GCSE Maths Paper 1 Analysis With Recommended Revision List For GCSE Maths Paper 2 Topics and Paper 3 Topics (2025)

This article was originally published on 19th May 2025

Here is your expert analysis of the GCSE maths Paper 1 2025, covering both the Foundation and Higher tiers to give you some pointers on the GCSE maths paper 2 topics and paper 3 topics that might come up next.

Thursday 15th May marked the start of the GCSE maths exams for this year’s cohort, so with GCSE maths Paper 1 2025 behind us, it’s time to look at what might be coming up next to focus your maths paper 2 revision.

In this article, experienced maths teacher and exam marker, Christine Norledge, gives her recommendations for the hit list of top topics for your students to revise next, based on where the gaps were from the GCSE maths paper 1.

As in previous years, this analysis focuses on the Edexcel exam board GCSE Maths Paper 1 (non-calculator) Foundation and Higher Maths Paper and doesn’t cover AQA GCSE mathematics, OCR or IGCSE. It’s also specifically about GCSE mathematics, not A-level mathematics exams.

It will be followed by detailed commentary on Papers 2 and 3. Alongside the breakdowns, we’ll continue to share recommendations to help teachers guide revision and give students the best chance of success.

The question papers and mark schemes are yet to be formally released, and this analysis provides recommendations only. It is not an official report from Edexcel.

Once all three papers are finished, we’ll ask you, the teachers, maths leads and support staff involved in the maths GCSEs for 2025, your opinion on the exam series and post a more detailed analysis of the whole series.

GCSE MATHS 2025: STAY UP TO DATE

Join our email list to stay up to date with the latest news, revision lists and resources for GCSE maths 2025. We’re analysing each paper during the course of the 2025 GCSEs in order to identify the key topic areas to focus on for your revision.

GCSE dates 2025
GCSE results 2025 (when published)
Analysis of GCSE Maths Paper 1 2025
Analysis of GCSE Maths Paper 2 2025
GCSE Maths Teacher Survey Results 2025

Edexcel GCSE Maths Paper 1 2025: student thoughts and feelings

On the whole, it seems that the Edexcel Maths Paper 1 was hard, with a noticeable increase in difficulty compared to previous years. Students across the country took to TikTok to share their opinions on the ‘horrific’ first maths paper.

To help students prepare as much as they can for Papers 2 and 3, I’ve compiled a list of the most likely Foundation and Higher topics that could appear.

Revision lists for foundation and higher maths papers 2 and 3

If you want to jump straight into the revision lists for the next maths GCSE papers, the key revision areas for Edexcel GCSE Maths Papers 2 and 3 follow.

You can download the lists with links to the relevant revision resources below:

List of priority foundation GCSE maths paper 2 and paper 3 topics

These are the topics I’d recommend students focus on answering practice papers and questions on fluently before the next two papers. Included below is an image you can use in your revision slides for GCSE maths Paper 2 and Paper 3 or, if you prefer, an easy copy and paste text list.

Number topics to revise

• Ordering sets of numbers
• Order of operations and inverse operations
• Calculator use
• Simple number properties (squares, cubes, odd, even etc)
• Listing strategies
• Integer powers
• Convert percentages
• FDP calculations
• Percentage calculations
• Errors and bounds

Algebra topics to revise

• Substitution
• Formulae including change of subject
• Expand and factorise
• Laws of indices
• Algebraic vocabulary (expression, equation etc)
• Coordinates
• Draw and interpret linear graph (less likely as equation of a line and quadratic graph appeared on 1F)
• Identify non-linear graphs
• Cubic and reciprocal graphs (less likely as we’ve had a quadratic graph on 1F)
• Two-step (or more) linear equations
• Form and solve equations or inequalities
• Represent linear inequalities on a number line
• Solve linear inequalities
• Linear simultaneous equations
• Linear and non-linear sequences

Ratio and Proportion topics to revise

• Compound measures
• Distance- and speed-time graphs and other real-life graphs
• Ratio notation
• Inverse proportion
• Proportion graphs
• Percentage change
• Compound percentage change

Geometry topics to revise

• Properties of circles (naming etc)
• Constructions and loci
• Transformations
• Congruence and similarity
• Representing 3D shapes (plans and elevations etc)
• Lines and angles (measuring)
• Perimeter and area of rectilinear shapes
• Perimeter and area of circles and part-circles
• Cylinders and prisms (volume and SA)
• Cones, spheres and pyramids (volume and SA)
• Volume and SA with compound measures
• Pythagoras and trigonometry in RA triangles

Probability topics to revise

• Single-event probability
• Frequency trees and tree diagrams
• Sets and Venns
• Independent and dependent combined events

Statistics topics to revise

• Data collection and sampling
• Time-series data
• Frequency polygons
• Scatter graphs
• Averages and range from listed ungrouped data
• Frequency tables
• Averages and range from grouped data

List of priority topics for your higher GCSE maths paper 2 and paper 3

Number topics to revise

• Fraction calculations
• Calculator use
• Combinations and permutations
• Integer powers
• Fractional powers
• Problem solving with FDP
• Error intervals and bounds

Algebra topics to revise

• Algebraic expressions
• Change of subject
• Expand and factorise
• Laws of indices
• Complete the square
• Algebraic fractions
• Coordinates
• Equation of a line
• Parallel and perpendicular lines
• Identify non-linear graphs
• Cubic and reciprocal graphs
• Exponential and trig graphs
• Graph and equation of a circle
• Graph transformations
• Form and solve linear equations or inequalities
• Represent linear inequalities, including graphs
• Form and solve quadratic equations/inequalities
• Simultaneous equations (all types)
• Iteration
• Linear sequences
• Quadratic and geometric sequences

Ratio and Proportion topics to revise

• Standard measures
• Compound measures
• Real-life graphs (velocity-time on 1H)
• Direct and inverse proportion (simple)
• Proportion graphs
• Percentage change
• Compound percentage change
• Growth and decay

Geometry topics to revise

• Properties of polygons
• Circle theorems
• Scale drawing and bearings
• Perimeter and area of rectilinear shapes
• Perimeter and area of circles and part-circles
• Cylinders and prisms (volume and SA)
• Cones, spheres and pyramids (volume and SA)
• Volume and SA with compound measures
• Pythagoras and trigonometry in right-angled triangles
• Further trigonometry
• Using exact trig values in calculations (show that)
• Vector notation, calculation and proofs

Probability topics to revise

• Tree diagrams
• Sets and Venns
• Independent and dependent combined events

Statistics topics to revise

• Sampling
• Time-series data
• Frequency polygons
• Cumulative frequency graphs and box plots
• Scatter graphs
• Average calculations for grouped data

How best to share revision recommendations

If you’re worried that students might read too much into the revision focus lists, you could present them differently. For example, a booklet of exam questions from GCSE maths past papers based on selected topics.

Within the accompanying resource for this blog, you’ll find links to targeted GCSE Maths revision materials, including questions and worksheets for each of the key topics. This could be a handy starting point for producing Paper 2 and 3 revision materials.

GCSE maths paper 1 2025: topics tested in depth 

This is what I observed in terms of topic and question detail from GCSE maths paper 1

Foundation Maths Paper 1

There weren’t any unusual skews in favour of one topic area over another, with proportions roughly in line with the previous June series. However, in my years of maths GCSE experience, Number was slightly on the low side for Paper 1 compared to historic data. We might see this balance out on Papers 2 and 3.

Topics that appeared on Paper 1 in depth and are therefore less likely to appear again included: 

• Decimal arithmetic
• Standard form calculations
• Estimating calculations by rounding
• Function machines
• Reading timetables
• Angles in polygons
• Column vector arithmetic
• Bar charts
• Stem and leaf plots

Within Algebra, there was a fair amount of focus on graph work, with the equation of a line and quadratic functions both assessed towards the end of the paper.

In Statistics, students were presented with questions involving a bar chart and a stem and leaf diagram. But, with two papers to go, we’re probably going to see a bit more statistical chart and graph work.

Higher Maths Paper 1

Topic strand distribution on the Higher Maths Paper 1 also followed general historical trends. However, there was quite a bit more work in Ratio and Proportion, and less work on Number and Geometry than in the two most recent June series.

Unlike previous years, the June 2025 Edexcel Higher Maths Paper 1 had an unusually small number of questions. Every previous Edexcel Higher paper has had at least 20 questions, with an average of 22 questions per paper.

Consequently, this paper provided students with a higher proportion of multi-mark questions which required in-depth thinking or problem-solving approaches. This may explain why some students found Paper 1 difficult.

Additionally, a few topics appeared on Paper 1 that, historically, are frequently examined on Calculator papers. This includes work with graphs, transformations and similar shapes. 

Topics that appeared on this paper in depth and are therefore less likely to appear again included:

• Systematic listing
• Rationalising the denominator
• Converting a recurring decimal to a fraction
• Algebraic proof
• Composite functions
• Solving linear inequalities
• Estimating gradients and areas of non-linear graphs
• Direct and inverse proportion (linked equations)
• Standard transformations
• Proof with similar shapes
  

Many topics traditionally considered “higher-grade” appeared on this paper. Once students had finished both Foundation and Higher common questions at the start of the Higher paper, they were asked to tackle some pretty challenging questions. 

As with Foundation, students faced a lot of graph work, with quadratic graphs in the common questions, and estimating gradients and areas further on.

Unusually, proof featured highly with an algebraic proof and geometric proof for a total of 5 marks.

Topics likely to come up on Paper 2 or 3 

While there is, of course, no certainty about which topics will or will not appear of Papers 2 and 3, based on the GCSE Maths Paper 1 2025 and previous series of GCSE maths paper series, these topics are likely to come up on the next two papers. You may want to make a note of the information below to help students action a revision plan.

Foundation papers topic analysis

Number 

Foundation Paper 1 is usually pretty calculation-heavy, and this paper wasn’t an exception to the rule. So far, there’s been little work on number properties, or powers or order of operations – although the latter is less likely on a calculator paper.

Other than some fraction arithmetic, students haven’t seen much on fractions, decimals and percentages yet. We can expect to see some more problem-solving work involving these topics.

Algebra

There was comparatively little work in equations and substitution domains, and nothing yet on sequences. These may prove good revision focus for Papers 2 and 3.

When looking at equations in more depth, it appears students have only been asked to solve a one-step simple equation. Prepare students to expect some more difficult work on equations or inequalities involving two or more steps on the next two papers. 

Additionally, we’ve not seen much work on algebraic manipulation (expand, factories, etc.), these might be some straightforward marks to target.

Ratio and Proportion 

Paper 1 already provided students with a couple of types of ratio questions and a straightforward recipe-based proportion problem. However, as this is such a broad topic, there will likely be more in the next two papers, potentially something easier earlier on in the paper.

Time was covered fairly comprehensively, but there’s been nothing yet on other standard measures, or compound measures such as speed, pressure and density.

Geometry 

Most of the Geometry work on Maths Paper 1 was on shape properties, with very little on measuring and calculating. However, Perimeter, area and volume usually form a decent chunk of marks at Foundation; we can expect to see something on this on Papers 2 or 3. 

We can also expect to see some Pythagoras, trigonometry or both in at least one of these papers. It’s very unusual to have a series where neither topic appears in some form.

Probability 

Historically, frequency trees and tree diagrams are an Edexcel favourite. Remarkably, we’ve not seen either yet, these could likely appear in the next two papers. Sets and Venn diagrams are yet to be seen.

Although we saw a mutually exclusive events question in the common section of the paper, we’re likely to see more simple probability somewhere else in the series.

Statistics

Students haven’t yet completed any work with averages or range and should expect some of these calculations on the next papers.

Grouped data hasn’t featured in the last couple of June or November papers, but this could crop up. And, with two papers still to go, there will likely be some more work on charts or graphs – possibly a scatter graph, time series chart or a pie chart.

Higher papers topic analysis

Number 

Students have completed quite a bit of work with surds on Paper 1, but none so far on power calculations. It might be worth working on negative and fractional indices.

We’re likely to see more problem-solving with fractions, decimals and percentages, and there’s been nothing yet on error intervals and bounds.

Algebra

As with Foundation, students have completed a lot of graph work but not much on algebraic manipulation or solving equations. Students also haven’t had to solve any quadratic equations yet, this is highly likely to come up. As the next 2 papers are the Calculator, they may need to use the quadratic formula to solve them.

If the pattern of more multi-mark questions continues, it might be worth working on context-based problems where students have to form and then solve equations, particularly linked with perimeter or area.

Ratio and Proportion 

With the Calculator papers approaching, students will probably have to complete some work with compound interest or depreciation.

Generally, percentage calculations have been assessed very little so far, there might be some more in-depth problem-solving with FDP conversions and ratios across the next few papers.

Look out for work on compound measures – there’s usually some work involving at least one of speed, pressure and density, and there’s been nothing so far.

Geometry 

All Geometry work on Higher Paper 1 focused on shape properties; nothing on measuring and calculating. We’re very likely to see some significant work on shape mensuration on Papers 2 and 3, perhaps combined with pressure or density.

Also expect to see some trigonometry, both in right-angled triangles and more advanced Higher-only work – it is very unusual to have a series where neither topic appears in some form.

Probability 

Again, like Foundation, sets or Venn diagrams are yet to appear; they likely may in the next two papers.

Students have solved a couple of Probability problems, but nothing involving combined events yet. They may see a tree diagram or face a more in-depth problem to tackle.

Statistics

Students haven’t worked with averages or range yet, so we might see a problem-solving question involving means or calculations with grouped data.

It’s likely to see more work on statistical charts or graphs, this could be:

• Scatter graphs;
• Cumulative frequency graphs;
• Box plots.

Frequently tested calculator paper topics

The topics in these lists are either:

• Frequently examined topics with a high proportion (<80%) of appearances on the calculator papers;
• Topics that have appeared in 75% or more of all series of live exam papers, either on Paper 2, Paper 3, or both.

This would be a good place to start when collating a “general calculator paper” practice booklet for students. All the resources you need to do this are available from the bundle linked above or you can find them yourself from the GCSE maths revision section of the site.

Foundation paper 

Number

• Ordering numbers
• Calculations in context
• Use a calculator accurately
• Factors and multiples (HCF appeared on 1F)
• Standard form (appeared on 1F)
• Convert percentages
• Error intervals
• Rounding

Algebra

• Write algebraic expressions (appeared on 1F)
• Solve linear equations
• Find terms in a linear sequence

Ratio and Proportion

• Standard measures
• Compound measures
• Ratio notation and calculations
• Direct proportion
• Proportion graphs
• Compound interest and depreciation

Geometry

• Properties of polygons
• Angle facts and properties (appeared on 1F)
• Transformations
• Scale drawing and bearings (appeared on 1F)
• Find missing sides and angles using trigonometry

Probability

• Single-event probability

Statistics

• Pictogram, bar chart or pie chart (bar chart appeared on 1F)
• Grouped data calculations

Higher paper 

Number

• Standard form (appeared on 1H)
• Errors and bounds

Algebra

• Algebraic fractionsQuadratic graphs (appeared on 1H)

Ratio and Proportion

• Compound measures
• Ratio calculations
• Compound interest and depreciation

Geometry

• Circle theorems 
• Transformations (appeared on 1H in some depth)
• Congruence and similarity (appeared on 1H)
• Perimeter and area of circles or parts of circles
• Pythagoras and trigonometry in right-angled triangles

Probability

• Independent and dependent combined events

Statistics

• Histograms (appeared on 1H)
• Cumulative frequency graphs and box plots

Less frequently tested calculator paper topics

This selection of topics has only appeared occasionally in recent series as main topics (some may be embedded in other questions), and have not appeared on Paper 1.

These are topics to watch out for as they are assessed less frequently, but it could be their turn this year!

Some topics listed here, such as loci, are either very infrequently assessed or are demanding for that particular tier, such as quadratic equations on Foundation papers. 

Once students are secure with the core content for each paper, it can be useful to revisit these topics. However, they shouldn’t take up the bulk of students’ revision time.

Foundation paper 

Number

• Inverse operations

Algebra

• Formulae
• Algebraic vocabulary
• Identify graph shapes (non-linear)
• Draw cubic or reciprocal graphs
• Non-linear sequence

Geometry

• Cones, spheres and pyramids (volume or surface area)
• Vector notation (vector calculation on 1F)

Probability

• Data collection and sampling

Statistics

• Time-series graph

Higher paper 

Algebra

• Shade regions for inequalities on a graph
• Other non-linear sequences (e.g. Fibonacci)
• Plot cubic or reciprocal graphs
• Exponential graphs

Geometry

• Loci – finding a region (still no main topic appearance on Higher)

Probability

• Sample sizes and proportion

Statistics

• Finding the median class interval
• Time

What’s next for your GCSE maths revision?

The dates for the next two Edexcel GCSE Maths exams are:

• Paper 2 – Wednesday 4th June
• Paper 3 – Wednesday 11th June

For both Paper 2 and 3, students can use a calculator. Here are five top tips for helping students maximise marks on the calculator papers:

1. Check the calculator’s settings before the exam: Resetting the calculator to clear memory and restore defaults is useful before the exam. When tackling trigonometry problems, ensure the calculator is in degrees.
2. Write down all working out: Don’t assume the examiner is a mind-reader. Signpost where all intermediate bits of working have come from, and annotate calculations clearly in the exam paper.
3. Check that the answer makes sense: Re-read the question and check that the answer is a sensible size for the context. Estimation can help here! 
4. Write the answer in the correct form: Calculator papers often require answers to be rounded to a certain number of decimal places or significant figures. Encourage students to check the question to make sure they’ve followed all instructions.
5. Use the calculator to check all calculations: Even if it’s a simple bit of mental arithmetic, students should check every answer using a calculator to avoid silly mistakes. There is often less tolerance for calculation errors on the mark schemes for Calculator papers
   

Good luck with Maths Paper 2

We recommend students complete as many GCSE maths past papers, practice papers and predicted papers as possible, specifically focusing on the questions covering the topics listed above ahead of their next GCSE maths exams to ensure they are ready.

We’ll be back after the 4th June with an updated hit list and further analysis between Papers 2 and 3. 

Just like after the GCSE maths paper 1 2024 analysis, the suggested list of topics won’t change significantly between these two exam papers, but we’ll be able to narrow down the hit list for Paper 3 once students sit Paper 2.

GCSE maths paper 1 2025 FAQs