Differentiation and integration

  • Derivative of f(x) as the gradient of the tangent to the graph of y = f(x) at a point

  • Derivative as rate of change

  • Use of standard notations

  • Derivatives of x^n , for any rational n, sin x, cos x, tan x, e^x, and In x together with constant multiples, sums and differences

  • Derivatives of products and quotients of functions

  • Use of Chain Rule

  • Increasing and decreasing functions

  • Stationary points (maximum and minimum turning points and stationary points of inflexion)

  • Use of second derivative test to discriminate between maxima and minima

  • Apply differentiation to gradients, tangents and normals, connected rates of change and maxima and minima problems

  • Integration as the reverse of differentiation

  • Integration of x^n for any rational n, sinx, cos x, sec^2 x and e^x , together with constant multiples, sums and differences

  • Integration of ( ax+b)^n for any rational n, sin (ax + b), cos (ax + b) and e^(ax+b)

  • Definite integral as area under a curve

  • Evaluation of definite integrals

  • Finding the area of a region bounded by a curve and line(s) (excluding area of region between 2 curves)

  • Finding areas of regions below the x-axis

  • Application of differentiation and integration to problems involving displacement, velocity and acceleration of a particle moving in a straight line