15 Common Mistakes in A-Level Maths Exams (and How to Stop Making Them)

Every summer, examiners' reports for A-Level Maths list almost identical mistakes. They are not usually about a lack of knowledge — they are about habits, exam technique and small slips that snowball into lost marks. If you have worked through enough past papers, you will recognise most of these. The good news is that every mistake below is fixable with deliberate practice.

1. Sign errors when rearranging equations

The single most common source of lost marks in algebra is a dropped or flipped negative sign, especially when moving terms across an equals sign or expanding brackets with a negative in front. When you rearrange, rewrite the whole line rather than editing in your head, and get into the habit of substituting your answer back into the original equation to check it balances.

2. Radians vs degrees

Calculators default to degree mode, and switching between modes mid-paper is a classic trap, particularly in mechanics and any question involving calculus with trigonometric functions (you cannot differentiate or integrate sin x and cos x correctly unless x is in radians). Before starting any trigonometry question, check your calculator's mode indicator. If a question asks for an exact answer involving π, that is your cue that radians are expected.

3. Forgetting the constant of integration

Every indefinite integral needs "+ c". Examiners will withhold the final accuracy mark for an otherwise perfect integration if c is missing, and it is also easy to forget when a question later asks you to find the value of c using a boundary condition. Build the habit of writing "+ c" the instant you write the integral sign, not as an afterthought.

4. Ignoring the domain or validity of a binomial expansion

Binomial expansions of the form (1 + ax)^n for non-integer n are only valid for |ax| < 1. Students frequently expand correctly but forget to state the range of validity, which is worth marks in its own right and is often tested explicitly. Always write the validity condition as a final line of your answer.

5. Not showing full method on "show that" questions

"Show that" and "prove" questions are marked on method, not just the final answer. If the answer is given to you in the question, a bald assertion that you got the same value earns nothing. Write every algebraic step, including the substitution of given values, so an examiner can follow your logic line by line.

6. Rounding too early

Rounding an intermediate value and carrying that rounded figure through the rest of a calculation is one of the most penalised errors in numerical and mechanics questions. Keep full calculator accuracy (or exact surds and fractions) throughout your working, and only round the final answer to the number of significant figures the question asks for.

7. Misreading command words

"Solve", "simplify", "factorise", "hence" and "hence or otherwise" all mean different things, and examiners choose them precisely. "Hence" means you must use the result from the previous part; using a different method may score zero even if your answer is correct. Underline the command word before you start writing.

8. Calculator misuse

Common calculator errors include forgetting to close brackets, entering a negative index incorrectly, or using the wrong statistical mode for hypothesis tests. Learn your specific calculator model thoroughly before the exam rather than during it — five minutes practising the exact functions you'll need (inverse normal, binomial cdf, numerical solve) is worth far more than extra content revision the night before.

9. Losing marks on unsimplified answers

A correct but unsimplified surd, fraction, or trigonometric expression can lose the final accuracy mark if the question asks for an answer "in simplest form" or "as a single fraction". Always look back at the wording of the question before moving on.

10. Confusing mean and expectation, or variance and standard deviation

In statistics, mixing up variance (σ²) and standard deviation (σ) is extremely common, particularly under time pressure. Write out which quantity you are calculating before you calculate it, and check units make sense — standard deviation should be in the same units as the data, variance in squared units.

11. Sketching graphs without labelling key features

Graph sketches are marked on specific features: intercepts, asymptotes, turning points and behaviour as x tends to infinity. A beautifully drawn but unlabelled curve can lose most of the marks available. Mark coordinates explicitly, even approximately, and show asymptotes as dashed lines with their equations written next to them.

12. Not resolving forces correctly in mechanics

In mechanics questions involving inclined planes or connected particles, a frequent error is resolving forces along the wrong axis or forgetting to include friction or the normal reaction. Draw a full force diagram before writing any equations — this single habit prevents the majority of mechanics errors. Our mechanics revision guide covers the standard force-diagram approach for every question archetype.

13. Misapplying the formula booklet

Students often assume a result is in the formula booklet when it isn't, or misquote a formula that is provided but slightly misremembered. Know exactly what is and isn't given — see our companion article on what's in the formula booklet and what you must memorise.

14. Choosing the wrong integration method

Integration questions are frequently attempted with the wrong technique — for example, trying to integrate by parts when a substitution would be far quicker, or missing that a fraction needs splitting via partial fractions first. A systematic decision process avoids this; see our guide to choosing the right integration method.

15. Poor time allocation and not attempting every mark

Many students run out of time because they get stuck on one difficult question rather than moving on and returning later. Every mark is worth the same regardless of the question it's attached to. Practise past papers under timed conditions so you develop an instinct for how long two, three or five marks should take, and always attempt every part of a question, even if it's just writing down a relevant formula for partial credit.

How to turn this into a revision plan

Spotting these patterns in past papers is only useful if you act on them. After each timed past paper, keep a short error log: write down exactly which of the fifteen mistakes above you made, not just "I got it wrong". Over a few papers you will see the same one or two categories recurring, and that tells you precisely where to focus.

A structured revision timetable can help you build in regular past-paper practice alongside targeted topic revision, rather than leaving exam technique to chance in the final weeks. If you consistently struggle with the same category of error despite practice — for example, mechanics force diagrams or integration method selection — working with a tutor through A-Level Maths Tutoring can help you identify the underlying gap much faster than self-study alone.

It's also worth checking your target grade against recent exam performance using a grade boundary predictor, so you know how many of these small errors you can realistically afford before they start affecting your final grade.

Takeaway

None of these fifteen mistakes require new mathematical knowledge to fix — they require discipline: writing full method, checking calculator mode, not rounding early, reading command words carefully, and drawing proper diagrams in mechanics. Work through past papers with an error log, correct the same mistake category each time it appears, and these avoidable marks will stop disappearing from your scripts.

Building error awareness into daily practice

Most students revise by working through new questions, marking them, and moving on. This misses the biggest opportunity to fix recurring mistakes: reviewing why an error happened, not just noting that it happened. When you mark a past paper, resist the urge to simply write "sign error" in the margin and move on. Instead, ask three questions: at what exact step did the error occur, what were you thinking at that point, and what specific habit would have caught it before you submitted the answer. This kind of granular review is slower per paper but compounds quickly, because it turns vague awareness ("I sometimes make sign errors") into a specific, checkable habit ("I always rewrite the full equation line by line when rearranging").

It also helps to separate mistakes into two categories: conceptual gaps, where you genuinely didn't know the correct method, and execution slips, where you knew the method but made an error applying it. The fifteen mistakes in this article are almost all execution slips, which means more content revision won't fix them — only deliberate, repeated practice of the specific habit will. Trying to "revise harder" when the real issue is rushing through algebra, or not checking your calculator mode, wastes time that would be better spent on focused technique drills.

Exam-day checklist

In the final few minutes before submitting a paper, run through a short mental checklist rather than simply stopping when you run out of time:

• Have you included "+ c" on every indefinite integral?
• Have you stated validity conditions on any binomial expansions?
• Have you checked your calculator is in the correct angle mode for every trigonometry question?
• Have you simplified every answer as far as the question requires?
• Have you shown full method on every "show that" question, even where the working feels obvious?
• Have you labelled every force in your mechanics diagrams and defined a positive direction?
• Have you attempted every part of every question, even for partial credit?

This checklist takes under two minutes to run through but reliably recovers marks that would otherwise be lost to habit rather than knowledge. Building it into your timed past-paper practice, rather than trying it for the first time in the real exam, is what makes it effective on the day.