Learn how a rational function can be expressed in terms of its partial fractions. Cases will include denominators not more complicated than repeated linear terms. The degree of the numerator may equal or exceed the degree of the denominator. This technique will be applied to other topics such as integration, differentiation and series expansions.
The formula for the binomial series is extended to cover any rational n and any function of the form (ax+b)n and then used to find approximations for square and cube roots.
Learn about parametric equations of curves and conversion between Cartesian and parametric forms. Students will not be expected to sketch a curve from its parametric equations although some activities here illustrate the connection between parametric equations and their curves.
There are three main areas of study here: differentiation of implicit and parametric functions, including finding tangent and normals to curves; exponential growth and decay; and formation of simple differential equations, including connected rates of change.
Learn how to integrate ex,1/x, sinx, cosx and functions based on them. Learn the standard methods of integration: standard forms, substitution, parts, use of trig identities and partial fractions, and how to apply these techniques to finding volumes of revolution and solving separable first order differential equations. Learn how to apply the trapezium rule to functions met in recent modules.
Understand vectors in two and three dimensions. Learn about: Magnitude of a vector, algebraic operations of vector addition and multiplication by scalars, and their geometrical interpretations, position vectors, the distance between two points, vector equations of lines and the scalar product.