If you are unsure where to start with GCSE maths, begin with the skills that other topics depend on. Fractions help with percentages and probability. Equations help with graphs and geometry. Understanding those connections makes the course easier to work through.
The order
Number skills → fractions, percentages and ratio → core algebra → sequences and graphs → geometry and measures → probability and statistics → further topics for your tier.
Use that as your main route, with short reviews and exam questions along the way. You do not need to complete every topic in one stage before trying anything else, but it helps to secure the relevant basics before moving to a more demanding application.
Here is what to study at each stage, why it belongs there and how to check whether you are ready to continue.
The best order to learn GCSE maths topics at a glance
| Stage | Learn these topics | Why they come here |
|---|---|---|
| Number foundations | Arithmetic, negative numbers, order of operations, factors, multiples, powers, roots, decimals and rounding | These calculations appear throughout GCSE maths |
| Fractions, percentages and ratio | Fraction calculations, conversions, percentages, ratio, scaling and proportion | These develop the skills used in comparisons, rates and probability |
| Core algebra | Simplifying, substitution, brackets, factorising, equations, inequalities and rearranging formulae | These help you work with unknown values and mathematical relationships |
| Sequences and graphs | Linear sequences, coordinates, tables of values, straight-line graphs and real-life graphs | These build on substitution, equations and number patterns |
| Geometry and measures | Angles, perimeter, area, volume, transformations, constructions, similarity, Pythagoras and right-angled trigonometry | These bring together number, algebra, proportion and spatial reasoning |
| Probability and statistics | Averages, charts, frequency tables, sample spaces, probability diagrams and combined events | More demanding questions use the fraction and proportion skills learned earlier |
| Further topics for your tier | Extend your algebra, graphs, geometry and data handling using your specification checklist | These become more manageable once their prerequisites are secure |
Note
This is a suggested learning order, rather than a complete syllabus checklist. Basic averages, charts, angles and shapes can be studied earlier. Exam-style questions should appear at every stage, rather than being saved until you have finished the course.
Start with number foundations
The first stage is becoming reliable with the calculations you will need everywhere else. Work through:
- Addition, subtraction, multiplication and division.
- Negative numbers.
- Order of operations.
- Decimal calculations.
- Factors, multiples and prime numbers.
- Squares, cubes, powers and roots.
- Rounding, significant figures and estimation.
If these already feel comfortable, test yourself and move on. You do not need to spend several sessions repeating material you can do independently.
Why number comes first
Worked example
Substituting a negative. Substitute x = −3 into 2x² − 5.
You need to understand negative numbers, powers and the order of operations:
2(−3)² − 5 = 2(9) − 5 = 13
Common mistake: treating (−3)² as −9. A student might understand substitution perfectly but still get this wrong.
That is why it is worth repairing number weaknesses early. Otherwise, the same error can follow you into algebra, graphs and geometry.
Before you move on
Try a short mixed set containing negatives, decimals, powers and rounding. If one calculation type keeps going wrong, give it some focused practice. You can continue to the next stage while keeping that skill in your daily warm-up.
Learn fractions, percentages and ratio
Once your basic calculations are reasonably secure, move on to working with parts, proportions and comparisons. A useful order is:
- Equivalent fractions and simplifying fractions.
- Comparing fractions.
- Adding and subtracting fractions.
- Multiplying and dividing fractions.
- Converting between fractions, decimals and percentages.
- Finding fractions and percentages of amounts.
- Percentage change and reverse percentages.
- Simplifying ratios and sharing in a ratio.
- Scaling, unit rates and proportion.
Fractions should come before the harder percentage and ratio questions because they help you understand what part of an amount you are working with.
How the topics connect
Worked example
One relationship, three forms. A club has 180 members and 35% are juniors.
35% = 35/100 = 7/20, so the number of juniors is 7/20 × 180 = 63.
Now suppose the ratio of junior to adult members is 7 : 13. There are 20 parts altogether, so juniors again represent 7/20 of the membership.
Fractions, percentages and ratios can describe the same relationship in different forms. Learning them together makes it easier to recognise what a question is telling you.
Learn ratio questions in increasing difficulty
Begin with sharing a known total. Then try questions where one share is given, followed by questions where the difference between the shares is given.
Worked example
A difference between shares. Two amounts are in the ratio 4 : 7. The larger amount is £27 more than the smaller amount. Find both amounts.
The difference is 7 − 4 = 3 parts, so one part is 27 ÷ 3 = 9.
The amounts are 4 × 9 = £36 and 7 × 9 = £63.
Common mistake: dividing £27 by the total number of parts. The £27 is the difference, not the total.
Before you move on
Make sure you can recognise whether you have been given a total, one share, a difference or an original amount. If you can perform the calculations but keep choosing the wrong one, practise a mixed set of question types.
Build core algebra
Next, learn how to describe relationships and work with unknown values. Study core algebra in this order:
- Algebraic notation and like terms.
- Substitution, including negative values.
- Expanding a single bracket.
- Factorising by taking out a common factor.
- One-step and two-step equations.
- Equations with brackets and unknowns on both sides.
- Forming equations from written information.
- Simple inequalities.
- Rearranging formulae.
You can begin this stage while still practising percentages and ratio. The essential preparation is being comfortable with arithmetic, negatives and the meaning of fractions.
Why equations should come before harder applications
Worked example
An equation with brackets. Solve 4(x − 2) = 2x + 10.
Expand the bracket: 4x − 8 = 2x + 10
Subtract 2x, then add 8: 2x = 18
x = 9
Once you can do this reliably, you can use the same process inside angle, perimeter and other worded problems.
For example, if the angles in a triangle are x, x + 20 and 2x, you can form x + (x + 20) + 2x = 180. The geometry fact gives you the equation. Algebra lets you solve it.
Before you move on
Do more than solve equations that have already been written for you. Try a short worded problem and form the equation yourself. Also check that you can substitute your answer back into the original equation to verify it.
Move on to sequences and graphs
Sequences and graphs become easier once you can substitute, simplify and solve basic equations.
| Sequences | Graphs |
|---|---|
| Continuing a sequence | Coordinates in all four quadrants |
| Using a term-to-term rule | Reading scales |
| Using a position-to-term rule | Completing tables of values |
| Finding the nth term of a linear sequence | Plotting straight-line graphs |
| — | Understanding gradient and intercepts |
| — | Finding and using equations of lines |
| — | Interpreting graphs in real situations |
Start with the relationship between position and value
Worked example
The nth term. Find the nth term of 6, 10, 14, 18, …
The terms increase by 4, so begin with 4n. This gives 4, 8, 12, 16, … Each value is two less than the required term, so the rule is 4n + 2.
The 25th term is therefore 4(25) + 2 = 102.
That same substitution skill helps you complete a table of values for a graph such as y = 4x + 2.
Understand what a graph represents
For the line y = 3x − 4, the gradient is 3, meaning y increases by 3 whenever x increases by 1. The line crosses the vertical axis at −4.
Try connecting the equation, a table of values and the plotted line. Understanding how they describe the same relationship is more useful than learning each representation separately.
Before you move on
Make sure you can work in both directions: use an equation to plot a graph, and use a graph to interpret a relationship. Always check the scale before reading coordinates or calculating a gradient.
Study geometry and measures in smaller groups
Geometry covers too much to learn as one block. Work through related groups, using the number and algebra skills you have already developed. A practical sequence is:
- Angle facts and properties of shapes.
- Perimeter and area.
- Circles and composite shapes.
- Volume and surface area.
- Transformations and scale drawings.
- Bearings, constructions and loci.
- Similarity.
- Pythagoras' theorem.
- Right-angled trigonometry.
Some of these can be studied earlier. Basic angles and area, for example, do not require you to finish all of algebra first.
Key point
The more important connections are within the groups. Learn area before surface area, scale factors before similarity, and squares and roots before Pythagoras.
Why Pythagoras comes before more demanding triangle problems
Worked example
Finding the hypotenuse. A right-angled triangle has shorter sides of 9 cm and 12 cm. Find its hypotenuse.
c² = 9² + 12²
c² = 81 + 144 = 225
c = 15 cm
To complete this, you need to identify the hypotenuse, square the lengths and take a square root.
Right-angled trigonometry then introduces relationships between side lengths and angles. It becomes more manageable when you can already label a triangle, work with ratios and rearrange simple equations.
Before you move on
Practise choosing a method as well as carrying it out. When faced with a triangle question, can you explain why Pythagoras or trigonometry is appropriate? When finding an area, can you identify the perpendicular height?
Watch out
Also check units. A correct calculation with the wrong unit can reveal that you have confused length, area or volume.
Develop probability and statistics
This stage brings together data handling and probability. You can learn the simpler topics much earlier, but return to them here and extend your understanding.
| Statistics | Probability |
|---|---|
| Reading tables and charts | The probability scale |
| Mean, median, mode and range | Listing possible outcomes |
| Frequency tables | Probabilities as fractions, decimals and percentages |
| Grouped data and estimated means | Sample spaces |
| Pie charts and scatter graphs | Expected frequencies |
| Further statistical diagrams required for your tier | Venn diagrams and tree diagrams |
| — | More demanding combined-event questions |
Why fractions should come before probability trees
Worked example
Without replacement. A bag contains five green counters and three yellow counters. Two counters are taken without replacement. Find the probability that both are yellow.
3/8 × 2/7 = 6/56 = 3/28
You need two kinds of understanding here. First, the probability changes after a yellow counter is removed. Second, you must multiply the fractions correctly.
If the fraction calculation is the problem, revisit fraction multiplication. If you keep using 3/8 for the second draw, revisit what "without replacement" means.
Before you move on
For statistics, make sure you can interpret an answer in context, rather than only calculate it. For probability, explain why you are adding or multiplying and whether the number of available outcomes changes.
Add further topics according to your tier
Once the main foundations are secure, extend each subject area using your exam board's specification.
Watch out
Avoid putting every difficult-looking topic into a "Higher-only" category. Foundation includes right-angled trigonometry, some quadratic work and linear simultaneous equations. Check the particular skills required, rather than judging by the topic name alone.
For further study, the following learning sequences are useful:
| Topic area | Sensible learning sequence |
|---|---|
| Quadratics | Expanding double brackets → factorising simple quadratics → solving by factorising → further solving methods where required |
| Simultaneous equations | Linear equations → two linear simultaneous equations → linear–quadratic simultaneous equations where required |
| Algebraic fractions | Numerical fractions → factorising expressions → simplifying algebraic fractions → calculations and equations |
| Further trigonometry | Right-angled trigonometry → sine and cosine rules → mixed triangle problems |
| Circle theorems | Basic angle facts → circle vocabulary → individual theorems → problems combining theorems |
| Vector proof | Vector notation and arithmetic → expressing routes → using ratios → constructing geometric arguments |
You do not have to finish every topic in one branch before extending another. If your algebra is strong, you can progress with quadratics while still practising geometry.
Key point
The key is to secure the particular skills the next topic depends on.
When should you start exam questions?
Use exam questions throughout this learning order.
After learning fractions, try exam questions involving fractions. After learning equations, try both direct equation questions and problems where you must form an equation.
As you cover more topics, introduce mixed sets. These make you decide which method to use without a worksheet heading giving it away.
Full past papers become more useful once you have covered enough of the course to attempt a substantial proportion of the questions: Starley has AQA, Edexcel and OCR GCSE Maths papers. If you have already studied the syllabus, you can use a paper at the start of revision to identify gaps. For a timeline, see when to start GCSE Maths past papers.
Remember
Do not wait until you feel completely ready. Exam practice helps you discover what still needs work.
How do you know when you are ready for the next topic?
You are ready to progress when you can answer ordinary questions independently and understand the main steps in the method.
Before moving on, try
- a straightforward question without notes;
- a question with different wording or a different layout;
- a question that combines the skill with something you learned earlier;
- a fresh question after a few days.
You do not need perfect scores before continuing. If a minor error remains, keep practising it alongside the next topic. If you still cannot perform a skill that the next topic relies on, spend longer repairing it.
For example, occasional rounding errors should not stop you from learning equations. Being unable to add fractions is a stronger reason to pause before attempting algebraic fractions.
Should you follow the same order when revising?
If you are learning GCSE maths from the beginning, the sequence above gives you a clear route.
If you are revising material you have already been taught, use it more selectively. Start with a mixed assessment, identify the gaps and work backwards to any missing foundations.
Quick tip
Suppose you struggle with quadratic equations because you cannot factorise. Begin with factorising. You do not need to restart with basic arithmetic if that is already secure.
If an exam is close, prioritise specific weaknesses shown by your recent work: see how to revise GCSE Maths effectively. If you have more time, work through the sequence steadily and revisit earlier topics each week, using a plan such as our GCSE Maths revision timetable.
Frequently asked questions
What GCSE maths topic should I learn first?
Start with essential number skills: arithmetic, negative numbers, order of operations, decimals, powers and roots. Then develop fractions, percentages and ratio. If you already know these, check them briefly and begin at your first significant gap.
Should I learn algebra before geometry?
Learn core algebra early because it helps with many geometry problems. However, basic angles, perimeter and area can be studied alongside it. More demanding geometry becomes easier once you can form and solve equations.
Should I finish Foundation topics before studying Higher topics?
Secure the relevant foundations first, but you do not need to complete every Foundation topic before attempting any Higher work. Follow the prerequisites within each topic area and keep checking your overall syllabus coverage.
Can I study statistics before finishing algebra?
Yes. Basic charts, averages and probability can be studied early. More demanding questions may require stronger fraction, proportion or algebra skills.
What if I get stuck halfway through a topic?
Find the first step you cannot complete. It might be a missing fact, an unfamiliar method or an earlier calculation skill. Practise that step, then return to the original topic with a fresh question.
What is the simplest revision order to follow?
Begin with number, then fractions and proportion, then algebra. Build towards graphs, geometry, probability and statistics, before extending each area to the level required for your tier. Keep reviewing earlier skills and answering exam questions as you go. For the topics that turn up most often, see GCSE Maths topics that come up every year.