Pure Mathematics A-Level Notes – Booklet 3: Geometry & Probability

Take your A-Level Mathematics preparation to the next level with Booklet 3. This comprehensive 110-page booklet covers nine major topics, providing clear explanations, important formulae, visual diagrams and fully worked examples to guide you through the syllabus.

Whether you are learning a topic for the first time, consolidating your understanding or preparing for examinations, these notes provide a structured resource to support your studies.

What's Included?

This booklet covers the following nine topics:

1. Coordinate Geometry – Gradients, equations of straight lines, intersections, midpoints, distances, perpendicular lines and perpendicular bisectors.

2. Trigonometry 1 & 2 – Trigonometric identities, radians, circular measure, graphs, equations, compound angles, double angles and advanced trigonometric methods.

3. The Circle – Circle equations, geometrical properties and related coordinate geometry techniques.

4. Polar Curves – Understanding polar coordinates, equations and curves.

5. Vectors 1 – Vector notation, magnitude, direction and vector operations.

6. Vectors 2 – Further vector techniques and applications in geometry.

7. Matrices 1 – Matrix notation, operations and calculations.

8. Matrices 2 – Further matrix methods and applications.

9. Probability – Sample spaces, tree diagrams, permutations, combinations, Venn diagrams, independent and mutually exclusive events, conditional probability and Bayes-style reverse probability.

Why Choose These Notes?

• Detailed explanations: Understand the mathematical concepts rather than simply memorising formulae.

• Fully worked examples: Follow step-by-step solutions to see how different questions are approached.

• Clear diagrams: Visual representations help simplify complex mathematical concepts.

• Important methods highlighted: Key rules and techniques are easy to identify when revising.

• Exam preparation: Develop confidence in applying mathematical methods to different types of questions.

• Structured learning: Topics are organised into sections, making it easier to study independently and revisit specific concepts.

Who Is This For?

Ideal for A-Level Mathematics students who want comprehensive notes to support classroom learning, independent study, topic revision and examination preparation.