A student can genuinely understand how to solve an NMTC Part B problem and still lose most of the marks — because the written solution doesn't clearly show the reasoning a grader needs to see. Writing a full-marks solution is a distinct, learnable skill.
The Structure of a Full-Marks Solution
- State what is given and what needs to be proven, in your own words, before starting the working — this shows the grader you understood the problem.
- Justify every non-obvious step. If you use a theorem or property, name it and confirm the conditions for using it are actually met.
- Avoid logical leaps. A step that feels "obvious" to the student writing it may not be obvious to the grader reading it — write the connecting reasoning explicitly.
- End with a clear final statement confirming what was proven, not just a number circled at the bottom of the page.
Common Reasons Students Lose Marks Despite Knowing the Answer
| Mistake | Why It Costs Marks |
|---|---|
| Skipping "obvious" steps | Graders can only credit reasoning that is actually written down |
| Using a result without justification | An unproven claim is treated as a gap in the argument |
| Working backward without saying so | A solution that assumes the answer to prove itself is circular unless flagged |
| Messy, unordered working | Graders may not follow scattered reasoning even if it is technically complete |
A Practice Method That Works
After solving a problem mentally or on rough paper, rewrite the solution from scratch as if explaining it to someone who has never seen the problem. This single habit — writing for an unfamiliar reader rather than for yourself — is the fastest way to close the gap between "I know how to solve this" and "I wrote a full-marks solution."