Summary A sequence is a set of numbers in a given order with a rule for obtaining the terms, written as:   . The nth term of a sequence is an expression that will allow us to calculate the term that is in the nth position of the sequence i.e    is the first term … Read more


Summary Random errors: an error that affects only some observed values and can be reduced by taking average of large number of readings. Systematic Error: an error which is built in the measurement device, it cannot be reduced, however it can be removed if we know the exact error and then we subtract it from … Read more


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


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