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CSEC Additional Mathematics · May/June 2008 · Paper 2

32 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(i)2 marksFind the value of a and of b.
  2. 1(ii)1 markFind the coordinates of the turning point of the curve.
  3. 2(a)(i)2 marksIllustrate A ∩ B = Ø using a Venn diagram.
  4. 2(a)(ii)2 marksIllustrate (C ∪ D) ⊆ E using a Venn diagram.
  5. 2(b)2 marksExpress, in set notation, the set represented by the shaded region.
  6. 35 marksFind the coordinates of the points where the straight line y = 2x - 3 intersects the curve x² + y² + xy + x = 30.
  7. 4(i)3 marksSketch, on the same diagram, the graphs of y = |x - 3| and y = |2x - 9|.
  8. 4(ii)2 marksSolve the equation |2x - 9| = |x - 3|.
  9. 5(i)2 marksFind the coefficient of x³ in the expansion of (1 + 3x)⁸.
  10. 5(ii)3 marksFind the coefficient of x³ in the expansion of (1 - 4x)(1 + 3x)⁸.
  11. 6(a)2 marksGiven that sin x = p, find an expression, in terms of p, for sec²x.
  12. 6(b)4 marksProve that sec A cosec A - cot A = tan A.
  13. 7(i)1 markWrite down an expression, in terms of x, for (OP)².
  14. 7(ii)2 marksDenoting (OP)² by S, find an expression for dS/dx.
  15. 7(iii)3 marksFind the value of x for which S has a stationary value and the corresponding value of OP.
  16. 8(i)3 marksSolve the equation 2^(2x + 1) = 20.
  17. 8(ii)4 marksSolve the equation 5^(4y - 1) / 25^y = 125^(y + 3) / 25^(2 - y).
  18. 9(i)2 marksCalculate AB.
  19. 9(ii)2 marksCalculate BC.
  20. 9(iii)4 marksFind the matrix X such that AX = B.
  21. 10(a)(i)2 marksFind ∫ 12/(2x - 1)⁴ dx.
  22. 10(a)(ii)3 marksFind ∫ x(x - 1)² dx.
  23. 10(b)(i)3 marksGiven that y = (x - 5)√(x + 4), show that dy/dx = 3(x + 1)/√(x + 4).
  24. 10(b)(ii)2 marksHence find ∫ (x + 1)/√(x + 4) dx.
  25. 11(i)1 markFind the range of f.
  26. 11(ii)1 markFind f²(1).
  27. 11(iii)3 marksFind an expression for f⁻¹(x).
  28. 11(iv)2 marksFind g⁻¹(2).
  29. 11(v)4 marksFind the value of x for which fg(x) = 38.
  30. 12 EITHER (i)5 marksFind the coordinates of A and of B.
  31. 12 EITHER (ii)5 marksFind the area of the shaded region.
  32. 12 OR10 marksFind the area of the quadrilateral ABCD.

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