This maths revision guide covers essential GCSE topics you'll encounter... Show more
Maths102 views·Updated May 24, 2026·9 pagesComprehensive GCSE Math Notes
Charlotte@charlotte26
1 / 9
1
of 9
Inequalities - The Basics
Ever wondered how to show that something is "greater than" or "at least" a certain value? Inequalities are your answer! They're like equations but instead of being exactly equal, they show relationships between values.
The symbols are pretty straightforward: > means greater than, < means less than, and adding an equals sign (≥ or ≤) means "or equal to" as well. When you're graphing these, remember that solid lines represent ≥ or ≤, whilst dotted lines show > or <.
💡 Quick tip: On number lines, use open circles (○) for > or < and closed circles (●) for ≥ or ≤. The length of your line doesn't matter - it's all about showing the direction!
Solving inequalities works just like equations - you can add, subtract, multiply or divide both sides. Just remember to flip the inequality sign if you multiply or divide by a negative number!
2
of 9
Bearings - Finding Your Way
Think of bearings like a compass reading that tells you exactly which direction something is. They're measured clockwise from north and always written as three figures (so 45° becomes 045°).
Here's the key trick: when finding bearings, always draw your north line from the point you're measuring from. If you're finding the bearing of point A from point B, draw north from B, then measure clockwise to A.
💡 Remember: If you need to find the bearing "back" (like B from A when you know A from B), add or subtract 180° to find the opposite direction. It's like turning around completely!
The three-figure rule is crucial for exams - even if your angle is just 45°, you must write it as 045°. Those zeros at the front matter!
3
of 9
Essential Maths Skills - Paper 2 Revision
Error intervals might seem tricky, but they're just about understanding rounding. If 6 is rounded to 1 decimal place, it could have been anything from 5.95 to 6.05 (but we write this as 6.0 ≤ x < 6.1).
Index laws are your best friend for simplifying expressions. Remember that anything to the power of 1 equals itself, and when multiplying powers with the same base, you add the indices. When dividing, you subtract them.
💡 Calculator tip: Always close your brackets properly and write down all the numbers before rounding. This prevents silly mistakes that cost marks!
Expanding brackets follows the same pattern every time - multiply everything in the first bracket by everything in the second. For factorising, look for common factors you can take out, like taking 3 out of 3x + 15 to get 3.
4
of 9
Equations and Quadratic Inequalities
Solving linear equations is all about doing the same thing to both sides. Your goal is to get the letter on its own, so work backwards through the order of operations. If there are letters on both sides, collect them together first.
Word problems become easier when you define your variables clearly. If Chris is x years old and Adam is 8 years older, then Adam is x + 8. Always check your answer makes sense in the original problem!
💡 Parallel lines trick: Lines are parallel when they have the same gradient (the number before x). Rearrange equations into y = mx + c form to spot this quickly.
Quadratic inequalities give you a range of answers rather than just one value. Factorise the quadratic, find where it equals zero, then test which region satisfies your inequality. The answer will be between or outside these values.
5
of 9
Sequences and Algebraic Fractions
Linear sequences have a constant difference between terms. To find the nth term, work out this common difference, then adjust for the first term. For 3, 7, 11, 15... the difference is 4, so the nth term is 4n - 1.
Quadratic sequences are trickier - their differences aren't constant, but the second differences are. Start with n², then adjust to match your sequence. Fibonacci sequences simply add the two previous terms together.
💡 Sequence tip: Always check your nth term formula by substituting n = 1, 2, 3... to see if you get the original sequence back.
Algebraic fractions work just like number fractions. To simplify, factorise the top and bottom, then cancel common factors. When adding or subtracting, find a common denominator first - usually by multiplying the denominators together.
6
of 9
Functions and Real-Life Maths
Inverse functions undo what the original function does. To find f⁻¹(x), swap x and y in your equation, then rearrange to make y the subject. It's like working backwards through the function's steps.
Composite functions like gf(x) mean "do f first, then g". Substitute the entire f(x) expression into g(x). Be careful with your algebra when expanding - it's easy to make sign errors!
💡 Function tip: Always substitute carefully and show each step clearly. Examiners love to see your working, especially with composite functions.
Depreciation problems are just repeated percentage decreases. Each year, the car keeps 80% of its value (if it depreciates by 20%). You can multiply by 0.8 repeatedly or use the formula: original value × (multiplier)ⁿ.
7
of 9
Proportionality and Currency
Currency conversion requires careful attention to exchange rates. Always check which currency gives better value by converting both to the same currency. Don't forget that £1 = $1.29 means you multiply pounds by 1.29 to get dollars.
Direct proportion means as one quantity increases, the other increases at the same rate. If y ∝ x, then y = kx where k is your constant. Use given values to find k, then use it to find unknown values.
💡 Proportion tip: Write down your relationship clearly before substituting numbers. This prevents confusion between direct and inverse proportion.
Inverse proportion is the opposite - as one increases, the other decreases. If A ∝ 1/B, then A = k/B. The key is identifying which type of relationship you're dealing with from the context.
8
of 9
Advanced Topics - Pressure and Circle Theorems
Pressure calculations use the formula Pressure = Force ÷ Area. Watch out for unit conversions - you might need to convert cm² to m² by dividing by 10,000 .
Circle theorems are essential geometry rules. Angles in the same segment are equal, the angle in a semicircle is 90°, and the angle between a tangent and radius is always 90°.
💡 Circle theorem tip: Always mark equal angles with the same symbols and clearly state which theorem you're using. Examiners want to see you know the rules!
The alternate segment theorem states that the angle between a tangent and chord equals the angle in the alternate segment. These theorems often combine, so look for multiple relationships in complex diagrams.
9
of 9
Statistics - Box Plots and Data Analysis
Box plots show five key values: minimum, lower quartile, median, upper quartile, and maximum. The interquartile range (IQR) is UQ - LQ and shows how spread out the middle 50% of data is.
When comparing box plots, discuss both average (median) and consistency (IQR or range). A higher median means higher average values, whilst a smaller IQR means more consistent data.
💡 Statistics tip: Always relate your statistical comments back to the real-world context of the problem. Don't just say "the median is higher" - explain what this means in practical terms.
Stem and leaf diagrams organise data clearly whilst preserving original values. Always include a key and remember to order the leaves from smallest to largest. They make finding the mode, median, and range much easier.
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.
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.
1079,7766,318
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
92,6740
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
Maths102 views·Updated May 24, 2026·9 pagesComprehensive GCSE Math Notes
Charlotte@charlotte26
This maths revision guide covers essential GCSE topics you'll encounter in your exams. From inequalities and bearings to functions and statistics, these concepts form the backbone of your mathematical toolkit.
1
of 9Sign up to see the content. It's free!
- Access to all documents
- Improve your grades
- Join milions of students
Inequalities - The Basics
Ever wondered how to show that something is "greater than" or "at least" a certain value? Inequalities are your answer! They're like equations but instead of being exactly equal, they show relationships between values.
The symbols are pretty straightforward: > means greater than, < means less than, and adding an equals sign (≥ or ≤) means "or equal to" as well. When you're graphing these, remember that solid lines represent ≥ or ≤, whilst dotted lines show > or <.
💡 Quick tip: On number lines, use open circles (○) for > or < and closed circles (●) for ≥ or ≤. The length of your line doesn't matter - it's all about showing the direction!
Solving inequalities works just like equations - you can add, subtract, multiply or divide both sides. Just remember to flip the inequality sign if you multiply or divide by a negative number!
2
of 9Sign up to see the content. It's free!
- Access to all documents
- Improve your grades
- Join milions of students
Bearings - Finding Your Way
Think of bearings like a compass reading that tells you exactly which direction something is. They're measured clockwise from north and always written as three figures (so 45° becomes 045°).
Here's the key trick: when finding bearings, always draw your north line from the point you're measuring from. If you're finding the bearing of point A from point B, draw north from B, then measure clockwise to A.
💡 Remember: If you need to find the bearing "back" (like B from A when you know A from B), add or subtract 180° to find the opposite direction. It's like turning around completely!
The three-figure rule is crucial for exams - even if your angle is just 45°, you must write it as 045°. Those zeros at the front matter!
3
of 9Sign up to see the content. It's free!
- Access to all documents
- Improve your grades
- Join milions of students
Essential Maths Skills - Paper 2 Revision
Error intervals might seem tricky, but they're just about understanding rounding. If 6 is rounded to 1 decimal place, it could have been anything from 5.95 to 6.05 (but we write this as 6.0 ≤ x < 6.1).
Index laws are your best friend for simplifying expressions. Remember that anything to the power of 1 equals itself, and when multiplying powers with the same base, you add the indices. When dividing, you subtract them.
💡 Calculator tip: Always close your brackets properly and write down all the numbers before rounding. This prevents silly mistakes that cost marks!
Expanding brackets follows the same pattern every time - multiply everything in the first bracket by everything in the second. For factorising, look for common factors you can take out, like taking 3 out of 3x + 15 to get 3.
4
of 9Sign up to see the content. It's free!
- Access to all documents
- Improve your grades
- Join milions of students
Equations and Quadratic Inequalities
Solving linear equations is all about doing the same thing to both sides. Your goal is to get the letter on its own, so work backwards through the order of operations. If there are letters on both sides, collect them together first.
Word problems become easier when you define your variables clearly. If Chris is x years old and Adam is 8 years older, then Adam is x + 8. Always check your answer makes sense in the original problem!
💡 Parallel lines trick: Lines are parallel when they have the same gradient (the number before x). Rearrange equations into y = mx + c form to spot this quickly.
Quadratic inequalities give you a range of answers rather than just one value. Factorise the quadratic, find where it equals zero, then test which region satisfies your inequality. The answer will be between or outside these values.
5
of 9Sign up to see the content. It's free!
- Access to all documents
- Improve your grades
- Join milions of students
Sequences and Algebraic Fractions
Linear sequences have a constant difference between terms. To find the nth term, work out this common difference, then adjust for the first term. For 3, 7, 11, 15... the difference is 4, so the nth term is 4n - 1.
Quadratic sequences are trickier - their differences aren't constant, but the second differences are. Start with n², then adjust to match your sequence. Fibonacci sequences simply add the two previous terms together.
💡 Sequence tip: Always check your nth term formula by substituting n = 1, 2, 3... to see if you get the original sequence back.
Algebraic fractions work just like number fractions. To simplify, factorise the top and bottom, then cancel common factors. When adding or subtracting, find a common denominator first - usually by multiplying the denominators together.
6
of 9Sign up to see the content. It's free!
- Access to all documents
- Improve your grades
- Join milions of students
Functions and Real-Life Maths
Inverse functions undo what the original function does. To find f⁻¹(x), swap x and y in your equation, then rearrange to make y the subject. It's like working backwards through the function's steps.
Composite functions like gf(x) mean "do f first, then g". Substitute the entire f(x) expression into g(x). Be careful with your algebra when expanding - it's easy to make sign errors!
💡 Function tip: Always substitute carefully and show each step clearly. Examiners love to see your working, especially with composite functions.
Depreciation problems are just repeated percentage decreases. Each year, the car keeps 80% of its value (if it depreciates by 20%). You can multiply by 0.8 repeatedly or use the formula: original value × (multiplier)ⁿ.
7
of 9Sign up to see the content. It's free!
- Access to all documents
- Improve your grades
- Join milions of students
Proportionality and Currency
Currency conversion requires careful attention to exchange rates. Always check which currency gives better value by converting both to the same currency. Don't forget that £1 = $1.29 means you multiply pounds by 1.29 to get dollars.
Direct proportion means as one quantity increases, the other increases at the same rate. If y ∝ x, then y = kx where k is your constant. Use given values to find k, then use it to find unknown values.
💡 Proportion tip: Write down your relationship clearly before substituting numbers. This prevents confusion between direct and inverse proportion.
Inverse proportion is the opposite - as one increases, the other decreases. If A ∝ 1/B, then A = k/B. The key is identifying which type of relationship you're dealing with from the context.
8
of 9Sign up to see the content. It's free!
- Access to all documents
- Improve your grades
- Join milions of students
Advanced Topics - Pressure and Circle Theorems
Pressure calculations use the formula Pressure = Force ÷ Area. Watch out for unit conversions - you might need to convert cm² to m² by dividing by 10,000 .
Circle theorems are essential geometry rules. Angles in the same segment are equal, the angle in a semicircle is 90°, and the angle between a tangent and radius is always 90°.
💡 Circle theorem tip: Always mark equal angles with the same symbols and clearly state which theorem you're using. Examiners want to see you know the rules!
The alternate segment theorem states that the angle between a tangent and chord equals the angle in the alternate segment. These theorems often combine, so look for multiple relationships in complex diagrams.
9
of 9Sign up to see the content. It's free!
- Access to all documents
- Improve your grades
- Join milions of students
Statistics - Box Plots and Data Analysis
Box plots show five key values: minimum, lower quartile, median, upper quartile, and maximum. The interquartile range (IQR) is UQ - LQ and shows how spread out the middle 50% of data is.
When comparing box plots, discuss both average (median) and consistency (IQR or range). A higher median means higher average values, whilst a smaller IQR means more consistent data.
💡 Statistics tip: Always relate your statistical comments back to the real-world context of the problem. Don't just say "the median is higher" - explain what this means in practical terms.
Stem and leaf diagrams organise data clearly whilst preserving original values. Always include a key and remember to order the leaves from smallest to largest. They make finding the mode, median, and range much easier.
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.
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.
1079,7766,318
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
92,6740
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