Quelpr

CSEC Mathematics · May/June 2016 · Paper 2

59 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 marksCalculate 3 3/8 - 2 1/4 / 1 1/2, giving your answer as a fraction in its lowest terms.
  2. 1(a)(ii)2 marksCalculate (2.86 + 0.75) + 0.481^2 giving your answer correct to 2 decimal places.
  3. 1(b)(i)2 marksCalculate the selling price (paid cash).
  4. 1(b)(ii)2 marksCalculate the profit or loss as a percentage of the cost price.
  5. 1(c)3 marksWhich size of orange juice is the most cost-effective buy? Justify your answer.
  6. 2(a)(i)2 marksFactorize completely: 4a^2 - 16.
  7. 2(a)(ii)2 marksFactorize completely: 3y^2 + 2y - 8.
  8. 2(b)5 marksSolve the simultaneous equations: 2x + y = 3 and 5x - 2y = 12.
  9. 2(c)3 marksCalculate the values of t and u.
  10. 3(a)(i)2 marksWrite an expression, in x, in its simplest form, for the TOTAL number of students in the class.
  11. 3(a)(ii)2 marksState whether the following relationships are true or false: H U F = U and H ∩ F' = Ø.
  12. 3(a)(iii)2 marksDetermine the number of students who study BOTH History and French.
  13. 3(b)(i)4 marksUsing a ruler, a pencil and a pair of compasses, construct triangle PQR with PQ = 5 cm, ∠ PQR = 60° and ∠ QPR = 90°.
  14. 3(b)(ii)2 marksMeasure and state the length of PR and the measure of ∠ PRQ.
  15. 4(a)2 marksCalculate the volume of the box using the external measurements.
  16. 4(b)(i)1 markComplete the statement: The internal length of the box is 30 cm – 2 × 1.5 cm =
  17. 4(b)(ii)2 marksComplete the statement: The internal width of the box is
  18. 4(b)(iii)1 markComplete the statement: The internal depth of the box is
  19. 4(c)2 marksCalculate the internal volume of the box.
  20. 4(d)3 marksThe box is made of silver which has a mass of 10.5 g for each cm³. Calculate the mass of the silver box, giving your answer in kg.
  21. 5(a)(i)2 marksDetermine, giving reasons for EACH of your answers, the value of x.
  22. 5(a)(ii)2 marksDetermine, giving reasons for EACH of your answers, the value of y.
  23. 5(a)(iii)2 marksDetermine, giving reasons for EACH of your answers, the value of w.
  24. 5(b)(i)3 marksDescribe FULLY the transformation which maps RST onto R'S'T'.
  25. 5(b)(ii)3 marksTriangle RST is reflected in the line x = 6. On the graph above, draw triangle R'' S'' T'', the image of Δ RST, after the reflection. Write down the coordinates of R''.
  26. 6(a)(i)2 marksDetermine the equation of the line which is parallel to the line x + y = 3 and passes through the origin.
  27. 6(a)(ii)2 marksDetermine the equation of the line which is perpendicular to the line x + y = 3 and passes through the midpoint of AB.
  28. 6(b)(i)2 marksComplete the table by calculating and inserting the missing values of y.
  29. 6(b)(ii)2 marksOn the same axes used in Part (a) on page 16, draw the graph of y = x^2 - 2x – 3.
  30. 6(b)(iii)3 marksUsing information from your graph, complete EACH of the following statements: The minimum value of y = x^2 - 2x – 3 occurs when x = (blank) and The values of x for which x^2 - 2x - 3 = x + 3 are x = (blank) and x =…
  31. 7(a)4 marksComplete the frequency table for the data shown above.
  32. 7(b)(i)1 markFor the class interval 21-30, state the upper class boundary.
  33. 7(b)(ii)1 markFor the class interval 21-30, state the class width.
  34. 7(b)(iii)1 markFor the class interval 21-30, state the class midpoint.
  35. 7(c)4 marksOn the grid on page 19, using a scale of 2 cm to represent 10 kg on the x-axis, and 1 cm to represent 1 bag on the y-axis, draw a histogram to represent the data contained in your frequency table above.
  36. 8(a)2 marksDraw Figure 4 of the sequence.
  37. 8(b)(i)2 marksComplete the table by inserting the missing values in the row numbered (i) for N=4.
  38. 8(b)(ii)3 marksComplete the table by inserting the missing values in the row numbered (ii) where S=255.
  39. 8(b)(iii)3 marksComplete the table by inserting the missing values in the row numbered (iii) for N=10.
  40. 9(a)(i)4 marksWrite an expression, in terms of x, for EACH of the following: f^-1(x), g^-1(x), fg(x).
  41. 9(a)(ii)3 marksShow that (fg)^-1(5) = g^-1 f^-1(5).
  42. 9(b)(i)1 markState the time of day at which the car arrived at Town C.
  43. 9(b)(ii)2 marksCalculate the TOTAL time, in minutes, for which the car stopped during the journey.
  44. 9(b)(iii)2 marksDetermine the constant speed of the car during Stage 2 of the journey.
  45. 9(b)(iv)3 marksCalculate the average speed of the car for the time during which it was moving.
  46. 10(a)(i)2 marksCalculate, giving reasons for your answer, the measure of ∠EHF.
  47. 10(a)(ii)2 marksCalculate, giving reasons for your answer, the measure of ∠FGH.
  48. 10(a)(iii)2 marksCalculate, giving reasons for your answer, the measure of ∠JHE.
  49. 10(a)(iv)2 marksCalculate, giving reasons for your answer, the measure of ∠JGH.
  50. 10(b)(i)1 markCalculate, giving your answer to 1 decimal place where appropriate, the measure of ∠RTS.
  51. 10(b)(ii)3 marksCalculate, giving your answer to 1 decimal place where appropriate, the length of ST.
  52. 10(b)(iii)3 marksCalculate, giving your answer to 1 decimal place where appropriate, the height of the tower, FT.
  53. 11(a)(i)3 marksExpress in the form (x, y) the vectors AB and AC.
  54. 11(a)(ii)3 marksHence, determine whether A, B and C are collinear, giving the reasons for your answer.
  55. 11(b)2 marksDetermine the value of x for which the matrix (3, x; 2, 4) is singular.
  56. 11(c)(i)1 markDetermine NP.
  57. 11(c)(ii)1 markGiven that PN = (19, 11; 11, 4), determine whether matrix multiplication is commutative.
  58. 11(c)(iii)2 marksDetermine N^-1, the inverse of N.
  59. 11(c)(iv)3 marksHence, calculate the values of x and y for which (4, 1; 3, 2) * (x, y) = (1, 2).

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