Quelpr

CSEC Mathematics · May/June 2012 · Paper 2

61 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 1/5 - 2/3) / (2 4/5), giving your answer as a fraction in its lowest terms.
  2. 1(b)4 marksCopy and complete the table below, inserting the missing values at (i) and (ii).
  3. 1(c)1 markCalculate the value of EC 1 in TT .
  4. 1(c)(ii)1 markCalculate the value of US 80 in EC .
  5. 1(c)(iii)3 marksCalculate the value of TT 648 in US .
  6. 2(a)(i)2 marksFactorise completely: 2x²y + 6x²y².
  7. 2(a)(ii)1 markFactorise completely: 9x² - 4.
  8. 2(a)(iii)2 marksFactorise completely: 4x² + 8xy - xy - 2y².
  9. 2(b)3 marksSolve for x: (2x-3)/3 + (5-x)/2 = 3.
  10. 2(c)4 marksSolve the simultaneous equations: 3x - 2y = 10 and 2x + 5y = 13.
  11. 3(a)2 marksCopy and complete the Venn diagram below to show the number of students in the subsets marked y and z.
  12. 3(a)(ii)a)1 markWrite an expression in x to represent the TOTAL number of students in the survey.
  13. 3(a)(ii)b)2 marksWrite an equation in x to represent the total number of students in the survey and hence solve for x.
  14. 3(b)(i)2 marksCopy the diagram and label it to show the points Q and R, and the distances 20 km and 15 km.
  15. 3(b)(ii)2 marksCalculate PR, the shortest distance of the ship from the port where the journey started.
  16. 3(b)(iii)3 marksCalculate the measure of angle QPR, giving your answer to the nearest degree.
  17. 4(a)(i)2 marksCalculate the length of the arc ABC.
  18. 4(a)(ii)2 marksCalculate the perimeter of the sector OABC.
  19. 4(a)(iii)2 marksCalculate the area of the sector OABC.
  20. 4(b)(i)2 marksCalculate the volume of the prism.
  21. 4(b)(ii)2 marksCalculate the mass of the prism, to the nearest kg, given that 1 cm³ of tin has a mass of 7.3 kg.
  22. 5(a)(i)4 marksUsing a ruler, a pencil and a pair of compasses, construct triangle PQR with PQ = 8 cm, ∠PQR = 60° and ∠QPR = 45°.
  23. 5(a)(ii)1 markMeasure and state the length of RQ.
  24. 5(b)(i)2 marksDetermine the gradient of the line, l.
  25. 5(b)(ii)2 marksDetermine the equation of the line, l.
  26. 5(b)(iii)1 markDetermine the midpoint of the line segment, TS.
  27. 5(b)(iv)2 marksDetermine the length of the line segment, TS.
  28. 6(a)2 marksLocate the centre of enlargement, showing your method clearly.
  29. 6(b)2 marksState the scale factor and the coordinates of the centre of the enlargement.
  30. 6(c)2 marksDetermine the value of Area of PQR / Area of LMN.
  31. 6(d)2 marksDraw and label triangle ABC with coordinates (-4, 4), (-1, 4) and (-1, 2) respectively.
  32. 6(e)3 marksDescribe fully the single transformation which maps triangle LMN on to triangle ABC.
  33. 7(a)2 marksCopy and complete the table to show the cumulative frequency.
  34. 7(b)5 marksUsing a scale of 2 cm to represent 10 years on the x-axis and 1 cm to represent 5 persons on the y-axis, draw the cumulative frequency curve for the data.
  35. 7(c)(i)2 marksUse your graph drawn at (b) above to estimate the median age for the data.
  36. 7(c)(ii)2 marksUse your graph drawn at (b) above to estimate the probability that a person who visited the clinic was 75 years or younger. Draw lines on your graph to show how these estimates were obtained.
  37. 8(a)2 marksOn the answer sheet provided, draw the fourth figure (Figure 4) in the sequence.
  38. 8(b)(i)2 marksStudy the patterns in the table below, and on your answer sheet, complete the row numbered (i) for Figure 4.
  39. 8(b)(ii)2 marksStudy the patterns in the table below, and on your answer sheet, complete the row numbered (ii) where the Area of Triangle is 100.
  40. 8(b)(iii)2 marksStudy the patterns in the table below, and on your answer sheet, complete the row numbered (iii) for Figure 20.
  41. 8(b)(iv)2 marksStudy the patterns in the table below, and on your answer sheet, complete the row numbered (iv) for Figure n.
  42. 9(a)(i)5 marksSolve the pair of simultaneous equations: y = 8 - x and 2x² + xy = -16.
  43. 9(a)(ii)2 marksState, giving the reason for your answer, whether the line y = 8 - x is a tangent to the curve 2x² + xy = -16.
  44. 9(b)(i)3 marksWrite THREE inequalities for the constraints given.
  45. 9(b)(ii)1 markOn the answer sheet provided, shade the region of the graph which represents the solution set for the inequalities in (b)(i).
  46. 9(b)(iii)1 markState the coordinates of the points which represent the vertices of the region showing the solution set.
  47. 9(b)(iv)3 marksThe florist sells a bouquet of flowers to make a profit of 3 on each rose and 4 on each orchid. Determine the MAXIMUM possible profit on the sale of a bouquet.
  48. 10(a)(i)3 marksCalculate the length of RS.
  49. 10(a)(ii)3 marksCalculate the measure of ∠QTS.
  50. 10(b)(i)a)2 marksCalculate, showing working where necessary, the measure of angle OUZ.
  51. 10(b)(i)b)3 marksCalculate, showing working where necessary, the measure of angle UVY.
  52. 10(b)(i)c)2 marksCalculate, showing working where necessary, the measure of angle UWO.
  53. 10(b)(ii)a)1 markName the triangle in the diagram which is congruent to triangle ZOU.
  54. 10(b)(ii)b)1 markName the triangle in the diagram which is congruent to triangle YXU.
  55. 11(a)(i)a)2 marksExpress in the form (x, y) the vector BA.
  56. 11(a)(i)b)2 marksExpress in the form (x, y) the vector BC.
  57. 11(a)(ii)1 markState ONE geometrical relationship between BA and BC.
  58. 11(a)(iii)2 marksDraw a sketch to show the relative positions of A, B and C.
  59. 11(b)(i)3 marksCalculate the values of a and b such that (a-4, b) * (2, -4; 1, -3) = (20, 0; 0, 2).
  60. 11(b)(ii)2 marksHence, or otherwise, write down the inverse of (2, -4; 1, -3).
  61. 11(b)(iii)3 marksUse the inverse of (2, -4; 1, -3) to solve for x and y in the matrix equation (2, -4; 1, -3) * (x, y) = (12, 7).

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