A-Level Maths OCR A H240

Understand and be able to use the structure of mathematical proof, proceeding from given assumptions through a series of logical steps to a conclusion.

In particular, learners should use methods of proof including proof by deduction and proof by exhaustion.

Understand and be able to use the logical connectives $≡$, $\implies$, $\iff$.

Learners should be familiar with the language associated with the logical connectives: “congruence”, “if..... then” and “if and only if” (or “iff”).

Be able to show disproof by counter example.

*Learners should understand that this means that, given a statement of the form “if $P(x)$ is true then $Q(x)$ is true”, finding a single $x$ for which $P(x)$ is true but $Q(x)$ is false is to offer a disproof by counter example.

Questions requiring proof will be set on content with which the learner is expected to be familiar e.g. through study of GCSE (9-1) or AS Level Mathematics.

Learners are expected to understand and be able to use terms such as “integer”, “real”, “rational” and “irrational”.*

Understand and be able to use proof by contradiction.

*In particular, learners should understand a proof of the irrationality of $\sqrt{2}$ and the infinity of primes.

Questions requiring proof by contradiction will be set on content with which the learner is expected to be familiar e.g. through study of GCSE (9-1), AS or A Level Mathematics.*