CSEC Additional Mathematics · 2014 · Paper 1

44 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 choiceWhen 2x^3 + 3x^2 - 2x + 3 is divided by 2x - 1 the remainder is
2. Q21 mark · multiple choiceThe expression ab + 3c - 3b - ac is equal to
3. Q31 mark · multiple choiceWhich of the following graphs BEST represents f(x) = x(1 - x)?
4. Q41 mark · multiple choiceThe number of visas, V(x), issued by an embassy annually is given by V(x) = 7x^2 - 42x + 72. The LEAST number of visas issued in a particular year, x, is
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 choiceThe value of g^{-1}[f(3)] is
10. Q101 mark · multiple choiceWhich of the graphs below is a function?
11. Q111 mark · multiple choiceA function is defined by f: x \to \frac{1}{x + 1}, x \neq -1. The value of f^{-1}(1) is
12. Q121 mark · multiple choice\sqrt[4]{3 \times 27^m} is equal to
13. Q131 mark · multiple choiceThe value of x for which 4^{x+1} = 2 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 choice\frac{2^{-1}}{8^{\frac{1}{2}}} simplifies to
17. Q171 mark · multiple choiceWhich of the following is NOT an arithmetic sequence?
18. Q181 mark · multiple choiceThe sum of the ODD integers between 10 and 50 is
19. Q191 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
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 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 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 P and Q. The coordinates of P and Q respectively are
24. Q241 mark · multiple choiceTwo vectors are equal
25. Q251 mark · multiple choiceGiven that \vec{OA} = \begin{pmatrix} -17 \\ 25 \end{pmatrix} and \vec{OB} = \begin{pmatrix} 4 \\ 5 \end{pmatrix} the vector \vec{AB} =
26. 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…
27. Q271 mark · multiple choiceThe exact value of \frac{\sin 150^\circ}{\cos 150^\circ} is given as
28. Q281 mark · multiple choiceThe size of the missing angle X, measured in radians, is
29. Q301 mark · multiple choiceThe smallest positive angle for 0 \le \theta \le 2\pi, for which the equation (2\cos\theta - 1)(\cos\theta - 2) = 0 is positive is
30. Q311 mark · multiple choice\sin(\alpha + 45^\circ) is equal to
31. Q321 mark · multiple choiceThe value of \frac{4\pi}{5} radians expressed as degrees is
32. Q331 mark · multiple choiceIf \sin\theta = \frac{5}{13} and \theta is obtuse, then \tan\theta =
33. Q341 mark · multiple choiceThe trigonometrical expression \frac{\sin x}{1 - \cos x} + \frac{\sin x}{1 + \cos x} is identical to
34. Q351 mark · multiple choiceGiven that y = (5 - 2x)^5, then \frac{dy}{dx} =
35. Q361 mark · multiple choiceThe gradient at x = \frac{\pi}{6} on the curve y = \cos x is
36. 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
37. Q381 mark · multiple choiceGiven y = \cos 2x, then \frac{dy}{dx} =
38. 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
39. Q401 mark · multiple choiceThe value of a for which \int_0^a (x^2 - 5)\,dx = \frac{50}{3} is
40. Q411 mark · multiple choice\int (2x - 4)^3\,dx =
41. Q421 mark · multiple choiceIf X = \int_a^b f(x)\,dx and a < c < b then
42. 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, in units^2, of R is
43. Q441 mark · multiple choiceIf \int_1^3 f(x)\,dx = 5, then \int_1^3 [2f(x) + 3]\,dx =
44. Q451 mark · multiple choice\int (\sin x - \cos x)\,dx =