CSEC Mathematics · 2022 · Paper 2

55 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.

1. 1(a)(i)a)1 markUsing a calculator, or otherwise, find the EXACT value of \frac{7}{8} + \frac{1}{6} \div \frac{2}{9}.
2. 1(a)(i)b)1 markFind the EXACT value of \frac{8}{0.4^3}.
3. 1(a)(ii)1 markFind the value of \sqrt{26.8 - 2.5^{\frac{3}{2}}}, correct to 2 decimal places.
4. 1(b)(i)2 marksBananas cost $3.85 per kilogram. Ms Rekha buys 25 kg of bananas and receives a discount of 12%. How much money does she spend on bananas?
5. 1(b)(ii)2 marksMs Rekha spends $165.31, inclusive of a sales tax of 15%, on oranges. Calculate the original price of the oranges.
6. 1(b)(iii)2 marksThe ratio of the number of bananas to the number of oranges is 2:3. Furthermore, there are 24 more oranges than bananas. Calculate the number of bananas Ms Rekha bought.
7. 2(a)(i)2 marksFactorize completely the quadratic expression 5x^2 - 9x + 4.
8. 2(a)(ii)1 markHence, solve the equation 5x^2 - 9x + 4 = 0.
9. 2(b)3 marksMake v the subject of the formula w = \frac{5+v}{v-3}.
10. 2(c)(i)1 markWrite an equation showing the relationship between h and p.
11. 2(c)(ii)2 marksGiven that h = 5.4 when p = 1.44, determine the value of h when p = 2.89.
12. 3(a)(i)3 marksDescribe fully the single transformation that maps shape P onto shape Q.
13. 3(a)(ii)2 marksDescribe fully the single transformation that maps shape P onto shape R.
14. 3(a)(iii)3 marksDescribe fully the single transformation that maps shape P onto shape S.
15. 3(b)1 markOn the grid provided on page 10, draw the image of shape P after a translation by the vector \begin{pmatrix}-2\\3\end{pmatrix}. Label this image T.
16. 4(a)(i)1 markDetermine g\left(\frac{1}{3}\right).
17. 4(a)(ii)2 marksDetermine f^{-1}(-3).
18. 4(b)(i)2 marksWrite the equation of the line L in the form y = mx + c.
19. 4(b)(ii)a)1 markWrite down the coordinates of the point where Q crosses the x-axis.
20. 4(b)(ii)b)1 markWrite down the coordinates of the point where Q crosses the y-axis.
21. 4(b)(ii)c)1 markOn the grid on page 14, draw the graph of the line Q.
22. 4(b)(iii)1 markComplete the statement: According to the graph, the solution of the system of equations consisting of L and Q is _______.
23. 5(a)3 marksComplete the table and use the information to calculate an estimate of the mean height of the students, giving your answer correct to 1 decimal place.
24. 5(b)1 markUsing the information provided, and your response in (a), comment on the distribution of the heights of the students in both Class A and Class B.
25. 5(c)(i)1 markComplete the cumulative frequency table below and use the information to construct the cumulative frequency curve on the grid provided on page 19.
26. 5(c)(ii)a)1 markUse your cumulative frequency curve to find an estimate of the median height of the group of students.
27. 5(c)(ii)b)1 markUse your cumulative frequency curve to find the probability that a student chosen at random would be taller than 130 cm.
28. 6(a)4 marksCalculate the TOTAL surface area of the solid. [The surface area, A, of a cylinder with radius r is A = 2\pi r^2 + 2\pi r h].
29. 6(b)3 marksCalculate the volume of the solid.
30. 6(c)2 marksThe solid is made from gold. One cubic centimetre of gold has a mass of 19.3 grams. The cost of 1 gram of gold is $42.62. Calculate the cost of the gold used to make the solid.
31. 7(a)2 marksDraw the diagram for 4 tables using Arrangement L.
32. 7(b)(i)2 marksComplete the row numbered (i) for T = 4 tables in the table provided.
33. 7(b)(ii)2 marksComplete the row numbered (ii) where the number of chairs in Arrangement M is 130.
34. 7(b)(iii)2 marksComplete the row numbered (iii) giving the number of chairs for n tables for both Arrangement L and Arrangement M.
35. 7(c)2 marksLeon needs to arrange tables to seat 70 people for a birthday party. Which of the arrangements, L or M, will allow him to rent the LEAST number of tables? Use calculations to justify your answer.
36. 8(a)3 marksWrite down THREE inequalities, in terms of x and/or y, other than x \ge 0 and y \ge 0, to represent this information.
37. 8(b)1 markA car can carry 4 people and a minivan can carry 6 people. There are at most 60 persons to be taken on a tour. Show that 2x + 3y \le 30.
38. 8(c)5 marksOn the grid below, plot the four lines associated with the inequalities in (a) and (b). Shade and label the region that satisfies ALL four inequalities R.
39. 8(d)(i)2 marksDetermine the two combinations for the MINIMUM number of cars and minivans that can be used to carry EXACTLY 60 people on the tour.
40. 8(d)(ii)1 markThe company charges 75 to rent a car and 90 to rent a minivan. Show that the MINIMUM rental cost for this tour is $990.
41. 9(a)(i)a)1 markExplain, giving a reason, why angle HJM = 38^\circ.
42. 9(a)(i)b)1 markExplain, giving a reason, why angle MJK = 90^\circ.
43. 9(a)(ii)a)2 marksDetermine the value of Angle MLJ. Show detailed working where appropriate.
44. 9(a)(ii)b)1 markDetermine the value of Angle LJK.
45. 9(a)(ii)c)1 markDetermine the value of Angle JHM.
46. 9(b)(i)1 markComplete the diagram above by inserting the value of angle RLT.
47. 9(b)(ii)2 marksCalculate RT, the distance between the two ships.
48. 9(b)(iii)3 marksDetermine the bearing of T from R.
49. 10(a)(i)1 markWrite the coordinates of P', the image of the point P(7, 11) after it undergoes a rotation by 90^\circ anticlockwise about the origin, O.
50. 10(a)(ii)2 marksT is the combined transformation of A followed by B. Determine the elements of the matrix representing the transformation T.
51. 10(a)(iii)2 marksDescribe, geometrically, the transformation represented by T.
52. 10(b)2 marksDetermine the value of k, given that the matrix C is singular.
53. 10(c)(i)1 markExpress \vec{BX} in terms of u and v.
54. 10(c)(ii)a)1 markExpress \vec{BM} in terms of u and v.
55. 10(c)(ii)b)3 marksUsing a vector method, show that the ratio YM : YA is 1 : 3. Show ALL working.