A-Level Maths Edexcel 9MA0

Understand and use the structure of mathematical proof, proceeding from given assumptions through a series of logical steps to a conclusion; use methods of proof, including:

Proof by deduction

e.g. using completion of the square, prove that $n^2-6n+10$ is positive for all values of $n$ or, for example, differentiation from first principles for small positive integer powers of $x$ or proving results for arithmetic and geometric series. This is the most commonly used method of proof throughout this specification

Proof by exhaustion

Given that $p$ is a prime number such that $3 < p < 25$, prove by exhaustion, that $(p - 1)(p + 1)$ is a multiple of 12.

Disproof by counter example

e.g. show that the statement "$n^2 - n + 1$ is a prime number for all values of $n$" is untrue

Proof by contradiction (including proof of the irrationality of $\sqrt{2}$ and the infinity of primes, and application to unfamiliar proofs).