Exam-style question
Try this first
When using a counterexample to disprove a statement, which check matters most?.
- A.A1: check notation, restrictions and final form
- 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: check notation, restrictions and final form.
- It is correct because a counterexample only disproves a universal statement if the chosen value satisfies the original conditions and clearly makes the statement false.
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: check notation, restrictions and final form, is best because a counterexample only disproves a universal statement if the chosen value satisfies the original conditions and clearly makes the statement false. This A1 item tests disproof by counterexample: the counterexample must sit inside the allowed domain, use the original wording, and demonstrate failure of the claim.
Maths method check
- Topic focus: Pure Mathematics.
- Question style: practice.
- Reasoning demand: application.
- 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.