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CSEC Additional Mathematics · 2013 · Paper 2

40 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)2 marksUse the factor theorem to show that x + 4 is a factor of f(x).
  2. 1(a)(ii)3 marksDetermine the other linear factors of f(x).
  3. 1(b)(i)3 marksFind an expression for the inverse function f⁻¹(x).
  4. 1(b)(ii)2 marksWrite an expression for the composite function, fg(x). Simplify your answer.
  5. 1(c)4 marksShow that x = 2(log5 + log7) / (log125 - log7).
  6. 2(a)(i)3 marksExpress f(x) in the form a(x + h)² + k where h and k are constants.
  7. 2(a)(ii)1 markState the minimum value of f(x).
  8. 2(a)(iii)1 markDetermine the value of x for which f(x) is a minimum.
  9. 2(b)4 marksFind the set of values of x for which 2x² + 3x - 5 ≥ 0.
  10. 2(c)5 marksFind the sum to infinity of the following series: 1/4 + 2/4² + 1/4³ + 2/4⁴ + ... .
  11. 3(a)(i)3 marksExpress the equation of the circle in the form x² + y² + hx + gy + k = 0, where h, g and k are integers to be determined.
  12. 3(a)(ii)3 marksFind an equation for l.
  13. 3(b)3 marksFind the value of λ such that OP and OQ are perpendicular.
  14. 3(c)3 marksFind the unit vector in the direction of AB.
  15. 4(a)4 marksWhat is its area?
  16. 4(b)5 marksSolve the equation 2 cos²θ + 3 sin θ = 0 for 0 ≤ θ ≤ 360°.
  17. 4(c)3 marksUse the appropriate compound angle formula to find the value of the acute angle α.
  18. 5(a)(i)5 marksFind the coordinates of the stationary points of y.
  19. 5(a)(ii)5 marksFind the second derivative of y and hence determine the nature of EACH of the stationary points.
  20. 5(b)4 marksDifferentiate y = (5x + 3)³sin x with respect to x, simplifying your result as far as possible.
  21. 6(a)2 marksFind ∫(5x² + 4) dx.
  22. 6(b)4 marksEvaluate ∫₀^(π/2) (3 sin x - 5 cos x) dx.
  23. 6(c)8 marksFind the area of the finite region bounded by the curve in the first quadrant.
  24. 7(a)(i)2 marksCopy and complete the following tree diagram, by putting in all the missing probabilities, to show this information.
  25. 7(a)(ii)3 marksWhat is the probability that a customer pays for petrol with cash?
  26. 7(a)(iii)4 marksDetermine which is the more likely event: Event T or Event V.
  27. 7(b)(i)1 markState ONE advantage of using a stem and leaf diagram versus a box and whiskers plot to display the data.
  28. 7(b)(ii)3 marksConstruct a stem and leaf diagram to show the data.
  29. 7(b)(iii)2 marksDetermine the median mark.
  30. 7(b)(iv)3 marksCalculate the semi inter-quartile range of the marks.
  31. 7(b)(v)2 marksDetermine the probability that both scored less than 50 on the exam.
  32. 8(a)(i)3 marksOn the graph paper provided, draw a velocity-time graph to illustrate the motion of the particle.
  33. 8(a)(ii)a)4 marksFrom your graph determine the total distance, in metres, travelled by the particle.
  34. 8(a)(ii)b)2 marksFrom your graph determine the average velocity of the particle for the entire journey.
  35. 8(b)(i)3 marksCalculate the values of t when the particle is instantaneously at rest.
  36. 8(b)(ii)3 marksCalculate the distance travelled by the particle between 1 second and 3 seconds.
  37. 8(b)(iii)a)2 marksCalculate the value of dv/dt when t = 2 seconds.
  38. 8(b)(iii)b)1 markCalculate the value of dv/dt when t = 3 seconds.
  39. 8(b)(iv)a)1 markGive an interpretation for the value in 8(b)(iii)a).
  40. 8(b)(iv)b)1 markGive an interpretation for the value in 8(b)(iii)b).

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