CSEC Additional Mathematics · May/June 2017 · 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 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} + rac{3}{x^2 - 9} expressed as a single fraction is
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 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 set of values of x for which \frac{5x - 2}{2 - 3x} \ge 0 is given by
7. Q71 mark · multiple choiceThe set of values of x for which 3x + 2 > x - 2 is
8. Q91 mark · multiple choiceThe functions f and g are defined as follows: f : x \to \frac{x+1}{x-1}, \quad x \ne 1, x \in \mathbb{R} g : x \to 2x + 1, \quad x \ne \frac{1}{2}, x \in \mathbb{R} The function fg(x) is given by
9. Q101 mark · multiple choiceIf function m : x \to 5 + 2x, then m(4 - 2a) is
10. Q111 mark · multiple choiceIf f^{-1} : x \to x^2 - 1, x \ge 0, then
11. Q121 mark · multiple choice\frac{2^{-1}}{8^{\frac{1}{3}}} simplifies to
12. Q131 mark · multiple choice\sqrt[n]{3 \times 27^m} is equal to
13. Q141 mark · multiple choiceThe value of 2^z where z = 5 + \log_2 3 is
14. Q151 mark · multiple choiceGiven that \log_2 x^3 = 6, then the value of x is
15. Q161 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. Q171 mark · multiple choiceThe common ratio of the geometric sequence 8, 12, 18, \dots is
17. Q181 mark · multiple choiceThe sum of the first n terms of a series is given by \sum_{r=1}^n (5 - 3r). The sum of the first 10 terms is
18. Q191 mark · multiple choiceThe expression \sum_{r=1}^5 (-1)^r (3)^{r+1} =
19. Q201 mark · multiple choiceThe sum of the odd integers between 10 and 50 is
20. Q211 mark · multiple choiceA line L passes through the point (6, 5) and is perpendicular to a line whose equation is 3x + 4y - 7 = 0. The equation of L is
21. Q221 mark · multiple choiceThe lines 7x - 4y + 25 = 0 and 3x - y - 5 = 0 intersect at the point P. The coordinates of P are
22. Q231 mark · multiple choiceA circle C has centre (3, -2) and radius 4. The equation of C is
23. Q241 mark · multiple choiceTwo vectors are equal if they
24. Q251 mark · multiple choiceThe vector \mathbf{a} is given as 5\mathbf{i} + 12\mathbf{j}. A unit vector parallel to \mathbf{a} is
25. Q261 mark · multiple choiceGiven that \vec{OA} = \begin{pmatrix} -17 \\ 25 \end{pmatrix} and \vec{OB} = \begin{pmatrix} 4 \\ 5 \end{pmatrix}, then the vector \vec{AB} =
26. Q271 mark · multiple choiceThe exact value of \frac{\sin 150^\circ}{\cos 150^\circ} is given as
27. Q281 mark · multiple choiceThe size of the missing angle X, measured in radians, is
28. Q291 mark · multiple choice\frac{4\pi}{5} radians converted to degrees is
29. Q301 mark · multiple choiceThe smallest positive angle in radians, within the range 0 \le \theta \le 2\pi that satisfies the equation (2\cos\theta - 1)(\cos\theta - 2) = 0 is
30. Q311 mark · multiple choice\sin(\alpha + 45^\circ) is equal to
31. Q321 mark · multiple choiceIf \sin\theta = \frac{5}{13} and \theta is obtuse, then \tan\theta =
32. Q331 mark · multiple choiceIf \sin(x + 20^\circ) = \cos x, then the value of x is
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 choice\frac{d}{dx} \sqrt{(7x^2 + 4)} =
35. Q361 mark · multiple choiceAt the point (7, 4) on the curve y = f(x), \frac{dy}{dx} = 0 and \frac{d^2y}{dx^2} = -5. The point (7, 4) is
36. Q371 mark · multiple choiceThe gradient at x = \frac{\pi}{6} on the curve y = \cos x is
37. Q381 mark · multiple choiceGiven y = 2x^2 + 3\cos x, then \frac{dy}{dx} =
38. 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 the point (-2, 5) is
39. Q401 mark · multiple choiceIf \int_1^4 f(x)\,dx = 6, then \int_1^4 4f(x)\,dx + 5 =
40. Q411 mark · multiple choice\int (\cos x - 2\sin x)\,dx =
41. Q421 mark · multiple choiceThe region bounded by the curve y = 2x^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 calculated by
42. Q431 mark · multiple choiceIf y = 3x^2 + \cos x then \int y\,dx
43. Q441 mark · multiple choice\int_1^2 (1 + x + x^2)\,dx =
44. Q451 mark · multiple choiceThe region R is enclosed by the x-axis, the curve y = -x^2 + 2 and the lines x = 0 and x = 1. The area of R is