# The GCSE Maths Topics Your Year 10 And Year 11 Should Revise For Their Foundation Exam In 2024

**Here we take a look at the GCSE maths topics to focus on with your Foundation exam groups in 2024. Look out for links to the one to one tuition support and lots of free resources also available for your students.**

### GCSE maths topic list

These are the 6 GCSE maths topics

- Number
- Algebra
- Ratio, proportion and rates of change
- Geometry and measure
- Probability
- Statistics

These topics apply across Edexcel, AQA and OCR. More detail is provided below for each of them.

### What is the current picture for GCSE maths?

The past few years have been very challenging for the education sector, particularly in the domain of examinations (or lack thereof) and assessments. With the complications of teacher-assessed grades and advanced information behind us GCSEs make a full return to their standard, pre-pandemic form in 2024.

Update: The formula sheets which were given in maths, physics, and combined science in 2023 as a concessionary measure for students who had experienced learning disruption due to the pandemic are also to be made available in 2024. That said, candidates will still benefit from memorising some of the key GCSE maths formulae.

**Download free:** GCSE Maths formula booklet

**GCSE Maths 2024: Stay up to date**

Join our email list to stay up to date with the latest news, revision lists and resources for GCSE maths 2024. We’ll be bringing in our expert contributors to analyse each paper and identify key topic areas to focus your revision.

GCSE 2024 dates

GCSE 2024 results (when published)

GCSE results 2023

Analysis of GCSE Maths Paper 1 (2023)

Analysis of GCSE Maths Paper 2 (2023)

Analysis of GCSE Maths Paper 3 (2023)

Summary of ALL GCSE Maths Papers (2023)

### A note on how we teach these GCSE maths topics in one to one tuition sessions

GCSE maths is interconnected, and that’s how we approach our online GCSE maths tuition programme. When designing the programme, we focus on each individual high-value lesson as part of an interconnected web, rather than teaching each main topic differently. This allows our tutors to adjust their teaching depending on the student and their level.

Within these individual lessons, our GCSE tutor slides follow a similar structure to support the revision of a topic. We move from a warm-up question to the actual lesson split into three learning objectives, which cover the topic.

In response to the student’s understanding, each learning objective moves through an exam-style question, a ‘support’ slide and an ‘assess’ slide. The lesson ends with the option of a ‘challenge’ slide to build on the previous learning objectives.

Practice Paper Pack: Edexcel Foundation 2023

Download a free pack of GCSE foundation exam practice papers to help students prepare for Maths GCSE

Download Free Now!### Breakdown of GCSE maths topics

The detail for each topic below covers the following

- Number
- Structure and calculation
- Fractions, decimals and percentages
- Measures and accuracy

- Algebra
- Notation, vocabulary and manipulation
- Graphs
- Solving equations and inequalities
- Sequences

- Ratio, proportion and rates of change
- Geometry and measure
- Properties and constructions
- Mensuration and calculation
- Vectors

- Probability
- Statistics

In addition, there are three assessment objectives that will be tested:

- AO1: Use and apply standard techniques
- AO2 Reason, interpret, and communicate mathematically
- AO3: Solve problems within mathematics and in other contexts

These are all taken from The DfE’s subject content and assessment objectives for GCSE mathematics.

### The GCSE maths topics we think you should be learning

This article focuses on the most important GCSE maths topics and strategies for Foundation tier exam preparation. Many of the suggestions in this article are applicable to all three major exam boards, including AQA. However, where we refer to topics that may have appeared on past papers, or content of past paper questions, this draws on our extensive research and analysis of all the Edexcel foundation maths papers since 2017.

We believe that all students should experience a broad and balanced curriculum, and choice of teaching topics should first and foremost be commensurate with their current mathematical attainment. As such, the suggestions in this article should not be used to narrow teaching content.

However, in preparing for GCSE exams, there are some topics that are assessed frequently and widely across the papers, and some which do not appear as often, or tend to be assessed in particular ways. Exam preparation and revision could reflect this, allowing students more time to focus on the skills which typically attract more marks.

This article looks at the specific topics and approaches you can use to maximise revision time with your students and minimise exam anxiety.

For each of the GCSE maths topic areas below, we’ve provided links to the relevant GCSE maths revision guides. In each guide, you’ll find step-by-step examples, practice questions, exam questions, and a worksheet.

### 1. GCSE maths topic: Number

**Key topics**

- Context-rich work on four operations and calculation skills, including basic arithmetic, fractions, decimals and negative numbers, order of operations.
- Real-life contexts including bank accounts, utility bills, wage increases, recipes, and best-buys.
- Procedural work on place value, standard form, indices, rounding and estimation, factors, multiples, HCF, LCM and product of primes.

##### Infrequently appearing topics

- Problem-solving or rich problems using HCF, LCM, product of primes, standard form.

#### What do we know from the GCSE paper analysis?

One thing highlighted by the GCSE paper analysis is that numeracy skills and proportional reasoning are the backbone of the current GCSE Foundation programme of study. A significant amount of this is assessed in a non-standard manner or using ‘real-life’ contexts. At Foundation, being able to work confidently with arithmetic and apply this to unfamiliar problems is absolutely key.

It was clear from the Sample Assessment Materials, and the messaging from exam boards, that one of the goals for GCSE maths 2015 was to increase the demand in problem-solving, and also to ask more questions requiring connections to be made between topics. In conjunction with the need for these skills beyond school in many circumstances, I cannot see any considerable change in this regard to exams from 2023 and beyond.

#### What should you be teaching this year?

Students need plenty of practice on number skills (four operations including fractions and decimals, calculations, percentages etc) so these are not limiting their ability to access the context-based problems. Ample time and opportunity should also be spent working with number skills in a wide variety of contexts; these should include more common real-life contexts such as:

- Shopping and best buys
- Planning the cost of a holiday
- Calculating deposits and monthly payments
- Meter readings
- Working out quantities of materials needed for decorating/gardening

Some number topics are typically assessed in a fairly procedural or context-free way; these include:

- Place value and standard form
- Ordering
- Order of operations
- Inverse operations
- Powers and roots
- FDP conversions
- Rounding and estimation

While there is some lovely rich teaching content in these topics, it is less likely to be assessed on GCSE Foundation. That said, there is very little content in the number and proportion strand that could be considered non-essential.

**Don’t miss: **80+ GCSE maths revision guides for Number.

### 2. GCSE maths topic: Algebra

**Key topics**

- The ‘algebra toolkit’ of simplifying, expanding, factorising, laws of indices, which ensures that students can reliably apply methods to standard problems.
- Solving linear equations and inequalities.
- Applying mathematical formulae to a variety of real-life and unfamiliar contexts.
- Sequences, functions and graphs, with focus on procedural ‘easy wins’ in graph work and sequences.

**Infrequently appearing topic**s

- Quadratic equations, particularly factorising and solving the form x
^{2}+ bx + c = 0. - Limited work on quadratic expressions.
- Algebraic vocabulary (identify formula/equation/identity etc).
- Finding terms in quadratic and geometric sequences.
- Cubic and reciprocal graphs.
- Parallel lines.

#### What do we know from the GCSE paper analysis?

In the Foundation tier, a significant amount of algebra is assessed in procedural, context-free ways; this suggests there is less value in spending a lot of vital exam preparation time on rich problems for these topics. It is worth remembering that, while the complexity and degree of problem-solving expected for algebra at Foundation is relatively low, students find the topics themselves more challenging, and so these are not necessarily easier marks.

Furthermore, we need to consider the frequency at which high-end algebra topics, such as parallel lines, quadratic and geometric sequences, non-linear graphs (other than quadratics), quadratic expressions and equations, appear on Foundation papers, and think critically about the amount of teaching time spent on these for borderline grade 4/5 candidates.

#### What should you be teaching this year?

It is crucial that students’ basic algebra skills are secure, focusing on fluency and the ability to tackle procedural problems over significant amounts of problem-solving or rich content. I would consider spending less time on the less frequently occuring topics listed above, in favour of more time on graphs, sequences and functions, particularly as these are traditionally tackled poorly by candidates.

The 2018 Chief Examiner’s report states that “beyond drawing a simple graph of an equation, there appears to be little understanding of the relationship between equation[s] and graph[s], between graphs of parallel lines, or finding an equation from a straight-line graph.”

Although problem-solving in Foundation algebra is fairly limited, it is worth ensuring that grade 4/5 students can apply algebra skills to geometry problems (e.g. Nov21 1F Q16), many of which require them to form and solve an equation or inequality.

**Read more:**

**Don’t miss: **70+ GCSE maths revision guides for Algebra.

### 3. GCSE maths topic: Ratio and proportion

**Key topics**

- Context-rich problems requiring students to work flexibly with fractions, percentages and ratios.
- Splitting into a ratio and combining ratios, particularly in context.
- ‘Number-puzzle’ problems where students are asked to work out a missing amount when the other proportions are given as a mixture of fractions, percentages, and ratios (e.g. June 2018 P1 Q14).
- Time calculations, particularly misconceptions around fractions of an hour, and the use of a calculator for time problems.

**Infrequently appearing topics**

- Inverse proportion
- Real life graphs that
*aren’t*speed, distance and time

**What do we know from the GCSE paper analysis?**

There is a large amount of problem-solving at Foundation within Ratio and proportion, particularly direct proportion (recipes, best buys etc), using ratio notation, splitting into a ratio and combining ratios. Compound measures also contains a lot of problem-solving or context-based work, and has appeared on almost all series to date.

There are some topics that are more likely to be assessed procedurally, including:

- Distance- and speed-time graphs
- Standard measures (i.e. unit conversions)
- Proportion graphs
- Reverse percentages
- Simple and compound interest

**What should you be teaching this year?**

Speed, distance and time featured more heavily than other compound units work, such as pressure or density, and most real-life graph work also uses distance-time or speed-time graphs. That said, a strong understanding of all compound measures work is vital, particularly for students aiming for a grade 4 or above.

Addressing misconceptions around fractions of an hour, and the use of a calculator for time problems is also extremely useful. Quite a lot of the content here (such as compound measures, reverse percentages and repeated percentage change) tend to appear in crossover content towards the end of the paper, so these are crucial skills for grade 4 and 5 candidates.

**Don’t miss: **20+ GCSE maths revision guides for Ratio and Proportion.

### 4. GCSE maths topic: Geometry and measure

**Key topics**

- Perimeter, area and volume, particularly context-based problems
- Applying compound measures to shape problems (e.g. use density with volume of a shape)
- Scale drawing work and bearings
- Procedural work on 2D shape (such as polygons) and angle properties (particularly angles on a line, around a point, in a triangle) and vectors

##### Infrequently appearing topics

- Constructions and loci
- Trigonometry, particularly exact values
- 3D shape and angle properties
- Surface area and volume of spheres, cones and pyramids

#### What do we know from the GCSE paper analysis?

One thing that I noted from the Edexcel paper analysis was a large amount of problem-solving based around perimeter, area and volume. There were relatively few procedural problems, instead of real-life contexts and unfamiliar abstract situations. As well as ensuring students can reliably apply standard methods, they must be able to flexibly apply these skills to other problems.

#### What should you be teaching this year?

Students should be given plenty of practice on problem-solving and context-based problems in units on perimeter, area and volume. Typical contexts include:

- Calculating costs for fencing or boundaries (e.g. Jun18 2F Q19)
- Covering an area with grass seed, paving slabs or paint

Many similar shapes involved in area work are standard: squares, rectangles, triangles and circles, with less on compound shapes. Also featuring highly is crossover work with compound measures. Density and pressure are linked fairly frequently with volume or area calculations.

I would also recommend plenty of coverage on the correct use of mathematical equipment, such as scale drawing work and bearings, as these come up frequently for a fair number of marks, and students may have had varying degrees of success working on these remotely.

3D shape properties can represent easy wins, but come up relatively infrequently.

The traditionally ‘higher’ surface area and volume work, such as spheres, cones and pyramids, also comes up infrequently, so it might be advisable to skim this in favour of spending more time on, for example, problem-solving using circumference and area of a circle.

Read more:

Read more:

- Pythagoras Theorem Questions And Practice Problems (KS3 & KS4)
- Trigonometry Questions And Practice Problems (KS3 & KS4)

**Don’t miss: **125+ GCSE maths revision guides for Geometry and Measure.

### 5. GCSE maths topic: Probability

**Key topics**

- Procedural work on listing outcomes, Venn diagrams, frequency trees
- Application of fraction, decimal and ratio skills to problems about mutually exclusive events

##### Infrequently appearing topics

- Tree diagrams

#### What do we know from the GCSE paper analysis?

Like algebra, a significant amount of probability and statistics is assessed at Foundation in procedural, context-free ways. Again, there is less value in terms of exam preparation in spending lots of time on rich problems.

#### What should you be teaching for 2023?

In the probability strand, one topic that does attract a fair amount of non-standard problems is mutually exclusive events, which often embed skills using fractions or ratios, so it is worth focusing on problem-solving skills there.

Procedural work on ‘newer’ topics such as Venns, listing outcomes and frequency trees would be valuable, as these topics seem to appear frequently. In fact, frequency trees were heavily favoured over standard tree diagrams, so I would be tempted to skim the latter, plugging gaps once advance information has been released if necessary.

**Don’t miss**: 35+ revision guides for Probability.

### 6. GCSE maths topic: **Statistics**

**Key topics**

- Presenting data; drawing and interpreting a wide variety of graphs
- Estimating the mean

**Infrequently appearing topics**

- Frequency polygons
- Data collection and sampling

**What do we know from the GCSE paper analysis?**

Similar to algebra and probability, much of the statistics at Foundation level is assessed procedurally, so more focus should be given to procedural fluency over engaging with rich problems when considering exam preparation.

**What should you be teaching this year? **

In statistics, the emphasis is more heavily on presenting data rather than processing data, with equal focus on drawing or completing charts and graphs, and interpreting or critiquing existing representations. Pictograms and pie charts feature frequently, with fewer bar charts. Scatter graphs usually include a drawing and interpreting component. Estimating the mean comes up on quite a few papers. Data collection and sampling does not appear on every series, and questions can usually be answered in a fairly intuitive way.

**Don’t miss**: 40+ revision guides for Statistics.

**Read more:** Probability Questions And Practice Problems (KS3 & KS4).

### Teaching strategies for these GCSE maths topics

Based on analysis across all GCSE maths papers (Foundation) since 2017, the following points become clear:

- There needs to be a continued strong emphasis on number and proportion work, particularly in applying these in other contexts.
- Basic numeracy work needs to be continually revised and practised.
- Standard procedures, such as expanding, factorising, simplifying, and using formulae need work too.
- We need to ensure that students are familiar with connections within the Foundation content eg

– using linear equations to solve 2D shape and angle problems

– using fractions and ratios in probability calculations. - For lower-attaining students spend less time on rich content and problem-solving within those select topics in number, algebra, and most of statistics which are unlikely to come up in the exam.

### Recommended free resources to support these GCSE maths teaching strategies

- Use GCSE Fluent in Five Arithmetic Pack to build arithmetic skills and mathematical fluency through regular daily practice
- Or, in the settler/starter portion of the lesson, focus on five or ten key topics for a few weeks at a time; GCSE Exam Questions can help you here.
- When planning exam preparation in Year 11, continual, low-stakes formative assessment (regular mini-quizzes, or using the starting portion of the lesson for a Top 5/10) is more crucial than ever for identifying gaps in learning. These Diagnostic Questions are ideal for identifying misconceptions.

Have you got a group of students who need more targeted GCSE intervention strategies.

We are here to help! The best way to plug individual gaps is to give each student personalised and one to one tutoring for the support they may not be able to access in a class of 30.

Third Space Learning’s weekly online interventions feature an initial diagnostic assessment to identify the most impactful lessons from our GCSE maths revision programme for that particular student.

You can find out more about our GCSE maths revision programme here or book a call with one of our schools team.

### What GCSE maths topics appear in the first five questions at foundation?

The first five questions of Edexcel Foundation papers consist mainly of one-mark standard procedural questions. They’re designed to ease students into the paper, as well as testing key skills in a simple manner. Many of the topics in this section are absolutely fundamental to success in GCSE Maths, so these could be skills to target with frequent retrieval practice.

To summarise briefly, there is:

- A heavy skew towards Number topics
- Some inclusion of simple Algebra and Ratio and proportion topics
- Very little Geometry or Statistics, no Probability

The most frequently appearing topics are:

- Metric unit conversions
- Place value calculations
- Rounding to integers
- Ordering integers, fractions and decimals
- Factors and multiples
- Convert between FDP
- Find fractions of amounts
- Algebraic notation/simplify (easier)
- Order of operations
- Calculator use
- Square and cube numbers and their roots

For further detail and analysis read this: Edexcel GCSE maths topics and questions from the 2017-2023 papers.

### Which GCSE maths topics appear in the first ten questions at foundation?

Expanding to the first ten questions on the paper, we see a much wider range of topics cropping up. The next five questions (Q6-10) contain a much wider mix of topics, more reflective of the general proportions of the paper. Most lower-grade Foundation topics appear somewhere in here on one series or another, but there are a few very common topics or types of questions that crop up between question 6 and 10 on most papers. Interestingly, there is also a greater proportion of Statistics in Q6-10 compared to the whole paper.

The most frequently appearing topics in Q6-10 are:

- Money calculations
- Probability scale
- Using coordinates in four quadrants
- Bar chart
- Pictogram
- Time calculations
- One-step linear equations
- Simple averages and range
- Using correct algebraic notation
- Parts of a circle
- Angles at a point, on a line, vertically opposite

For further detail and analysis see Get Ahead In Foundation GCSE Maths With This Comprehensive Question & Topic Analysis Of GCSE Foundation Maths Papers 2017-2023.

### Which are the most common crossover questions?

Crossover or common questions are those which appear on both tiers of paper. On average, this is around 20-25 questions per series, split over three papers. So a typical Foundation paper will contain approximately 8 common questions (often split into parts), carrying nearly a third of the overall marks per paper.

The most frequently appearing common questions are on the following topics:

- Quadratic graphs
- Compound measures
- Standard form
- Scatter graphs
- HCF, LCM and PPF
- Pythagoras and trigonometry in RA triangles
- Writing as a ratio
- Ratio and fraction links
- Combining ratios
- Laws of indices
- Sets and Venns
- Angle facts and properties
- Fraction calculations

For more detailed analysis of the crossover portion of Edexcel’s exam papers, see my analysis piece: Get Ahead In Foundation GCSE Maths.

### Tiers of entry

When deciding tiers, it is worth bearing in mind that when the new specification came in in 2015, exam boards encouraged more Foundation entries, particularly those who would have previously been considered ‘weak grade Cs’. This messaging has not changed; exam boards are keen to dissuade Higher entries for candidates who will not be able to access the majority of the paper.

We can see that the most recent live exams have settled at just over 40% of candidates being entered for Higher, a large contrast to the pre-2015 specification, where over three-quarters of candidates were regularly entered for Higher.

A recent development relevant to tiering decisions is Ofsted’s Coordinating Mathematical Success report, which suggests that tiering decisions are being made too early, are restricting the KS4 curriculum and having a negative impact on students’ experience of mathematics. The report acknowledges that external pressures are often the driver of this, and it will be interesting the implementation of their recommendation that the DfE and Ofqual explore this further.

### Which GCSE maths topics should be taught to borderline candidates?

That said, it is definitely appropriate to leave tiering decisions later for some groups, particularly those identified in typical “borderline 4-5” teaching groups. For these students, a decent grasp of and fluency with all crossover content is vital. There are also some topics that appear on the Higher paper only that can be cherry-picked as easier marks, or often asked in more procedural ways. Generally speaking, you’re looking for topics that satisfy one of these criteria:

- Encountered at Foundation, but may be asked with more context, complexity or a deeper problem-solving element (such as reverse percentages).
- Build in small steps on key top-end skills at Foundation (such as expanding triple brackets).
- Higher-only stand alone content that’s accessible and is unlikely to be included in multi-topic problems (such as box plots or cumulative frequency).

This suggested starting topic list is based on the most frequently occuring, highest scoring topics in the first half of the Higher paper, excluding crossover content.

Topics in italics are Higher-only.

- Calculating using standard form, including context-based
- Laws of indices, including
*positive fractional powers*and simple negative powers *Product rule for counting*- Find and interpret gradient in context
- Simultaneous equations, including writing from contexts
*Expand triple brackets**Add and subtract algebraic fractions*- Compound interest and depreciation
- Percentage change and reverse percentages, usually with some element of problem-solving
- Density, mass, volume
- Use Pythagoras’ theorem in context
- Find missing sides and angles using trigonometry
- Similar areas and volumes
- Enlargements (positive
*and negative*scale factors) *Sine rule and cosine rule**Circle theorems*- Tree diagrams
*Box plots (draw and interpret)**Cumulative frequency graphs (draw, interpret, estimate values)*

**Read more:**

### Building maths skills for the future

There is a balance to be struck between preparing students for their GCSE maths exams and providing them with skills for onward life and study. We must be mindful that the sole purpose of education is not to enable students to pass exams. This point has been raised in the most recent mathematics subject report from Ofsted, who have some concerns about the extent to which external examinations are driving curriculum planning.

At GCSE level, a school-wide approach may be necessary, collaborating with colleagues to work out what skills are fundamental to success for post-16 study. This will depend on the school’s individual setting and demographic.

For example, it might be important to ensure that statistical content necessary for the study of AS/A Level Psychology is covered, or that students have sufficient algebra and graphing skills to be able to access A-level Sciences.

**Additional useful GCSE maths revision resources for schools**

As part of the Third Space Learning offer to schools, the personalised online GCSE maths tuition can be supplemented by hundreds of **free** GCSE maths revision resources from the secondary maths resources library including:

– GCSE maths past papers

– GCSE maths worksheets

– GCSE maths questions

– GCSE maths topic list

### GCSE maths topics FAQs

**How many topics are in GCSE maths?**

There are 6 main GCSE maths topics: Number, Algebra, Ratio, proportion and rates of change, Geometry and measure, Probability, Statistics.

**What are the hardest GCSE maths topics?**

The hardest GCSE maths topics vary from person to person but from our research the most complex questions are to be found in proportional reasoning, perimeter, area and volume, and substitution and formulae. Although students traditionally struggle with probability and statistics the questions asked in GCSE Mathematics are sometimes easier than in other topics.

**What are the 3 GCSE maths papers?**

The 3 GCSE maths papers are:

Paper 1: Non-Calculator

Paper 2: Calculator

Paper 3: Calculator

If you have followed the foundation syllabus these will all be foundation papers. If you’ve followed the higher tier syllabus the three papers will all be higher papers.

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Learn about the GCSE revision programme or request a personalised quote for your school to speak to us about your school’s needs and how we can help.