CSEC Additional Mathematics · 2018 · Paper 2

38 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)4 marksFind the inverse function, f⁻¹(x), stating its domain.
2. 1(a)(ii)2 marksOn the grid provided below, sketch f⁻¹(x).
3. 1(a)(iii)2 marksState the relationship between f(x) and f⁻¹(x).
4. 1(b)3 marksDerive the polynomial, P(x), of degree 3 which has roots equal to 1, 2 and -4.
5. 1(c)(i)2 marksUse logarithms to derive an equation of the form y = mx + c that can be used to find the values of k and a.
6. 1(c)(ii)1 markIf a graph of y versus x from the equation in Part (c) (i) is plotted, a straight line is obtained. State an expression for the gradient of the graph.
7. 2(a)(i)3 marksExpress g(x) in the form a(x + h)^2 + k where a, h and k are constants.
8. 2(a)(ii)3 marksOn the grid provided below, sketch the graph of g(x), showing the maximum point and the y-intercept.
9. 2(b)4 marksDetermine the sum of the first four terms.
10. 2(c)4 marksDetermine the value of 1/alpha^2 + 1/beta^2.
11. 3(a)3 marksDetermine the equation of the circle that has centre (5, -2), and passes through the origin.
12. 3(b)2 marksDetermine whether the following pair of lines is parallel: x + y = 4 and 3x - 2y = -3.
13. 3(c)(i)4 marksCalculate the magnitude of AB.
14. 3(c)(ii)3 marksCalculate the angle AÔB, giving your answer to the nearest whole number.
15. 4(a)4 marksDetermine, in radians, the angle of the sector, giving your answer in terms of pi.
16. 4(b)4 marksSolve the equation sin^2(theta) + 3 cos(2*theta) = 2 for 0 <= theta <= pi. Give your answer(s) to 1 decimal place.
17. 4(c)4 marksProve the identity 1/(1 - sin x) - 1/(1 + sin x) = 2 tan x / cos x.
18. 5(a)(i)5 marksDetermine the coordinates of the stationary points.
19. 5(a)(ii)5 marksDetermine the nature of EACH stationary point.
20. 5(b)4 marksDifferentiate y = 2x * sqrt(4 - 8x) with respect to x, simplifying your answer.
21. 6(a)6 marksShow, using integration, that the finite area of the curve y = sin x in the first quadrant bounded by the line x = 4pi/3 is smaller than the finite region of y = cos x in the same quadrant and bounded by the same line.
22. 6(b)4 marksDetermine the volume of the solid of revolution formed.
23. 6(c)4 marksFind the equation of the curve.
24. 7(a)(i)2 marksDetermine the median score.
25. 7(a)(ii)3 marksCalculate the interquartile range of the scores.
26. 7(a)(iii)4 marksIn the space below, construct a box-and-whisker plot to illustrate the data and comment on the shape of the distribution.
27. 7(b)(i)3 marksIllustrate this information on a tree diagram showing ALL the probabilities on ALL branches.
28. 7(b)(ii)3 marksAn insecticide is selected at random, determine the probability that it is unsuccessful.
29. 7(c)(i)2 marksCalculate the probability of obtaining a 5 on the 2nd toss, given that a 5 was obtained on the 1st toss.
30. 7(c)(ii)2 marksDetermine the probability that a 5 is obtained on both tosses.
31. 7(c)(iii)1 markExplain why the answers in (c) (i) and (c) (ii) are different.
32. 8(a)(i)2 marksDetermine its velocity when t = 2.
33. 8(a)(ii)4 marksDetermine the values of t when the particle is at rest.
34. 8(a)(iii)3 marksDetermine the distance between the rest points.
35. 8(a)(iv)3 marksDetermine the time at which the maximum velocity occurs.
36. 8(b)(i)3 marksOn the grid provided on page 27, draw a distance-time graph to illustrate the motion of the bus.
37. 8(b)(ii)2 marksDetermine the distance from Station B to Station C.
38. 8(b)(iii)3 marksDetermine the average speed from Station A to Station B, in km/h.