Course Outline

Aim

• To build confidence and understanding of mathematical ideas.
• To enable the student to interpret and solve mathematical problems.
• To improve examination technique and to make the student aware of common examination errors.
• To make the student fully aware of the content and emphasis of the specification.
• To strengthen revision methods.

Key Topics Covered

1. Algebra and functions

• Rational functions. Partial fractions (denominators not more complicated than repeated linear terms).

2. Coordinate geometry in the (x, y) plane

• Parametric equations of curves and conversion between Cartesian and parametric forms.

3. Sequence and series

• Binomial series for any rational n.

4. Differentiation

• Differentiation of simple functions defined implicitly or parametrically.
• Exponential growth and decay.
• Formation of simple differential equations.

5. Integration

• Integration of
• Evaluation of volume of revolution.
• Simple cases of integration by substitution and integration by parts. These methods as the reverse processes of the chain and product rules respectively.
• Simple cases of integration using partial fractions.
• Analytical solution of simple first order differential equations with separable variables.
• Numerical integration of functions.

6. Vectors

• Vectors in two and three dimensions.
• 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.
• The scalar product. Its use for calculating the angle between two lines.