Friday, 18 December 2009

Trigonometry: Cosine Rule

A good animated example

You need to be familiar with how to find a side and how to find an angle using the cosine rule

1. When all three sides of a triangle are known or can be calculated. In this situation, the Cosine Rule can be used to find any and all of the three angles

2. When two sides are known, and the included angle is either known or can be calculated (e.g. using the other two angles). In such a situation, the length of the third side can be calculated, and so can the other angles.

3. If two sides and an angle besides the included angle is known, the Cosine Rule can still be used, but the Sine Rule is easier to use.

Bitesize Revision

Thursday, 17 December 2009

Trigonometry: Sine Rule

Can be used in triangles without right angles when given

Two sides and an angle opposite to one of the sides
One side and any two angles


This video lasts 10 minutes but goes through examples

Statistics: Histograms

Histograms are a favourite GCSE topic, you need to know

  • what grouped data is
  • how to calculate the frequency density

The frequency on a Histogram is shown by the area in the box (frequency density x class width)
The class width is often unequal

Histograms are most often used with grouped data

In the diagram below

  • there are 20 people aged between 60 and 100
  • there are 42 people aged between 40 and 60

Statistics: Moving Averages

A pdf file with worked examples of GCSE questions - useful when you revise
Bitesize gives a simple example and a graph to show why we do them

Wednesday, 16 December 2009

Algebra: Surds

Surds are numbers left in 'square root form' (or 'cube root form' etc). They are therefore irrational numbers. The reason we leave them as surds is because in decimal form they would go on forever and so this is a very clumsy way of writing them. (See here for notes and examples )

Skills needed to answer GCSE questions
  • Using Surds in calculations
  • Simplifing Surds
  • Rationalise Surds (which needs you to remember the difference of 2 squares)

    Helpful resources, examples and links


    BBC Bitesize is always good

    GCSE Maths tutor - technical but some worksheets and videos

    Some people fing watching a YouTube video can help, but be aware that they use real Maths teachers

    MyMaths Surds1 goes through the topics in a gentle way.
    Surds2 - a little harder

  • Monday, 14 December 2009

    Revision Guides - Higher Edexcel

    I think the following at around £3.50 each are well worth the money.

    GCSE Success Edexcel Maths Higher Revision Guide
    This book puts all the notes you need in one place with limited examples. All of the Specification is set out.
    GCSE Success Edexcel Maths Higher Workbook (GCSE Success Revision Guides and Workbooks)
    This gives lots of examples with answers to reinforce your ideas.
    There are lots of sites that give you help (videos, worked examples, etc). This one is the BBC Bitesize – Statistics Site