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CAPE Pure Mathematics Unit 1 · 2008 (Rest of Region) · Paper 1

41 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.

Practise this paper
  1. Q11 mark · multiple choiceIn the real number system, the inverse of addition is represented by
  2. Q21 mark · multiple choiceWhich of the following statements is true?
  3. Q31 mark · multiple choiceThe (k + 1)\text{th} term in \sum_{r=1}^{n} r(r - 1) is
  4. Q41 mark · multiple choiceThe basic wage W_b and the overtime wage W_o of a shop attendant never differ by more than \100$. An inequality representing this statement is
  5. Q51 mark · multiple choiceIf |x + b| = |x|; x, b \in \mathbb{N}, then the value of x in terms of b is
  6. Q61 mark · multiple choiceThe polynomial P(x) = 2x^3 + x^2 - 13x + 6, when divided by (x - 1), gives a remainder of
  7. Q71 mark · multiple choice(4x)^3 - (4y)^3 can be expressed in the form
  8. Q81 mark · multiple choiceIf \alpha and \beta represent roots of the equation x^2 - px + q = 0, then the value of \alpha^2 + \beta^2 is
  9. Q91 mark · multiple choiceThe exact value of \left(\frac{25}{16}\right)^{-\frac{1}{2}} is
  10. Q101 mark · multiple choiceRationalising \frac{\sqrt{2} - 1}{\sqrt{2} + 1} gives
  11. Q111 mark · multiple choiceThe expression 2 - 4x + 3x^2 can be written as
  12. Q121 mark · multiple choiceWhich of the following mapping diagrams does NOT represent a function?
  13. Q131 mark · multiple choiceThe function f(x) is decreasing for the range
  14. Q141 mark · multiple choiceThe general quadratic equation with roots \alpha and \beta may be written as
  15. Q151 mark · multiple choiceThe sketch below shows a function y = f(x). The function y = |f(x)| is represented by
  16. Q161 mark · multiple choiceIf \mathbf{a} = 5\mathbf{i} + \mathbf{j} and \mathbf{b} = \lambda\mathbf{i} + 5\mathbf{j} are parallel vectors, then the value of \lambda is
  17. Q191 mark · multiple choiceThe function \sin\left(x + \frac{\pi}{2}\right) can be simplified to
  18. Q201 mark · multiple choiceWhich of the following sketches BEST represents the curve \[ y = \cos\frac{1}{2}x, \quad (0 \le x \le 2\pi)? \]
  19. Q211 mark · multiple choice\sin(30^\circ - A) is equal to
  20. Q221 mark · multiple choiceIf \beta is an acute angle and \cos\beta = \frac{5}{13}, then \sec\beta =
  21. Q231 mark · multiple choice2\sin\theta\cos\phi is equivalent to
  22. Q241 mark · multiple choiceIf 2\cos\theta + 9\sin\theta = r\cos(\theta - \alpha), where r > 0 and 0 < \alpha < \frac{\pi}{2}, then the maximum value of the expression is
  23. Q251 mark · multiple choiceWhich of the following equations BEST represents the graph shown above?
  24. Q261 mark · multiple choiceThe point A has coordinates (3, -2). The vector 3\vec{OA} is
  25. Q291 mark · multiple choiceThe line passing through the centre of the circle (x - 3)^2 + (y + 2)^2 = 25 and parallel to the x-axis, has the equation
  26. Q301 mark · multiple choiceThe curve with parametric representation x = 2t, y = t^2 has equation
  27. Q311 mark · multiple choiceIn the diagram above showing the graph of y^2 = x, y is NOT defined for
  28. Q321 mark · multiple choiceThe function f(x) = \frac{x^2 - 2}{x + 2} is discontinuous for the domain value of
  29. Q331 mark · multiple choice\lim_{x \to 3} \frac{x^2 - 9}{x - 3} is
  30. Q341 mark · multiple choiceGiven that \lim_{x \to 0} \frac{\sin x}{x} = 1, where x is measured in radians, then the value of \lim_{x \to 0} \frac{\sin 4x}{x} is
  31. Q351 mark · multiple choiceGiven that f(x) = (2x + 1)^3, then f'(2) equals
  32. Q361 mark · multiple choiceAn expression for obtaining the volume generated by rotating the bounded, shaded region through 360^\circ about the x-axis is
  33. Q371 mark · multiple choiceThe first derivative of -\frac{1}{x^2 - 1} is
  34. Q381 mark · multiple choiceIf \frac{dy}{dx} = \cos x, then
  35. Q391 mark · multiple choiceThe area of the finite region shaded in the diagram is
  36. Q401 mark · multiple choiceThe stationary point of the function y = (x - 1)^2 is
  37. Q411 mark · multiple choiceThe gradient of the normal to the curve y = \ln x at x = 2 is
  38. Q421 mark · multiple choice\int_{0}^{\frac{\pi}{2}} 2\cos 5x \, dx is
  39. Q431 mark · multiple choiceGiven \frac{dy}{dx} = 2x, a sketch of y versus x may be represented by I. II. III. IV.
  40. Q441 mark · multiple choiceA curve is defined by the equation y = -5(2x - 1)^2. Given that x increases at a rate of 1\text{ unit per second} when x = 1, what is the corresponding rate of change for y?
  41. Q451 mark · multiple choiceFrom the diagram above, which of the following statements are true? I. f'(1) < 0 II. f(1) > k III. f(2) = 0 IV. f'(2) = k

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