GCSE Maths Topics That Come Up Every Year (And How to Actually Get the Marks)

Here's something nobody tells you in Year 10: GCSE maths is much more predictable than it feels.

Not the exact questions. Those change every year, and anyone who says they know what's on this summer's paper is guessing. But the topics? A big chunk of them turn up year after year after year. Percentages. Ratio. Solving equations. Angles. Pythagoras. Probability. You could open almost any paper from the last eight years and find most of them in there.

That isn't laziness from the exam boards. Edexcel, AQA and OCR have to test the whole specification, and some topics are so central that leaving them out would make no sense. You can't really test algebra without equations, or geometry without angles.

So this guide is about using that to your advantage. We'll go through:

• which topics come up pretty much every year (Foundation and Higher)
• how they usually get asked, with worked examples
• the small mistakes that quietly lose marks
• how mark schemes actually give out marks
• a 6-week revision plan, an exam-day checklist and a quick self-test

Let's get into it.

02What "comes up every year" actually means

Let's be honest about this before anything else.

When we say a topic "comes up every year", we mean it appears somewhere across the set of papers in almost every exam series. Most boards (Edexcel, AQA and OCR) give you three papers, each 1 hour 30 minutes long: one non-calculator and two calculator. A topic like percentages might show up on Paper 2 one year and Paper 3 the next. It might be a 2-mark question one year and hidden inside a 5-mark problem the next.

So a few rules:

• No topic is guaranteed on a particular paper. If percentages were all over Paper 1, don't assume they're "done" for Papers 2 and 3.
• The wording changes, the method doesn't. A ratio question might be about paint, recipes, money or students in a school. It's still ratio.
• Common topics get disguised. On Higher especially, a "Pythagoras question" is often a Pythagoras step inside a bigger problem about area or perimeter.

The goal is to know the methods so well that the disguise doesn't matter.

03The quick list: topics that turn up almost every year

If you're short on time, start here. These are the topics that appear in nearly every exam series.

Both tiers (Foundation and Higher)

Number

• Fractions, decimals and percentages (including percentage change and reverse percentages)
• Ratio and proportion (sharing, simplifying, best buys)
• Prime factors, HCF and LCM
• Standard form
• Rounding, estimation and error intervals
• Compound measures (speed, density, pressure)
• Simple and compound interest

Algebra

• Simplifying, expanding and factorising
• Solving linear equations
• Inequalities (solving them and showing them on a number line)
• Sequences and the nth term
• Straight-line graphs (y = mx + c)
• Rearranging formulae
• Substitution

Geometry and measures

• Angle rules, including parallel lines and polygons
• Area and perimeter (including circles and compound shapes)
• Volume and surface area
• Pythagoras' theorem
• Transformations
• Constructions and loci (less often, but regular)
• Bearings and scale drawings

Statistics and probability

• Averages and range (including from frequency tables)
• Charts and graphs, especially scatter graphs
• Probability (including tree diagrams and Venn diagrams)
• Frequency trees (more Foundation)

Extra topics that come up a lot on Higher

• Quadratics: factorising, solving, the quadratic formula, completing the square
• Simultaneous equations (linear, and linear with quadratic)
• Trigonometry (SOHCAHTOA, sine rule, cosine rule, ½ab sin C)
• Circle theorems
• Similar shapes (including area and volume scale factors)
• Direct and inverse proportion
• Surds and indices (including fractional and negative indices)
• Histograms and cumulative frequency
• Vectors
• Functions (composite and inverse)
• Algebraic proof
• Recurring decimals to fractions
• Iteration
• Graph transformations and gradients/areas under curves

04Why the same topics keep coming back

GCSE maths is built around three things the exam boards are required to test:

Some topics are perfect for all three. Percentages can be a 1-mark "find 20% of £45" or a 5-mark problem about a salary rise, tax and a savings account. Angles can be a quick calculation or a full reasoning question where you have to give reasons for every step.

Topics like that are useful to examiners, so they keep using them. Which makes them useful to you too.

05Number: the topics that turn up everywhere

Fractions, decimals and percentages

This is the most common area on the whole paper. At Foundation it starts with conversions and "find 35% of…". At Higher it becomes multi-step problems, reverse percentages and compound interest.

Learning multipliers is one of the best things you can do for GCSE maths. Once you get them, a lot of questions become one line.

Ratio and proportion

Ratio is everywhere: recipes, maps, mixing paint, sharing money. It also gets combined with fractions, percentages and area on Higher.

A sneakier version (very common now): "Amy and Ben share some money in the ratio 3 : 5. Ben gets £18 more than Amy. How much does Amy get?"

The difference is 5 − 3 = 2 parts, so 2 parts = £18 and 1 part = £9. Amy gets 3 × 9 = £27.

If you can spot whether you've been given the total, the difference or one person's share, you can do any ratio question.

Prime factors, HCF and LCM

This is a regular on non-calculator papers.

Standard form

Loads of students lose the final mark here by leaving the answer as 15 × 10¹⁰.

Rounding, estimation and error intervals

Estimation: round every number to 1 significant figure unless the question says otherwise, then work it out. Always show the rounded numbers, because that's where the method mark is.

Estimate (48.7 × 3.12) ÷ 0.51 ≈ (50 × 3) ÷ 0.5 = 150 ÷ 0.5 = 300

(Dividing by 0.5 is the same as doubling. That comes up a lot.)

Error intervals: x = 5.2, correct to 1 decimal place. Write the error interval.

5.15 ≤ x < 5.25

That "<" on the right-hand side matters. 5.25 would round up to 5.3, so x can't actually equal it.

Truncation is different. If x = 3.7 truncated to 1 decimal place (the extra digits are just chopped off), then 3.7 ≤ x < 3.8.

Compound measures

Speed, density and pressure come up every year, often hidden in a wordy context.

Converting minutes to hours (divide by 60) is one of the most common places to lose marks on the whole paper.

06Algebra: where a lot of the marks are

Algebra makes up a big share of the marks, especially on Higher. The good news is that the core skills come up constantly, so practising them pays off quickly.

Expanding and factorising

Expand: (x + 3)(x − 5)

x² − 5x + 3x − 15 = x² − 2x − 15

Use FOIL, the grid method or whatever works for you. Just be careful with negatives.

Factorise: x² + 5x + 6

Find two numbers that multiply to 6 and add to 5: that's 2 and 3. (x + 2)(x + 3)

Always expand your answer back out in your head to check it.

Solving linear equations and inequalities

These are close to guaranteed across the papers.

Number line reminder:

• A filled-in circle (●) means the number is included (≤ or ≥)
• An empty circle (○) means it isn't included (< or >)

Integer questions: "List the integers that satisfy −2 < n ≤ 3" means −1, 0, 1, 2, 3. Students often include −2 by mistake.

Rearranging formulae

The rule: undo things in the reverse order they were done to r. Here r was squared and then multiplied by π, so you divide by π first and square root second.

Sequences and the nth term

A common follow-up: "Is 100 in this sequence?" Set 3n + 1 = 100, so 3n = 99 and n = 33. That's a whole number, so yes, it's the 33rd term. If you'd got a decimal, the answer would be no. Always write a sentence explaining your answer.

Straight-line graphs

y = mx + c, where m is the gradient and c is where the line crosses the y-axis.

Higher extras: Parallel lines have the same gradient. Perpendicular gradients multiply to −1, so if one line has gradient 2, a perpendicular line has gradient −½.

Simultaneous equations

Solving quadratics (Higher, and sometimes Foundation)

If it won't factorise, or the question says "give your answer to 2 decimal places", that's a big hint to use the quadratic formula.

07Geometry and measures: where marks hide in the reasons

Angle rules

You need these off by heart:

• Angles on a straight line add up to 180°
• Angles around a point add up to 360°
• Vertically opposite angles are equal
• Angles in a triangle add up to 180°
• Angles in a quadrilateral add up to 360°
• Alternate angles are equal (Z shape)
• Corresponding angles are equal (F shape)
• Co-interior angles add up to 180° (C shape)

Area, perimeter and volume

Make sure you know:

Pythagoras' theorem

a² + b² = c², where c is the hypotenuse (the longest side, opposite the right angle).

• Finding the hypotenuse: legs 6 and 8. c = √(6² + 8²) = √100 = 10
• Finding a shorter side: hypotenuse 13, one side 5. a = √(13² − 5²) = √144 = 12

Pythagoras often turns up on Higher as part of a bigger question, like finding the perimeter of a shape or the distance between two coordinates.

Trigonometry

SOHCAHTOA:

• sin θ = opposite ÷ hypotenuse
• cos θ = adjacent ÷ hypotenuse
• tan θ = opposite ÷ adjacent

Exact trig values come up on non-calculator papers, so learn sin, cos and tan of 0°, 30°, 45°, 60° and 90°. For example, sin 30° = ½ and tan 45° = 1.

Transformations

There are four. Each needs specific details to get full marks:

Two very common ways to lose marks:

• Describing more than one transformation when the question asks for "a single transformation". That gets zero marks.
• Forgetting the centre of rotation or enlargement.

Ask for tracing paper. You're allowed it in the exam, and it makes rotations much easier.

Bearings

Three rules to remember:

1. Measure from North
2. Measure clockwise
3. Always write three figures: 045°, not 45°

Back bearings: if the bearing of B from A is less than 180°, add 180° to get the bearing of A from B. If it's more than 180°, subtract 180°.

Higher geometry favourites

• Circle theorems: like angle rules, you need to state the theorem to get the reasoning marks.
• Similar shapes: if the length scale factor is k, the area scale factor is k² and the volume scale factor is k³. So if lengths are 3 times bigger, areas are 9 times bigger and volumes are 27 times bigger.
• Sine and cosine rules: use the sine rule when you have a side and its opposite angle. Use the cosine rule when you have all three sides, or two sides and the angle between them.
• Vectors: usually a proof at the end (show that points are on a straight line, or that lines are parallel). Show every step of your route.

08Statistics and probability: often the easiest marks

Averages and range

From a frequency table: multiply each value by its frequency, add those up, then divide by the total frequency. A very common mistake is dividing by the number of rows instead.

Grouped data (estimate of the mean): use the midpoint of each group. It's an estimate because you don't know the exact values.

Comparing two sets of data: when you're asked to compare, write two things:

1. A comparison of an average, e.g. "On average, Class A scored higher because their median was greater."
2. A comparison of spread, e.g. "Class B's scores were more consistent because their range was smaller."

Always say what it means in the context of the question, not just "the mean is bigger".

Scatter graphs

You should be able to:

• describe correlation: positive, negative or none
• draw a line of best fit: a single straight line following the trend, roughly the same number of points on each side, not forced through the origin
• use the line to estimate values
• explain why estimating outside the data range (extrapolation) is unreliable
• identify an outlier

And remember: correlation doesn't mean causation. Two things going up together doesn't prove one causes the other.

Probability

The basics:

• Probabilities go from 0 to 1
• All the possible outcomes add up to 1
• P(not A) = 1 − P(A)
• AND means multiply. OR means add (for mutually exclusive events).

"Without replacement" is your signal that the second set of probabilities changes.

Expected outcomes: if P(red) = 0.3 and you spin 200 times, you'd expect 0.3 × 200 = 60 reds.

Venn diagrams: always start in the middle (the overlap) and work outwards. Then make sure everything adds up to the total, including anything outside both circles.

Higher statistics regulars

• Histograms: frequency density = frequency ÷ class width. The area of the bar is the frequency, not the height.
• Cumulative frequency: plot at the upper end of each group, read the median at half the total, and find the interquartile range from the quartiles.
• Box plots: often used to compare two sets of data (median and IQR).
• Conditional probability: "given that…" means the total you're working from has changed.

09How marks are actually given (and how to collect more of them)

Most students never look at a mark scheme properly. That's a mistake, because mark schemes tell you exactly what examiners reward.

The codes you'll see in mark schemes

What this means for you

• Always show your working. On a 4-mark question you might get 3 marks with the wrong final answer, as long as your method is clear. A wrong answer with no working gets 0.
• Never leave a question blank. Write down anything relevant: a formula, a first step, a conversion. Method and process marks are given for partial progress.
• Don't cross out working unless you've replaced it. If you cross something out and don't write anything new, the examiner can't mark it.
• "Show that" questions: you're given the answer, so the marks are for the steps. Show every line, and give your answer to more decimal places than the one you were given.
• Write a sentence when asked to "explain", "decide" or "compare". A number with no conclusion often loses the communication mark.

Command words worth knowing

10Timing: the skill nobody practises

On Edexcel and AQA, each paper is 80 marks in 90 minutes, which is roughly 1 minute per mark with about 10 minutes spare. (OCR papers are 100 marks in 90 minutes, so it's tighter.)

Some practical tips:

• A 2-mark question shouldn't take 8 minutes. If you're stuck, write what you can, put a star next to it and move on. Come back at the end.
• Questions generally get harder as the paper goes on, but not always. There are often easier marks hidden near the end, so don't give up on the last few pages.
• Use the spare time to check, especially the questions where you used a calculator. Re-type the calculation in a slightly different way to see if you get the same answer.
• Practise full papers with a timer. Knowing the maths and finishing in time are two different skills.

11Calculator skills that save time

On calculator papers, knowing your calculator properly can give you a real advantage.

• Use the fraction button for fraction calculations, and the S⇔D button to switch between fraction and decimal.
• Use brackets properly. Type (3 + 5) ÷ 2, not 3 + 5 ÷ 2.
• Use the ANS button in multi-step questions so you don't round halfway through.
• Don't round until the end. Rounding in the middle of a trig or compound interest question can push your final answer out of the allowed range.
• Check the mode: degrees (D) for trig.
• Use the table function (if your calculator has it) to plot graphs and find values quickly.

And don't rely on it too much. One of your three papers is non-calculator, and many students lose easy marks there because they never practised fractions, long multiplication or division without one.

12Formula sheets: what you get and what you still need to know

Students taking GCSE maths have been given a formulae sheet in recent years, and at the time of writing this has been confirmed through the 2027 exams. Check with your teacher or exam board for your exam year, because these things can change.

Even with a sheet, you should still learn the common formulas. Here's why:

• Looking things up takes time you don't have.
• The sheet tells you the formula, not when to use it.
• Lots of things you need aren't on it: angle rules, polygon angle sums, circle theorems, the nth term method, bounds, standard form rules and probability rules.

Treat the sheet like a safety net, not a crutch.

13Mistakes that keep costing students marks

These come up in examiner reports year after year:

1. Treating predictions as promises. Predicted papers are great practice, but revise the method, not one question style.
2. Skipping non-calculator practice. Fraction arithmetic and long division are worth more marks than people think.
3. Doing steps in your head. If it's not written down, you can't get method marks.
4. Rounding too early. Keep full values on your calculator until the end.
5. Forgetting units. cm, cm², cm³, £, km/h. Sometimes there's a mark just for this.
6. Mixing up area and perimeter, or radius and diameter.
7. Reverse percentages done forwards. If you're working back to the original, divide by the multiplier.
8. Time conversions. 1 hour 15 minutes is 1.25 hours, not 1.15.
9. Not reading the last line of the question. "Give your answer to 3 significant figures", "in terms of π", "in its simplest form": these are mark-losers if you miss them.
10. Lazy reasons in geometry. "Z angles" isn't enough. Write "alternate angles are equal".
11. Not checking whether the answer makes sense. A person who's 15 metres tall or a probability of 1.4 means something's gone wrong.

14How to revise these topics properly

The best revision isn't "do everything". It's doing the right things in the right order.

The three-pass method

1. Rebuild the method. Pick a topic. Watch a short revision video and make brief notes, just the method and one example. Don't spend ages making them look nice.
2. Topic practice. Do practice questions on just that topic, then mark them yourself using the mark scheme. Pay attention to where the marks go, not just whether you got the answer.
3. Mixed paper practice. Do full papers or predicted papers under timed conditions. This is where you find out what you actually know when topics are mixed up and you're under pressure.

Keep a mistakes log (seriously, do this)

Every time you lose marks, write down:

• the topic
• what went wrong (didn't know the method? silly slip? misread it? ran out of time?)
• the correct method in one line

After a few papers you'll see patterns. Maybe you keep messing up bounds, or always forget units. Those patterns are your revision list. It's far more useful than revising topics you're already good at because it feels nice.

Prioritise the right topics

15A 6-week revision plan

You can stretch or squeeze this depending on how long you have.

16Quick self-test: can you do these?

Try them without looking back. The answers are hidden below.

1. A phone costs £240 after a 25% discount. What was the original price?
2. Share £120 in the ratio 2 : 3 : 5.
3. Write 0.000 47 in standard form.
4. Solve 3(x − 2) = 2x + 5.
5. Find the nth term of 5, 9, 13, 17, …
6. Find the interior angle of a regular pentagon.
7. A right-angled triangle has a hypotenuse of 17 cm and one side of 8 cm. Find the other side.
8. The length of a pencil is 14 cm, correct to the nearest cm. Write the error interval.
9. A bag has 4 green and 6 yellow sweets. Two are taken without replacement. Find P(both green).
10. (Higher) Write 0.4545… (recurring) as a fraction in its simplest form.

AnswersShow answersHide answers

1. 240 ÷ 0.75 = £320
2. 10 parts, so £12 each: £24, £36, £60
3. 4.7 × 10⁻⁴
4. 3x − 6 = 2x + 5, so x = 11
5. 4n + 1
6. Exterior = 360 ÷ 5 = 72°, so interior = 108°
7. √(17² − 8²) = √225 = 15 cm
8. 13.5 ≤ L < 14.5
9. 4/10 × 3/9 = 12/90 = 2/15
10. Let x = 0.4545…, so 100x = 45.4545… Subtract: 99x = 45, so x = 45/99 = 5/11

Got 8 or more? You're in a good place. Fewer than 6? Go back to the topics you missed first. That's your revision plan sorted.

17Exam-day checklist

The night before

• Calculator with fresh batteries (and a spare if you can)
• Black pens (at least two), pencil, rubber, sharpener
• Ruler, protractor and compasses
• A clear pencil case
• Get some sleep. Seriously. Cramming at 1am does more harm than good.

In the exam

• Read every question twice, especially the last line
• Underline key words: estimate, exact, give reasons, 3 s.f.
• Ask for tracing paper for transformations
• Do the questions you're confident on first if that helps your nerves
• Never leave a blank. Write something.
• Use spare time to check calculator answers and units

18Frequently asked questions

Are there GCSE maths topics that definitely come up every year?

No topic is ever 100% guaranteed, but some are as close as it gets: percentages, ratio, solving equations, angles, area, Pythagoras and probability have appeared in almost every exam series. Revise them first, but don't skip the rest of the specification.

How are Foundation and Higher different for these topics?

Many of the same topics are on both papers. Foundation tends to ask them more directly, while Higher combines them with other topics and adds harder twists. For example, a Foundation percentage question might ask you to find 15% of an amount, while a Higher one might involve reverse percentages and compound interest together. There's some overlap in the middle: the grade 4 and 5 questions are often the same on both tiers.

What's the best way to use past papers without wasting time?

Don't just do the paper and check your score. Mark it properly with the mark scheme, write every mistake in your mistakes log, then go back and practise those specific topics before doing another paper. One paper done properly is worth more than three rushed ones.

Are predicted papers worth doing?

Yes, as practice. They're a good way to get timed, mixed-topic practice. Just don't treat them as a preview of the real exam. The real paper will have questions you haven't seen, and that's fine if you know the methods.

How many past papers should I do?

Quality beats quantity. Aim to do at least one full set of three papers under timed conditions in the last few weeks. Before that, focus on topic practice to fix your weak areas.

I'm doing A Level maths next. Is this still worth revising properly?

Definitely. A Level maths builds directly on GCSE algebra, especially rearranging, quadratics, surds, indices, graphs and trig. Students who are shaky on GCSE algebra find the jump to A Level much harder. Getting it solid now will make Year 12 much easier.

What if I'm really behind and the exam is soon?

Focus on the topics in the "both tiers" list, especially number and basic algebra. They come up the most and are often the most accessible marks. Do short, focused sessions every day rather than trying to cover everything at once. Even a few weeks of consistent practice can make a big difference.

19Bringing it all together

GCSE maths papers change the story each year, but they keep testing the same skills. Percentages, ratio, equations, angles, area, Pythagoras and probability are the foundations, and they show up again and again.

Revise those properly and you stop feeling like you need to guess what's coming. You'll know you can handle whatever version of it you get.