SCool Revision Summary
SCool Revision Summary
Indices
Basic rules to learn are:
When using surds remember that:
Logarithms
Definition:
Logarithm Rules:
An exponential equation is in the form: = value, and is solved by taking logs.
Binomial Expansion
To expand where n is a positive integer :

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

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

Add Binomial Coefficients from Pascals triangle, or by using: .
To expand , where n is not a positive integer:

Rearrange to get

Use the general formula
Remember the condition
Partial Fractions
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.