Variation 2 · answer guide

Combinatorics — Symmetric sides

Question

Three points on each side of a triangle (9 points total). Number of triangles?

This practice question was inspired by Question 7 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.

Set up the solution: count a simple unrestricted set first, then add or subtract the arrangements that break the condition.; three collinear triples, one per side.
Finish the calculation, then check that the result meets the question’s conditions..
Match the result to the choices and state the correct option.Therefore option A is correct.

Common mistake: changing so many features that the new example no longer tests the same mathematical idea.

Verification: Only full side-triples are collinear among the chosen points.

Any mark labels are a TestMum study aid, not an official NESA marking allocation.