number of students who take Drama ONLY.
  12. 3(b)(i)5 marksWrite down the equation of this line in the form y = mx + c.
  13. 3(b)(ii)2 marksShow that this line is parallel to the line 2x - 3y = 0.
  14. 4(a)5 marksIs a medium pizza twice as large as a small pizza? Use calculations to support your answer.
  15. 4(b)5 marksA medium pizza is cut into 3 equal parts, and each part is sold for 15.95. A small pizza is sold for 12.95. Which is the better buy? Use calculations to support your answer.
  16. 5(a)3 marksOn graph paper, draw the x-axis and the y-axis. Using a scale of 1 cm to represent 1 unit on both axes, draw the triangle DEF with vertices D (1, 1), E (3, 1) and F(1, 4).
  17. 5(b)(i)5 marksDraw the image of ΔDEF under reflection in the line x = 4. Name the image ΔD'E'F'.
  18. 5(b)(ii)1 markDraw the image of ΔD'E'F' under the translation [0, -3]. Name the image D"E"F".
  19. 5(b)(iii)1 markName the type of transformation that maps ΔDEF onto ΔD"E"F".
  20. 5(c)4 marksCalculate, to the NEAREST degree, the angle of elevation of the sun.
  21. 6(a)(i)4 marksCalculate the size of the angle marked x°. Show all steps in your calculations and give reasons for your answers.
  22. 6(a)(ii)1 markCalculate the size of the angle marked y°. Show all steps in your calculations and give reasons for your answers.
  23. 6(b)(i)8 marksEvaluate g(3) + g(-3)
  24. 6(b)(ii)1 markEvaluate f⁻¹(6)
  25. 6(b)(iii)1 markEvaluate fg(2)
  26. 7(a)5 marksUsing a horizontal scale of 2 cm to represent a height of 5 cm and a vertical scale of 2 cm to represent 50 applicants, draw a cumulative frequency curve of the heights. Start your horizontal scale at 150 cm.
  27. 7(b)(i)1 markUse your graph to estimate the number of applicants whose heights are less than 170 cm.
  28. 7(b)(ii)2 marksUse your graph to estimate the median height of applicants.
  29. 7(b)(iii)2 marksUse your graph to estimate the height that 25% of the applicants are less than.
  30. 7(b)(iv)2 marksUse your graph to estimate the probability that an applicant selected at random has a height that is no more than 162 cm.
  31. 8(a)(i)7 marksStudy the number pattern in the table below and complete lines (i), (ii) and (iii) in your answer booklet.
  32. 8(a)(ii)1 markStudy the number pattern in the table below and complete lines (i), (ii) and (iii) in your answer booklet.
  33. 8(a)(iii)1 markStudy the number pattern in the table below and complete lines (i), (ii) and (iii) in your answer booklet.
  34. 8(b)3 marksShow that (a-b)² (a + b) + ab(a+b) = a³ + b³.
  35. 9(a)4 marksWrite 5x² + 2x - 7 in the form a(x + b)² + c, where a, b, and c are real numbers.
  36. 9(b)(i)3 marksHence, or otherwise, determine the minimum value of the function y = 5x² + 2x - 7.
  37. 9(b)(ii)1 markHence, or otherwise, determine the value of x at which the minimum occurs.
  38. 9(c)3 marksFind the values of x for which 5x² + 2x - 7 = 0.
  39. 9(d)(i)5 marksSketch the graph of y = 5x² + 2x - 7, clearly showing the coordinates of the minimum point.
  40. 9(d)(ii)1 markSketch the graph of y = 5x² + 2x - 7, clearly showing the value of the y-intercept.
  41. 9(d)(iii)1 markSketch the graph of y = 5x² + 2x - 7, clearly showing the points where the graph cuts the x-axis.
  42. 10(a)(i)6 marksUsing the graph, calculate the acceleration of the cyclist during the first 15 seconds.
  43. 10(a)(ii)1 markUsing the graph, calculate the distance traveled by the cyclist between the period t = 15 and t = 35 seconds.
  44. 10(b)(i)5 marksWhat was the average speed during the first 2 hours?
  45. 10(b)(ii)1 markWhat did the athlete do between 2 and 3 hours after the start of the journey?
  46. 10(b)(iii)1 markWhat was the average speed on the return journey?
  47. 10(c)(i)1 markWrite the equation of the line HK.
  48. 10(c)(ii)3 marksWrite the set of three inequalities which define the shaded region GHK.
  49. 11(a)(i)6 marksCalculate the size of angle PXQ, expressing your answer correct to the nearest degree.
  50. 11(a)(ii)1 markCalculate the area of triangle YXZ.
  51. 11(b)(i)(a)3 marksCalculate the size of angle SJM.
  52. 11(b)(i)(b)1 markCalculate the size of angle JKM.
  53. 11(b)(ii)(a)6 marksCalculate, expressing your answer correct to ONE decimal place, the length of MJ.
  54. 11(b)(ii)(b)1 markCalculate, expressing your answer correct to ONE decimal place, the length of JK.
  55. 12(a)6 marksDraw a sketch of the earth showing the location of Antigua and of Belize, their associated circles of latitude and longitude, the equator, and the Greenwich Meridian.
  56. 12(b)5 marksCalculate the shortest distance between Antigua and Belize measured along their common circle of latitude.
  57. 12(c)4 marksCalculate the shortest distance between Antigua and Bahia Blanka measured along the common circle of longitude.
  58. 13(a)(i)5 marksExpress in terms of x and y: AB
  59. 13(a)(ii)1 markExpress in terms of x and y: BD
  60. 13(a)(iii)1 markExpress in terms of x and y: DP
  61. 13(b)2 marksShow that AP = x - 2y.
  62. 13(c)4 marksProve that A, P and E are collinear.
  63. 13(d)4 marksUse a vector method to prove that triangle AED is isosceles.
  64. 14(a)(i)7 marksShow that M is a non-singular matrix.
  65. 14(a)(ii)1 markWrite down the inverse of M.
  66. 14(a)(iii)1 markWrite down the 2x2 matrix which is equal to the product M x M⁻¹.
  67. 14(a)(iv)1 markPre-multiply both sides of the following matrix equation by M⁻¹: [[2, 5], [7, 15]] * [[x], [y]] = [[-3], [17]]. Hence solve for x and y.
  68. 14(b)(i)8 marksWrite down the 2x2 matrix, R, which represents a reflection in the y-axis.
  69. 14(b)(ii)1 markWrite down the 2x2 matrix, N, which represents a clockwise rotation of 180° about the origin.
  70. 14(b)(iii)1 markWrite down the 2x1 matrix, T, which represents a translation of -3 units parallel to the x-axis and 5 units parallel to the y-axis.
  71. 14(b)(iv)1 markDetermine the coordinates of P' and P''.

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