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CSEC Additional Mathematics · May/June 2009 · Paper 2

31 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)1 markExpress, in set notation, the set represented by the shaded region.
  2. 1(b)(i)1 markIllustrate this information using a Venn diagram.
  3. 1(b)(ii)1 markFind the number of students studying neither of these subjects.
  4. 1(b)(iii)1 markFind the number of students studying exactly one of these subjects.
  5. 24 marksFind A⁻¹ and hence solve the simultaneous equations 7x + 6y = 17, 3x + 4y = 3.
  6. 34 marksSketch the graph of y = |x² - 8x + 12|.
  7. 4(i)2 marksFind the coefficient of x⁴ in the expansion of (1+2x)⁶.
  8. 4(ii)3 marksFind the coefficient of x⁴ in the expansion of (1 - x/4)(1+2x)⁶.
  9. 5(i)2 marksObtain an expression for dy/dx.
  10. 5(ii)3 marksUse your expression to find the approximate change in the value of y when x increases from 2 to 2.04.
  11. 6(i)1 markFind the range of f.
  12. 6(ii)2 marksFind an expression for f⁻¹(x).
  13. 6(iii)2 marksFind gf(12).
  14. 7(i)1 markFind logₚ √X.
  15. 7(ii)1 markFind logₚ (1/X).
  16. 7(iii)2 marksFind logₚ (XY).
  17. 7(iv)2 marksFind log_Y X.
  18. 8(i)2 marksFind the length of PQ in terms of t and hence show that the area, A square units, of PQRS is given by A = 54t - 2t³.
  19. 8(ii)3 marksGiven that t can vary, find the value of t for which A has a stationary value.
  20. 8(iii)3 marksFind this stationary value of A and determine its nature.
  21. 9(i)2 marksCalculate the number of ways the 4 pieces can be chosen if there are no restrictions.
  22. 9(ii)3 marksCalculate the number of ways the 4 pieces can be chosen if there must be 2 pieces by Beethoven, 1 by Handel and 1 by Sibelius.
  23. 9(iii)4 marksCalculate the number of ways the 4 pieces can be chosen if there must be at least one piece by each composer.
  24. 109 marksFind the equation of the perpendicular bisector of AB.
  25. 11(a)(i)3 marksFind all the angles between 0° and 360° which satisfy 2sin x - 3cos x = 0.
  26. 11(a)(ii)5 marksFind all the angles between 0° and 360° which satisfy 2sin² y - 3cos y = 0.
  27. 11(b)3 marksFind, correct to 2 decimal places, all the values of z for which sin(2z + 1) = 0.9.
  28. 12 EITHER (i)5 marksFind, in terms of e, the y-coordinate of Q.
  29. 12 EITHER (ii)5 marksFind, in terms of e, the x-coordinate of R.
  30. 12 OR (i)4 marksFind the coordinates of B.
  31. 12 OR (ii)6 marksFind the area of the shaded region.

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