Pure mathematics

This is the foundation module on which subsequent, university level pure mathematics is based.

Logic, Proof and Sets: Mathematical statements and proof. Some basic logic. Quantifiers and proof by contradiction. Set notation and operations on sets.
Algebra: Polynomial division. The factor and remainder theorems. Solving polynomial equations. The relationship between the roots of a polynomial and its coefficients. Partial fractions. The binomial theorem.
Trigonometry: Trigonometric functions and the Pythagorean identities. The compound angle formulae. Using trigonometric identities to simplify and evaluate trigonometric expressions. Solving trigonometric equations.
Calculus: Differentiating implicitly defined functions. Integration by substitution. Integration by parts. Using trigonometric identities and partial fractions in integration.
Differential Equations: Separable and linear first‐order differential equations with some applications.
Coordinate Geometry: Conic sections. Tangents and normals. Parametric equations and using them to find gradients.
Vectors: Vector addition and scalar multiplication. The dot product and the angle between two vectors. The vector equation of a straight line. Normal vectors and planes. The Cartesian and vector equations of a plane.

If you complete the module successfully, you should be able to:

Use the concepts, terminology and methods covered in the course to solve mathematical problems
Solve unseen mathematical problems involving understanding of these concepts and applications of these methods
See how mathematics can be used to solve problems in economics and related subjects
Demonstrate knowledge and understanding of the underlying mathematical principles.

Unseen written exam (Two-hour 15 minutes).

Bostock, L. and Chandler, F. S. (2013) Core Maths for Advanced Level. 3rd edition. Stanley Thornes.