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CSEC Additional Mathematics · 2014 · Paper 2

41 questions and parts 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. 1(a)(i)1 markShow that f is NOT one-to-one.
  2. 1(a)(ii)a)2 marksFind fg(x), and clearly state its domain.
  3. 1(a)(ii)b)3 marksDetermine the inverse, g⁻¹, of g and sketch on the same pair of axes, the graphs of g and g⁻¹.
  4. 1(b)3 marksDetermine the value of the constant a.
  5. 1(c)5 marksfind the values of x and y (the dimensions of the kitchen).
  6. 2(a)(i)3 marksExpress f(x) in the form k+ a (x+h)², where a, h and k are integers to be determined.
  7. 2(a)(ii)1 markState the maximum value of f(x).
  8. 2(a)(iii)1 markDetermine the value of x for which f(x) is a maximum.
  9. 2(b)4 marksFind the set of values of x for which 3 + 5x - 2x² ≤ 0.
  10. 2(c)(i)3 marksShow that this series is geometric.
  11. 2(c)(ii)2 marksFind the sum to infinity of this series, giving your answer as an exact fraction.
  12. 3(a)(i)3 marksDetermine the value of k such that the lines x + 3y = 6 and kx + 2y = 12 are perpendicular to each other.
  13. 3(a)(ii)3 marksA circle of radius 5 cm has as its centre the point of intersection of the two perpendicular lines in (i). Determine the equation for this circle.
  14. 3(b)(i)4 marksShow that TRS = 90°.
  15. 3(b)(ii)2 marksDetermine the length of the hypotenuse. [Hint: A rough drawing of RST might help].
  16. 4(a)(i)2 marksFind the area of the sector OAB.
  17. 4(a)(ii)4 marksHence, find the area of the shaded region, H.
  18. 4(b)2 marksshow that cos(x + π/6) = (1/2)(√3 cos x - sin x), where x is acute.
  19. 4(c)4 marksProve the identity (tan θ sin θ)/(1 - cos θ) = 1 + 1/cos θ.
  20. 5(a)4 marksFind the equation of the tangent to the curve at P, giving your answer in the form ax + by + c = 0, where a, b, c, ∈ Z.
  21. 5(b)(i)5 marksFind ALL the stationary points of f(x).
  22. 5(b)(ii)5 marksDetermine the nature of EACH of the stationary points of f(x).
  23. 6(a)4 marksEvaluate ∫₂⁴ x (x² - 2) dx.
  24. 6(b)4 marksEvaluate ∫₀^(π/3) (4 cos x + 2 sin x) dx, leaving your answer in surd form.
  25. 6(c)(i)3 marksDetermine the equation of the curve.
  26. 6(c)(ii)3 marksFind the area of the finite region bounded by the curve, the x-axis, the line x = 3 and the line x = 4.
  27. 7(a)(i)3 markswhat is the probability that the student is studying both Mathematics and Biology?
  28. 7(a)(ii)2 marksBiology only?
  29. 7(b)(i)1 markCopy and complete the sample space diagram below.
  30. 7(b)(ii)a)2 marksFind P (S > 9)
  31. 7(b)(ii)b)1 markP (S≤4).
  32. 7(c)(i)4 marksFind the median and quartiles for the data given.
  33. 7(c)(ii)4 marksConstruct a box-and-whisker plot to illustrate the data given and comment on the distribution of the data.
  34. 7(c)(iii)3 marksFind the values of a, b and c.
  35. 8(a)(i)2 marksWhat distance did the car travel from Point A towards Point B before starting to decelerate?
  36. 8(a)(ii)5 marksCalculate the deceleration of the car as it goes from 25 m s⁻¹ to 10 m s⁻¹.
  37. 8(a)(iii)1 markFor how long did the car maintain the speed of 10 m s⁻¹?
  38. 8(a)(iv)2 marksDetermine the average velocity of the car over the journey from Point A to Point C.
  39. 8(b)(i)3 marksFind the time when the velocity is at its maximum.
  40. 8(b)(ii)2 marksDetermine the maximum velocity.
  41. 8(b)(iii)5 marksFind the distance moved by the particle from P to the point where the particle attains its maximum velocity.

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