Differentiating Powers of x How do I differentiate expressions involving powers of?x? Powers of?x?are differentiated according to the following formulae: Differentiating terms with positive integer...
Definition of Derivatives What is the derivative of a function?? Differentiation?is an operation that calculates the?rate of change?of a?function?with respect to a variable This means how much the ...
Definition of Gradient What is the gradient of a curve? At a given point the?gradient?of a curve is defined as the gradient of the?tangent?to the curve at that point A?tangent?to a curve is a line ...
Modelling with Sequences & Series What do I need to know about modelling with progressions? Many real-life situations can be modelled using progressions If a quantity is changing repeatedly by ...
Recurrence Relations What do I need to know about recurrence relations? A?recurrence relation?describes each term in a progression as a function of the previous term – ie?un+1?= f(un) Along with th...
Sigma Notation What is sigma notation? The symbol Σ is the capital Greek letter sigma – that's why it's called 'sigma notation'! 'Σ' stands for 'sum' – the expression to the right of the Σ tells yo...
Language of Sequences & Series What is a progression/sequence? A?progression?(or?sequence) is an?ordered?set of numbers with a rule for finding all the numbers in the progression The numbers in...
Geometric Series How do I find the sum of a geometric progression? The?sum?of the terms of a?geometric progression?is sometimes called a?geometric series The following formulae will let you find th...
Geometric Sequences What do I need to know about geometric progressions? In a?geometric progression?(also called?geometric sequence)?there is a?common ratio?between consecutive terms in the sequenc...
Arithmetic Series How do I find the sum of an arithmetic progression? The?sum?of the terms of an?arithmetic progression?is sometimes called an?arithmetic series The following formulae will let you ...
Arithmetic Sequences What do I need to know about arithmetic progressions? In an?arithmetic progression?(also called?arithmetic sequence), the difference between consecutive terms in the sequence i...
Binomial Expansion What is the binomial expansion? Look at the pattern Start at?nC0, then?nC1,?nC2, etc Powers of?a?start at?n?and decrease by 1 Powers of?b?start at 0 and increase by 1 There are s...
