GCSE Maths Syllabus: A Clear & Simple Guide

10/08/2023 / Maths Tutoring

GCSE mathematics is crucial for so many reasons. It’s key in so many professions and provides a foundation for numerous other subjects such as science, geography and more. Of course, GCSE maths is also compulsory for all students in England, Wales and Northern Ireland.

However, the GCSE maths syllabus can be complex and hard to understand. That’s why we’re here to help with a simple guide to the topics learned in GCSE maths. With a read through our article today, you should be prepared to know exactly what you’ll face during your GCSE mathematics course.

GCSE maths differences in England, Wales and Northern Ireland

Before we start, it’s worth remembering that GCSEs in England, Wales and Northern Ireland work slightly differently. This handy graphic from the UK government outlines some of the main differences:

• Students in England will receive marks using the 1-9 grading system, and exams are taken only at the end of the course (linear qualification)
• Students in Wales will more often receive marks using the A*-G grading system, but sometimes might receive marks using the 1-9 system. Some GCSEs have grading that is based on modules during the course (modular qualification), while some use the linear qualification method
• Students in Northern Ireland might receive marks using either grading system and either qualification method, depending on the GCSE they take.

What’s more, the topics covered in the GCSE maths syllabus differ between exam specifications regulated by Ofqual in England, exams regulated by Qualifications Wales and exams regulated by the Council for the Curriculum Examinations and Assessment in Northern Ireland.

If this sounds confusing, don’t worry! We’ll break it all down for you.

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GCSE maths syllabus in England

If your GCSE exam specification is AQA, Edexcel, Eduqas or OCR, your GCSE maths syllabus will cover these six main topic categories:

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

Now let’s dig a little deeper to see what’s covered in each topic area. Topics covered are mostly the same for all four exam specifications mentioned above – we’ll highlight any points where there are differences.

Number

Number is a category covering some basic mathematical concepts, including things you’ll likely have studied in previous years like decimals and fractions. Within the topic of Number, you’ll study:

• Whole numbers
• Decimals
• Converting between fractions, decimals and percentages
• Approximation
• Fractions
• Multiples and factors (for OCR, this is multiples, factors, powers and roots)
• Laws of indices
• Standard form
• Surds (for Eduqas, Edexcel and OCR, this is only on the Higher tier paper)
• Financial mathematics

Algebra

Algebra of course includes algebraic formulae, but it also covers many kinds of graphs and graphical depictions of algebraic expressions. Within the topic of Algebra, you’ll study:

• Algebraic expressions
• Algebraic formulae
• Solving linear equations
• Solving simultaneous equations
• Solving quadratic equations
• Inequalities
• Sequences
• Straight line graphs
• Other graphs
• Transformation of curves (Higher tier paper only)
• Algebraic fractions
• Using and interpreting graphs

Ratio, proportion and rates of change

Ratio, proportion and rates of change is a smaller category. Within this topic, you’ll study:

• Ratio in context
• Percentages
• Direct and inverse proportion

Geometry and measure

Geometry and measure includes some simpler sub-topics such as 2-dimensional shapes as well as some more advanced ideas like trigonometry and vectors. Within the topic of Geometry and Measure, you’ll study:

• Angles, lines and polygons
• Loci and constructions
• 2-dimensional shapes
• 3-dimensional shapes (3-dimensional solids for OCR)
• Circles, sectors and arcs
• Circle theorems (Higher tier paper only)
• Transformations
• Pythagoras’ theorem
• Units of measure
• Trigonometry
• Vectors

Probability

For all four above exam boards, probability isn’t divided into sub-topics.

Statistics

And our last topic area is a small one, focused on practical uses of statistics:

• Collecting data
• Representing data
• Analysing data

GCSE maths syllabus in Wales

The WJEC exam specification has a syllabus that’s slightly different from the one outlined above. Its main categories are:

• Number
• Algebra
• Geometry and measure
• Statistics

In other words, the topic areas of probability and ratio, proportion and rates of change that are present in the above exam specifications aren’t used here. However, the some of the material in those areas is present but just organised under a different category. For example, “ratio” is listed under the “number” topic rather than in its own topic of “ratio, proportion and rates of change.”

We’ll explore the subtopics in the WJEC exam specification to see the differences. Keep in mind that WJEC has Foundation, Intermediate and Higher tier papers, so not all topics will be covered at all tiers.

Number

Number here is a smaller area than we’ve seen before. It includes:

• Prime factors
• Index notation
• Venn diagrams
• Standard form
• Ratio
• Approximate measurements (Intermediate and Higher tier paper only)
• Mathematical terminology

Algebra

• Equations of lines
• Equations of curves (Intermediate and Higher tier paper only)
• Basic algebra
• Equations and formulae
• Factorising (Intermediate and Higher tier paper only)
• Quadratic expressions (Intermediate and Higher tier paper only)
• Sequences
• Functions (Higher tier paper only)
• Inequalities (Intermediate and Higher tier paper only)
• Simultaneous equations (Intermediate and Higher tier paper only)

Geometry and measure

• Sector, segment and arc (Higher tier paper only)
• Loci and constructions
• Polygons
• Circles (Intermediate and Higher tier paper only)
• Transformations

Statistics

• Histograms (Higher tier paper only)
• Probability
• Further probability (Intermediate and Higher tier paper only)

GCSE maths syllabus in Northern Ireland

CCEA is the last exam specification we’ll look at, and this is used in Northern Ireland. This syllabus is interesting because it’s quite different from the ones we’ve looked at already. The main topic areas are:

• Number and algebra
• Geometry and measure
• Handling data.

Let’s delve a little deeper

Number and algebra

Many sub-topics fall within this category. They include:

• Whole numbers
• Decimals
• Fractions
• Percentages
• Converting decimals, fractions and percentages
• Approximation and estimation
• Multiples, factors, powers and roots
• Standard form (Higher tier paper only)
• Surds (Higher tier paper only)
• Personal finance
• Household finance
• Business finance
• Foreign money and exchange rates
• Binary
• Ratio in context
• Algebraic expressions
• Algebraic formulae
• Law of indices
• Solving linear equations
• Solving quadratic equations (Higher tier paper only)
• Solving simultaneous equations
• Trial and improvement
• Inequalities
• Sequences
• Straight line graphs
• Using and interpreting graphs
• Equations of circles (Higher tier paper only)
• Proportion and graphs
• Problem solving introduction
• Solving number problems
• Solving algebraic problems
• Solving graphical problems

Geometry and measure

Here’s another large category. It includes:

• Angles
• 2-dimensional shapes
• 3-dimensional shapes
• Circles, sectors and arcs
• Units of measure
• Timetables and schedules
• Pythagoras’ theorem
• Trigonometry (Higher tier paper only)
• Circle theorems (Higher tier paper only)
• Maps and scale drawings
• Bearings
• Polygons
• Transformations
• Congruent and similar shapes
• Constructions and loci
• Solving geometric problems

Handling data

The last category here includes just a few sub-topics:

• Collecting data
• Analysing data
• Representing data
• Probability
• Solving statistical problems

How to use your GCSE maths syllabus

There’s a lot of information to take in when it comes to GCSE maths, but we hope that our breakdown of the topics covered in the GCSE maths syllabus can help empower you to take control of your learning.

What’s the next step if you’re preparing for GCSE mathematics? Now that you know the learning goals that your teachers are aiming for, keep track of the topics you’re covering and consider how you’re feeling about each one.

Did the lesson go a little too quickly and you need to review? Was anything unclear? Or is this a topic that’s firmly under your belt, so you don’t need to worry about it any more? Being in charge of your learning this way will help you to feel more confident and to grow your skills by seeking help when you need it.

What if you decide that you do need more help? There are so many great resources on the internet for mathematics, including BBC Bitesize and Khan Academy on YouTube.

Working with an online GCSE mathematics tutor is another great option to boost your self-assurance and your skills in mathematics. Sometimes what you need is one-on-one time to ask questions and work through maths problems step by step. In this case, tutoring might be just right for you.

Finding the roadmap to GCSE maths success with Principal Tutors

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Ready to start conquering that GCSE maths syllabus with the help of a qualified tutor? You can get in touch with us by phone on 0800 772 0974, or just use our online form to get started requesting a tutor.