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CSEC Additional Mathematics · 2012 · Paper 2

37 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 markDetermine the composition function g(f(x)).
  2. 1(a)(ii)1 markState the range of g(f(x)).
  3. 1(a)(iii)2 marksDetermine the inverse of g(f(x)).
  4. 1(b)2 marksIf x + 2 is a factor of f(x) = 2x³ - 3x² - 4x + a, find the value of a.
  5. 1(c)5 marksSolve the equation 3^(2x) – 9(3^(-2x)) = 8.
  6. 1(d)(i)2 marksExpress x³ = 10^(-3) in the form log₁₀x = ax + b.
  7. 1(d)(ii)1 markHence, state the value of the gradient of a graph of log₁₀x versus x.
  8. 2(a)5 marksCalculate the value of α² + β².
  9. 2(b)4 marksFind the range of values of x for which (2x - 5) / (3x + 1) > 0.
  10. 2(c)5 marksCalculate the TOTAL amount of money repaid at the end of the 24th month.
  11. 3(a)(i)3 marksA line has equation x + y + 1 = 0. Show that this line passes through the centre of the circle.
  12. 3(a)(ii)4 marksFind the equation of the tangent to the circle at the point A (-6, 3).
  13. 3(b)(i)2 marksWrite BP in terms of a and b.
  14. 3(b)(ii)3 marksFind |BP|.
  15. 4(a)(i)5 marksCalculate, giving your answer in terms of π, the area of the shape OACMN.
  16. 4(a)(ii)5 marksCalculate, giving your answer in terms of π, the perimeter of the shape OACMN.
  17. 4(b)3 marksEvaluate without using calculators, the exact value of cos(7π/12).
  18. 4(c)4 marksProve the identity 1 / (sec θ + tan θ) = (1 - sin θ) / cos θ.
  19. 5(a)4 marksDifferentiate the following expression with respect to x, simplifying your answer: (3x + 4) / (x - 2).
  20. 5(b)(i)5 marksFind equations for the tangent to the curve at P.
  21. 5(b)(ii)5 marksFind equations for the normal to the curve at P.
  22. 5(c)5 marksFind the rate of increase of the area when the length of the side is 5 cm.
  23. 6(a)4 marksEvaluate ∫₁² (16 - 7x)³ dx.
  24. 6(b)3 marksDetermine the equation of the curve.
  25. 6(c)3 marksCalculate the area between the curve y = 2 cos x + 3 sin x and the x-axis from x = 0 to π/3.
  26. 6(d)4 marksCalculate the volume of the solid formed when the area enclosed by the curve y = x² + 2 and the x-axis, from x = 0 to x = 3, is rotated through 360° about the x-axis. [Leave your solution in terms of π].
  27. 7(a)4 marksDetermine the proportion that own NEITHER a laptop NOR a desktop computer.
  28. 7(b)(i)3 marksFind the probability that the marbles drawn are ALL of the SAME colour.
  29. 7(b)(ii)3 marksFind the probability that the marbles drawn contain EXACTLY 1 red marble.
  30. 7(c)(i)3 marksIllustrate this information on a tree diagram showing the probability on all branches.
  31. 7(c)(ii)a)3 marksA garage is chosen at random, determine the probability that the taxi will arrive late.
  32. 7(c)(ii)b)4 marksA garage is chosen at random, determine the probability that the taxi will come from garage C given that it is late.
  33. 8(a)(i)3 marksUsing the graph sheet provided, draw a velocity-time graph to illustrate the motion of the car.
  34. 8(a)(ii)3 marksDetermine the TOTAL distance travelled by the car.
  35. 8(a)(iii)4 marksCalculate the length of time after the first car started that this second car meets it.
  36. 8(b)(i)5 marksDetermine its velocity when t = 4.
  37. 8(b)(ii)5 marksDetermine its displacement from O when t = 3.

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