Examples of how to factorise expressions whose terms don't have any common factor (other than 1) by grouping pairs that do have factors in common.

Examples of how to factorise expressions whose terms don't have any common factor (other than 1) by grouping pairs that do have factors in common.

We investigate inequalities involving quadratic expression and show how to use a combination of algebraic rearrangement and graph sketching to find solutions. The solutions are written as inequalities and as intervals.

We use the known result for Laplace transform of a derivative sF(s) to speculate about the result for the transform of an integral. We guess that it might involve division by s. This result is proven using a double integration method.

Examples are given of the visual interpretation of systems of 3 simultaneous linear equations in 3 unknowns for the case where there is a unique solution, an infinite number of solutions, and no solutions.

After a brief review of circular polar coordinates, a double integral is written using Cartesian coordinates. We draw the region of integration and describe it in terms of polar coordinates in order to rewrite the integral in polar coordinates.

Outlines the general formula for finding the Inverse of a 2x2, then goes through one simple example.

The general definition of logarithms is given and the general principle of solving equations of from a^x=b is introduced. Two examples to apply this method are then given.

The general principle of changing base of logs (logarithms) is given and then this is illustrated with a specific example.

This recording first explains what a transition curves is and gives formulae to calculate the angle theta as well as any point on the curve (x,y). It then works through an example.