The mathematics is not the only thing being assessed. At A-level, AP, and IB levels, the write-up carries marks of its own — method marks, communication marks, accuracy marks — which can be awarded even when the final answer is incorrect. The student who understands this scoring structure recovers marks that the student who writes only answers loses.
How A-level and AP marking schemes work
A worked solution in A-level or AP mathematics is typically broken into:
M marks (method marks): awarded for correct method, independent of accuracy. A marks (accuracy marks): depend on the correct preceding M marks. B marks (independent marks): awarded for specific correct values or statements.
If you make an arithmetic error on line 3 of a 7-line solution, you lose the accuracy mark on line 3 — but you may still earn the method marks for lines 4–7 if your subsequent reasoning is correct, given your (wrong) line 3 value. This is called "following through" (f.t.) on an error.
A solution that shows the method earns method marks even with computational errors. A solution that shows only a final answer earns full marks only if correct, and zero if incorrect. The write-up is an insurance policy.
The required structural elements
1. A clear statement of what you are finding at each step. 2. Working shown at every non-trivial step (examiners do not award marks they cannot see). 3. Units on final answers (and intermediate answers involving physical quantities). 4. A box or underline around the final answer so it is unambiguous. 5. Logical connectives between steps — "therefore," "since," "from (*)," not just a sequence of disconnected equations.
The presentation errors that cost marks
Unmarked equal signs: writing a series of expressions separated by = without verifying equality at each step. Students sometimes write "x = 3 = y" meaning "x = 3 and y = 3" — which is wrong notation. Each equality sign is a claim.
Substituting before naming: writing 4(2) + 3 = 11 without stating "let x = 2" first. If the marker cannot tell what value was substituted and why, method marks are at risk.
Crossing out correct work: if you cross out a correct line of working and replace it with an incorrect one, only the uncrossed-out version is marked. Never cross out work without being certain it is wrong.
The integration example
Find ∫₀² x(x−1) dx.
Poor write-up: x(x−1) = x²−x → [x³/3 − x²/2] → 8/3 − 2 = 2/3.
Full-marks write-up:
∫₀² x(x−1) dx = ∫₀² (x² − x) dx
= [x³/3 − x²/2]₀²
= (8/3 − 4/2) − (0 − 0)
= (8/3 − 2)
= 8/3 − 6/3
= 2/3
The steps — expanding, integrating (with brackets and limits shown), substituting both limits, computing the arithmetic — each correspond to a mark on the scheme.
Frequently Asked Questions
Should I write in pen or pencil?
Most examiners prefer ink, and many mark schemes specify it. Pencil can smear or be difficult to scan. Use black ink for working and diagrams. If you must cross something out, use a single horizontal line (not scribble) so the original is still legible for potential recovery marks.
How long should my solution be?
Long enough to show every non-trivial step; no longer. Examiners read hundreds of scripts — padding with explanation of trivial steps earns no marks and wastes your time. The benchmark: could a competent peer follow your logic from your write-up alone, without additional explanation?