Quelpr

CSEC Mathematics

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)(i)2 marksUsing a calculator, or otherwise, calculate 5 1/2 ÷ 3 2/3 + 1 4/5, giving your answer as a fraction in its lowest terms.
  2. 1(a)(ii)1 mark165 × 0.38², giving your answer as an EXACT value.
  3. 1(b)(i)1 markWrite your answer in (a)(ii) correct to two decimal places.
  4. 1(b)(ii)1 markWrite your answer in (a)(ii) correct to three significant figures.
  5. 1(b)(iii)1 markWrite your answer in (a)(ii) correct to the nearest whole number.
  6. 1(c)(i)1 markDetermine the simple interest earned.
  7. 1(c)(ii)2 marksDetermine the annual interest rate paid by the credit union.
  8. 1(c)(iii)2 marksDetermine the length of time it will take for Mr Adams' investment to be doubled, at the same rate of interest.
  9. 2(a)(i)2 marksDetermine the value of 1 * 2.
  10. 2(a)(ii)3 marksDetermine whether the operation denoted by * is commutative. Justify your answer.
  11. 2(b)(i)2 marksSolve the inequality 3 - 2x > 5.
  12. 2(b)(ii)1 markRepresent your answer in (b)(i) on the number line shown below.
  13. 2(c)(i)2 marksLet x represent the cost of an adult ticket and y the cost of a ticket for a child. Write TWO equations in x and y to represent the information above.
  14. 2(c)(ii)2 marksSolve the equations to determine the cost of an adult ticket.
  15. 3(a)(i)1 markState the value of n(P ∩ R).
  16. 3(a)(ii)a)2 marksList the members of M ∩ P.
  17. 3(a)(ii)b)2 marksList the members of M ∪ R'.
  18. 3(b)(i)4 marksUsing a ruler, a pencil and a pair of compasses, construct triangle PQR with PQ = 8 cm, angle PQR = 120° and QR = 5 cm.
  19. 3(b)(ii)1 markMeasure and state the length of the side PR.
  20. 3(b)(iii)2 marksOn your diagram in (b)(i), construct the point S, such that PQRS forms a parallelogram.
  21. 4(a)(i)2 marksWrite the equation of the line, l, in the form y = mx + c.
  22. 4(a)(ii)1 markHence, determine the gradient of the line, l.
  23. 4(a)(iii)2 marksThe point P with coordinates (r, 2) lies on the line l. Determine the value of r.
  24. 4(a)(iv)2 marksFind the equation of the straight line passing through the point (6, 0) which is perpendicular to l.
  25. 4(b)(i)2 marksDraw the straight lines x + y = 10 and y = x on the grid below.
  26. 4(b)(ii)2 marksOn the same grid, shade the region which satisfies the FOUR inequalities x ≥ 0, y ≥ 0, x + y ≤ 10 and x ≥ y.
  27. 5(a)(i)1 markWhat is the name of the polygon shown above?
  28. 5(a)(ii)1 markCalculate the perimeter of the polygon EFGHIJ.
  29. 5(a)(iii)2 marksDetermine the size of each interior angle of the polygon.
  30. 5(a)(iv)3 marksShow, by calculation, that the area of the polygon, to the nearest whole number, is 65 cm².
  31. 5(b)(i)3 marksDetermine the capacity of the tank, in litres.
  32. 5(b)(ii)2 marksCalculate the height, h, in metres, of the tank.
  33. 6(a)1 markState the coordinates of R.
  34. 6(b)(i)2 marksOn the diagram above, draw ΔP'Q'R', a reflection of ΔPQR in the line y = 1.
  35. 6(b)(ii)2 marksOn the diagram above, draw ΔP''Q''R'', a reflection of ΔP'Q'R' in the line x = 0.
  36. 6(c)3 marksDescribe, fully, the single transformation that maps ΔP''Q''R'' onto ΔPQR.
  37. 6(d)2 marksTriangle PQR undergoes an enlargement of scale factor 2. Calculate the area of its image.
  38. 7(a)(i)1 markFor the data above, determine the range.
  39. 7(a)(ii)1 markFor the data above, determine the median.
  40. 7(a)(iii)2 marksFor the data above, determine the interquartile range.
  41. 7(a)(iv)2 marksDetermine the probability that a student chosen at random scores less than half the total marks in the test.
  42. 7(b)6 marksOn the grid on page 23, using a scale of 2 cm to represent 5 units on the x-axis and 1 cm to represent 1 unit on the y-axis, draw a frequency polygon to represent the information in the table.
  43. 8(a)2 marksDraw Figure 4 of the sequence.
  44. 8(b)(i)2 marksComplete the row numbered (i) for Figure 4.
  45. 8(b)(ii)2 marksComplete the row numbered (ii) where the perimeter of the figure is 19 + 20 + 2 = 41.
  46. 8(b)(iii)2 marksComplete the row numbered (iii) where the number of toothpicks in the pattern is 127.
  47. 8(b)(iv)2 marksComplete the row numbered (iv) for Figure n.
  48. 9(a)(i)3 marksShow, by calculation, that the EXACT roots of the quadratic equation x² + 2x - 5 = 0 are -1 ± √6.
  49. 9(a)(ii)4 marksHence, or otherwise, solve the simultaneous equations 2 + x = y and xy = 5.
  50. 9(b)(i)2 marksComplete the table for the function y = 2ˣ.
  51. 9(b)(ii)4 marksOn the grid provided on page 27, draw the graph of y = 2ˣ, using a scale of 2 cm to represent 1 unit on the x-axis and 1 cm to represent 1 unit on the y-axis.
  52. 9(b)(iii)2 marksDrawing appropriate lines on your graph, determine the value of x for which 2ˣ = 11.
  53. 10(a)(i)2 marksCalculate, giving reasons for EACH step of your answer, the measure of ∠ACD.
  54. 10(a)(ii)2 marksCalculate, giving reasons for EACH step of your answer, the measure of ∠AED.
  55. 10(a)(iii)2 marksCalculate, giving reasons for EACH step of your answer, the measure of ∠OAC.
  56. 10(a)(iv)2 marksCalculate, giving reasons for EACH step of your answer, the measure of ∠ABC.
  57. 10(b)(i)1 markA straight adjustable wire connects R to P along the top of the cuboid. Calculate the length of the wire RP.
  58. 10(b)(ii)2 marksThe connection at P is now adjusted and moved to T. Calculate the length of the wire RT.
  59. 10(b)(iii)2 marksCalculate the angle TRV.
  60. 10(b)(iv)2 marksComplete the following statements: The size of the angle through which the wire moves from RP to RT is _____. An angle which is the same in size as RTV is _____.
  61. 11(a)(i)2 marksDetermine the vector OQ.
  62. 11(a)(ii)1 markShow that OQ is parallel to RS, giving a reason for your answer.
  63. 11(b)(i)1 markExpress XZ in terms of a and b.
  64. 11(b)(ii)3 marksExpress MY in terms of a and b.
  65. 11(c)(i)2 marksDetermine A⁻¹, the inverse of A.
  66. 11(c)(ii)2 marksShow that A⁻¹A = I, the identity matrix.
  67. 11(c)(iii)2 marksDetermine the matrix A².
  68. 11(c)(iv)a)1 markExplain why the matrix product AB is NOT possible.
  69. 11(c)(iv)b)1 markWithout calculating, state the order of the matrix product BA.

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