Problem Solving in Pure Mathematics

Problem solving in pure mathematics requires you to connect different mathematical topics, apply knowledge in unfamiliar contexts, and construct solutions to problems that do not have an immediately obvious method. This is assessed under AO3 (Solve problems within mathematics and in other contexts) in the AQA A-Level Mathematics specification (7357), and typically accounts for around 10% of the total marks across all three papers.

AO3 questions are designed to be unstructured — they do not tell you which technique to use. You must identify the relevant mathematical concepts, select appropriate methods, and link ideas across different areas of the specification.

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What Makes a Problem "Problem Solving"?

A problem-solving question is characterised by one or more of the following:

• It connects two or more topics (e.g., trigonometry and calculus, algebra and coordinate geometry).
• It requires you to interpret information and decide on an approach.
• The method is not immediately obvious from the question.
• It may involve modelling a real-world situation mathematically.
• It may require you to work backwards from a given result.

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Connecting Topics: Examples

Example 1: Algebra meets Coordinate Geometry