Video in which Dr Bill Foster works through an example of how to find the equation of a straight line with a negative gradient.

A video of Dr Bill Foster showing how to rearrange a fraction with polynomial denominator into partial fractions.

Having factorised the denominator and written down the partial fractions with unknown numerators, the next step is to equate the coefficients of each power of x, and hence find the numerators of the partial fractions.

This is a video of Prof Robin Johnson demonstrating an example of how to solve a quadratic equation by completing the square.

A video of Prof Robin Johnson comparing the curves defined by two different equations.

They both represent a circle of radius 2 centred at the origin, but one is given implicitly by an equation in x and y, but in the other x and y are given explicitly in terms of cos and sin.

A video of Prof Robin Johnson demonstrating how to factorise a quadratic by completing the square. 

Simply trying to look at a quadratic and guessing which numbers produce the correct factors can be quite tricky, so a more mechanical method can be useful. By completing the square, you can rewrite a quadratic as the difference of two squares, and the factorisation can then be written down easily, with no guesswork involved.

A video of Dr Bill Foster demonstrating how to find the equation of a straight line with positive gradient.

This is a video in which Prof Robin Johnson finds the equation of a circle.

By beginning with a quadratic equation in X and Y, it is shown that it can be rewritten in the canonical form of the equation of a circle, by completing the square. After rearranging, you can easily see where the centre of the circle is and what its radius is.

A video of Dr Bill Foster demonstrating how to rewrite an algebraic fraction with repeated linear factors as partial fractions.

In this video Dr Phil Ansell demonstrates how to use the law of total probability to find the total probability of an event, given the conditional probabilities of the event.

Given the probabilities that voters for each political party support tax cuts, and the probabilities of a voter supporting each party, we find the probability that any voter supports tax cuts.

In this video, Prof Robin Johnson investigates what the modulus does to a function, by sketching its graph.