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Exam Syllabuses 2007 - Additional Mathematics

7.
Differentiation from first principles. Differentiation ofpowers of x and trigonometric functions. Differentiation of a sum, a product and a quotient of functions. Differentiation of a composite function and an implicit function. Second derivatives.
(The differentiation of inverse trigonometric functions will not be examined.)

Application of differentiation to gradients, rates of change,tangents and normals to a curve, maxima and minima, and sketching of simple curves.
(Excluding points of inflexion and asymptotes.)

8.
Indefinite integration as the reverse process of differentiation.
(Excluding integration of 1/x and integration by parts.)

The integrals of (ax + b)^n (excluding n = –1), sin(ax + b) and cos(ax + b).
(Integration by substitution is not required.)

Definite integrals and their simple properties.
Applications in finding plane areas and finding volume of solids of revolution formed by revolving about the coordinate axes.
(Proofs of these properties are not required.)

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