![]() ![]() ![]() Pupils should be taught to integrate using partial fractions that are linear in the denominator more. Pupils should be taught to construct simple differential equations in pure mathematics and in context, (contexts may include kinematics, population growth and modelling the relationship between price and demand) more. Pupils should be taught to carry out simple cases of integration by substitution and integration by parts understand these methods as the inverse processes of the chain and product rules respectively (Integration by substitution includes finding a suitable substitution and is limited to cases where one substitution will lead to a function which can be integrated integration by parts includes more than one application of the method but excludes reduction formulae) more. Pupils should be taught to differentiate simple functions and relations defined implicitly or parametrically, for first derivative only more. Pupils should be taught to understand and use numerical integration of functions, including the use of the trapezium rule and estimating the approximate area under a curve and limits that it must lie between more. Pupils should be taught to Understand and use Pupils should be taught to differentiate using the product rule, the quotient rule and the chain rule, including problems involving connected rates of change and inverse functions more. Pupils should be taught to evaluate definite integrals use a definite integral to find the area under a curve and the area between two curves more. Identify where functions are increasing or decreasing more. Pupils should be taught to apply differentiation to find gradients, tangents, normals, maxima, minima and points of inflection. ![]() Integrate e kx, 1/x, sin kx, cos kx and related sums, differences and constant multiples more. Pupils should be taught to integrate x n (excluding n = -1) and related sums, differences and constant multiples. Understand and use the derivative of ln x more. Differentiate e kx and a kx, sin kx, cos kx, tan kx and related sums, differences and constant multiples. Pupils should be taught to differentiate x n, for rational values of n, and related constant multiples, sums and differences. Pupils should be taught to know and use the Fundamental Theorem of Calculus more. 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 more. 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. Pupils should be taught to 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, ![]()
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