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CAIE A Level Mathematics 9709

Differentiation (AS) questions

Exam-style questions on Differentiation (AS), 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. 2 marksFoundationDifferentiate the following function with respect to x: f(x) = 2x^3 - 2x^-2 + 1
  2. 2 marksFoundationDifferentiate the following function with respect to x: f(x) = 3x^3 + x^-2 + 5x^(1)/(2).
  3. 3 marksStandardThe curve y = 6x^2 + 12x has a stationary point. Find the x-coordinate of this stationary point.
  4. 3 marksStandardFind the gradient of the curve y = x^2 - x - 2 at the point where x = 1.
  5. 4 marksStandardThe curve C has equation y = x^2 + x + 4. Find the equation of the tangent to C at the point where x = 3.
  6. 4 marksStandardThe curve C has equation y = x^2 + 3x. Find the equation of the normal to C at the point where x = 3. Give your answer in the form Ax + By + C = 0, where A, B and C are integers.
  7. 3 marksStandardThe curve y = x^2 - 4x + 3 has a stationary point. Find the x-coordinate of this stationary point.