CSEC Mathematics · 2021 · Paper 2

57 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)2 marksUsing a calculator, or otherwise, calculate the EXACT value of 1\frac{4}{7} \div \frac{2}{3} - 1\frac{5}{7}.
2. 1(b)1 markWhen Meghan started working, she was paid $85 each week. After a six-month probationary period, her pay was increased by 20%. How much was she paid each week after the increase?
3. 1(c)(i)a)1 markWrite the population in 2015 correct to 3 significant figures.
4. 1(c)(i)b)1 markWrite the population in 1965 in standard form.
5. 1(c)(ii)2 marksDetermine the percentage increase in the population from 1965 to 2015.
6. 1(d)2 marksThe ratio of teachers to male students to female students in a school is 3:17:18. If the TOTAL number of students in the school is 630, determine the number of teachers in the school.
7. 2(a)(i)1 markFind the value of n when T = 49.
8. 2(a)(ii)1 markMake T the subject of the formula.
9. 2(b)(i)2 marksWrite expressions in terms of x for Jim's age and Chris' age.
10. 2(b)(ii)3 marksIn two years' time, the product of Ally's age and Chris' age will be the same as the square of Jim's present age. Show that the equation x^2 - 4x - 21 = 0 represents the information given above.
11. 2(b)(iii)2 marksCalculate Ally's present age.
12. 3(a)(i)1 markCalculate the size of angle PRQ.
13. 3(a)(ii)2 marksCalculate the length of the side RQ.
14. 3(b)(i)1 markTriangle X is mapped onto Triangle Y by a reflection. State the equation of the mirror line.
15. 3(b)(ii)2 marksDescribe fully the transformation which maps Triangle X onto Triangle Z.
16. 3(b)(iii)1 markOn the diagram on page 10, translate Triangle Y using the vector \begin{pmatrix}-7 \\ 1\end{pmatrix}. Label this image V.
17. 3(b)(iv)2 marksOn the diagram on page 10, enlarge Triangle X about the centre, C(0, 0), and scale factor \frac{1}{2}. Label this image W.
18. 4(a)(i)1 markExpress the equation of the line L_1 in the form y = mx + c.
19. 4(a)(ii)1 markState the gradient of the line L_1.
20. 4(a)(iii)2 marksHence, determine the equation of the line L_2.
21. 4(b)(i)1 markDetermine the value of f(9).
22. 4(b)(ii)2 marksCalculate the value of fg(-3).
23. 4(b)(iii)2 marksDetermine the value of x, for which g(x) = \frac{5}{2}.
24. 5(a)(i)a)1 markUsing the table, determine the modal class of the amount of money spent.
25. 5(a)(i)b)2 marksCalculate an estimate of the mean amount of money spent, giving your answer correct to 2 decimal places.
26. 5(a)(ii)1 markDamion reports that the median amount spent is $84. Briefly explain why Damion's report could be correct.
27. 5(b)(i)2 marksComplete the table by inserting the missing values.
28. 5(b)(ii)1 markA student is selected at random. What is the probability that he/she was being driven to school on that day?
29. 5(b)(iii)2 marksOne of the girls is selected at random. What is the probability that she did NOT cycle to school?
30. 6(a)3 marksShow, by calculation, that the internal capacity (volume) of the trough is 8\,091\,000\text{ cm}^3.
31. 6(b)3 marksCalculate the volume of wood needed to make a trough.
32. 6(c)3 marksFarmer Brown must paint the INTERNAL surface of the trough. Given that 1 gallon of paint covers approximately 280\,000\text{ cm}^2 of surface, determine the TOTAL amount of paint, in litres, that is needed to paint…
33. 7(a)2 marksDraw Figure 4 of the pattern in the space provided.
34. 7(b)(i)2 marksComplete the row for Figure 5.
35. 7(b)(ii)2 marksComplete the row where the Number of Lines (L) is 66.
36. 7(b)(iii)2 marksComplete the row for Figure n.
37. 7(c)2 marksWrite a simplified expression, in terms of n, for the difference, d, between the number of lines and the perimeter of any figure, n.
38. 8(a)(i)1 markMarla must not spend more than $1\,200. Write an inequality to represent this information.
39. 8(a)(ii)1 markThe number of B-Flo phones must be greater than or equal to the number of C-Flex phones. Write down an inequality in x and y to show this information.
40. 8(a)(iii)4 marksRepresent the two inequalities on the grid shown. Label as R the region which satisfies both inequalities.
41. 8(a)(iv)1 markThe total number of mobile phones is represented by x + y. According to the graph on page 23, what is the largest possible value of x + y?
42. 8(b)(i)3 marksOn the grid provided on page 25, plot the remaining 4 points and draw the graph of the function y = x^2 + x - 4 for -4 \le x \le 3.
43. 8(b)(ii)1 markWrite down the maximum or minimum value of the function.
44. 8(b)(iii)1 markUsing a ruler, draw the axis of symmetry on the graph on page 25.
45. 9(a)(i)2 marksDetermine the value of angle ECD and give a reason to support your answer.
46. 9(a)(ii)2 marksDetermine the value of angle CEG and give a reason to support your answer.
47. 9(a)(iii)2 marksDetermine the value of angle CGF and give a reason to support your answer.
48. 9(b)(i)1 markComplete the diagram to show the information given.
49. 9(b)(ii)3 marksCalculate QR, the distance between the two ships, to the nearest km.
50. 9(b)(iii)2 marksCalculate how far due south is Ship R of the harbour, H.
51. 10(a)(i)2 marksCalculate the matrix product \begin{pmatrix}5 & 4 \\ -3 & -2\end{pmatrix}\begin{pmatrix}2 & 1 & -4 \\ 0 & 3 & 6\end{pmatrix}.
52. 10(a)(ii)1 markState why the two matrices in (a)(i) are conformable for multiplication.
53. 10(b)2 marksDetermine the inverse of \begin{pmatrix}5 & 4 \\ -3 & -2\end{pmatrix}.
54. 10(c)(i)2 marks\vec{CD}
55. 10(c)(ii)2 marks\vec{OE}
56. 10(d)(i)1 markWrite \vec{OR} as a column vector.
57. 10(d)(ii)2 marksDetermine |\vec{QR}|.