This collection covers essential GCSE maths topics you'll definitely encounter... Show more
Maths998 views·Updated May 28, 2026·6 pagesComprehensive GCSE AQA Maths Notes for Paper 3
E
Eren Gregg@renregg_deipnwscuzce
1 / 6
1
of 6
Algebraic Fractions
Working with algebraic fractions is just like handling regular fractions, but with letters thrown into the mix. The key is spotting the highest common factor and cancelling it out to simplify.
When you're adding or subtracting algebraic fractions, you need a common denominator first. If the denominators are the same, just add or subtract the numerators and keep the denominator unchanged.
For fractions with different denominators, multiply each fraction to create matching denominators. Then combine the numerators as usual.
Quick tip: Always look for common factors in brackets like – they cancel out just like numbers do!
2
of 6
Bounds and Probability
Bounds help you understand the range of possible values when numbers are rounded. For a number rounded to the nearest 10, remember the lower bound includes the equals sign, but the upper bound doesn't.
The product rule makes counting combinations dead simple – just multiply all your options together. Restaurant menus, dice combinations, clothing choices – it works for everything.
Probability calculations often use sample space diagrams (like the dice table shown). Count your successful outcomes, divide by total possible outcomes, and you've got your answer.
Remember: When finding bounds, think about what values would round to give your number – this helps you set the correct inequalities.
3
of 6
Interest and Iteration
Simple interest stays constant each year – just calculate the percentage once and multiply by the number of years. Compound interest grows because you earn interest on your previous interest too.
Iteration is a clever method for solving equations that are too tricky for normal algebra. You use a formula repeatedly, plugging each answer back in until the values stop changing.
The iteration process continues until your answers stabilise to the required number of decimal places. It's like mathematical trial and improvement, but much more systematic.
Pro tip: With compound interest, each year's calculation becomes the starting amount for the next year – that's where the "compounding" happens!
4
of 6
Line Equations and Bearings
Parallel lines share identical gradients – that's literally all you need to remember. Change the y-intercept, keep the gradient the same, and you've got a parallel line.
Perpendicular lines use negative reciprocal gradients. If your original gradient is 2, the perpendicular gradient becomes -1/2. Flip the fraction and change the sign.
Bearings follow three strict rules: measured from North, measured clockwise, and always written with three figures (like 045° instead of 45°).
Memory trick: Perpendicular gradients multiply together to give -1, so 2 × (-1/2) = -1.
5
of 6
Angles in Parallel Lines
When parallel lines are cut by a transversal, you get four types of angle relationships that are absolute exam favourites. Alternate angles are equal and sit in a 'Z' pattern.
Corresponding angles are equal and sit in an 'F' pattern. Vertically opposite angles are equal where two lines cross.
Co-interior angles (also called allied angles) are different – they add up to 180° and sit in a 'C' pattern between the parallel lines.
Exam hack: Learn to spot these patterns quickly – angle questions often test multiple relationships in one diagram.
6
of 6
We thought you’d never ask...
What is the Knowunity AI companion?
Our AI Companion is a student-focused AI tool that offers more than just answers. Built on millions of Knowunity resources, it provides relevant information, personalised study plans, quizzes, and content directly in the chat, adapting to your individual learning journey.
Where can I download the Knowunity app?
You can download the app from Google Play Store and Apple App Store.
Is Knowunity really free of charge?
That's right! Enjoy free access to study content, connect with fellow students, and get instant help – all at your fingertips.
Similar content
Most popular content in Maths
9MathsComprehensive Maths Concepts
Explore essential mathematical concepts including powers, geometry, statistics, and probability. This resource features 65 pages of detailed explanations, diagrams, and examples to enhance your understanding of topics such as right triangles, volume calculations, and data representation. Ideal for students seeking to strengthen their numeracy skills and grasp complex mathematical principles.
1079,7556,318
MathsGCSE Maths (Higher) // Revision Guide
The only GCSE maths (higher) revision guide you need to get a grade 9! Contains every topic, each with all potential question types and their solutions.
102,33054
M
MathsMedium Level alerbra
Master challenging maths concepts with this medium level flashcard set designed for grade 7/8 students. Strengthen your problem-solving skills and boost your confidence in maths!
75533
MathsComprehensive Maths Concepts
Explore essential mathematical concepts including polynomial theorems, logarithmic properties, trigonometric functions, and integration techniques. This resource covers everything from solving inequalities to understanding exponential functions, providing a solid foundation for A-level mathematics. Ideal for students aiming for top grades.
1221,9901,818
M
MathsMastering Maths: Essential Concepts for Grade 10
Boost your math skills with this comprehensive flashcard set covering key concepts for grade 10. Perfect for exam preparation and building a strong foundation in mathematics.
104261
M
MathsMastering Medium-Level Maths: Essential Flashcards for Grade 11 Students
Boost your Maths skills with this comprehensive set of flashcards designed specifically for Grade 11 students. Covering medium-level topics, these cards will help you ace your exams and build a solid foundation for advanced Maths.
118823
MathsComprehensive Maths Concepts
Explore essential higher mathematics concepts including calculus, trigonometry, polynomials, and vector analysis. This summary covers key topics such as differentiation, integration, quadratic equations, and the properties of circles, providing a solid foundation for exam preparation. Ideal for students seeking a concise yet thorough review of advanced mathematical principles.
S51,93757
P
MathsPercentage,fractions and decimals
how well do you know percentages,fractions and decimals
72703
M
Mathsmaths SOHCAHTOA
Trigonometric ratios SOHCAHTOA for calculating angles and sides in right-angled triangles.
111740
Most popular content
9
SociologySociology of Education Overview
Explore comprehensive A-Level Sociology notes on the education system, covering key theories, policies, and sociological perspectives. This resource includes insights on marketisation, gender roles, cultural deprivation, and educational inequalities, providing a thorough understanding of how education shapes social stratification and individual achievement. Ideal for exam preparation and in-depth study.
12102,3893,038
CriminologyCriminology: Crime & Punishment Overview
Comprehensive mindmaps covering key concepts in the Crime and Punishment topic for WJEC Criminology Unit 4. This resource includes detailed insights into the Criminal Justice System, crime prevention strategies, sentencing models, and the roles of various agencies. Ideal for A-Level revision, ensuring you grasp essential theories and legislative processes to excel in your exams.
1254,8131,059
SociologySociology of Families: Comprehensive Revision
Dive into an extensive overview of family dynamics, perspectives, and patterns in sociology. This resource covers key concepts such as family diversity, gender roles, marriage, and the impact of social policies on family structures. Perfect for A-Level Sociology students preparing for Paper 2.
1273,2392,304
English LiteratureAn Inspector Calls: Character Insights
Explore in-depth analysis and key quotes for characters in J.B. Priestley's 'An Inspector Calls'. This resource covers Gerald Croft, Inspector Goole, Sheila Birling, Mrs. Birling, Eric Birling, and Eva Smith, focusing on themes of class, gender roles, and social responsibility. Ideal for students aiming for Grade 8 and above.
1025,231901
CriminologyWJEC Unit 4 Criminology
Criminology unit 4 detailed revision note
127,120124
CriminologyCriminology Theories Overview
Explore key criminology theories and their implications on crime and deviance. This comprehensive summary covers biological, psychological, and sociological perspectives, including labelling theory, right realism, and the impact of social campaigns on policy development. Ideal for A-Level criminology students seeking to understand the complexities of criminal behaviour and the factors influencing crime prevention strategies.
129,746211
English LiteratureRomeo and Juliet: Key themes
Key Romeo and Juliet themes and analysed quotes
106,619197
C
BiologyCell Biology and Cell structure
cell structures
92,6560
English LiteratureMacbeth: Guilt and Ambition
Explore the complex themes of guilt and ambition in Shakespeare's 'Macbeth'. This analysis covers key characters, including Macbeth and Lady Macbeth, their moral dilemmas, and the tragic consequences of their ambition. Ideal for students studying character motivations, thematic elements, and the psychological impact of power. Includes insights on the natural order, manipulation, and the descent into madness.
918,818392
Can't find what you're looking for? Explore other subjects.
Students love us — and so will you.
4.6/5App Store
4.7/5Google Play
The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
Stefan SiOS user
This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha KlichAndroid user
Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
AnnaiOS user
Maths998 views·Updated May 28, 2026·6 pagesComprehensive GCSE AQA Maths Notes for Paper 3
E
Eren Gregg@renregg_deipnwscuzce
This collection covers essential GCSE maths topics you'll definitely encounter in your exams. From algebraic fractions to circle geometry, these concepts build on each other and appear regularly in both coursework and final assessments.
1
of 6Sign up to see the content. It's free!
- Access to all documents
- Improve your grades
- Join milions of students
Algebraic Fractions
Working with algebraic fractions is just like handling regular fractions, but with letters thrown into the mix. The key is spotting the highest common factor and cancelling it out to simplify.
When you're adding or subtracting algebraic fractions, you need a common denominator first. If the denominators are the same, just add or subtract the numerators and keep the denominator unchanged.
For fractions with different denominators, multiply each fraction to create matching denominators. Then combine the numerators as usual.
Quick tip: Always look for common factors in brackets like – they cancel out just like numbers do!
2
of 6Sign up to see the content. It's free!
- Access to all documents
- Improve your grades
- Join milions of students
Bounds and Probability
Bounds help you understand the range of possible values when numbers are rounded. For a number rounded to the nearest 10, remember the lower bound includes the equals sign, but the upper bound doesn't.
The product rule makes counting combinations dead simple – just multiply all your options together. Restaurant menus, dice combinations, clothing choices – it works for everything.
Probability calculations often use sample space diagrams (like the dice table shown). Count your successful outcomes, divide by total possible outcomes, and you've got your answer.
Remember: When finding bounds, think about what values would round to give your number – this helps you set the correct inequalities.
3
of 6Sign up to see the content. It's free!
- Access to all documents
- Improve your grades
- Join milions of students
Interest and Iteration
Simple interest stays constant each year – just calculate the percentage once and multiply by the number of years. Compound interest grows because you earn interest on your previous interest too.
Iteration is a clever method for solving equations that are too tricky for normal algebra. You use a formula repeatedly, plugging each answer back in until the values stop changing.
The iteration process continues until your answers stabilise to the required number of decimal places. It's like mathematical trial and improvement, but much more systematic.
Pro tip: With compound interest, each year's calculation becomes the starting amount for the next year – that's where the "compounding" happens!
4
of 6Sign up to see the content. It's free!
- Access to all documents
- Improve your grades
- Join milions of students
Line Equations and Bearings
Parallel lines share identical gradients – that's literally all you need to remember. Change the y-intercept, keep the gradient the same, and you've got a parallel line.
Perpendicular lines use negative reciprocal gradients. If your original gradient is 2, the perpendicular gradient becomes -1/2. Flip the fraction and change the sign.
Bearings follow three strict rules: measured from North, measured clockwise, and always written with three figures (like 045° instead of 45°).
Memory trick: Perpendicular gradients multiply together to give -1, so 2 × (-1/2) = -1.
5
of 6Sign up to see the content. It's free!
- Access to all documents
- Improve your grades
- Join milions of students
Angles in Parallel Lines
When parallel lines are cut by a transversal, you get four types of angle relationships that are absolute exam favourites. Alternate angles are equal and sit in a 'Z' pattern.
Corresponding angles are equal and sit in an 'F' pattern. Vertically opposite angles are equal where two lines cross.
Co-interior angles (also called allied angles) are different – they add up to 180° and sit in a 'C' pattern between the parallel lines.
Exam hack: Learn to spot these patterns quickly – angle questions often test multiple relationships in one diagram.
6
of 6Sign up to see the content. It's free!
- Access to all documents
- Improve your grades
- Join milions of students
We thought you’d never ask...
What is the Knowunity AI companion?
Our AI Companion is a student-focused AI tool that offers more than just answers. Built on millions of Knowunity resources, it provides relevant information, personalised study plans, quizzes, and content directly in the chat, adapting to your individual learning journey.
Where can I download the Knowunity app?
You can download the app from Google Play Store and Apple App Store.
Is Knowunity really free of charge?
That's right! Enjoy free access to study content, connect with fellow students, and get instant help – all at your fingertips.
Similar content
Most popular content in Maths
9MathsComprehensive Maths Concepts
Explore essential mathematical concepts including powers, geometry, statistics, and probability. This resource features 65 pages of detailed explanations, diagrams, and examples to enhance your understanding of topics such as right triangles, volume calculations, and data representation. Ideal for students seeking to strengthen their numeracy skills and grasp complex mathematical principles.
1079,7556,318
MathsGCSE Maths (Higher) // Revision Guide
The only GCSE maths (higher) revision guide you need to get a grade 9! Contains every topic, each with all potential question types and their solutions.
102,33054
M
MathsMedium Level alerbra
Master challenging maths concepts with this medium level flashcard set designed for grade 7/8 students. Strengthen your problem-solving skills and boost your confidence in maths!
75533
MathsComprehensive Maths Concepts
Explore essential mathematical concepts including polynomial theorems, logarithmic properties, trigonometric functions, and integration techniques. This resource covers everything from solving inequalities to understanding exponential functions, providing a solid foundation for A-level mathematics. Ideal for students aiming for top grades.
1221,9901,818
M
MathsMastering Maths: Essential Concepts for Grade 10
Boost your math skills with this comprehensive flashcard set covering key concepts for grade 10. Perfect for exam preparation and building a strong foundation in mathematics.
104261
M
MathsMastering Medium-Level Maths: Essential Flashcards for Grade 11 Students
Boost your Maths skills with this comprehensive set of flashcards designed specifically for Grade 11 students. Covering medium-level topics, these cards will help you ace your exams and build a solid foundation for advanced Maths.
118823
MathsComprehensive Maths Concepts
Explore essential higher mathematics concepts including calculus, trigonometry, polynomials, and vector analysis. This summary covers key topics such as differentiation, integration, quadratic equations, and the properties of circles, providing a solid foundation for exam preparation. Ideal for students seeking a concise yet thorough review of advanced mathematical principles.
S51,93757
P
MathsPercentage,fractions and decimals
how well do you know percentages,fractions and decimals
72703
M
Mathsmaths SOHCAHTOA
Trigonometric ratios SOHCAHTOA for calculating angles and sides in right-angled triangles.
111740
Most popular content
9SociologySociology of Education Overview
Explore comprehensive A-Level Sociology notes on the education system, covering key theories, policies, and sociological perspectives. This resource includes insights on marketisation, gender roles, cultural deprivation, and educational inequalities, providing a thorough understanding of how education shapes social stratification and individual achievement. Ideal for exam preparation and in-depth study.
12102,3893,038
CriminologyCriminology: Crime & Punishment Overview
Comprehensive mindmaps covering key concepts in the Crime and Punishment topic for WJEC Criminology Unit 4. This resource includes detailed insights into the Criminal Justice System, crime prevention strategies, sentencing models, and the roles of various agencies. Ideal for A-Level revision, ensuring you grasp essential theories and legislative processes to excel in your exams.
1254,8131,059
SociologySociology of Families: Comprehensive Revision
Dive into an extensive overview of family dynamics, perspectives, and patterns in sociology. This resource covers key concepts such as family diversity, gender roles, marriage, and the impact of social policies on family structures. Perfect for A-Level Sociology students preparing for Paper 2.
1273,2392,304
English LiteratureAn Inspector Calls: Character Insights
Explore in-depth analysis and key quotes for characters in J.B. Priestley's 'An Inspector Calls'. This resource covers Gerald Croft, Inspector Goole, Sheila Birling, Mrs. Birling, Eric Birling, and Eva Smith, focusing on themes of class, gender roles, and social responsibility. Ideal for students aiming for Grade 8 and above.
1025,231901
CriminologyWJEC Unit 4 Criminology
Criminology unit 4 detailed revision note
127,120124
CriminologyCriminology Theories Overview
Explore key criminology theories and their implications on crime and deviance. This comprehensive summary covers biological, psychological, and sociological perspectives, including labelling theory, right realism, and the impact of social campaigns on policy development. Ideal for A-Level criminology students seeking to understand the complexities of criminal behaviour and the factors influencing crime prevention strategies.
129,746211
English LiteratureRomeo and Juliet: Key themes
Key Romeo and Juliet themes and analysed quotes
106,619197
C
BiologyCell Biology and Cell structure
cell structures
92,6560
English LiteratureMacbeth: Guilt and Ambition
Explore the complex themes of guilt and ambition in Shakespeare's 'Macbeth'. This analysis covers key characters, including Macbeth and Lady Macbeth, their moral dilemmas, and the tragic consequences of their ambition. Ideal for students studying character motivations, thematic elements, and the psychological impact of power. Includes insights on the natural order, manipulation, and the descent into madness.
918,818392
Can't find what you're looking for? Explore other subjects.
Students love us — and so will you.
4.6/5App Store
4.7/5Google Play
The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
Stefan SiOS user
This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha KlichAndroid user
Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
AnnaiOS user