S-Cool Revision Summary

S-Cool Revision Summary

Indices

Basic rules to learn are:

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Copyright S-cool

When using surds remember that:

Logarithms

Definition: Copyright S-cool

Logarithm Rules:

  1. Copyright S-cool

  2. Copyright S-cool

  3. Copyright S-cool

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

Binomial Expansion

To expand Copyright S-cool where n is a positive integer Copyright S-cool:

  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: Copyright S-coolCopyright S-cool.

To expand Copyright S-cool, where n is not a positive integer:

  1. Rearrange to get Copyright S-cool

  2. Use the general formula Copyright S-cool

Remember the condition Copyright S-cool

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.