These aren't vague tips. These are the specific errors that appear in examiner reports, year after year.
Every summer, AQA, Edexcel and OCR publish something called an examiner report. It's a document written by the people who actually marked your papers, and it describes — in sometimes painful detail — the mistakes students made. Most students never read these reports. That's a mistake in itself.
This article pulls directly from those reports and from the patterns that emerge year after year in GCSE Maths algebra questions. These aren't general tips. They're specific, documented errors with specific fixes.
This comes up in almost every examiner report for GCSE Maths. The classic error is expanding (x + 3)(x + 5) and getting x² + 8 instead of x² + 8x + 15. What's happening is students are adding the constants (3 + 5 = 8) but forgetting to collect the middle terms properly.
❌ Wrong: (x + 3)(x + 5) = x² + 8
✓ Correct: (x + 3)(x + 5) = x² + 5x + 3x + 15 = x² + 8x + 15
The fix is mechanical: use FOIL every single time. First, Outer, Inner, Last. Write out all four terms before you simplify anything. It takes an extra five seconds and eliminates the error entirely. Examiners specifically note that students who skip steps and try to do it mentally are the ones who drop marks here.
A trickier version of this mistake shows up with negative signs. (x − 4)(x + 2) trips people up because students forget to multiply the negative through properly. The outer term is +2x, the inner term is −4x, not +4x. Write. Every. Term. Out.
This sounds like something you'd never do wrong after year 8. But examiner reports consistently show it happening at GCSE level, especially in multi-step equations where there are more opportunities to slip up.
The most common version involves dividing. A student solving 3x + 6 = 21 will subtract 6 correctly to get 3x = 15, then divide only the left side by 3 and write x = 5. That's actually right here — but the habit of not writing the division on both sides causes catastrophic errors in harder questions.
❌ Wrong: 4x + 8 = 20 → 4x = 12 → x = 12 (forgot to divide 12 by 4)
✓ Correct: 4x + 8 = 20 → 4x = 12 → x = 12 ÷ 4 = 3
Write every operation on both sides of the equals sign. Every time. Don't take shortcuts on paper even if you think you can do it in your head — at GCSE level, the questions are designed to catch exactly those shortcuts.
Factorising quadratics is one of the most heavily tested algebra skills at GCSE. And sign errors are responsible for a huge proportion of lost marks. The question x² − 5x + 6 = 0 requires factors that multiply to +6 and add to −5. The answer is (x − 2)(x − 3). But a very common wrong answer is (x + 2)(x − 3), where the student gets the numbers right but mixes up the signs.
The fix: always expand your factorised answer back out to check. It takes fifteen seconds and guarantees you haven't made a sign error. This is explicitly recommended in mark scheme guidance — if you check and correct your own error in working, you can still get method marks even if your initial attempt was wrong.
Always expand your brackets back out to verify. If it doesn't give you the original expression, something is wrong with your signs.
A related error appears in difference of two squares questions. x² − 25 should factorise to (x + 5)(x − 5). Students often write (x − 5)(x − 5) or forget that this type of factorisation exists at all and try to use the quadratic formula instead — which works but wastes time and introduces more opportunities for arithmetic errors.
Rearranging formulae is a skill that appears throughout the paper — in algebra questions but also in physics-style calculations within maths, distance-speed-time, and compound interest. The most common error is performing an operation correctly but then losing track of what the subject of the formula should be.
Take this example: make r the subject of A = πr². Students correctly divide both sides by π to get A/π = r², then stop. They've forgotten to square root both sides. The answer should be r = √(A/π). Examiner reports note this as one of the most frequent partial-credit situations — students get one mark for the correct first step and then lose the second mark for not completing the rearrangement.
Before you start, write at the top of your working: "I am making ___ the subject." Then at each step, check: is what I'm doing moving me toward that goal? This sounds trivial but it genuinely prevents the mistake of stopping one step early, which is exactly what examiners report happening.
Another variant: make x the subject of y = 3x + 7. Students subtract 7 to get y − 7 = 3x, then write x = y − 7 without dividing by 3. The final answer should be x = (y − 7) / 3. Same error, same cause — stopping one operation too early.
Substituting values into expressions and formulae is one of the most reliably tested topics at GCSE. And it's one where small errors compound quickly. The most dangerous situation is substituting a negative number into an expression with a squared term.
If you're asked to find the value of 3x² − 2x + 1 when x = −3, the correct working is:
3(−3)² − 2(−3) + 1 = 3(9) + 6 + 1 = 27 + 6 + 1 = 34
The two places students go wrong: first, writing (−3)² = −9 instead of +9. Squaring a negative always gives a positive. Always. Second, writing −2(−3) = −6 instead of +6. Two negatives multiplied give a positive.
❌ Wrong: 3(−3)² = 3 × (−9) = −27
✓ Correct: 3(−3)² = 3 × 9 = 27 (squaring a negative gives a positive)
The fix is to use brackets religiously when substituting. Write (−3) with the brackets every time, not just −3. It sounds fussy but it's a visual reminder that the negative sign is part of the number being squared, and it reduces errors significantly.
This one is Higher tier but it's worth knowing even if you're on Foundation, because it shows up in harder Foundation questions too. When you multiply or divide both sides of an inequality by a negative number, the inequality sign flips direction.
So −2x > 8 does not give x > −4. It gives x < −4. The sign flips because you divided by −2. Most students either don't know this rule or forget it under exam pressure.
Dividing or multiplying an inequality by a negative number reverses the inequality sign. This is one of the most commonly missed rules in GCSE algebra.
The AQA specification explicitly lists this as an assessed skill. You can find the full algebra content in the AQA GCSE Mathematics specification, and Edexcel's equivalent is available on the Edexcel GCSE Mathematics page.
Algebraic fractions appear mostly at Higher tier and they catch a lot of students out. The error pattern mirrors the numerical fraction mistake that students thought they'd left behind in year 7: adding the numerators and denominators separately.
1/x + 1/3 is not 2/(x+3). This is completely wrong. You need a common denominator, which is 3x, giving you 3/(3x) + x/(3x) = (3 + x)/(3x). Students who are comfortable with numerical fractions but haven't practised algebraic ones tend to panic and default to incorrect rules under exam pressure.
The method is exactly the same as numerical fractions. Find the common denominator. Rewrite both fractions with that denominator. Add the numerators. Simplify if possible. Don't try to invent shortcuts.
Drawing and interpreting graphs of functions is tested across all exam boards. The most common error isn't the algebra — it's the plotting. Students correctly calculate the y-values for a table of x-values, then plot one point in the wrong place and draw a curve through the incorrect point, dragging the whole graph off course.
The fix: after plotting all points, step back and look at the overall shape before drawing the curve. For a quadratic, you should see a U-shape (or upside-down U). For a cubic, an S-curve. If one point looks wildly out of place compared to the others, recalculate that one before drawing through it. Examiners award marks for a smooth curve through correctly plotted points — one rogue point can cost you the graph mark even if nine others are correct.
PaperPlus generates unlimited algebra practice questions for AQA, Edexcel and OCR — with detailed mark schemes so you can see exactly where you're going wrong.
Start Practising Free →Reading a list of mistakes is not the same as fixing them. The only way to genuinely fix these errors is to practise algebra questions, make the mistakes yourself, catch them with mark schemes, and then practise the same type of question again until the correct method becomes automatic.
This is why past papers are so valuable — but also why they have a limit. Once you've done every available past paper, you need a different source of practice questions. That's exactly the problem PaperPlus was built to solve.
It's also worth reading the actual examiner reports for your specific exam board. They're free, publicly available, and they contain specific commentary on the questions students found hardest. AQA publishes theirs on their website under each subject's assessment resources. Edexcel and OCR do the same. Most students never look at them. The ones who do have a genuine advantage.