Find all the turning points of y=x^{1/x} for x>0 and decide whether each is a maximum or minimum. Give a sketch of the graph.

Draw graphs of the sine and modulus functions and explain the humps.

Build series for the sine and cosine functions by adding one term at a time, alternately making the approximation too big then too small but getting ever closer.

What functions can you make using the function machines RECIPROCAL and PRODUCT and the operator machines DIFF and INT?

What is the quickest route across a ploughed field when your speed around the edge is greater?

An article introducing the ideas of differentiation.

Put your complex numbers and calculus to the test with this impedance calculation.

Look at the calculus behind the simple act of a car going over a step.

Get started with calculus by exploring the connections between the sign of a curve and the sign of its gradient.

How many eggs should a bird lay to maximise the number of chicks that will hatch? An introduction to optimisation.

Can you hit the target functions using a set of input functions and a little calculus and algebra?

A point moves on a line segment. A function depends on the position of the point. Where do you expect the point to be for a minimum of this function to occur.

What is the longest stick that can be carried horizontally along a narrow corridor and around a right-angled bend?

This function involves absolute values. To find the slope on the slide use different equations to define the function in different parts of its domain.

Match the charts of these functions to the charts of their integrals.

Generalise the sum of a GP by using derivatives to make the coefficients into powers of the natural numbers.