MEX-P1
The Nature of Proof
Construct rigorous proofs using various techniques including contradiction, contrapositive and counterexample.
Sample questions
- 1.Prove by contradiction that √3 is irrational.
- 2.Prove the contrapositive: if n² is even, then n is even.
Exam weighting
3–5 marks — proof questions typically appear early in Section II.
Common student mistakes
- ·Assuming the result during a proof by contradiction instead of negating it
- ·Confusing contrapositive (¬Q → ¬P) with converse (Q → P)
- ·Not providing a valid counterexample that disproves both the statement and its converse
MEX-P2
Further Proof by Mathematical Induction
Prove results involving inequalities and series using strong and recursive induction.
Sample questions
- 1.Prove by induction that 2ⁿ ≥ n + 1 for all n ≥ 1.
Exam weighting
3–4 marks.
Common student mistakes
- ·Weak induction used where strong induction is required
- ·Inequality direction errors in the inductive step
Other Extension 2 topics
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