CSEC Additional Mathematics · 2015 · Paper 1

42 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 expression x - 2 is a factor of
2. Q21 mark · multiple choiceThe expression ab + 3c - 3b - ac is equal to
3. Q31 mark · multiple choiceIf x^2 - 6x + 13 = a(x + h)^2 + k then
4. Q41 mark · multiple choiceThe roots of the equation 3x^2 - 6x - 5 = 0 are
5. Q51 mark · multiple choiceThe values of x for which (x + 15)^2 = 64x are
6. Q61 mark · multiple choiceThe range of values for which x^2 - 7x + 10 < 0 is
7. Q81 mark · multiple choiceFunctions f and g are defined by f : x \rightarrow 2x - 5 \text{ and } g : x \rightarrow 4 + \frac{3}{x}, x \neq 0. The composite function gf is defined by
8. Q101 mark · multiple choiceIf function m : x \rightarrow 5 + 2x, then m(4 - 2a) is
9. Q111 mark · multiple choiceIf f : x \rightarrow 2\left(\frac{x}{3} + 5\right), then f^{-1}(x) is equal to
10. Q121 mark · multiple choiceGiven that 3 \times 27^{2x} = 9^x, the value of x is
11. Q131 mark · multiple choice\sqrt[n]{3 \times 27^m} is equal to
12. Q141 mark · multiple choiceThe value of x for which 4^{x+1} = 2 is
13. Q151 mark · multiple choiceGiven that \log_2 x^3 = 6, then the value of x is
14. Q161 mark · multiple choiceGiven that \alpha and \beta are the roots of the equation x^2 + 3x + 4 = 0, what is the value of (\alpha + \beta)^2?
15. Q171 mark · multiple choiceThe common ratio of the geometric sequence 8, 12, 18, \dots is
16. Q181 mark · multiple choiceThe sum of the ODD integers between 10 and 50 is
17. Q191 mark · multiple choiceFor the arithmetic progression -12, -7, -2, 3, 8 \dots the n^{\text{th}} term is given by
18. Q201 mark · multiple choiceThe first four terms of a convergent geometric progression (GP) is given by 500, 200, 80, 32. The sum to infinity of this GP is
19. Q211 mark · multiple choiceA line L passes through the point (6, 5) and is perpendicular to the line whose equation is 3x + 4y - 7 = 0. The equation of L is
20. Q221 mark · multiple choiceThe line y = 2x - 7 and the line x + 3y = 7 intersect at the point
21. Q231 mark · multiple choiceA circle C has centre (3, -2) and radius 4. The equation of C is
22. Q241 mark · multiple choiceTwo vectors are equal if they
23. Q251 mark · multiple choiceThe vector \mathbf{a} is given as 5\mathbf{i} + 12\mathbf{j}. A unit vector parallel to \mathbf{a} is
24. Q261 mark · multiple choiceThe position vector of the point P relative to an origin O is given as \mathbf{p} = 5\mathbf{i} + 2\mathbf{j} and the position vector of Q relative to an origin O is given as…
25. Q271 mark · multiple choiceThe EXACT value of \frac{\sin 150^\circ}{\cos 150^\circ} is given as
26. Q281 mark · multiple choiceThe size of angle X, measured in radians, is
27. Q291 mark · multiple choiceWhich of the following graphs represents y = \sin x?
28. Q301 mark · multiple choiceThe smallest positive angle within the range 0 \le \theta \le 2\pi that satisfies the equation (2\cos\theta - 1)(\cos\theta - 2) = 0 is
29. Q311 mark · multiple choice\sin(\alpha - 45^\circ) is equal to
30. Q321 mark · multiple choice\frac{4\pi}{5} radians converted to degrees is
31. Q331 mark · multiple choiceIf \sin\theta = \frac{5}{13} and \theta is obtuse, then \tan\theta =
32. Q341 mark · multiple choiceThe trigonometrical expression \frac{\sin x}{1 - \cos x} + \frac{\sin x}{1 + \cos x} is identical to
33. Q351 mark · multiple choice\frac{d}{dx}\sqrt{(7x^2 + 4)} =
34. Q371 mark · multiple choiceGiven that y = \cos 2x, then \frac{dy}{dx} =
35. Q381 mark · multiple choiceIf y = \frac{x^2}{x + 3}, then \frac{dy}{dx} is
36. 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
37. Q401 mark · multiple choiceIf \int_2^a (6 + 3x)\,dx = 72, where a > 2, then a =
38. 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:
39. Q421 mark · multiple choice\int (2x - 5)^3\,dx =
40. Q431 mark · multiple choiceIf y = 3x^2 + \cos x then \int y\,dx =
41. Q441 mark · multiple choice\int_1^2 (1 + x + x^2)\,dx =
42. Q451 mark · multiple choiceThe region R is enclosed by the x-axis, the curve y = -x^2 + 2, the lines x = 0 and x = 1. The area of R is