pure mathematics
Topics covered

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.
Learning outcomes
If you complete the course 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.
Essential reading

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