These are the statements describing what students need to learn:
[Higher Level only statements are in blue]
- introduction to the concept of a limit. Derivative interpreted as gradient function and as rate of change
- increasing and decreasing functions. Graphical interpretation of f'(x)>0, f'(x)=0,f'(x)<0
- derivative of f(x)=axn is f'(x)=anxn-1, The derivative of functions of the form f(x)=axn+bxn-1+… where all exponents are integers
- tangents and normals at a given point, and their equations
- introduction to integration as anti-differentiation of functions of the form f(x)=axn+bxn-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
- values of x where the gradient of a curve is zero. Solution of f'(x)=0. Local maximum and minimum points
- optimisation problems in context
- approximating areas using the trapezoidal rule
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