Proof
Mathematical proof — proof by deduction, proof by exhaustion, proof by contradiction, and disproof by counterexample.
Start practising →Sample questions
- Hard Proof by induction No Calculator [7]
- Hard Induction — sum of cubes No Calculator [7]
- Hard Induction — divisibility by 3 No Calculator [7]
About this topic
These are original, exam-style questions written to match the IB Mathematics syllabus for Analysis & Approaches HL. Every question comes with a full step-by-step worked solution showing the method, with mark allocations matching real IB marking schemes. Questions are labelled Paper 1 (no calculator) or Paper 2 (calculator allowed) so you practise under realistic exam conditions.
How to practise
- Open the question bank using the button above.
- Attempt the question, writing out your working.
- Reveal the full worked solution and compare your method step by step.
- Use the difficulty and calculator filters to focus on what you need most.