Mathematical Reasoning & Proof

Topic overview

Direct proof, proof by cases, proof by contradiction, counterexamples, and necessary/sufficient conditions; mathematical induction is not required.

Key concepts

Limits of rational powers in calculus and sums and differences after simplification; differentiation of exponential/trigonometric functions, variance, distributions of random variables, or mathematical induction are not required. Basic expected frequencies remain within the syllabus.

Key points

◆Follow the prerequisite knowledge requirements given by the examination body; new concepts may only be used when the question provides sufficient guidance.
◆The examples on this site are training with a limited scope and do not represent full syllabus coverage or official difficulty.

Worked examples

Try each example yourself before checking the explanation.

1Basic examples within scope

For integers $n$ , the statement ‘if $n^2$ is even then $n$ is even’ is:

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