Simple examples showing the geometric and algebraic effect on magnitude and direction of vectors when multiplying vectors by positive and negative scalars.

Calculates the MacLaurin series for the trigonometric function sine x. Comments on the pattern of the series.

Calculates the MacLaurin series for the exponential function. Also discusses the MacLaurin series for e^2x derived from the corresponding series for e^x.

Calculates the MacLaurin series for a composite function e^{sinx}. Highlights the fact that this series must be a polynomial.

Worked example of finding the magnitude of the horizontal and vertical component of a soccer balls velocity.

Explaination of how to resolve a vector into its horizontal and vertical components.

Introduction to combined inequalities. Example of forming a combined inequality from a given word statement and worked example of solving a combined inequality consisting of the word 'or' and solutions checked.

Forming a combined inequality statement from a given word statement using symbols instead of the words 'or' or 'and' and solving this combined inequality. Solutions also checked.

Forming a combined inequality from a given word problem to estimate the distance between two homes, given the distance from both homes to Dublin Airport.

Worked example of forming and solving a combined inequality statement from a given word statement. Term 'conjunction' explained and solutions checked.