Master the essential maths formulas you'll need for your GCSE...
Maths163 views·Updated May 29, 2026·2 pagesGCSE Higher Maths: Essential Formulas and Circle Theorems
brooke crotty@brookecrotty_movl
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Essential GCSE Maths Formulas
Trigonometry might seem intimidating, but once you've got these six key formulas down, you'll tackle any triangle problem with confidence. Start with Pythagoras' theorem - it's your foundation for right-angled triangles.
The three basic trig ratios are straightforward: sin uses opposite over hypotenuse, cos uses adjacent over hypotenuse, and tan uses opposite over adjacent. Remember the acronym SOH-CAH-TOA to keep them straight.
For more complex triangles, you've got the sine rule and cosine rule. The sine rule works brilliantly when you know some angles and sides. The cosine rule is perfect when you're dealing with three sides or two sides and the included angle.
Quick Tip: Practice identifying which formula to use by looking at what information you're given in the question - this saves loads of time in exams!
2
of 2
Area and Volume Calculations
Area formulas are exam favourites, so nail these basics first. Rectangles use length × width, whilst triangles can be calculated using ½ × base × height or the trig version (½ab sin C) when you know two sides and the included angle.
Don't forget parallelograms (base × height) and trapeziums - the trapezium formula uses the average of the parallel sides multiplied by height: /2 × height. For circles, it's π × radius², and circumference is π × diameter.
Volume calculations follow predictable patterns that'll boost your marks. Prisms use area of cross-section × height, cylinders use π × radius² × height, and pyramids use ⅓ × base area × height. The key is identifying the shape type first.
Exam Strategy: Always write down the formula before substituting numbers - examiners often award marks for showing the correct formula even if your calculation goes wrong!
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Maths163 views·Updated May 29, 2026·2 pagesGCSE Higher Maths: Essential Formulas and Circle Theorems
brooke crotty@brookecrotty_movl
Master the essential maths formulas you'll need for your GCSE exams! This quick reference guide covers trigonometry, area calculations, and volume formulas that regularly appear on test papers.
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of 2
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Essential GCSE Maths Formulas
Trigonometry might seem intimidating, but once you've got these six key formulas down, you'll tackle any triangle problem with confidence. Start with Pythagoras' theorem - it's your foundation for right-angled triangles.
The three basic trig ratios are straightforward: sin uses opposite over hypotenuse, cos uses adjacent over hypotenuse, and tan uses opposite over adjacent. Remember the acronym SOH-CAH-TOA to keep them straight.
For more complex triangles, you've got the sine rule and cosine rule. The sine rule works brilliantly when you know some angles and sides. The cosine rule is perfect when you're dealing with three sides or two sides and the included angle.
Quick Tip: Practice identifying which formula to use by looking at what information you're given in the question - this saves loads of time in exams!
2
of 2Sign up to see the content. It's free!
- Access to all documents
- Improve your grades
- Join milions of students
Area and Volume Calculations
Area formulas are exam favourites, so nail these basics first. Rectangles use length × width, whilst triangles can be calculated using ½ × base × height or the trig version (½ab sin C) when you know two sides and the included angle.
Don't forget parallelograms (base × height) and trapeziums - the trapezium formula uses the average of the parallel sides multiplied by height: /2 × height. For circles, it's π × radius², and circumference is π × diameter.
Volume calculations follow predictable patterns that'll boost your marks. Prisms use area of cross-section × height, cylinders use π × radius² × height, and pyramids use ⅓ × base area × height. The key is identifying the shape type first.
Exam Strategy: Always write down the formula before substituting numbers - examiners often award marks for showing the correct formula even if your calculation goes wrong!
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
9Most popular content
9Can'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