CSEC Additional Mathematics · 2017 · Paper 2

40 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 marksDetermine the inverse of f(x).
2. 1(a)(ii)1 markIf f⁻¹(8) = 5, find the value of p.
3. 1(b)4 marksDetermine the values of a and b.
4. 1(c)(i)1 markUse logarithms to reduce the equation to linear form.
5. 1(c)(ii)3 marksUsing a suitable scale, plot the best fit line of the equation in (c)(i) on the graph paper provided on page 9. Use the space below to show your working.
6. 1(c)(iii)3 marksHence, estimate the constants A and k.
7. 2(a)4 marksCalculate the value of 1/α + 1/β.
8. 2(b)4 marksDetermine the range of values of x for which (2x + 3) / (x + 1) ≥ 0.
9. 2(c)(i)4 marksCalculate the amount paid in the first year.
10. 2(c)(ii)2 marksCalculate the TOTAL salary earned at the end of the contract.
11. 3(a)(i)2 marksExpress the equation in the form (x + f)² + (y + g)² = r².
12. 3(a)(ii)2 marksState the coordinates of the centre and the value of the radius of circle C.
13. 3(a)(iii)4 marksDetermine the points of intersection of circle C and the equation y = 4 - x.
14. 3(b)(i)1 markDetermine the product of the two vectors, p and q.
15. 3(b)(ii)3 marksDetermine the angle between the two vectors.
16. 4(a)(i)1 markIf the building space is 50π/3 m², calculate the angle ACB in radians.
17. 4(a)(ii)4 marksWorking in radians, calculate the area used for farming.
18. 4(b)4 marksShow without using a calculator that cos(π/4 - π/3) / sin(2π/3) = (√2 + √6) / (2√3).
19. 4(c)3 marksProve the identity 1 - cos²θ / (1 + sinθ) = sinθ.
20. 5(a)4 marksDifferentiate the expression (1 + 2x)³ (x + 3) with respect to x, simplifying your answer.
21. 5(b)5 marksDetermine the equation of the normal to the curve at point P.
22. 5(c)5 marksDetermine the rate of increase of the volume of water in the container in terms of π.
23. 6(a)4 marksShow that ∫₀^(π/4) (sin x + 4 cos x) dx = (3√2 + 2) / 2.
24. 6(b)3 marksDetermine the equation of a curve whose gradient function dy/dx = x + 2, and which passes through the point P(2, 3).
25. 6(c)3 marksEvaluate ∫₁² (4 - x)² dx.
26. 6(d)4 marksCalculate the volume of the solid formed when the area enclosed by the straight line y = x/2 and the x-axis for x = 0 to x = 6 is rotated through 2π about the x-axis.
27. 7(a)(i)4 marksDraw a tree diagram to illustrate the information above.
28. 7(a)(ii)4 marksDetermine the probability that the student will be accepted for an internship programme.
29. 7(b)(i)2 marksDetermine the mean length.
30. 7(b)(ii)1 markDetermine the modal length.
31. 7(b)(iii)1 markDetermine the median length.
32. 7(b)(iv)2 marksDetermine the interquartile range for the data.
33. 7(c)(i)4 marksCalculate the probability that the first patty selected was saltfish.
34. 7(c)(ii)2 marksGiven that the first patty was saltfish, calculate the probability that the second patty was NOT saltfish.
35. 8(a)(i)3 marksDetermine the velocity of the particle at t = 3.5 s, clearly stating the correct unit.
36. 8(a)(ii)3 marksIf the particle is momentarily at rest, find the time, t, at this position.
37. 8(b)(i)3 marksIn the space below, sketch a velocity-time graph to illustrate the motion of the vehicle.
38. 8(b)(ii)7 marksCalculate the length of time the vehicle maintains constant speed.
39. 8(b)(iii)2 marksCalculate the maximum velocity attained.
40. 8(b)(iv)2 marksDetermine the acceleration of the vehicle.