CSEC Additional Mathematics · 2016 · Paper 1

45 multiple-choice items from this paper. Open one to see it in full, then practise it on Quelpr and get it marked against the mark scheme.

1. Q11 mark · multiple choiceThe function f(x) = 2x^3 - x^2 + hx - 6 can be expressed as f(x) = (2x + 1)(x + 2)(x - 3). What is the value of h?
2. Q21 mark · multiple choice\frac{1}{x + 3} + \frac{3}{x^2 - 9} expressed as a single fraction is
3. Q31 mark · multiple choiceWhich of the following graphs BEST represents f(x) = x(1 - x)?
4. Q41 mark · multiple choiceGiven that f(x) = ax^2 + bx + c, f(x) can be expressed in the form
5. Q51 mark · multiple choiceA quadratic equation is such that the sum of its roots is -\frac{2}{3} and the product of its roots is \frac{3}{4}. The quadratic equation is
6. Q61 mark · multiple choiceThe range of values for which x^2 - 7x + 10 < 0 is
7. Q71 mark · multiple choiceThe set of values of x for which \frac{2x + 1}{x - 1} \ge 0 is
8. Q81 mark · multiple choiceIf f(x) = \frac{1}{8}x^3, x \in \mathbb{R} and -2 \le x \le 4, then
9. Q91 mark · multiple choiceThe functions f and g are defined by f: x \to 2x - 5 and g: x \to 4 + \frac{3}{x}, x \ne 0. The composite function gf is defined by
10. Q101 mark · multiple choiceWhich of the following graphs is a function?
11. Q111 mark · multiple choiceA function is defined by f: x \to \frac{1}{x + 1}, x \ne -1. The value of f^{-1}(1) is
12. Q121 mark · multiple choice\sqrt[n]{3 \times 27^m} is equal to
13. Q131 mark · multiple choiceThe value of x for which 9^{x + 1} = 3 is
14. Q141 mark · multiple choiceGiven that \log_p X = 6 and \log_p Y = 4, the value of \log_p \left(\frac{X}{Y}\right) is
15. Q151 mark · multiple choiceThe expression \frac{\sqrt{5} - 1}{1 + \sqrt{5}} when simplified is equal to
16. Q161 mark · multiple choiceThe value of x for which \log_3(2x + 1) = 2 + \log_3(3x - 11) is
17. Q171 mark · multiple choiceThe series -2 + \frac{4}{3} - \frac{8}{9} + \dots converges to the limit
18. Q181 mark · multiple choiceWhat is the sum of the ODD integers between 10 and 50?
19. Q191 mark · multiple choiceThe sum of the first n terms of a geometric series is S_n = 4^n - 1. For this series I. the common ratio is 4 II. the first 3 terms are 3, 15 and 63 III. S_{2n} = 2^{4n} - 1 Which of the statements above are…
20. Q201 mark · multiple choiceThe sum of \sum_{k=1}^3 \frac{1}{k} is
21. Q211 mark · multiple choiceThe coordinates of the centre of a circle with equation (x - 1)^2 + (y + 3)^2 = 36 is
22. Q221 mark · multiple choiceThe line through the points Q(h, 2) and R(4, 8) is parallel to the line with equation 2x + y - 10 = 0. The value of h is
23. Q231 mark · multiple choiceThe points of intersection of the line with equation y - x - 2 = 0 and the circle with equation x^2 + y^2 = 10 are
24. Q241 mark · multiple choiceTwo vectors are equal if they
25. Q251 mark · multiple choiceThe vector \mathbf{a} is given as 5\mathbf{i} + 12\mathbf{j}. A unit vector parallel to \mathbf{a} is
26. Q261 mark · multiple choiceThe position vectors of A and B relative to an origin O are \begin{pmatrix} 2 \\ 3 \end{pmatrix} and \begin{pmatrix} 3 \\ -1 \end{pmatrix} respectively. The acute angle AOB is given by
27. Q271 mark · multiple choiceGiven that x is acute and \cos x = \frac{3}{5}, then the value of \sin 2x is
28. Q281 mark · multiple choiceWhat is the arc length, x, in metres, along the outer edge of the protractor?
29. Q291 mark · multiple choiceThe graph of y = \sin 2x is
30. Q301 mark · multiple choiceIf \sin(x + 20^\circ) = \cos x, then the value of x is
31. Q311 mark · multiple choice\sin(\alpha + 45^\circ) is equal to
32. Q321 mark · multiple choice\frac{8\pi}{5} radians converted to degrees is
33. Q331 mark · multiple choiceIf \sin\theta = \frac{5}{13} and \theta is obtuse, then \tan\theta =
34. Q341 mark · multiple choiceThe trigonometrical expression \frac{\sin x}{1 - \cos x} + \frac{\sin x}{1 + \cos x} is identical to
35. Q351 mark · multiple choiceGiven that y = \sqrt{5 - x}, then \frac{dy}{dx} is
36. Q361 mark · multiple choiceThe gradient at x = \frac{\pi}{6} on the curve y = \cos x is
37. Q371 mark · multiple choiceThe curve C is given by the equation y = 2x^3 - 3x^2 - 12x + 6. The values of x at which stationary points occur are
38. Q381 mark · multiple choiceGiven y = 2x^2 + 3\cos x, then \frac{dy}{dx} =
39. Q391 mark · multiple choiceThe curve C with equation y = f(x) has a stationary point at (-2, 5). If f''(x) = x^4 - 15, then (-2, 5) is
40. Q401 mark · multiple choiceIf \int_2^a (6 + 3x)\,dx = 72, where a > 2, then a =
41. Q411 mark · multiple choiceThe region bounded by the curve y = x^2, the x-axis and the lines x = 0 and x = 1 is rotated 360^\circ about the x-axis. The volume of the solid generated can be found from
42. Q421 mark · multiple choiceIf X = \int_a^b f(x)\,dx and a < c < b then
43. Q431 mark · multiple choiceThe region R is enclosed by the x-axis, the curve y = x^2 + 2x - 1, the lines x = 2 and x = 3. The area of R in units^2 is
44. Q441 mark · multiple choiceIf \int_1^4 f(x)\,dx = 6, then \int_1^4 4f(x)\,dx + 5 =
45. Q451 mark · multiple choice\int(\cos x - 2\sin x)\,dx =