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CSEC Additional Mathematics · May/June 2007 · 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. 13 marksCalculate the range of values of x for which the area of the triangle is greater than 3 m².
  2. 2(i)3 marksFind the value of c.
  3. 2(ii)3 marksFind the value of b.
  4. 2(iii)3 marksFind the value of a.
  5. 35 marksWithout using a calculator, express p/q in the form m+√n, where m and n are integers.
  6. 4(i)2 marksFind the number of different selections she can make.
  7. 4(ii)3 marksIn how many of these selections will there be more watercolour paintings than oil paintings?
  8. 5(i)1 markExpress 1/√32 as a power of 2.
  9. 5(ii)1 markExpress (64)^(1/3) as a power of 2.
  10. 5(iii)3 marksHence solve the equation (64)^(1/3) = 1/(2^x √32).
  11. 6(i)2 marksDifferentiate x² ln x with respect to x.
  12. 6(ii)4 marksUse your result to show that ∫(from 1 to e) 4x ln x dx = e² + 1.
  13. 7(i)3 marksFind the matrix X such that X = A² + 2B.
  14. 7(ii)4 marksFind the matrix Y such that YA = B.
  15. 8(i)4 marksFind the largest value of the integer k for which L intersects C.
  16. 8(ii)4 marksIn the case where k = – 2, show that the line joining the points of intersection of L and C is bisected by the line y = 2x + 5.
  17. 9(i)4 marksBy finding the magnitude of the vectors PR, RQ and QP, show that angle PQR is 90°.
  18. 9(ii)2 marksFind the unit vector parallel to PR.
  19. 9(iii)3 marksGiven that OQ = mOP + nOR, where m and n are constants, find the value of m and of n.
  20. 10(i)3 marksObtain expressions for f⁻¹ and g⁻¹.
  21. 10(ii)3 marksDetermine the value of a for which f⁻¹g(4) = 2.
  22. 10(iii)3 marksIf a = 9, show that there is only one value of x for which g(x) = g⁻¹(x).
  23. 11(i)4 marksFind the acceleration of the particle at A and at B.
  24. 11(ii)2 marksFind the greatest speed of the particle as it travels from A to B.
  25. 11(iii)4 marksFind the distance AB.
  26. 12(EITHER)(i)5 marksFind the coordinates of B.
  27. 12(EITHER)(ii)3 marksFind the coordinates of C.
  28. 12(EITHER)(iii)2 marksFind the coordinates of D.
  29. 12(OR)(a)(i)2 marksEvaluate b.
  30. 12(OR)(a)(ii)2 marksEvaluate a.
  31. 12(OR)(a)(iii)1 markEvaluate c.
  32. 12(OR)(b)5 marksSolve the equation x³ + 3x² = 2, giving your answers to 2 decimal places where necessary.

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