Positive integer powers of the binomial (a+b) are examined. It is shown how to expand the brackets to obtain a finite series using coefficients from the Pascal triangle. Later these coefficients are identified as the nCr coefficients.

Shows two incorrect solutions to finding the derivative of (3x+5)^2x and discusses why they are incorrect. The correct approach is then explained.

An example of using the multivariate chain rule, where in this case we are finding dz/dx given z = f(x,y) and y = y(x).

Example of solving a second-order linear ordinary differential equation with constant coefficients in the case where the auxiliary equation has a repeated root and the right hand side of the equation is a polynomial.

A demonstration of how to tranpose the formula y=(ae^t+be^(-t))/(ce^t+de^(-t)) to make t the subject.

3 completed examples of differentiating trigonometric functions. Similar questions at the end for students to try themselves, solutions provided also.

An example of solving a second order differential equation (where the right hand side is an exponential function), given specific initial conditions y(0) and y'(0) are also provided

We continue the theme of half range series and examine how the integrations can be simplified using the symmetry of the function. Here we examine a half-range cosine series for a linear f(t).

We state what is meant by a series, express series using the summation sign, define the partial sums and briefly discuss convergence and divergence giving examples.

Three basic laws of logarithms are introduced and two examples then demonstrate how these laws can be used to simply logarithmic expressions.