An example of calculating partial fractions when one of the factors on the denominator is an irreducible quadratic factor

Several examples are given of rewriting composite circular functions, where the inner function is an inverse trigonometric function, as an algebraic function in terms of x.

Outlines the general process for setting up and solving a related rates problem (where related quantities change over time). This is then applied to an example involving a chemical being drained out of a cylindrical tank.

Outlines the general process for setting up and solving a related rates problem (where related quantities change over time). This is then applied to an example involving the relative speed and distance apart of two bicycles at a specified time.

Basic explanation of what factorising is, why it is used, and a couple of simple examples.

An example of using the scalar product to determine the work done on an object by a force, when the force is expressed in vector form.

An example of calculating partial fractions when one of the factors on the denominator is a repeated linear factor.

An example of calculating partial fractions when the denominator can be factorised into single distinct linear factors

Demonstrates the general method and two examples of using the definitions of sinh(x) and cosh(x) to prove hyperbolic function identities

We derive the formula for the Laplace transform of df/dt in terms of that for f(t) and f(0). It is then shown how to extrapolate the rule to write down the transforms for 2nd, 3rd and higher derivatives.