Because NMTC Part B is graded on the written argument, not just the final answer, most of the marks students lose come from a small, repeatable set of mistakes — not from lacking the mathematical idea.
Mistake 1: Assuming What Needs to Be Proven
A surprisingly common error is using the result you're trying to prove somewhere inside the proof itself — a circular argument. This often happens when a student "sees" the answer is true and reverse-engineers a proof without checking that each step is independently justified.
Mistake 2: Treating a Special Case as the General Proof
Checking a problem for one or two specific numbers and concluding it's true "in general" is a very common trap, particularly in number theory and algebra problems. A full-marks proof needs to hold for every valid case, not just the ones tested.
Mistake 3: Missing Edge Cases in Geometry
Geometry solutions that assume a specific configuration (a particular type of triangle, a specific point placement) without checking whether the proof holds for all valid configurations often lose marks even when the core insight is correct.
Mistake 4: Running Out of Time Mid-Proof
A rushed, incomplete Part B answer under time pressure usually scores worse than a shorter, complete answer to a slightly easier question. Time management — knowing which Part B question to attempt first — matters as much as the mathematics itself.
How to Fix These, Systematically
- Practice identifying circular reasoning in your own past solutions, not just in worked examples.
- Explicitly ask "does this hold for every case, or just the one I checked?" before finalizing any proof.
- Time-box Part B practice attempts realistically, including the time needed to write the full solution, not just find the idea.