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CSEC Additional Mathematics · 2016 · Paper 2

38 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 marksDetermine the range of the function.
  2. 1(a)(ii)1 markFind f⁻¹(x).
  3. 1(a)(iii)2 marksSketch the graphs of f(x) and f⁻¹(x) on the same axes.
  4. 1(a)(iv)1 markComment on the relationship between the two graphs.
  5. 1(b)4 marksSolve the equation 2^(2x + 1) + 5(2^x) – 3 = 0.
  6. 1(c)(i)2 marksGiven that T = kp^(b/c), make c the subject of the formula.
  7. 1(c)(ii)2 marksSolve the equation log(x + 1) + log(x - 1) = 2 log(x + 2).
  8. 2(a)(i)1 markDetermine the nature of the roots of the quadratic equation 2x² + 3x – 9 = 0.
  9. 2(a)(ii)5 marksGiven that f(x) = 2x² + 3x – 9, sketch the graph of the quadratic function, clearly indicating the minimum value.
  10. 2(b)3 marksEvaluate Σ (from n=1 to 25) 3⁻ⁿ.
  11. 2(c)5 marksCalculate the total dividends on his investment by the end of 2016.
  12. 3(a)(i)5 marksDetermine the equation of circle C.
  13. 3(a)(ii)3 marksFind the equation of the tangent to the circle C at the point P(-1, 6).
  14. 3(b)4 marksFind the coordinates of OP.
  15. 4(a)4 marksCalculate the area of the shaded region in terms of x.
  16. 4(b)5 marksWithout the use of a calculator, evaluate cos 105°, in surd form, giving your answer in the simplest terms.
  17. 4(c)3 marksProve that the identity sin(θ + α) / (cos θ cos α) = tan θ + tan α.
  18. 5(a)4 marksFind dy/dx given that y = √(5x² - 4), simplifying your answer.
  19. 5(b)5 marksDetermine the equation of the normal to the curve at the point P.
  20. 5(c)5 marksObtain the equation for EACH of the two tangents drawn to the curve y = x² at the points where y = 16.
  21. 6(a)(i)3 marksFind ∫(3 cos θ - 5 sin θ) dθ.
  22. 6(a)(ii)4 marksEvaluate ∫(from 1 to 3) [(2/x²) - 3 + 2x³] dx.
  23. 6(b)4 marksCalculate the area of the region R.
  24. 6(c)3 marksFind the equation of the curve.
  25. 7(a)(i)3 marksConstruct a stem-and-leaf diagram to represent the given data.
  26. 7(a)(ii)1 markState an advantage of using the stem-and-leaf diagram to represent the given data.
  27. 7(a)(iii)1 markDetermine the mode.
  28. 7(a)(iv)2 marksDetermine the median.
  29. 7(a)(v)3 marksDetermine the interquartile range.
  30. 7(b)(i)2 marksDetermine P(A∩B).
  31. 7(b)(ii)2 marksDetermine P(A | B).
  32. 7(b)(iii)2 marksState, giving a reason, whether or not A and B are independent events.
  33. 7(c)4 marksFind the probability that the balls drawn are all of the same colour.
  34. 8(a)(i)5 marksOn the following grid, draw a displacement-time graph to display this information.
  35. 8(a)(ii)3 marksCalculate the average speed for the whole journey.
  36. 8(a)(iii)3 marksCalculate the average velocity of the whole journey.
  37. 8(b)(i)3 marksFind the velocity of the particle in terms of t.
  38. 8(b)(ii)6 marksCalculate the displacement of the particle in the interval of time t = π to t = 2π.

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