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CAPE Pure Mathematics Unit 1 · 2008 (T&T) · 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.

Practise this paper
  1. Q11 mark · multiple choice\sqrt{8} + \sqrt{32} - \sqrt{162} can be simplified as
  2. Q21 mark · multiple choiceThe range of values for x such that 5x + 7 > 10x - 13 is
  3. Q31 mark · multiple choiceWhich of the following statements is true?
  4. Q41 mark · multiple choice\sum_{r=1}^{50} (r + 2) is equal to
  5. Q51 mark · multiple choiceIf a remainder of 3 is obtained when 8x^3 + 4x + k is divided by x - 1, then k equals
  6. Q61 mark · multiple choice3\log_2 2q - 2\log_2 3q + 1 expressed as a single logarithm in its SIMPLEST form is
  7. Q71 mark · multiple choiceThe annual growth, g(x), (in thousands) of the population in a country for x years is represented by g(x) = 2^x. In how many years will a growth of 32 thousand be achieved?
  8. Q81 mark · multiple choiceWhich of the following sets of ordered pairs represent functions?\nI. \{(-1, 1), (0, 2), (1, 3), (4, 6)\}\nII. \{(-2, 4), (1, 1), (1, 4), (2, 4)\}\nIII. \{(-1, 1), (0, 0), (1, 1), (-3, 9)\}\nIV.…
  9. Q91 mark · multiple choiceIf g(x) is the inverse of f(x) then the correct diagram is
  10. Q101 mark · multiple choiceIf f(x) = 3x - 4 and fg(x) = x, then g(x) is
  11. Q111 mark · multiple choiceIf |x - 1|^2 + 2|x - 1| = 3, then x is
  12. Q121 mark · multiple choiceRationalising \frac{\sqrt{2} - 1}{\sqrt{2} + 1} gives
  13. Q131 mark · multiple choiceGiven that the roots of x^2 - 5x + a = 0 are equal, then a =
  14. Q141 mark · multiple choiceIf \alpha and \beta are the roots of the quadratic equation -x^2 + 10x + 2 = 0, then \alpha^2 + \beta^2 =
  15. Q151 mark · multiple choiceThe solution set of 5 + |2m - 9| \le 6 is
  16. Q161 mark · multiple choiceThe radius of the circle 2x^2 + 2y^2 - 4x + 12y + 11 = 0 is
  17. Q171 mark · multiple choiceThe value of \sin\left(\frac{\pi}{2} - p\right) is
  18. Q181 mark · multiple choiceIf \beta is an acute angle and \cos\beta = \frac{5}{13}, then \sec\beta =
  19. Q191 mark · multiple choiceWhich of the following sketches BEST illustrates the curve y = \cos x?
  20. Q201 mark · multiple choiceThe expression \sin 6A + \sin 4A may be written as
  21. Q211 mark · multiple choiceIf 2\cos\theta + 9\sin\theta \equiv r\cos(\theta - \alpha) where r > 0 and 0 < \alpha < \frac{\pi}{2}, then the maximum value of the expression is
  22. Q221 mark · multiple choiceWhich of the following equations BEST represents the graph shown above?
  23. Q231 mark · multiple choiceThe equation of the line passing through (0, -21) and perpendicular to x + 5y + 27 = 0 is
  24. Q241 mark · multiple choiceThe equation of the circle with centre (-3, 5) and radius 6 is
  25. Q251 mark · multiple choiceA circle has centre (-1, -1). The equation of the tangent to the circle at the point (0, -3) on the circle is
  26. Q261 mark · multiple choiceThe curves y^2 = x + 7 and xy = 6 intersect in three points. The y coordinates of these points are
  27. Q271 mark · multiple choiceThe curve with parametric representation x = 2t, y = t^2 has Cartesian equation
  28. Q281 mark · multiple choiceGiven that the vector (k+1)\mathbf{i} + 3\mathbf{j} is parallel to the vector 2\mathbf{i} - 6\mathbf{j}, the value of k is
  29. Q291 mark · multiple choiceGiven that \mathbf{p} = \begin{pmatrix} -2 \\ 3 \end{pmatrix} and \mathbf{r} = \begin{pmatrix} 5 \\ -2 \end{pmatrix}, then \mathbf{p} \cdot \mathbf{r} equals
  30. Q301 mark · multiple choiceThe cosine of the angle between the vectors -6\mathbf{j} and \mathbf{i} + \mathbf{j} is
  31. Q311 mark · multiple choiceGiven that f(x) = \begin{cases} 3x + 5 & \text{for } x < 3 \\ ax + 2 & \text{for } x \ge 3. \end{cases} For the function to be continuous at x = 3, the value of 'a' should be
  32. Q321 mark · multiple choiceThe value of \lim_{x \to 0} \frac{e^{2x} - 1}{e^x - 1} is
  33. Q331 mark · multiple choiceA dial on a plane preparing for landing registers the number 200 + 5\left(\frac{\sin h}{h}\right), where h is the height above the ground. Just as the plane lands the dial reads
  34. Q341 mark · multiple choiceGiven that f(x) = (2x + 1)^3, f'(2) equals
  35. Q351 mark · multiple choiceGiven f(x) = x^3, f'(x) is
  36. Q361 mark · multiple choiceIf y = \frac{(x^2 + 8)^4}{3} then \frac{\mathrm{d}y}{\mathrm{d}x} =
  37. Q371 mark · multiple choiceThe radius of a circle is increasing at a rate of 0.1\text{ cm s}^{-1}. At the instant when the radius is 3\text{ cm}, the rate of increase of the area in \text{cm}^2\text{ s}^{-1} is
  38. Q381 mark · multiple choiceAt x = 0, the gradient of the function x^3 - 2x^2 is
  39. Q391 mark · multiple choiceThe number of stationary points of the function g(x) = \frac{2}{x - 3}, x \in \mathbb{R}, and x \ne 3, is
  40. Q401 mark · multiple choiceWhich of the following is true given that f'(x) and f''(x) can be expressed in terms of x?
  41. Q411 mark · multiple choice\int_0^{\frac{\pi}{2}} \cos 5x\,\mathrm{d}x is
  42. Q421 mark · multiple choiceIf f'(x) = \sin x, then f(x) =
  43. Q431 mark · multiple choice\int [2x^{2n-1} + x^{3n-1}]\,\mathrm{d}x is equal to
  44. Q441 mark · multiple choiceGiven that \int_2^5 4f(x)\,\mathrm{d}x = 9, the value of \int_2^5 [3 - f(x)]\,\mathrm{d}x is
  45. Q451 mark · multiple choiceThe TOTAL shaded area in the diagram below is given by

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