This collection covers essential GCSE maths topics you'll definitely encounter...
Maths1,011 views·Updated 20 Aug 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.
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
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Maths1,011 views·Updated 20 Aug 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.
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of 6
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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
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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
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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
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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.
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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.
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We thought you’d never ask...
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.
You can download the app from Google Play Store and Apple App Store.
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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.
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Explore the fundamentals of trigonometry, including the tangent, sine, and cosine functions. This summary covers key concepts such as SOH CAH TOA, trigonometric ratios, and methods for finding angles and sides in right triangles. Ideal for students preparing for exams or needing a quick reference.
91,77159
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.
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MathsGCSE Maths 2018 Exam Insights
Explore the key concepts from the 2018 GCSE Maths Paper 2, including compound interest, probability, standard form, and geometric transformations. This comprehensive summary covers essential topics such as interest rates, area calculations, and Venn diagrams, providing students with a clear understanding of the exam's requirements. Ideal for exam preparation and practice.
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MathsUnderstanding Surds
Explore the concept of surds, including their definition, examples, and methods for simplifying them. This summary covers key techniques for simplifying surds, such as identifying square factors and combining terms. Ideal for students looking to master radical expressions and enhance their understanding of square roots.
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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.
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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