Worked example shows how to apply knowledge of vectors to determine the true course of a boat travelling across a river.

Worked example shows how to apply knowledge of vectors to determine the work done in pulling a cart a certain distance.

Worked example explains how to multiply numbers and letters. Also explains the concepts of expressions, constants and coefficients.

Worked examples of adding and subtracting vectors algebraically in terms of i and j and also using the result of the proof of vector ab = vector b - vector a.

Solving an inequality statement containing an absolute value symbol by isolating the absolute value term at one side of the inequality and solutions checked.

Worked example of solving an absolute value inequality statement and solutions checked.

Definition of absolute value using simple examples. Worked example of solving an equation consisting of an absolute value symbol and checking solutions.

Worked example of solving an inequality containing two absolute value symbols, solutions checked and graph of absolute values also shown to illustrate solution set.

Discusses reciprocal trigonometric identities and investigates numerous examples, some of which involve reading the differentiation tables.

Explains the partial fraction expansion procedure when the denominator has repeated linear roots, and applies this technique to a simple example. Then applies this expansion to conduct the integration. Uses substitution in the resulting integrals.