Everything you need to prepare for your GCSE (or IGCSE) maths exams. Below is a full list of topics and resources to revise Year 11 Maths at ease.
Note: This guide follows the Edexcel IGCSE curriculum. Other exam boards vary slightly.
Complete GCSE Topics
1. Changing the Subject of a Formula
| Learning Objective | Revision Resource | Practice |
| Be able to change the subject a formula. | Changing the Subject of the Formula Video | Changing the Subject Exam Questions Mark Scheme for above |
2 Algebra
Completing the Square
| Learning Objective | Revision Resource | Practice | Extension |
| Revision: Be able to factorise harder quadratics. (Year 10 topic) | Factorising Harder Quadratics | Factorising Harder Quadratics Exam Questions Mark Scheme for above | Revise all of Quadratics |
| Be able to complete the square for quadratic equations. | Completing the Square video | Completing the Square Transum 1 Completing the Square Transum 2 | Completing the Square Exam Questions |
Algebraic Proofs
| Learning Objective | Revision Resource | Practice | Extension |
| Be able to prove mathematical statements using algebraic logic. | Algebraic Proofs Video | Algebraic Proofs Exam Questions | Dr Austin Maths: Show That and Proof Questions Mark Scheme for Above |
Our top tips to improve your revision!
3. Upper and Lower Bounds
| Learning Objective | Revision Resource | Practice | Extension |
| Identify the upper and lower bounds on na value after it has been rounded, and express this as an inequality. | Upper and Lower Bounds Revision Video | Upper and Lower Bounds Transum Limits of Accuracy – Corbett Maths | |
| Apply upper and lower bounds to state the degree of accuracy of a calculated value. | (see above video) | Applying Limits of Accuracy Textbook Questions | Limits of Accuracy Exam Questions |
| Be able to answer a variety of GCSE questions on this topic. | Dr Frost Full Coverage: Bounds |
Casio ClassWizz Guide
Your calculator is your best friend. Make sure you learn how to use it effectively with our quick and easy guide! 😊
4. Trigonometry
Revise all of GCSE Trigonometry with our dedicated Trigonometry page! 🆕
Trigonometry for Non Right Angles Triangles
| Learning Objective | Revision Resource | Practice | Extension |
| Be able to use the Sine Rule to find lengths and angles of non triangles. | Sine Rule Video | Sine Rule Transum | |
| Be able to use the Sine Rule to find lengths and angles of non triangles. | Cosine Rule Video | Cosine Rule Transum | Sine and Cosine Rule Exam Questions |
| Be able to use the formula for the area of any triangle | Area of a Triangle Using Sine Video | Area of Triangle Using Sine Transum | Area of any Triangle Worksheet Grade 7+ Exam Style Questions Video |
3D Trigonometry
| Learning Objective | Revision Resource | Practice | Extension |
| Be able to visualise the distance and angles inside 3D objects. | Geogebra: Diagonal Distance in a Cuboid Geogebra: Angles in a Cuboid Geogebra: Angles in a Pyramid Use the links above to explore the distances and angles inside 3D objects. | ||
| Understand how to use Pythagoras to calculate distance in 3D | 3D Trigonometry Video | Transum: 3D Pythagoras | |
| Understand how to use trigonometry to calculate distances and angles in 3D. | See above | Transum: 3D SOHCAHTOA | Dr Austin Maths 3D Trig Practice Dr Austin MarkScheme |
| Solve problems involving trigonometry in 3D shapes. | See above | MathsGenie: 3D Trig MathsGenie Markscheme |
5. Solving Quadratic Equations
Revise all of Quadratics equations with our dedicated Quadratics page!
6. Arithmetic Sequences
🆕🎉Arithmetic Series revision page!
| Learning Objective | Revision Resource | Practice | Extension |
| Revision: Be able to find the nth term of an arithmetic sequence. | Nth term Revision Video | nth term transum | Sequences with Fractions Interwoven Maths |
| Be able to use the formula for the sum of an arithmetic sequence. | Sum of an arithmetic sequence Video. | Sum of an Arithmetic Sequence | |
| Be able to solve exam-style problems about arithmetic sequences. | (see above video) | Exam Style Questions on Arithmetic Sequences Maths Genie Addvance Maths Exams Questions! |
7. Vectors
| Learning Objective | Revision Resource | Practice | Extension |
| Know that vectors are like ‘arrows’, they have a magnitude and a direction. Know that a scalar refers to a simple number which can multiply vectors. | Introduction to Vectors Video | Vectors Worksheet | |
| Understand and use vector notation. | (see above video) | ||
| Be able to do basic operations with vectors, including: 1. Multiplying by a scalar 2. Factorising out a scalar. 3. Be able to add and subtract vectors. 4. Be able to calculate the magnitude of a vector. | (see above video) | Vectors Exam Questions | |
| Be able to understand how to split a vector in a given ratio. | (see below video) | ||
| Solve vector problems from exam questions. | Vector Problems Revision Video | ||
| Be able to prove geometrical properties using vectors. | Vector Proofs Revision Video | Vector Proofs MathsGenie Vector Proofs Exam Mark Scheme | |
| Be able to answer all possible exam questions on the vectors topic. | Dr Frost Full Coverage: Vectors |
8. Function Notation, Composite Functions and Inverse Functions
| Learning Objective | Revision Resource | Practice | Extension |
| Know and use function notation. | Functions and Composite Functions Video | Introduction to Functions Worksheet | |
| Be able to solve problems involving functions. | (See video above) | ||
| Understand the terms domain and range of a given function. | Functions: Domain and Range Revision Video | ||
| Be able to find a composite function, and solve problems relating to this. | Functions and Composite Functions Video | ||
| Be able to find an inverse function. | Inverse Functions Video | Exam Style Questions on Functions Dr Frost Full Coverage Functions |
Pause: Lets look back… is there something you’ve forgotten?
There are some topics in GCSE Maths that you would have studied back in Year 8, 9 and 10. These are easier topics, but still need to be revised. Check out these key topics below:
9. Graphs
Revise Straight Line Graphs!
Straight Line Graphs are a super important topic, make sure you revise the topic before we continue.
Quadratic, Reciprocal and Trigonometric Graphs
| Learning Objective | Revision Resource | Practice |
| Revision: Be able to plot and sketch quadratic and cubic graphs. | Plotting Quadratic Graphs Cubic Graphs Revision Video Quadratic Graphs Revision Video | Quadratic Graphs Exam Questions |
| Be able to recognise and plot reciprocal graphs. | Reciprocal Graphs Video | Reciprocal Graphs Exam Questions |
| Be able to recognise and plot sine, cosine and tangent graphs. | Sin, Cos and Tan Graphs Revision Video | Sine and Cos graphs MathsGenie Note: Exponential Graphs are included here, but are not on the IGCSE exam. Skip the exponential questions if you are doing IGCSE. |
| Use graphs to solve equations Know that the intersection of two curves is the solution to simultaneous equations. | Solving Equations on Graphs Simultaneous Equations on Graphs |
Graph Transformations
| Learning Objective | Revision Resource | Practice | Extension |
| Be able to sketch and recognise translations of graphs. Be able to identify the effect adding a constant to the function inside outside of the bracket will have. | Graph Transformations Translations Video | Graph Transformations Practice Questions | |
| Be able to sketch and recognise reflections of graphs. Be able to identify the effect a negative sign inside or outside of the brackets of a function will have. | Graph Transformations Reflections Video | (see above) | |
| Be able to sketch and recognise enlargements of graphs. Be able to identify the effect multiplying by a constant indie of outside of the brackets of a the function will have. | Graph Transformations Enlargements Video | (see above) | DrFrost Graph Transformations Worksheet |
| Be able to identify the effect of 2 transformations on a given function, and sketch the resulting curve. | Graph Transformations: Exam Questions Revision Video Transformations of Trigonometric Graphs Video | Transformations and Combinations of Transformations Transum |
Our Grade 7+ Guide for IGCSE and GCSE Maths!
Are you aiming high in GCSE Maths? Want a Grade 7, 8 or 9?
This is where you can find plenty of practice questions for those high level topics!
10. Quadratic Inequalities
| Learning Objective | Revision Resource | Practice |
| Solve quadratic inequalities, and represent their solutions as an inequality or on a number line. | Quadratic Inequalities Video | Transum Quadratic Inequalities Quadratic Inequalities Corbett Maths |
11. Differentiation
Note: Grade 4-6 students will struggle with the majority of this topic, however the first Learning Objective could be easy marks on the exam. The later sections of this topic are probably not worth practicing unless you are aiming for a Grade 8 or 9.
| Learning Objective | Revision Resource | Practice | Extension |
| Be able to differentiate polynomials. | Introduction to Differentiation Video | Differentiation Practice Transum Differentiation Practice 2 Transum | |
| Be able to find the gradient of a tangent by differentiating. | (see video above) | ||
| Be able to find stationary points by differentiation. | Stationary Points Revision Video | ||
| Be able to find the maximum or minimum of a value through differentiation. | Differentiation: Optimisation Video | ||
| Apply differentiation to kinematics and to other simple practical problems. | Differentiation: Kinematics | Differentiation IGCSE Questions Maths4Everyone (select Calculus in the drop down menu, then scroll to the differentiation questions) |
That’s all folks!
That’s the end of Year 11 Maths. You have now studied everything that could appear in IGCSE Maths. Well done!
It’s now time to revise weak topics and practice past papers. Good luck in your exams!
Further Maths?
Are you doing Further maths GCSE?
This is the revision guide for you, specifically for AQA Further Maths.
For more extension activities, please visit our UKMT resources page.
We also have a general page for more revision resources.
We hope this was useful, however we’d also appreciate your feedback.
Need help revising?
Aiming high? Check out these Grade 7+ Exam focus videos.
Have you revised everything?
You should now practice some Past Papers. You can find some here.
Disclaimer: This is a just a guide. Some schools may follow a different curriculum, and may teach different topics in different years. Addvance Maths is not responsible for content on external websites.
If you find an error, please let us know by emailing: addvancemaths@gmail.com
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