CSEC Additional Mathematics · 2013 · 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 expression x - 2 is a factor of
2. Q21 mark · multiple choiceThe expression ab + 3c - 3b - ac is equal to
3. Q31 mark · multiple choiceGiven that x + 2 is a factor of f(x) = 2x^3 - 3x^2 - 5x + p then p is equal to
4. Q41 mark · multiple choice2x^3 + x^2 - 7x - 6 factorizes completely as
5. Q51 mark · multiple choiceThe roots of the equation 5x^2 + 6x - 2 = 0 are
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 3x + 2 > x - 2 is
8. Q81 mark · multiple choiceIf f(x) = 3x - 4 and fg(x) = x, then g(x) is
9. Q91 mark · multiple choiceWhich one of the graphs below is a function?
10. Q101 mark · multiple choiceA function h is defined by h : x \rightarrow 5x + 2. What is h(2a + 3)?
11. Q111 mark · multiple choiceA function is defined by f : x \rightarrow \frac{2}{x - 3},\ x \neq 3 The value of f^{-1}(1) is
12. Q121 mark · multiple choice\frac{2^{-1}}{8^{\frac{1}{3}}} simplifies to
13. Q131 mark · multiple choice(8 + \sqrt{5})(2 - \sqrt{5}) can be expressed as
14. Q141 mark · multiple choiceThe value of x for which 4^{x+1} = 2 is
15. Q151 mark · multiple choiceGiven that \log_p X = 6 and \log_p Y = 4, the value of \log_p \left(\frac{X}{Y}\right) is
16. Q161 mark · multiple choiceGiven that a and b are the roots of the equation x^2 + 3x + 4 = 0, what is the value (a + b)^2?
17. Q171 mark · multiple choiceThe common ratio of the geometric sequence 8, 12, 18, \dots is
18. Q181 mark · multiple choiceThe sum of the ODD integers between 10 and 50 is
19. Q191 mark · multiple choiceFor the arithmetic progression -12, -7, -2, 3, 8\dots the n^{\text{th}} term is given by
20. Q201 mark · multiple choiceA long-distance runner runs the first kilometre of a race in 3 minutes 45 seconds but finds that his speed drops steadily so that each kilometre takes him 12 seconds more than the preceding one. The time taken to…
21. Q211 mark · multiple choiceThe lines 7x - 4y + 25 = 0 and 3x - y - 5 = 0 intersect at the point P. The coordinates of P is
22. Q221 mark · multiple choiceThe line through the points P(k, 2) and Q(6, 8) is parallel to the line with equation 3x + y - 21 = 0. The value of k is
23. Q231 mark · multiple choiceThe points of intersection of the line with equation x + y = 7 and the circle with equation x^2 + y^2 = 25 are A and B. The coordinates of A and B respectively are
24. Q241 mark · multiple choiceThe vector \mathbf{a} is given as 5\mathbf{i} + 12\mathbf{j}. A unit vector parallel to \mathbf{a} is
25. Q251 mark · multiple choiceIf \pi < \theta < 2\pi and 2\cos \theta = \sqrt{3}, then \theta is
26. Q261 mark · multiple choiceThe position vectors of A and B relative to an origin O are \begin{pmatrix} 2 \\ 5 \end{pmatrix} and \begin{pmatrix} 3 \\ -1 \end{pmatrix} respectively. The acute angle AOB is given by
27. Q271 mark · multiple choiceGiven that \cos x = \frac{3}{5}, 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 in the region of angle AOB?
29. Q291 mark · multiple choiceThe graph of y = \sin x is
30. Q301 mark · multiple choiceIf \sin(x^\circ + 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{4\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 choiceIf y = \sqrt{(1 + x^3)}, then \frac{dy}{dx} =
36. Q361 mark · multiple choiceThe gradient at x = \frac{\pi}{6} on the curve y = \sin x is
37. Q371 mark · multiple choiceThe equation of a curve is given by y = (x^2 + 2)(x - 1)^3. The gradient function, \frac{dy}{dx}, is given by
38. Q381 mark · multiple choiceIf y = \frac{x^2}{x + 3}, then \frac{dy}{dx} is
39. Q391 mark · multiple choiceThe curve C is given by the equation y = x^2 + \frac{16}{x}. The second derivative, \frac{d^2y}{dx^2}, is given by
40. Q401 mark · multiple choiceThe value of a for which \int_0^a (x^2 - 5)\,dx = \frac{50}{3} is
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 choice\int (2x - 5)^3\,dx =
43. Q431 mark · multiple choiceIf y = 3x^2 + \cos x then \int y\,dx =
44. Q441 mark · multiple choice\int (\sin x + 2\cos x)\,dx =
45. 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