The 10 most common A-Level Maths mistakes (and what they cost)

After a decade of marking students' working every week, the surprise isn't how many mistakes there are — it's how few. The same ten account for the overwhelming majority of avoidable lost marks I see, they recur from C-grade students to A*-chasers, and every one has a specific, trainable fix. Fixing even half of them is routinely worth a grade. Here they are, roughly in the order of total damage done, with what each costs and how to stop it.

The algebra slips: signs, brackets and lost solutions

One: sign errors under pressure. A minus sign dropped while expanding or rearranging — trivial in isolation, except it usually happens mid-question, poisoning everything downstream. Cost: one to three marks a time, several times a paper. The fix is mechanical, not moral: write one more line than feels necessary whenever negatives are in play, because sign errors live almost exclusively in skipped steps. Two: dividing when you should factorise. Dividing both sides of an equation by x — or by any expression that might be zero — silently deletes a solution, and the mark scheme notices even when you don't. Fix: rearrange to equal zero and factorise, every time; treat dividing by a variable as a small alarm bell. Three: the vanishing ± . Square-rooting both sides and keeping only the positive root, which quietly discards half the answer. Fix: the moment a square root enters, write ± before anything else does.

The calculus traps

Four: the missing chain rule. Differentiating composite functions as if they were plain ones — the single most common calculus error on any paper I mark. Cost: the method marks for the whole part, since the derivative is wrong from the first line. Fix: a habit of asking "function of a function?" before differentiating anything, and slowing down specifically when the inside isn't just x. Five: integrating without the constant, or losing it exactly when it matters. The dropped +c is a cheap mark thrown away — until the question involves finding the particular solution, at which point it's most of the question. Fix: +c on the same pen stroke as the integral sign's removal, no exceptions, and let the question tell you when it doesn't matter rather than deciding in advance.

The calculator and the numbers

Six: degree mode in a radian world. Calculus with trigonometry only works in radians, and a calculator sitting in degrees produces confident nonsense — often for the entire trig section before anyone notices. Fix: mode check as a written-down ritual at the start of every paper, and again the moment any answer looks implausible. Seven: rounding too early. Carrying a rounded intermediate value through three more steps, arriving just outside the mark scheme's tolerance, and losing accuracy marks for work that was conceptually perfect. Fix: full calculator accuracy all the way through — store intermediates in memory — and round once, at the end, to what the question asked for. Which is its own sub-error: not noticing what the question asked for.

The exam-craft failures

Eight: invisible working. Doing three steps in your head or on the calculator and writing only the answer — which converts a wrong answer from "method marks anyway" into zero, and a right answer into a gamble if the examiner can't see where it came from. In this subject the working is the product; the answer is just its last line. Fix: write like the reader is intelligent but cannot see inside your head, because that's exactly the situation. Nine: ignoring the question's own instructions. "Hence" means use what you just proved — a different method may earn little or nothing; "exact value" outlaws decimals; "show that" demands every step of the bridge, especially the one that feels obvious. Cost: some of the most painful marks on the paper, lost while doing correct mathematics. Fix: underline the command words as you read, and reread the question after answering it — half of this error is answering a question that wasn't asked. Ten: no plausibility check. Submitting a negative length, a probability of 1.4, a car accelerating at 400 metres per second squared — answers a two-second glance would have flagged. Fix: the two-second glance, institutionalised: after each answer, one breath, one question — "could this be true?" It's the cheapest checking protocol in existence and it catches the most embarrassing category of error entirely.

What connects them — and how to actually fix yours

Notice what's absent from the list: almost none of these are failures to understand the mathematics. They're failures of process under pressure — which is precisely why they're so fixable, and why the fix is never "revise more". The method that works: an error log. Every lost mark, one line — question, error, which of the ten it was. Within three past papers the log shows a personal pattern, because nobody commits all ten; most students live on two or three. Then the pattern trains the fix: your two errors become your personal start-of-paper checklist, your specific slow-down triggers. I've watched that one habit — log, pattern, checklist — move students a grade with no new mathematics learned at all. It's the closest thing to free marks this subject offers, which is exactly why examiners keep pricing these mistakes so heavily: they're testing discipline, and discipline is learnable.