SL 5.1  Introduction to the concept of a limit. 

             Derivative interpreted as gradient function and as rate of change. 

SL 5.2  Increasing and decreasing functions. Graphical interpretation of f ′(x) > 0, f ′(x) = 0, f ′(x) < 0. 

SL 5.3  Derivative of f(x) = axn is f ′(x) = anxn − 1 , n ∈ ℤ The derivative of functions of the form f x = axn + bxn − 1 +... where all exponents are

             integers. 

SL 5.4 Tangents and normals at a given point, and their equations. 

SL 5.5  Introduction to integration as anti-differentiation of functions of the form f(x) = axn + bxn − 1 + ...., where n ∈ ℤ, n ≠ − 1. 

             Anti-differentiation with a boundary condition to determine the constant term. 

             Definite integrals using technology. Area of a region enclosed by a curve y = f(x) and the x-axis, where f(x) > 0. 

SL 5.6  Values of x where the gradient of a curve is zero. Solution of f ′(x) = 0. Local maximum and minimum points. 

SL 5.7  Optimisation problems in context. 

SL 5.8  Approximating areas using the trapezoidal rule.