Sign In | Starter Of The Day | Tablesmaster | Fun Maths | Maths Map | Topics | More

These are the statements describing what students need to learn:

- understand and use the derivative of f (x) as the gradient of the tangent to the graph of y = f ( x) at a general point (x, y); the gradient of the tangent as a limit; interpretation as a rate of change, sketching the gradient function for a given curve, second derivatives, differentiation from first principles for small positive integer powers of x and for sin x and cos x. Understand and use the second derivative as the rate of change of gradient; connection to convex and concave sections of curves and points of inflection
- differentiate x
^{n}, for rational values of n, and related constant multiples, sums and differences. Differentiate e^{kx}and a^{kx}, sin kx, cos kx, tan kx and related sums, differences and constant multiples. Understand and use the derivative of ln x - apply differentiation to find gradients, tangents, normals, maxima, minima and points of inflection. Identify where functions are increasing or decreasing
- differentiate using the product rule, the quotient rule and the chain rule, including problems involving connected rates of change and inverse functions
- differentiate simple functions and relations defined implicitly or parametrically, for first derivative only
- construct simple differential equations in pure mathematics and in context, (contexts may include kinematics, population growth and modelling the relationship between price and demand)

Click on a statement above for suggested resources and activities from Transum.