To simplify algebraic fractions:
-Factorise
-Look for common factors in the top and bottom and cancel
-To divide by a fraction multiply by the reciprocal
-To add and subtract fractions find a common denominator

To divide polynomials use algebraic long division or compare coefficients (algebraic juggling is also an option) but read the question to see if a certain method is specified.
A polynomial can be written as (Quotient)(Divisor) + Remainder.
The divisor is the thing you divide by, the quotient is the answer, and the remainder is the bit left over.

One way of 'simplifying' algebraic fractions is by expressing them as partial fractions. To do this set the original fraction equal to 2 fractions with the denominator split, write as two fractions with numerators A and B, multiply both sides up to get rid of the fractions and then let x=a number to make one of the brackets 0 OR compare coefficients.

Parametric equations are when x and y are defined separately (in two equations) in terms of another parameter (usually t or \(\theta\). To find where graphs intersect equate the two equations, to find points of intersection with the axis set the equations equal to 0 and work out the t value then substitute it into the other equation.
Rearrange a parametric equation to make t the subject then substitute it into the other equation (using trig identities if required).

The binomial expansion formula is given in the formula book for the bracket: \[(1+x)^n\]
To use this the number at the front MUST be 1, if it isn't factorise the number out of the bracket to make it 1, but remember that when you factorise out the number is to the power n as well as the bracket left over.

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Mathematics: Core (Notes 1 of 1)