Quelpr

CSEC Mathematics · January 2017 · Paper 2

67 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: 3 1/2 × 1 2/5
  2. 1(a)(ii)2 marksUsing a calculator, or otherwise, calculate the EXACT value of: 5.47 - √(0.1014 / 1.5)
  3. 1(b)(i)1 markCalculate the value of P.
  4. 1(b)(ii)1 markCalculate the value of Q.
  5. 1(b)(iii)2 marksAn adult ticket is TWICE the cost of a youth ticket. Calculate the value of R.
  6. 1(b)(iv)3 marksThe bus company pays taxes of 15% on each ticket sold. Calculate the taxes paid by the bus company.
  7. 2(a)2 marksWrite as a single fraction: (2x+3)/3 + (x-4)/4
  8. 2(b)2 marksWrite the following statement as an algebraic expression. The sum of a number and its multiplicative inverse is five times the number.
  9. 2(c)(i)2 marksFactorize completely: x² - 36
  10. 2(c)(ii)2 marksFactorize completely: 2x² + 5x - 12
  11. 2(d)2 marksThe formula for the volume of a cylinder is given as V = πr²h. Make r the subject of the formula.
  12. 2(e)2 marksGiven that x² + ax + b = (x + 2)² – 3, work out the values of a and b.
  13. 3(a)(i)3 marksComplete the Venn diagram above to represent the information, showing the number of students in EACH subset.
  14. 3(a)(ii)2 marksCalculate the value of x.
  15. 3(b)7 marksUsing a ruler, a pencil and a pair of compasses, construct the trapezium ABCD with AB = 8 cm, BAD = 60°, AD = 6 cm, ABC = 90° and AB parallel to CD. (Credit will be given for clearly drawn construction lines.)
  16. 4(a)(i)2 marksDetermine the values of: g(0) + g(5)
  17. 4(a)(ii)2 marksDetermine the values of: fg(5)
  18. 4(a)(iii)2 marksDetermine the values of: f⁻¹(1)
  19. 4(b)(i)2 marksDetermine the gradient of PQ
  20. 4(b)(ii)2 marksDetermine the coordinates of the midpoint of PQ
  21. 4(b)(iii)2 marksDetermine the equation of the perpendicular bisector of PQ.
  22. 5(a)(i)2 marksComplete the following statement: In the diagram above, the corresponding angles of Δ PQR and Δ STR are __________ and the __________ of their corresponding sides are the same.
  23. 5(a)(ii)3 marksDetermine the length of PQ.
  24. 5(b)(i)1 markState the coordinates of the point E.
  25. 5(b)(ii)3 marksDescribe fully the transformation that maps triangle DEF to its image, D'E'F'.
  26. 5(b)(iii)2 marksOn the grid above, draw triangle D''E''F'', the reflection of triangle D'E'F' in the x-axis.
  27. 6(a)(i)2 marksDetermine, in km, the actual distance between Anderlin and Jersey.
  28. 6(a)(ii)2 marksHow many units apart are they on the map?
  29. 6(b)(i)2 marksShow that the diameter of the circle is 11√2 cm.
  30. 6(b)(ii)2 marksCalculate the area of the circle
  31. 6(b)(iii)2 marksCalculate the area of the square
  32. 6(b)(iv)1 markCalculate the area of the shaded section.
  33. 7(a)4 marksOn the graph paper provided on page 21, draw a bar chart to represent the data given in the table above using a scale of 1 cm to represent 1 year on the x-axis and 1 cm to represent 25 tonnes on the y-axis.
  34. 7(b)2 marksDetermine the range of the number of bananas produced between 2010 and 2015.
  35. 7(c)(i)1 markDuring which year was there the greatest production of bananas?
  36. 7(c)(ii)1 markHow is this information shown on the bar chart?
  37. 7(d)(i)1 markBetween which two consecutive years was there the greatest change in the production of bananas?
  38. 7(d)(ii)1 markHow is this information shown on the bar chart?
  39. 7(e)1 markGive ONE reason why the bar chart is unsuitable for predicting the number of bananas produced in 2016.
  40. 8(a)2 marksDraw Figure 4 of the sequence in the space provided above.
  41. 8(b)(i)2 marksComplete the rows numbered (i), (ii), (iii) and (iv). For Figure 4, fill in 'Number of Unit Squares' and 'Perimeter of Figure'.
  42. 8(b)(ii)2 marksComplete the rows numbered (i), (ii), (iii) and (iv). For 'Number of Unit Squares' = 45, fill in 'Figure' and 'Perimeter of Figure'.
  43. 8(b)(iii)2 marksComplete the rows numbered (i), (ii), (iii) and (iv). For 'Figure' = 30, fill in 'Number of Unit Squares' and 'Perimeter of Figure'.
  44. 8(b)(iv)2 marksComplete the rows numbered (i), (ii), (iii) and (iv). For 'Figure' = n, fill in 'Number of Unit Squares' and 'Perimeter of Figure'.
  45. 9(a)(i)1 markExpress y in terms of x and a constant k.
  46. 9(a)(ii)1 markCalculate the value of the constant k.
  47. 9(a)(iii)2 marksDetermine the values of a and b.
  48. 9(b)(i)2 marksUse the graph to solve the equation x² - 6x + 8 = 0.
  49. 9(b)(ii)1 markWrite down the coordinates of the minimum point in the form (x, y).
  50. 9(b)(iii)3 marksWrite x² - 6x + 8 in the form a(x + h)² + k where a, h and k are constants.
  51. 9(b)(iv)3 marksOn the same axes, draw the graph of the straight line g(x) = x - 2.
  52. 9(b)(v)2 marksHence, solve the equation x² - 6x + 8 = x - 2.
  53. 10(a)(i)2 marksCalculate, giving reasons for each step of your answer, the measure of HKL
  54. 10(a)(ii)2 marksCalculate, giving reasons for each step of your answer, the measure of JÔK
  55. 10(a)(iii)2 marksCalculate, giving reasons for each step of your answer, the measure of JÂK.
  56. 10(b)(i)2 marksIndicate on the diagram the bearing 030° and the distances 90 km and 310 km.
  57. 10(b)(ii)2 marksCalculate, to the nearest km, the distance between Bellville (B) and Comptin (C).
  58. 10(b)(iii)2 marksCalculate, to the nearest degree, the measure of ABC.
  59. 10(b)(iv)3 marksDetermine the bearing of Comptin (C) from Bellville (B).
  60. 11(a)(i)2 marksDetermine the values of c and d.
  61. 11(a)(ii)1 markDetermine the image of (-5, 4) under the transformation T.
  62. 11(a)(iii)2 marksDescribe fully the transformation T.
  63. 11(a)(iv)2 marksFind the matrix that maps the point Q back onto the point P.
  64. 11(b)(i)1 markWrite as a column vector in the form [x, y]: the vector OP
  65. 11(b)(ii)2 marksWrite as a column vector in the form [x, y]: the vector QR.
  66. 11(b)(iii)2 marksDetermine the magnitude of the vector QR.
  67. 11(b)(iv)3 marksOn the graph provided on page 33, draw the vector OS = [7, 4]. Show that PQRS is a parallelogram.

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