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Britain & the wider world: 1745 -1901
1l the quest for political stability: germany, 1871-1991
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Maths
8 Dec 2025
114
2 pages
brooke crotty @brookecrotty_movl
Master the essential maths formulas you'll need for your GCSE exams! This quick reference guide covers trigonometry, area... Show more
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!
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!
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.
That's right! Enjoy free access to study content, connect with fellow students, and get instant help – all at your fingertips.
1
Smart Tools NEW
Transform this note into: ✓ 50+ Practice Questions ✓ Interactive Flashcards ✓ Full Mock Exam ✓ Essay Outlines
Explore key concepts in circle geometry, including parts of a circle, essential formulae for circumference, area, and sector calculations. This summary provides step-by-step models and example questions to enhance your understanding of circle properties and their applications in GCSE Maths.
MathsExplore essential concepts of circles including circumference, diameter, radius, chords, tangents, sectors, arcs, and segments. This summary provides key formulas and properties crucial for GCSE Maths. Perfect for quick revision and understanding of circle geometry.
MathsExplore key concepts in geometry and pressure calculations, including formulas for the volume and surface area of cones, cylinders, and spheres. This summary covers essential topics such as arc length, sector area, and hydrostatic pressure, providing a comprehensive overview for students preparing for exams. Ideal for quick revision and understanding of 3D objects and circle properties.
MathsMaster the calculations for the area and circumference of circles with this comprehensive guide. Explore key concepts including formulas for circles, semicircles, and sectors, along with practical examples and problem-solving techniques. Ideal for GCSE students preparing for exams.
MathsExplore the fundamental components of circle geometry, including definitions and visual representations of the center, radius, diameter, chord, arc, segment, sector, and tangent. This summary provides a clear understanding of each part's role in circle mathematics.
MathsA comprehensive formula sheet for Year 11 students covering key concepts in geometry, algebra, circle theorems, probability, and graph transformations. Perfect for quick revision and exam preparation.
MathsApp Store
Google 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 S
iOS 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 Klich
Android 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.
Anna
iOS user
Best app on earth! no words because it’s too good
Thomas R
iOS user
Just amazing. Let's me revise 10x better, this app is a quick 10/10. I highly recommend it to anyone. I can watch and search for notes. I can save them in the subject folder. I can revise it any time when I come back. If you haven't tried this app, you're really missing out.
Basil
Android user
This app has made me feel so much more confident in my exam prep, not only through boosting my own self confidence through the features that allow you to connect with others and feel less alone, but also through the way the app itself is centred around making you feel better. It is easy to navigate, fun to use, and helpful to anyone struggling in absolutely any way.
David K
iOS user
The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!
Sudenaz Ocak
Android user
In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.
Greenlight Bonnie
Android user
very reliable app to help and grow your ideas of Maths, English and other related topics in your works. please use this app if your struggling in areas, this app is key for that. wish I'd of done a review before. and it's also free so don't worry about that.
Rohan U
Android user
I know a lot of apps use fake accounts to boost their reviews but this app deserves it all. Originally I was getting 4 in my English exams and this time I got a grade 7. I didn’t even know about this app three days until the exam and it has helped A LOT. Please actually trust me and use it as I’m sure you too will see developments.
Xander S
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE THE SCHOOLGPT. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮
Elisha
iOS user
This apps acc the goat. I find revision so boring but this app makes it so easy to organize it all and then you can ask the freeeee ai to test yourself so good and you can easily upload your own stuff. highly recommend as someone taking mocks now
Paul T
iOS user
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 S
iOS 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 Klich
Android 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.
Anna
iOS user
Best app on earth! no words because it’s too good
Thomas R
iOS user
Just amazing. Let's me revise 10x better, this app is a quick 10/10. I highly recommend it to anyone. I can watch and search for notes. I can save them in the subject folder. I can revise it any time when I come back. If you haven't tried this app, you're really missing out.
Basil
Android user
This app has made me feel so much more confident in my exam prep, not only through boosting my own self confidence through the features that allow you to connect with others and feel less alone, but also through the way the app itself is centred around making you feel better. It is easy to navigate, fun to use, and helpful to anyone struggling in absolutely any way.
David K
iOS user
The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!
Sudenaz Ocak
Android user
In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.
Greenlight Bonnie
Android user
very reliable app to help and grow your ideas of Maths, English and other related topics in your works. please use this app if your struggling in areas, this app is key for that. wish I'd of done a review before. and it's also free so don't worry about that.
Rohan U
Android user
I know a lot of apps use fake accounts to boost their reviews but this app deserves it all. Originally I was getting 4 in my English exams and this time I got a grade 7. I didn’t even know about this app three days until the exam and it has helped A LOT. Please actually trust me and use it as I’m sure you too will see developments.
Xander S
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE THE SCHOOLGPT. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮
Elisha
iOS user
This apps acc the goat. I find revision so boring but this app makes it so easy to organize it all and then you can ask the freeeee ai to test yourself so good and you can easily upload your own stuff. highly recommend as someone taking mocks now
Paul T
iOS user
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.
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
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!
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
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!
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.
That's right! Enjoy free access to study content, connect with fellow students, and get instant help – all at your fingertips.
1
Smart Tools NEW
Transform this note into: ✓ 50+ Practice Questions ✓ Interactive Flashcards ✓ Full Mock Exam ✓ Essay Outlines
Explore key concepts in circle geometry, including parts of a circle, essential formulae for circumference, area, and sector calculations. This summary provides step-by-step models and example questions to enhance your understanding of circle properties and their applications in GCSE Maths.
MathsExplore essential concepts of circles including circumference, diameter, radius, chords, tangents, sectors, arcs, and segments. This summary provides key formulas and properties crucial for GCSE Maths. Perfect for quick revision and understanding of circle geometry.
MathsExplore key concepts in geometry and pressure calculations, including formulas for the volume and surface area of cones, cylinders, and spheres. This summary covers essential topics such as arc length, sector area, and hydrostatic pressure, providing a comprehensive overview for students preparing for exams. Ideal for quick revision and understanding of 3D objects and circle properties.
MathsMaster the calculations for the area and circumference of circles with this comprehensive guide. Explore key concepts including formulas for circles, semicircles, and sectors, along with practical examples and problem-solving techniques. Ideal for GCSE students preparing for exams.
MathsExplore the fundamental components of circle geometry, including definitions and visual representations of the center, radius, diameter, chord, arc, segment, sector, and tangent. This summary provides a clear understanding of each part's role in circle mathematics.
MathsA comprehensive formula sheet for Year 11 students covering key concepts in geometry, algebra, circle theorems, probability, and graph transformations. Perfect for quick revision and exam preparation.
MathsApp Store
Google 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 S
iOS 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 Klich
Android 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.
Anna
iOS user
Best app on earth! no words because it’s too good
Thomas R
iOS user
Just amazing. Let's me revise 10x better, this app is a quick 10/10. I highly recommend it to anyone. I can watch and search for notes. I can save them in the subject folder. I can revise it any time when I come back. If you haven't tried this app, you're really missing out.
Basil
Android user
This app has made me feel so much more confident in my exam prep, not only through boosting my own self confidence through the features that allow you to connect with others and feel less alone, but also through the way the app itself is centred around making you feel better. It is easy to navigate, fun to use, and helpful to anyone struggling in absolutely any way.
David K
iOS user
The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!
Sudenaz Ocak
Android user
In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.
Greenlight Bonnie
Android user
very reliable app to help and grow your ideas of Maths, English and other related topics in your works. please use this app if your struggling in areas, this app is key for that. wish I'd of done a review before. and it's also free so don't worry about that.
Rohan U
Android user
I know a lot of apps use fake accounts to boost their reviews but this app deserves it all. Originally I was getting 4 in my English exams and this time I got a grade 7. I didn’t even know about this app three days until the exam and it has helped A LOT. Please actually trust me and use it as I’m sure you too will see developments.
Xander S
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE THE SCHOOLGPT. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮
Elisha
iOS user
This apps acc the goat. I find revision so boring but this app makes it so easy to organize it all and then you can ask the freeeee ai to test yourself so good and you can easily upload your own stuff. highly recommend as someone taking mocks now
Paul T
iOS user
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 S
iOS 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 Klich
Android 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.
Anna
iOS user
Best app on earth! no words because it’s too good
Thomas R
iOS user
Just amazing. Let's me revise 10x better, this app is a quick 10/10. I highly recommend it to anyone. I can watch and search for notes. I can save them in the subject folder. I can revise it any time when I come back. If you haven't tried this app, you're really missing out.
Basil
Android user
This app has made me feel so much more confident in my exam prep, not only through boosting my own self confidence through the features that allow you to connect with others and feel less alone, but also through the way the app itself is centred around making you feel better. It is easy to navigate, fun to use, and helpful to anyone struggling in absolutely any way.
David K
iOS user
The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!
Sudenaz Ocak
Android user
In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.
Greenlight Bonnie
Android user
very reliable app to help and grow your ideas of Maths, English and other related topics in your works. please use this app if your struggling in areas, this app is key for that. wish I'd of done a review before. and it's also free so don't worry about that.
Rohan U
Android user
I know a lot of apps use fake accounts to boost their reviews but this app deserves it all. Originally I was getting 4 in my English exams and this time I got a grade 7. I didn’t even know about this app three days until the exam and it has helped A LOT. Please actually trust me and use it as I’m sure you too will see developments.
Xander S
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE THE SCHOOLGPT. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮
Elisha
iOS user
This apps acc the goat. I find revision so boring but this app makes it so easy to organize it all and then you can ask the freeeee ai to test yourself so good and you can easily upload your own stuff. highly recommend as someone taking mocks now
Paul T
iOS user
Sociology