AS Level

  • Understand and use
    • the derivative of f(x) as the gradient of the tangent to the graph of y = f(x) at a general point (x, y);
    • the gradient of the tangent as a limit;
    • interpretation as a rate of change;
    • sketching the gradient function for a given curve;
    • second derivatives;
    • differentiation from first principles for small positive integer powers of x
  • Understand and use the second derivative as the rate of change of gradient
  • Differentiate xn, for rational values of n, and related constant multiples, sums and differences
  • Apply differentiation to find gradients, tangents and normals, maxima and minima and stationary points
  • Identify where functions are increasing or decreasing

A Level

  • connection to convex and concave sections of curves and points of inflection
  • Differentiate ekx and akx, sinkx, coskx ,tankx and related sums, differences and constant multiples
  • Understand and use the derivative of lnx
  • points of inflection
  • Differentiate using the product rule, the quotient rule and the chain rule, including problems involving connected rates of change and inverse functions
  • Differentiate simple functions and relations defined implicitly or parametrically, for first derivative only
  • Construct simple differential equations in pure mathematics and in context, (contexts may include kinematics, population growth and modelling the relationship between price and demand)