Exam-style question
Try this first
A1: A student claims that testing three examples proves a general statement. Explain why this is insufficient and describe the proof structure needed instead.
Model answer
What a good answer should say
- Begin by separating evidence from proof.
- Three examples may support a conjecture, but they do not prove a universal statement.
- For A1 mathematical proof, the student should state the assumption, use a recognised method such as deduction, exhaustion, counterexample or contradiction, and justify each implication.
- A common error is treating pattern spotting as proof.
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..
This question is anchored to A1 because it distinguishes examples from proof and requires a valid proof structure. It rewards explicit assumptions, justified logical steps and a conclusion that matches the original statement.
Maths method check
- Topic focus: Pure Mathematics.
- Question style: exam_style.
- Reasoning demand: recall.
- 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.