Lists of GCSE Maths Topics

Want to know what GCSE Maths topics you have to study for your exams? Maths is really a great choice for your GCSE, as it gives you many future benefits and various career opportunities. There are many GCSE MATHS TOPICS that you will be studying. But to make it short, GCSE has defined 5 fields in which they have included all the topics according to each field. These 5 fields are ‘Algebra’, ‘Probability and statistics’, ‘ratio, Proportion and rates of change’, ‘geometry and measures and ‘number’.

This blog will help you with all the information you are looking for on GCSE maths topics. Here, you will get a detailed understanding of each field. We will even mention the topics that you will be facing in your foundation batch and the ones in your Higher batch.

GCSE Maths Topics

There are three main 3 exams for GCSE maths in the UK, which include Edexcel person) AQA and OCR. All these exam boards must follow the set rules of the national curriculum, which is designed by the Department for Education; therefore, whatever you learn in your GCSE maths will stay the same for each exam.

The variations among the three exam boards are rather in the type of questions, the structure and marking of the exam, than the content itself. Nonetheless, as far as content is concerned, the Foundation and Higher levels have a lot to differ. These differences will be discussed as we consider the content under examination.

For all three 3 exams, the various topics that are covered in GCSE maths are combined into 5 fields. These 5 fields cover all the topics that you have to face in this subject.

1. Algebra

2. Number

3. Probability and Statistics

4. Ration, Proportion and rates of change

5. Geometry and Measures

Fields of GCSE Maths Topics

GCSE Maths topics are merged into 5 fields, each field representing its own nature of maths topics. In each field, there are two tiers: the first is the foundation tier, and the other is the higher tier. Topics in the foundation tier will be carried on in the Higher tier as well. You will gain an advanced level of knowledge of the same topics, and a few new topics will be added.

1. Number 

In GCSE mathematics, number is a basic subject area since it is the basis of numerical literacy. Topics in numbers include the learning of decimals, fractions, percentages, and arithmetic operations.

This, consequently, underlines more developed ideas like powers, standard form and properties of numbers.

The following table will be a summary of the various number topics taught at GCSE. There is a great similarity between the two Foundations and Higher, and a few significant differences exist between the tiers.

Whereas the Foundation level requires the use of the precise values, e.g. one should be able to compute the precise values with fractions or leave answers as 𝜋, at the Higher level, you are also expected to know how to use the surds in the computation.

Compared to the coverage of exam questions, about 15 per cent of questions in the exam paper that are of the Higher tier cover numbers content and about 25 per cent of the exam paper in the Foundation tier cover numbers content!

In Foundation, you will have to study the following topics:

• Number Toolkit, e.g., mathematical operations

• Types of Number, Prime Factors, HCF & LCM

• Powers, Roots & Standard Form

• Fractions

• Percentages

• Simple & Compound Interest, Growth & Decay

• Fractions, Decimals & Percentages

• Rounding, Estimation & Error Intervals

• Exact Values

• Using a Calculator

In the higher level, you will go through the same topics but at their advanced level, and one new topic will be added.

• Surds

2. Algebra

Another significant element in the GCSE maths curriculum is algebra. 

Despite the numerous topics of Algebra, which are taught at Foundation and Higher, there are undoubtedly more that are taught at Higher only. As an example, circle equations and graph transformations. 

More than this, even in the redundant material between the levels, subjects will frequently be covered to deeper levels at the Higher level than at the Foundation. As an example, algebraic reasoning is taught at the Foundation, and the algebraic formal proof is taught at the Higher level. 

This focus on algebraic ability is seen in that the Higher tier exams tend to contain a much greater proportion of algebraic content, about 30 versus about 20 with the Foundation tier exams. Here are the topics that you will be studying in the field of Algebra. 

Here are the Topics that you will be studying in your foundation of Algebra:

• Algebra Toolkit

• Algebraic Roots & Indices

• Expanding Brackets

• Factorising

• Rearranging Formulae

• Algebraic Reasoning

• Linear Equations

• Solving Quadratic Equations

• Simultaneous Equations

• Forming & Solving Equations

• Functions

• Coordinate Geometry

• Linear Graphs y = mx + c

• Graphs of Functions

• Real-Life Graphs

• Solving Inequalities

• Sequences

Among your foundation topics, at the higher level, these new topics will be added, although previous topics will be taught in more detail.

• Completing the Square

• Algebraic Fractions

• Algebraic Proof

• Iteration

• Equation of a Circle

• Estimating Gradients & Areas under Graphs

• Graphing Inequalities

• Transformations of Graphs

3. Ratio, Proportion and Rates of Change

Ratios, proportions and rates of change comprise about 25 per cent of the Foundation paper material and 20 per cent of the Higher paper material. They are questions which examine how quantities relate to one another. 

In this field, at both higher and foundation levels, you will be learning how to express ratios and solve equations using proportionality, with concepts of compound measure and unit conversions. Topics in both levels are the same; it's just at the higher level, you will be learning an advanced form of that which might be difficult from the foundation level. Let's understand this by example. At the foundation level, you will have to solve equations related to direct and inverse proportion of various quantities, whereas when you move to a higher level, you will be solving equations that even contain quantities that have powers.

Here are your topics for Foundation and higher level:

• Ratio Toolkit

• Ratio Problem Solving

• Direct & Inverse Proportion

• Standard & Compound Units

• Exchange Rates & Best Buys   

4. Geometry and Measures

In the field of geometry and measures, you will have the opportunity of learning the basics of shapes that are 2D and 3D, and you will go through the properties of each. Other than this, you will learn Pythagoras' theorem and transformation. Similar to other fields, there are many things that you will be further taught in higher level, like area and volume shapes and theorems of circles will be covered in the Higher tier. It even has some areas that are developed on the same lines as those of foundations to a higher level, for example, theorems related to Pythagoras and right-angled trigonometry for 2D shapes will be taught in the foundation, whereas 3D shapes will be taught in a higher level. 

The Foundation paper material that deals with these geometry and measures topics is about 15 per cent of the Foundation paper material, and the high paper material that deals with these is about 20 per cent, and the distribution of these is presented in the table below.

Topics that you will study in the Foundation level:

• Geometry Toolkit

• Angles in Polygons & Parallel Lines

• 2D & 3D Shapes

• Bearings, Scale Drawing, Constructions & Loci

• Area & Perimeter

• Circles, Arcs & Sectors

• Volume & Surface Area

• Congruence, Similarity & Geometrical Proof

• Pythagoras & Trigonometry

• Vectors

With all the foundation Topics, these new topics will also be added that you will study in your Higher level:

• Transformations

• Circle Theorems

• Area & Volume of Similar Shapes

• Right-Angled Triangles - Pythagoras & Trigonometry

• Sine, Cosine Rule & Area of Triangles

• 3D Pythagoras & Trigonometry

5. Probability and Statistics

The two are different fields of maths, but as two of the minor fields in the GCSE, one tends to lump them together. As a matter of fact, both the content in the Foundation paper and the Higher paper only address these two areas in about 15 per cent of the content. 

Foundation and higher level have the same topics just in an advanced level, but there will be some new topics as well, like Conditional probability, statistical diagrams, which will further include cumulative frequency of diagrams, histograms, and even box plots. 

Topics that you will study in your foundation level:

• Probability Toolkit

• Simple Probability Diagrams

• Tree Diagrams & Combined Probability

• Statistics Toolkit

• Statistical Diagrams

• Scatter Graphs & Correlation

Topics that will get added with your foundation level topics in your higher level:

• Combined & Conditional Probability

• Histograms

• Cumulative Frequency & Box Plots

What things are covered in the Different GCSE maths papers?

There is one answer to this question: every topic that is mentioned in this blog will be seen in all types of Papers. These three main bodies (AQA, Edexcel, and OCR) each have 3 exams, in which you are allowed to carry a calculator in two papers, and one is without a calculator. Topic which are covered in the paper where you are not allowed to carry a calculator includes fraction, expanding and factorising brackets, calculations, and for topic for higher-level topics are Surds. For other topics, you do not need to worry, as you have a calculator with you in these exams. Topics in which you can carry a calculator are compound interest, iteration and etc. However, you should note that the majority of the topics have not decided whether they will be a calculator or non-calculator paper, so you must prepare all topics without a calculator, so that you do not face any issue when you do not have a calculator. This will make you prepared for all types of situations. 

Conclusion

GCSE maths topics are indeed a lot, but they cover every aspect of maths, which will make it easy for you in future. As your base is clear with all these topics, whichever degree you want to pursue further in your career, you will surely benefit from the learning you have here. As mentioned in this blog, all 5 fields cover every aspect of mathematics. Number fields cover all decimals, fractions and many other topics; similarly, you have algebra, ratios, proportions and rates of change, geometry and measurements, and probability and statistics.