Gradients, Tangents & Normals Using the derivative to find the gradient of a curve To find the gradient of a curve y= f(x) at any point on the curve, substitute the x‑coordinate of the point in...
Chain Rule What is the chain rule? If y is a function of u, and u is a function of x, then the chain rule tells us that The chain rule allows us to differentiate more complicated expressions and c...
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...
