Quadratic Equations

Summary A quadratic equation is in the form  , A quadratic function has a minimum value when a > 0 A quadratic function has a maximum value when a < 0 Vertex is a point on the where the curve is either maximum or minimum To find the values of the maximum or minimum point … Read more

Functions

Summary A function is defined as a rule which assigns each element of set X, one and only one element of set Y.  i.e set   and set  Domain: elements of set X Range: elements of set Y One to One Function: for each element of set Y, there is a unique corresponding element in … Read more

Algebraic Long Division

Summary Polynomial long division is normal long division but with polynomials instead of just numbers. If a polynomial p(x) is to be divided by (x – a) and p(a) = 0 then we can say that (x – a) is a factor of the polynomial Revise the steps below to be able to carry out … Read more

Partial Fractions

Summary Remember these formulas of partial fractions for different types of fractions: We can recall from GCSE’s that to transform a function consisting of many fractions into a single fraction, we take LCM (lowest common factor) of the entire function i.e: if we have a function , we take its LCM and make it into … Read more

Surds

Summary Rational Number: A number that can be written as a fraction, where both the numerator and the denominator are whole numbers. E.g 3/4 Irrational Number: They cannot be written as a fraction. They can only be written as decimals numbers. E.g    which is equal to 1.7320…… A surd is a number that’s written … Read more

The Binomial Expansion

Summary Pascal’s Triangle can be used to multiply out a bracket. When we have large powers, we can use combination and factorial notation to help expand binomial expressions. What is a Binomial? A binomial is an expression which consists of two terms only i.e 2x + 3y and 4p – 7q are both binomials. What … Read more