Exam-style question
Try this first
For proof by contradiction, what is the safest first move before deriving an impossible statement?.
- A.A1: justify each step using the relevant mathematical proof and reasoning rule
- 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: justify each step using the relevant mathematical proof and reasoning rule.
- It is correct because contradiction begins by assuming the negation of the required result, then uses valid implications until a contradiction with a known fact or assumption appears.
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 A1 item isolates proof by contradiction. A successful answer must state the temporary opposite assumption clearly and justify the route to contradiction.
The wrong options either skip the assumption, treat examples as proof, or alter the statement so the contradiction no longer proves the intended result.
Maths method check
- Topic focus: Pure Mathematics.
- Question style: practice.
- Reasoning demand: understanding.
- 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.