AS-level Edexcel Pure Maths - Module 7: Algebraic methods|2023 LATEST UPDATE|GUARANTEED SUCCESS

Simplifying algebraic fractions - Factorise the numerator and denominator - Collect like terms Binomial An algebraic expression of the sum or the difference of two terms. E.g. x²-y³ Polynomial A finite expression with more than 2 terms. E.g. 6x²+24x+48 Dividend The base number that is being divided Divisor The number that is dividing into the dividend Quotient The whole number that results after dividing Remainder The number that is left over after a division Algebraic long division Factorising polynomials by factor theorem 1. Sub f(1) into f(x), then f(-1), then f(2), then f(-2)... 2. Stop when the answer is 0, sub this into (x-p). E.g. if f(2)=0, then (x-2) is a factor of the equation Factor theorem If f(x) is a polynomial then: - If f(p)=0 then (x-p) is a factor of f(x) - Conversely, if (x-p) is a factor of f(x), then f(p)=0 f(p)=0 is the same as saying p is a root of f(p) Term A single number or variable Expression A mathematical statement with variables and constants but which does not contain any relation symbol (,,=,...) E.g. 4x-7 Equation A mathematical statement with variables and constants which contains an equal sign 4x-7=13 Function An expression that processes an input to give an output f(x)=4x-7 Identity An expression that is true for all variables of x. Uses '≡' (a+b)²≡a²+2ab+b² Formula A mathematical relationship or rule expressed in numbers, symbols and variables E.g. A=πr² Counterexample An example used to disprove a statement Proof by deduction Starting with known and using logic to reach the desired conclusion Proving identities Use the expression on one side and manipulate is using algebra until it matches the other side. Don't solve like an equation