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CSEC Additional Mathematics · 2015 · Paper 2

36 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)2 marksFind the value of g(f(2)).
  2. 1(b)3 marksDetermine the inverse of h(x).
  3. 1(c)3 marksFactorize k(x) completely.
  4. 1(d)(i)2 marksSolve the equation: 16^(x+2) = 1/4.
  5. 1(d)(ii)4 marksSolve the equation: log3(x + 2) + log3(x - 1) = log3(6x - 8).
  6. 2(a)(i)3 marksExpress f(x) in the form a(x + b)^2 + c, where a, b and c are real numbers.
  7. 2(a)(ii)1 markState the coordinates of the minimum point of f(x).
  8. 2(b)4 marksFind the value of 1/α + 1/β.
  9. 2(c)3 marksDetermine the coordinates of the points of intersection of the curve 2x^2 - y + 19 = 0 and the line y + 11x = 4.
  10. 2(d)3 marksDetermine the annual salary that the employee should receive in the ninth year.
  11. 3(a)(i)2 marksDetermine the coordinates of the centre of the circle.
  12. 3(a)(ii)1 markFind the length of the radius.
  13. 3(a)(iii)3 marksDetermine the equation of the normal to the circle at the point (4, 10).
  14. 3(b)(i)3 marksDetermine the unit vector AB.
  15. 3(b)(ii)3 marksDetermine the acute angle AOB, in degrees, to one decimal place.
  16. 4(a)4 marksCalculate the area of the shaded region.
  17. 4(b)4 marksSolve the equation 8 sin^2 θ = 5 - 10 cos θ, where 0° ≤ θ ≤ 360°, giving your answer correct to one decimal place.
  18. 4(c)4 marksProve the identity (sin θ + sin 2θ) / (1 + cos θ + cos 2θ) = tan θ.
  19. 5(a)4 marksDifferentiate the expression (2x^2 + 3) sin 5x with respect to x, simplifying your answer.
  20. 5(b)(i)3 marksFind the coordinates of all the stationary points of the curve y = x^3 - 5x^2 + 3x + 1.
  21. 5(b)(ii)2 marksDetermine the nature of EACH point in (i) above.
  22. 5(c)5 marksCalculate, in terms of π, the rate at which the radius is increasing when the radius of the balloon is 10 cm.
  23. 6(a)4 marksEvaluate ∫(from π/6 to π/3) cos 3θ dθ.
  24. 6(b)(i)2 marksDetermine the value of k.
  25. 6(b)(ii)4 marksDetermine the equation of the curve.
  26. 6(c)4 marksCalculate, in terms of π, the volume of the solid formed when the area enclosed by the curve y = x^2 + 1 and the x-axis, from x = 0 to x = 1, is rotated through 360° about the x-axis.
  27. 7(a)(i)4 marksFind the probability that the motorist has to stop at ONLY ONE traffic light.
  28. 7(a)(ii)4 marksFind the probability that the motorist has to stop at AT LEAST TWO traffic lights.
  29. 7(b)4 marksUse the data in the following table to estimate the mean of x.
  30. 7(c)(i)4 marksDraw a probability tree diagram to illustrate the information, and show the probability on ALL of the branches.
  31. 7(c)(ii)4 marksDetermine the probability that it will rain on the Wednesday of that week.
  32. 8(a)(i)3 marksOn the answer graph sheet, provided as an insert, draw a velocity-time graph to represent the motion of the particle.
  33. 8(a)(ii)3 marksCalculate the acceleration of the particle.
  34. 8(a)(iii)4 marksDetermine the increase in displacement over the interval t = 0 to t = 4.
  35. 8(b)(i)5 marksFind the velocity when t = 4.
  36. 8(b)(ii)5 marksFind the displacement of the particle from O when t = 3.

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