Exam-style question
Try this first
After completing proof by exhaustion, what should the final line make explicit?.
- A.A1: connect the result back to the original question
- B.Use any familiar GCSE calculation even if it ignores the structure of mathematical proof
- C.Write only the final answer without showing the mathematical method
- D.Change the notation or restrictions to make the algebra look simpler
Model answer
What a good answer should say
- The correct answer is A1: connect the result back to the original question.
- It is correct because proof by exhaustion must cover every allowed case and then state that the cases together prove the required result.
This answer is tied to the objective: A1 Understand and use the structure of mathematical proof, proceeding from given assumptions through a series of logical steps to a conclusion; use methods of proof including proof by deduction and proof by exhaustion; use disproof by counter example; use proof by contradiction including proof of the irrationality of sqrt(2), the infinity of primes and application to unfamiliar proofs..
Explanation
Why this works
Use the explanation to connect the worked answer back to A1 Understand and use the structure of mathematical proof, proceeding from given assumptions through a series of logical steps to a conclusion; use methods of proof including proof by deduction and proof by exhaustion; use disproof by counter example; use proof by contradiction including proof of the irrationality of sqrt(2), the infinity of primes and application to unfamiliar proofs..
The correct option, A1: connect the result back to the original question, is best because proof by exhaustion must cover every allowed case and then state that the cases together prove the required result. This A1 item checks that the conclusion is not just a list of cases; it explicitly links those cases to the original claim.
Maths method check
- Topic focus: Pure Mathematics.
- Question style: practice.
- Reasoning demand: analysis.
- Check the operation, notation, units, and final answer form against the question before moving on.
Common mistake
No common mistake is linked to this question yet.