CSEC Additional Mathematics · 2018 · Paper 1

39 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 ab + 3c - 3b - ac is equal to
2. Q21 mark · multiple choiceThe linear factor of x^3 - 3x^2 - 3x - 4 is
3. Q31 mark · multiple choiceGiven that f(x) = 6 - x - 2x^2 is less than or equal to k, where k \in \mathbb{R}, then k is equal to
4. Q41 mark · multiple choiceGiven that f(x) = 1 - 4x - 2x^2, then 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 choiceGiven that x > 0, the set of values of x for which x - 2 < \frac{15}{x} is
7. Q71 mark · multiple choiceGiven that f(x) = 13x - 6 - 2x^2, the values of x for which f(x) < 0 are
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 choiceIf f : x \to 2\left(\frac{x}{3} + 5\right), then f^{-1}(x) is equal to
10. Q101 mark · multiple choiceIf f(x) = \frac{4x + 1}{x - 2}, x \ne 2, x \in \mathbb{R}, then ff(x) =
11. Q111 mark · multiple choiceWhich of the following graphs depicts a function?
12. Q121 mark · multiple choice\sqrt{3 \times 27^{2m}} 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_2 x^3 = 6, then the value of x is
15. Q151 mark · multiple choiceThe value of \sqrt{18} + \sqrt{50} is
16. Q161 mark · multiple choiceThe value of x for which 3^{x + 2} + 3^x = 90 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 common ratio of the geometric sequence 8, 12, 18, \dots is
20. Q201 mark · multiple choiceA sequence of positive integers \{U_n\} is defined by U_n = 3\left(\frac{1}{2}\right)^{n - 1}. The 10th term of the sequence is given by
21. Q211 mark · multiple choiceThe point (2, 3) is at one end of a diameter of a circle whose equation is x^2 + y^2 - 10x + 2y + 1 = 0. The coordinates of the other end of the diameter are
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 line y = 2x - 7 and the line x + 3y = 7 intersect at the point
24. Q241 mark · multiple choiceThe vectors \mathbf{i} and \mathbf{j} represent 1\text{ km/h} east and north respectively. A man sails a boat on a lake such that the velocity is -\mathbf{i} + 2\mathbf{j} when there is no current. If there is a…
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 vector of two points A and B relative to an origin O are given by \vec{OA} = \begin{pmatrix} 3 \\ 8 \end{pmatrix} and \vec{OB} = \begin{pmatrix} 8 \\ 5 \end{pmatrix} respectively. The modulus of…
27. Q271 mark · multiple choiceThe trigonometrical expression \frac{\sin x}{1 - \cos x} + \frac{\sin x}{1 + \cos x} is identical to
28. Q281 mark · multiple choiceItem 28 refers to the following protractor which represents half of a circle. The protractor has a radius of 1.5\text{ metres} and the angle AOB measures 45^\circ. What is the arc length, x, in metres, along…
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. Q371 mark · multiple choice\frac{\mathrm{d}}{\mathrm{d}x}\left(\frac{2x - 1}{5 - x}\right) =
32. Q381 mark · multiple choiceGiven y = 2x^2 + 3\cos x, then \frac{\mathrm{d}y}{\mathrm{d}x} =
33. 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
34. Q401 mark · multiple choice\int_0^2 (3x + 4)^3 \,\mathrm{d}x =
35. Q411 mark · multiple choiceThe solution to \int_{-1}^1 \frac{1}{(5x - 2)^2} \,\mathrm{d}x is
36. Q421 mark · multiple choice\int (2x - 4)^3 \,\mathrm{d}x =
37. Q431 mark · multiple choiceA curve C passes through the point (2, -5). The gradient of the curve at the point (x, y) is given by \frac{\mathrm{d}y}{\mathrm{d}x} = 7 - x^3. The equation of the curve is
38. Q441 mark · multiple choiceIf \int_1^4 f(x)\,\mathrm{d}x = 6, then \int_1^4 4f(x)\,\mathrm{d}x + 5 =
39. Q451 mark · multiple choice\int (\cos x - 2\sin x)\,\mathrm{d}x =