Unit 1: Number and Algebra
Topic 1.15: Proof by induction (HL only) Questions
Practice 20 exam-style questions for IB Math AA SL Topic 1.15. Review the question stems below, then unlock the full Question Bank to access markschemes, model answers, and AI grading.
11 mark
2026
To DISPROVE 'for all n, P(n) is true', a counterexample is a value where:
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2026
Why can ONE counterexample disprove a 'for all' statement?
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Unlock Question3Disprove2 marks
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Disprove: 'For all real x, if x > 1 then 1/x > 1.'
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2026
State the four steps you must write in any proof by induction.
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2026
Proof by contradiction relies on the fact that:
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2026
Which step proves that 'true for k' forces 'true for k + 1'?
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For 'aⁿ − bⁿ divisible by (a − b)', the base case checks:
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2026
Which is the WRONG way to start a contradiction proof of 'x is irrational'?
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Unlock Question10Disprove2 marks
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Disprove: 'For all real numbers x, √(x²) = x.'
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Disprove: 'If a number is divisible by 4, then it is divisible by 8.'
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A proof that omits the conclusion sentence is likely to:
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A counterexample to 'all multiples of 3 are odd' is:
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Which disproves 'x² > 0 for all real x'?
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Unlock Question15Disprove2 marks
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Disprove: 'For all positive integers n, 2ⁿ > n².'
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Unlock Question16Prove6 marks
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Prove by induction that 2 + 4 + 6 + … + 2n = n(n + 1) for all n ∈ ℤ⁺.
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2026
Disprove: 'The product of two irrational numbers is always irrational.'
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2026
In proving 6ⁿ − 1 divisible by 5, the step rewrites − 1 as:
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2026
Why isn't checking n = 1, 2, 3, …, 100 a valid proof for all n?
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Unlock Question20Explain1 mark
2026
Explain why the base case cannot be left out.
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