Basic rules to learn are:

When using surds remember that:

Definition:

Logarithm Rules:

An exponential equation is in the form: = value, and is solved by taking logs.

To expand where n is a positive integer :

1. Write down a in descending powers - (from n to 0)

2. Write down b in ascending powers - (from 0 to n)

3. Add Binomial Coefficients from Pascals triangle, or by using: .

To expand , where n is not a positive integer:

1. Rearrange to get

2. Use the general formula

Remember the condition

These are used to turn complex expressions into simple fractions, which can then be used to integrate the expression, or use the binomial expansion to get an approximation to the original expression.

Choose the appropriate formula from these:

Then add the separate fractions together and match the numerators. You will need to use simultaneous equations.