Exam-style question
Try this first
Which answer avoids the common misconception in the structure of mathematical proof?.
- A.A1: avoid assuming that checking examples is not the same as proving the general statement
- 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: avoid assuming that checking examples is not the same as proving the general statement.
- This option is best because state the assumption, justify each logical step, and identify the conclusion, then checks that the notation, restrictions and conclusion match the AQA A-level Mathematics objective.
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..
A1: avoid assuming that checking examples is not the same as proving the general statement is the correct option. It directly supports the structure of mathematical proof by requiring the student to state the assumption, justify each logical step, and identify the conclusion.
The other options are weaker because they hide the reasoning, ignore restrictions, or use a generic calculation that may not fit the objective.
Maths method check
- Topic focus: Pure Mathematics.
- Question style: practice.
- 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.