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Differentiation of algebraic and trigonometric expressions can be used for calculating rates of change, stationary points and their nature, or the gradient and equation of a tangent to a curve.

Integration is the inverse of differentiation of algebraic and trigonometric expressions involving brackets and powers. This can solve differential equations and evaluate definite integrals.

Optimization is used to find the greatest/least value(s) a function can take. This can involve creating the expression first. Also find the rate of change by differentiating then substituting.

The area above and below the x axis and the area between two curves is found by integrating, then evaluating from the limits of integration. Integration is also used to solve differential equations.