Variation 2 · answer guide
Mathematical induction — Modulo viewpoint
Question
Show and , and deduce .
This practice question was inspired by Question 12(f) in the 2022 NSW HSC Mathematics Extension 1 examination, © NESA. It is an original TestMum variation that practises the same mathematical idea, not an official NESA question.
Step by step
- Set up the solution: show the base case, state the assumption for n=k, and transform the k+1 case using that assumption..
- Finish the calculation, then check that the result meets the question’s conditions..
- State the final answer clearly in the form the question requested.Sum .
Common mistake: changing so many features that the new example no longer tests the same mathematical idea.
Verification: Congruence proof is shorter; induction is what the paper asks.
Any mark labels are a TestMum study aid, not an official NESA marking allocation.
← Back to 2022 HSC Extension 1 paper Question 12(f)