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Top 10 Mistakes Students Make in GCSE Maths Exams
Sir Faraz Hassan
12 Apr 2026
After marking thousands of mock papers and reviewing real exam scripts across AQA, Edexcel, and OCR, the same mistakes appear year after year. These are not gaps in knowledge — they are errors in technique, carelessness, and exam strategy that cost students between 20 and 40 marks per paper. The difference between Grade 7 and Grade 9 is often not what you know, but what you do not lose. Here are the ten most expensive mistakes I see, ranked by how many marks they typically cost, with the exact fix for each one.
20-40
marks lost per paper to avoidable errors
73%
of Grade 7 students make 3+ of these
5 min
of checking can recover 10+ marks
The 10 Costliest Mistakes
Ranked from most marks lost to least. Every mistake includes a real exam example and the exact fix. Be honest with yourself as you read — most students recognise at least four or five of these in their own work.
Mistake #1: Not Showing Working (costs 3–8 marks per paper)
This is the single most expensive habit in GCSE Maths. On a five-mark question, the final answer alone is typically worth just one mark — the remaining four are awarded for the method. Even if your answer is correct, you score 1 out of 5 without visible working. Worse, if your answer is wrong but the method is sound, you could have earned 3 or 4 marks through follow-through marks. Consider a “show that” question: “Show that x = 3.5 is a solution to 2x² − 3x − 14 = 0.” Writing “yes it works” scores zero. You must substitute, simplify each term, and write a conclusion: “2(3.5)² − 3(3.5) − 14 = 24.5 − 10.5 − 14 = 0, therefore x = 3.5 is a solution.”
Fix: Write one step per line
Treat every line of working as a potential mark. For “show that” questions, substitute the value, simplify each term on a separate line, and finish with a conclusion sentence. Even for straightforward two-mark questions, if the marks are for method and accuracy, there must be at least two lines of visible working. The golden rule: if a question is worth two or more marks, show the method.
Mistake #2: Premature Rounding (costs 2–6 marks per paper)
Students round intermediate values, then use those rounded figures in the next step. By the final answer the error has compounded enough to lose the accuracy mark. This is especially damaging in trigonometry: if sin(35°) = 0.57358… and you round to 0.57 before multiplying by 12, your answer is 6.84 instead of the correct 6.88. That tiny difference costs a mark. On multi-step questions involving Pythagoras, bearings, or compound area, premature rounding can cascade across three or four steps and produce a final answer that is noticeably wrong.
Fix: Only round at the FINAL step
Use the ANS button on your calculator to carry full precision through every intermediate step. Only round when the question explicitly asks you to — “give your answer correct to 3 significant figures” or “to 2 decimal places.” When you reach the final line, write the full calculator display first, then write the rounded version underneath. This way you have evidence of accuracy even if your rounding is slightly off.
Mistake #3: Misreading the Question (costs 2–5 marks per paper)
“Find the perimeter” but the student calculates area. “Give your answer in cm²” but the student writes cm³. “Write down” means one mark with no working required; “show that” means full algebraic working; “explain” means words, not just numbers. Students also miss critical trigger words: “hence” means use your previous answer, “state” means no working needed, “estimate” means round first then calculate, and “exact” means leave your answer as a surd or fraction with no decimals. A single misread command word can turn a correctly solved problem into zero marks.
Fix: Underline command words
Before writing a single line of working, underline the command word and the unit or form required. For example: “Find the exact area, giving your answer in terms of π.” Three things are underlined: exact, area, and terms of π. This takes five seconds and prevents the most frustrating type of mark loss — getting the mathematics right but answering the wrong question.
Mistake #4: Unit Errors and Conversions (costs 2–4 marks per paper)
Centimetres versus metres, cm² versus m², millilitres versus litres — these conversions trip students up constantly. The key misunderstanding is that area units square and volume units cube the linear conversion factor. One metre equals 100 centimetres, but one square metre equals 10,000 square centimetres, and one cubic metre equals 1,000,000 cubic centimetres. Students who memorise only the linear conversion and forget to square or cube it lose marks on every area or volume question that involves mixed units.
Fix: Convert BEFORE calculating
Before starting any calculation, convert all measurements to the same unit. Write the conversion factor explicitly on your working. For area questions, multiply the linear conversion factor by itself: 1 m² = (100)² cm² = 10,000 cm². For volume: 1 m³ = (100)³ cm³ = 1,000,000 cm³. Do the conversion first, calculate second. Never convert the final answer — convert the inputs.
Mistake #5: Sign Errors in Algebra (costs 3–6 marks per paper)
Expanding brackets with a negative sign is the single most common algebraic error. Students write −(2x − 3) = −2x − 3 instead of −2x + 3. The minus sign must multiply through every term inside the bracket, flipping each sign. This mistake cascades: one wrong sign in an expansion makes every subsequent line of solving incorrect. It also appears when solving equations (subtracting a negative), factorising quadratics (choosing the wrong signs for the bracket pair), and simplifying fractions with negative numerators.
Fix: Expand brackets one term at a time
Write each term of the expansion on a separate line. For negative brackets, multiply the minus sign through each term individually and write the result next to it. After expanding, do a quick check: substitute a simple value like x = 1 into both the original expression and your expanded version. If they give different numbers, you have made a sign error. This check takes fifteen seconds and catches the mistake before it contaminates the rest of your working.
Mistake #6: Calculator Input Errors (costs 2–4 marks per paper)
The most common calculator errors involve missing brackets. Typing 3+4/2 gives 5 instead of the intended (3+4)/2 = 3.5 because the calculator follows order of operations. Similarly, typing sin30² gives sin(900) instead of (sin30)² = 0.25. Another frequent issue is leaving the calculator in radian mode when the question uses degrees. Students also mistype negative signs — pressing the subtraction key instead of the negative key, which produces a syntax error or an incorrect computation.
Fix: Use brackets for EVERYTHING
When typing any fraction into your calculator, put the entire numerator in brackets and the entire denominator in brackets. Always. For expressions like sin²(30), type (sin(30))². Before any trigonometry question, glance at the top of your calculator display and confirm it says “D” for degrees, not “R” for radians. Make this a habit at the start of every paper — it takes two seconds.
Mistake #7: Graph Reading Errors (costs 1–3 marks per paper)
Students assume each grid square represents one unit when the scale might be 2, 5, or 0.2 units per square. They read coordinates inaccurately, especially on scatter graphs and cumulative frequency diagrams. Lines of best fit are drawn through the first and last points instead of through the middle of the data cloud. On histograms, students read the height of bars instead of calculating the frequency using frequency density multiplied by class width.
Fix: Check the scale first, every time
Before reading or plotting any point, count the small squares between two labelled gridlines and calculate what each square represents. Write it on the exam paper next to the graph: “1 square = 0.2 units.” For lines of best fit, make sure your line passes through the mean point of the data and has roughly equal numbers of points above and below it. For histograms, always use frequency = frequency density × class width.
Mistake #8: Solving But Not Answering (costs 1–3 marks per paper)
The student finds x = 5 but the question asked for “the length of the rectangle,” which is 2x + 3 = 13 cm. The algebra is perfect — full marks for method — but the final answer mark is lost because the student stopped one step too early. This also happens with simultaneous equations (finding x but not y), quadratics (factorising but not stating the solutions), and probability (finding individual probabilities but not combining them as the question requires).
Fix: Re-read the question AFTER solving
After completing your working, go back and re-read the original question. Does your final line actually answer what was asked? If the question says “find the length of the rectangle,” your final line should say “The length of the rectangle is 13 cm.” Writing a concluding sentence forces you to check that you have actually finished.
Mistake #9: Ratio and Proportion Errors (costs 2–4 marks per paper)
Students confuse part-to-part ratios with part-to-whole fractions. “Split £120 in the ratio 2:3” — many students divide by 2 and then by 3 separately instead of dividing by the total number of shares (5). Inverse proportion questions are another pitfall: students use y = kx when the relationship is y = k/x, or they set up a direct proportion table when the question clearly states “inversely proportional.” Percentage increase is confused with finding a percentage of a number — students calculate 15% of 80 as £12 but forget to add it to the original to get £92.
Fix: Always find 'one share' first
For every ratio question, add the parts together first (2 + 3 = 5 shares), divide the total by the number of shares (£120 ÷ 5 = £24 per share), then multiply each part (2 × £24 = £48, 3 × £24 = £72). For proportion, set up the equation explicitly: y = kx for direct or y = k/x for inverse. Find k using the given values, then substitute to solve. Writing the equation first prevents you from mixing up the two types.
Mistake #10: Running Out of Time (costs 5–15 marks per paper)
Students spend twelve to fifteen minutes on a three-mark question they cannot solve, then rush the final twenty marks or leave them blank entirely. On a 100-mark paper with 90 minutes, the rule of thumb is one mark per minute. A five-mark question should take roughly five minutes. If you have spent eight minutes on it with no progress, you are spending time you do not have. The last ten marks on a paper are often the hardest, but they are still marks — and leaving them completely blank guarantees zero.
Fix: The 90-second rule
If you have read a question twice and have no idea how to start, circle it and move on immediately. Come back after completing the rest of the paper. You will often find the method clicks on a second look — your subconscious has been working on it while you answered other questions. This approach ensures you attempt every question on the paper and do not sacrifice easy marks at the end for one difficult question at the start.
How Many of These Do You Make?
Be honest with yourself. Go through your last three mock papers and count how many of these mistakes appear. Most students make four to six of them regularly. The good news is that fixing just three of these patterns can improve your grade by a full level — without learning any new mathematics.
- I always show my working, even on easy questions
- I never round until the final step
- I underline command words before starting
- I check units and convert before calculating
- I expand negative brackets term by term
- I use brackets for every calculator fraction
- I check graph scales before reading values
- I re-read the question after solving
- I find one share first in ratio questions
- I move on from stuck questions within 90 seconds
📊
Students who actively eliminate these ten errors typically improve by 15 to 30 marks across their papers. That is the difference between Grade 7 and Grade 9. It is not about learning new mathematics — it is about stopping the marks you already earn from leaking away.
I have never seen a student who knew the maths but got Grade 7 because of one mistake. It is always the accumulation of small errors — five marks here, three marks there. Fix the pattern, fix the grade.
Sir Faraz Hassan — GCSE & IGCSE Maths Specialist
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