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CSEC Mathematics · May/June 2017 · Paper 2

68 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)(i)2 marksUsing a calculator, or otherwise, calculate the EXACT value of 4 1/3 - 1 2/5 ÷ 4/15
  2. 1(a)(ii)2 marksCalculate the EXACT value of (3.1-1.15)² / 0.005
  3. 1(b)(i)2 marksCalculate the TOTAL cost of a phone under Plan A.
  4. 1(b)(ii)2 marksDetermine which of the two plans, A or B, is the better deal. Justify your answer.
  5. 1(c)(i)2 marksCalculate the TOTAL amount that John pays for electricity consumption for the month of March 2016.
  6. 1(c)(ii)2 marksFor the next month, April 2016, John pays $2351.10 for electricity consumption. Determine his meter reading at the end of April 2016.
  7. 2(a)(i)2 marksFactorize the following expressions completely: 6y² - 18xy
  8. 2(a)(ii)1 markFactorize the following expressions completely: 4m² - 1
  9. 2(a)(iii)2 marksFactorize the following expressions completely: 2t² - 3t - 2
  10. 2(b)2 marksWrite as a single fraction and simplify (5p+2)/3 - (3p-1)/4
  11. 2(c)(i)2 marksDetermine the value of d when h = 29. Give your answer correct to 3 significant figures.
  12. 2(c)(ii)2 marksMake h the subject of the formula.
  13. 3(a)(i)1 markList the members of the subset M.
  14. 3(a)(ii)1 markList the members of the subset R.
  15. 3(a)(iii)4 marksDraw a Venn diagram that represents the relationship among the defined subsets of U.
  16. 3(b)(i)3 marksUsing a ruler, a pencil and a pair of compasses, construct accurately, the square ABCD, with sides 6 cm.
  17. 3(b)(ii)2 marksConstruct, as an extension of your drawing in (b)(i), the trapezium DABQ so that ∠ABQ = 120°. [Note: Credit will be given for clearly drawn construction lines.]
  18. 3(b)(iii)1 markHence, measure and state the length of BQ.
  19. 4(a)(i)2 marksFind the value of f(3) + f(-3).
  20. 4(a)(ii)2 marksCalculate the value of x for which f(x) = 5.
  21. 4(a)(iii)2 marksDetermine the inverse function f⁻¹(x).
  22. 4(b)(i)2 marksCalculate the gradient of the lines l₁ and l₂.
  23. 4(b)(ii)2 marksDetermine the equation of the line l₁.
  24. 4(b)(iii)2 marksWhat is the relationship between l₁ and l₂? Give a reason for your answer.
  25. 5(a)(i)2 marksDetermine, giving a reason for each step of your answer, the measure of angle RQT.
  26. 5(a)(ii)2 marksDetermine, giving a reason for each step of your answer, the measure of angle PRT.
  27. 5(a)(iii)2 marksDetermine, giving a reason for each step of your answer, the measure of angle SPT, given that angle SRT = 145° and angle PSR = 100°.
  28. 5(b)(i)3 marksDescribe completely the transformation that maps Δ ABC to Δ A'B'C'.
  29. 5(b)(ii)2 marksThe translation vector T = [4, -5] maps Δ A'B'C' to Δ A''B''C''. On the diagram above, draw the Δ A''B''C''.
  30. 6(a)(i)2 marksCalculate the area of the field.
  31. 6(a)(ii)3 marksCalculate the perimeter of the field.
  32. 6(b)(i)2 marksCalculate the area of the triangle ABC.
  33. 6(b)(ii)2 marksCalculate the length of the prism, if the volume is 540 cm³.
  34. 6(b)(iii)2 marksCalculate the surface area of the prism.
  35. 7(a)(i)1 markFor the class interval 20-39, as written in the table above, complete the following sentences: The upper class limit is ___________.
  36. 7(a)(ii)1 markFor the class interval 20-39, as written in the table above, complete the following sentences: The class width is ___________.
  37. 7(a)(iii)1 markFor the class interval 20-39, as written in the table above, complete the following sentences: Sixteen vehicles passed a checkpoint at no more than ___________ kmh⁻¹.
  38. 7(b)2 marksComplete the table shown above by inserting the missing values for the cumulative frequency column.
  39. 7(c)4 marksOn the grid provided on page 21, using a scale of 2 cm to represent 20 kmh⁻¹ on the x-axis, and 2 cm to represent 10 vehicles on the y-axis, draw the cumulative frequency curve to represent the information in the table.
  40. 7(d)(i)1 markOn your graph, draw reference lines to estimate the speed at which no more than 50% of the vehicles drove as they passed the checkpoint.
  41. 7(d)(ii)1 markWhat is the estimated speed?
  42. 8(a)2 marksDraw Figure 5 of the sequence in the space below.
  43. 8(b)1 markHow many dots would be in Figure 6?
  44. 8(c)2 marksComplete the row which corresponds to Figure 11 in the table above.
  45. 8(d)2 marksDetermine which figure in the sequence has 210 dots.
  46. 8(e)1 markWrite a simplified algebraic expression for the number of dots, d, in the Figure n.
  47. 8(f)2 marksShow that there is no diagram that has exactly 1000 dots.
  48. 9(a)(i)a)1 markCalculate the gradient of OA.
  49. 9(a)(i)b)1 markCalculate the gradient of AB.
  50. 9(a)(ii)3 marksComplete the following statements: The cyclist started from rest, where his velocity was ___________ ms⁻¹, and steadily increased his velocity by ___________ ms⁻¹ each second during the first 25 seconds. During the next…
  51. 9(a)(iii)3 marksDetermine the average speed of the cyclist over the 40-second period.
  52. 9(b)(i)2 marksWITHOUT solving, show that (1, 2) is a solution for the pair of simultaneous equations.
  53. 9(b)(ii)5 marksSolve the pair of simultaneous equations above to determine the other solution.
  54. 10(a)(i)2 marksUsing the geometrical properties of a circle to give reasons for each step of your answer, determine the measure of ∠SPQ.
  55. 10(a)(ii)3 marksUsing the geometrical properties of a circle to give reasons for each step of your answer, determine the measure of ∠OQS.
  56. 10(b)(i)2 marksOn the diagram below, not drawn to scale, label the known distances travelled and the known angles.
  57. 10(b)(ii)2 marksDetermine the measure of ∠ABC.
  58. 10(b)(iii)3 marksCalculate, to the nearest km, the distance AC.
  59. 10(b)(iv)3 marksShow that the bearing of A from C, to the nearest degree, is 260°.
  60. 11(a)(i)2 marksShow by multiplying A and B, that AB ≠ BA.
  61. 11(a)(ii)2 marksFind A⁻¹, the inverse of A.
  62. 11(a)(iii)1 markWrite down the 2 × 2 matrix representing the matrix product AA⁻¹.
  63. 11(b)(i)1 markWrite the following pair of simultaneous equations as a matrix equation.
  64. 11(b)(ii)2 marksWrite the solution of your matrix equation in (b)(i) as a product of two matrices.
  65. 11(c)(i)1 markExpress in the form [x, y], vector OS.
  66. 11(c)(ii)2 marksExpress in the form [x, y], vector PQ.
  67. 11(c)(iii)2 marksExpress in the form [x, y], vector RS.
  68. 11(c)(iv)2 marksState TWO geometrical relationships between PQ and RS.

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