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CAIE A Level Mathematics 9709

Differentiation (A2) questions

Exam-style questions on Differentiation (A2), ordered from foundation to challenge. Pick one, write your answer the way you would in the exam, and it comes back marked against the mark scheme, point by point.

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Written by Markquill to follow the Cambridge International syllabus. Markquill is independent and is not affiliated with or endorsed by Cambridge International.

  1. 3 marksFoundationGiven that y = cos(3x + 2), find (dy)/(dx).
  2. 3 marksFoundationFind the derivative of f(x) = sin(5x - 2) with respect to x.
  3. 4 marksStandardFind the gradient of the curve with equation y = -4x^3 + x^2 - 2 at the point where x = 3.
  4. 4 marksStandardFind the gradient of the curve y = (3x + 4)^2 at the point where x = 2.
  5. 4 marksStandardGiven that y = x e^-2x, find (dy)/(dx).
  6. 4 marksStandardA curve is defined parametrically by x = 3 cos t, y = 6 sin t, where t is a parameter. Find (dy)/(dx) in terms of t.
  7. 4 marksStandardThe parametric equations of a curve are given by x = 1 sin(t), y = 4 cos(2t), where t is a parameter. Find (dy)/(dx) in terms of t.
  8. 3 marksStandardFind the gradient of the normal to the curve y = x^2 + x at the point where x = 2.
  9. 5 marksChallengeThe curve C has equation x^2 + xy + y^2 = 7. The point P(1,2) lies on C. Find the gradient of C at P.
  10. 5 marksChallengeThe curve C is defined implicitly by the equation x^2 + y^2 + xy = 4^2 + 3^2 + 43. The point P(4, 3) lies on C.