CSEC Mathematics

52 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)2 marksEvaluate 3.8 × 10² + 1.7 × 10³, giving your answer in standard form.
2. 1(a)(ii)2 marksEvaluate (1/2 × 3/5) / (3 1/2), giving your answer as a fraction in its lowest terms.
3. 1(b)1 markExpress the number 6 as a binary number.
4. 1(c)2 marksJohn bought a car for $65 000. If the value of the car depreciates by 8% each year, how much will the car be worth at the end of 2 years?
5. 1(d)2 marksDetermine, as a percentage, the student's final mark for the Mathematics examination.
6. 2(a)(i)2 marksMake x the subject of the formula y = x/5 + 3p.
7. 2(a)(ii)2 marksSolve the following equation by factorization: 2x² - 9x = 0.
8. 2(b)2 marksGiven that the area enclosed by the fence is 378 square metres, show that l² - 3l - 378 = 0.
9. 2(c)(i)1 markRepresent this information as an equation in terms of F, e and an appropriate constant, k.
10. 2(c)(ii)2 marksUsing the equation obtained in (c)(i), or otherwise, determine the value of x and y.
11. 3(a)4 marksUsing a ruler, a pencil and a pair of compasses, construct the right-angled triangle ABC, such that AB = 5 cm, ∠ABC = 90° and ∠BAC = 60°.
12. 3(b)(i)a)1 markUsing the diagram, express c in terms of a and b.
13. 3(b)(i)b)2 marksWrite, in terms of a, b and c, an expression for sin θ + cos θ.
14. 3(b)(ii)2 marksUsing the results from (i) a) and b) on page 12, show that (sin θ)² + (cos θ)² = 1.
15. 4(a)(i)1 markDetermine the value of x for which the function is undefined.
16. 4(a)(ii)3 marksDetermine an expression for h⁻¹(x).
17. 4(b)(i)2 marksUsing the graph, determine the gradient of the line.
18. 4(b)(ii)1 markDetermine the equation of the line.
19. 4(b)(iii)2 marksDetermine the equation of the perpendicular line that passes through P.
20. 5(a)(i)2 marksIf this information is to be represented on a pie chart, what is the angle for the sector that will represent O-Fone?
21. 5(a)(ii)3 marksUsing the circle below, with radius shown, represent the information in the table above on a clearly labelled pie chart.
22. 5(b)(i)1 markA girl is chosen at random. Determine the probability that she achieves a Grade I.
23. 5(b)(ii)2 marksWhat percentage of the boys who took the exam achieved Grades I to III?
24. 5(b)(iii)1 markConsidering the standard deviations in the table on page 18, compare the performance of the boys and the girls.
25. 6(a)2 marksDraw a cross-sectional view of the container showing the measurements of the inner and outer radii.
26. 6(b)2 marksShow that the capacity of the container is 73 304 cm³.
27. 6(c)3 marksDetermine the volume of the material used to make the container.
28. 6(d)2 marksGiven that the density of the material used to make the container is 2.2 g/cm³, determine the mass, in kg, of the empty container (density = mass/volume).
29. 7(a)2 marksDraw Figure 4 of the sequence.
30. 7(b)(i)2 marksComplete the rows numbered (i).
31. 7(b)(ii)2 marksComplete the rows numbered (ii).
32. 7(b)(iii)2 marksComplete the rows numbered (iii).
33. 7(c)2 marksShow that no figure can have a perimeter of 100 units.
34. 8(a)(i)1 markComplete the table below for the function f(x) = 3 + 2x - x².
35. 8(a)(ii)2 marksComplete the grid below to show all the points in the table on page 25 and hence, draw the graph of the function f(x) = 3 + 2x - x² for -2 ≤ x ≤ 4.
36. 8(a)(iii)a)1 markUsing the graph on page 26, determine the coordinates of the maximum point of f(x).
37. 8(a)(iii)b)2 marksUsing the graph on page 26, determine the range of values of x for which f(x) > 0.
38. 8(a)(iii)c)1 markUsing the graph on page 26, determine the gradient of f(x) at x = 1.
39. 8(b)(i)2 marksWrite TWO inequalities to represent this information.
40. 8(b)(ii)2 marksWrite an inequality to represent this information.
41. 8(b)(iii)1 markShow that on any given day, it is NOT possible for Mr Thomas to make 50 bottles of juice and 12 cakes.
42. 9(a)(i)2 marksDetermine the value of Angle PTR. Show detailed working where necessary and give a reason to support your answer.
43. 9(a)(ii)2 marksDetermine the value of Angle TPQ. Show detailed working where necessary and give a reason to support your answer.
44. 9(a)(iii)2 marksDetermine the value of Obtuse angle POR where O is the centre of the circle. Show detailed working where necessary and give a reason to support your answer.
45. 9(b)(i)1 markComplete the diagram below by inserting the angles of depression and the distance between the ships.
46. 9(b)(ii)a)3 marksDetermine, to the nearest metre, the distance, TS₂, between the top of the lighthouse and Ship 2.
47. 9(b)(ii)b)2 marksDetermine, to the nearest metre, the height of the lighthouse, TB.
48. 10(a)(i)2 marksUsing a calculation to support your answer, explain whether matrix P is a singular or a non-singular matrix.
49. 10(a)(ii)3 marksGiven that PQ = R, determine the values of a and b.
50. 10(a)(iii)1 markState the reason why the matrix product QP is not possible.
51. 10(b)(i)3 marksComplete the diagram below to represent ALL the information given above.
52. 10(b)(ii)3 marksGiven that OX + OY = k(r + s), where k is a constant, using a vector method, find the value of k.