# Chapter one

Mathematical skills

## Section one: Logarithms, trigonometry, and binomial expansions

This chapter is on the theme of supporting mathematics that are needed for engineering problem solving, analysis, design and evaluation.

This section focuses on some basic pre-requisites that students should have studied before coming to university. They will be useful for students who are revising and trying to improve their problem solving skills.

Logarithms

We give a quick review of the key logarithm content on A level mathematics followed by a number of questions. The main contribution is to show how questions can be solved using simple techniques linked directly to the properties of logarithmic functions.

Trigonometry

Next we give a quick review of the key trigonometry content on A level mathematics followed by a number of questions. The main contribution is to show how questions can be solved using simple techniques linked directly to the properties of trigonometric functions.

Binomials

These videos give a quick review of the key binomial expansion content on A level mathematics followed by a number of questions. The main contribution is to show how questions can be solved using simple techniques linked directly to the formulae for binomial expansions.

### Logarithms

Logarithm revision examples one for A level students

A rapid review of rules of logarithms and the links to indices or powers. Followed by a number of worked examples showing how logarithms can be used to solved problems involving power functions.

A talk through video is on YouTube.

Logarithm revision examples two for A level students

A number of examples showing how the rules and properties of logarithms can be used in problem solving. Emphasises by example that familiarity with and use of core properties is most effective tool for questions that appear on typical A level papers.

A talk through video is on YouTube.

Logarithm revision examples three for A level students

Shows how to solve a number of more challenging problems that can appear on A level papers. Emphasises how knowledge of and application of the properties (or rules) of logs makes such problems relatively straightforward.

A talk through video is on YouTube.

### Trigonometry

Revision of A level trigonometry - questions and answers one

A rapid review of the core rules which students learn in GCSE such as SOH, CAH, TOA, sine rule, cosine rule, areas of triangles and Pythagoras.

A talk through video is on YouTube.

Revision of A level trigonometry - questions and answers two

Gives a general definition for the sine function and shows how this can be plotted for angles outside of 0 to 90 degrees. Uses the sketch of the sine function to show how problems involving sine have multiple solutions, and demonstrates with worked examples.

A talk through video is on YouTube.

Revision of A level trigonometry - questions and answers three

Gives a general definition for the cosine function and shows how this can be plotted for angles outside of 0 to 90 degrees. Uses the sketch of the cosine function to show how problems involving cosine have multiple solutions; demonstrates with worked examples.

A talk through video is on YouTube.

Revision of A level trigonometry - questions and answers four

Gives a general definition for the tangent function and shows how this can be plotted for angles outside of 0 to 90 degrees. Uses the sketch of the tangent function to show how problems involving tangent have multiple solutions; demonstrates with worked examples.

A talk through video is on YouTube.

Revision of A level trigonometry - questions and answers five

Introduces radians as a means of measuring angles. Gives a number of example problems to demonstrate how the problems tackled in videos two to four can equally be solved in radians rather than degrees.

Questions start around three minutes into video.

A talk through video is on YouTube.

Revision of A level trigonometry - questions and answers six

Looks at links between Pythagoras and sine/cosine, and gives a number of numerical examples showing how this link can be exploited to solve algebraic problems that commonly appear on A level papers.

Questions start almost immediately.

A talk through video is on YouTube.

### Binomials

Revision of A level binomial expansions - questions and answers one

A rapid review of the definition of a binomial expansion followed with some illustrations of how and why the coefficients are what they are. Demonstrates that the coefficients have a prescribed pattern.

A talk through video is on YouTube.

Revision of A level binomial expansions - questions and answers two

Builds on the insights of video one to give precise definitions or formulae for the coefficients of a binomial expansion. Students are usually provided with these formulae in an exam, but familiarity is always helpful.

A talk through video is on YouTube.

Revision of A level binomial expansions - questions and answers three

After a very brief reminder of key formulae which will be used, this video presents four introductory type questions from A level papers. It demonstrates a systematic solution methodology for them.

A talk through video is on YouTube.

Revision of A level binomial expansions - questions and answers four

After a very brief reminder of key formulae which will be used, this video presents four typical questions from A level papers. It demonstrates a systematic solution methodology for solving them.

A talk through video is on YouTube.

Revision of A level binomial expansions - questions and answers five

After a very brief reminder of key formulae which will be used, this video presents four less typical questions from A level papers. It demonstrates a systematic solution methodology for them.

There is a small typing error in part B of question four. It should ask for q/p.

A talk through video is on YouTube.