Unit 1: Number and Algebra
Topic 1.6: Proof Questions
Practice 20 exam-style questions for IB Math AA SL Topic 1.6. Review the question stems below, then unlock the full Question Bank to access markschemes, model answers, and AI grading.
1Prove2 marks
2026• Aimnova practice — 1.6.3
Prove the identity (x + 1)(x + 5) ≡ x² + 6x + 5.
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2026• Aimnova practice — 1.6.3
Prove the difference-of-squares identity a² − b² ≡ (a + b)(a − b).
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2026• Aimnova practice — 1.6.1
Show that 5n + 15 is a multiple of 5 for every integer n, and state the integer it is 5 times.
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2026• Aimnova practice — 1.6.2
Prove that the sum of any two consecutive integers is odd.
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2026• Aimnova practice — 1.6.1
Prove that the sum of any two even numbers is even.
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Unlock Question6Show3 marks
2026• Aimnova practice — 1.6.1
Show that (n + 2)² − n² = 4(n + 1) for all integers n.
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Unlock Question7Prove3 marks
2026• Aimnova practice — 1.6.2
Prove that the sum of any five consecutive integers is a multiple of 5.
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Unlock Question8Prove3 marks
2026• Aimnova practice — 1.6.2
Prove that the difference between the squares of two consecutive integers is always odd.
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Unlock Question9Prove3 marks
2026• Aimnova practice — 1.6.2
Prove that the sum of the squares of any two consecutive integers is always odd.
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Unlock Question10Prove4 marks
2026• Aimnova practice — 1.6.1
Prove that the square of any odd number is odd.
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Unlock Question11Prove3 marks
2026• Aimnova practice — 1.6.1
Prove that n² + n is even for every integer n.
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Unlock Question12Prove3 marks
2026• Aimnova practice — 1.6.3
Prove that (2x − 3)² ≡ 4x² − 12x + 9.
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Unlock Question13Prove3 marks
2026• Aimnova practice — 1.6.3
Prove the identity 1/x − 1/(x + 2) ≡ 2/(x(x + 2)).
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Unlock Question14Prove3 marks
2026• Aimnova practice — 1.6.3
Consider the product (x − 2)(x + 5).
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2026• Aimnova practice — 1.6.1
Prove that the sum of any three consecutive integers is a multiple of 3.
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Unlock Question16Prove2 marks
2026• Aimnova practice — 1.6.2
Prove that the sum of any four consecutive integers is even.
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2026• Aimnova practice — 1.6.3
Show that (x + 3)² − (x + 1)² ≡ 4(x + 2).
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2026• Aimnova practice — 1.6.1
An odd number is squared and then 3 is added.
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2026• Aimnova practice — 1.6.1
Prove that the product of any two consecutive integers is even.
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2026• Aimnova practice — 1.6.3
Show that (x + 4)² − (x − 4)² ≡ 16x.
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