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gracie keenan
11/08/2025
Maths
CCEA MATHS PURE NOTES
1,910
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11 Aug 2025
•
CCEA GCSE Maths: Indices, Trigonometry, Quadratics & Circle Theorems Notes
gracie keenan
@graciekeenan_
Mathematical Indices, Trigonometry, and More: CCEA GCSE Maths Overview
This page provides a comprehensive overview of key mathematical concepts covered in the CCEA GCSE Maths curriculum. It serves as a quick reference guide for students preparing for exams or seeking to reinforce their understanding of fundamental principles.
The page begins with a section on indices, presenting important rules and formulas. For example, it shows that (aᵐ)ⁿ = aᵐⁿ and a^(m-n) = aᵐ/aⁿ. These rules are essential for simplifying and manipulating expressions involving exponents.
Definition: Indices, also known as exponents, indicate how many times a number is multiplied by itself.
Next, the quadratic formula is presented, which is crucial for solving quadratic equations:
Highlight: The quadratic formula is given as x = (-b ± √(b² - 4ac)) / (2a), where a, b, and c are coefficients in the quadratic equation ax² + bx + c = 0.
The page then moves on to trigonometry, introducing the basic ratios of sine, cosine, and tangent. These are fundamental for solving problems involving right-angled triangles and have numerous applications in geometry and physics.
Vocabulary: Trigonometry is the study of relationships between the sides and angles of triangles.
Graph transformations are also covered, explaining how functions can be shifted, stretched, or reflected. For instance, y = f(x) + 2 adds 2 to all y-values, shifting the graph up by 2 units.
The equation of a circle is presented as (x - a)² + (y - b)² = r², where (a, b) is the center and r is the radius. This formula is essential for problems involving circular geometry.
Example: The equation (x - 3)² + (y + 1)² = 25 represents a circle with center (3, -1) and radius 5.
The discriminant of a quadratic equation is explained, showing how it determines the number of roots:
- When b² - 4ac > 0, there are two distinct roots
- When b² - 4ac = 0, there is one repeated root
- When b² - 4ac < 0, there are no real roots
Coordinate geometry concepts are also included, such as finding the gradient between two points and the distance formula.
Formula: The distance between two points (x₁, y₁) and (x₂, y₂) is given by √((x₂ - x₁)² + (y₂ - y₁)²).
The page concludes with advanced topics like the factor theorem, remainder theorem, circle theorems, and trigonometric identities. It also touches on the binomial expansion, which is crucial for higher-level mathematics.
This comprehensive overview serves as an excellent revision tool for students preparing for their CCEA GCSE Maths exams, covering a wide range of topics from basic algebra to advanced geometry and trigonometry.
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4.9/5
App Store
4.8/5
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
CCEA GCSE Maths: Indices, Trigonometry, Quadratics & Circle Theorems Notes
gracie keenan
@graciekeenan_
The CCEA GCSE Maths curriculum covers a wide range of mathematical concepts, including indices, trigonometry, quadratic equations, and circle theorems. This comprehensive summary provides an overview of key topics and formulas essential for success in CCEA GCSE Maths:
- Indices... Show more
Mathematical Indices, Trigonometry, and More: CCEA GCSE Maths Overview
This page provides a comprehensive overview of key mathematical concepts covered in the CCEA GCSE Maths curriculum. It serves as a quick reference guide for students preparing for exams or seeking to reinforce their understanding of fundamental principles.
The page begins with a section on indices, presenting important rules and formulas. For example, it shows that (aᵐ)ⁿ = aᵐⁿ and a^(m-n) = aᵐ/aⁿ. These rules are essential for simplifying and manipulating expressions involving exponents.
Definition: Indices, also known as exponents, indicate how many times a number is multiplied by itself.
Next, the quadratic formula is presented, which is crucial for solving quadratic equations:
Highlight: The quadratic formula is given as x = (-b ± √(b² - 4ac)) / (2a), where a, b, and c are coefficients in the quadratic equation ax² + bx + c = 0.
The page then moves on to trigonometry, introducing the basic ratios of sine, cosine, and tangent. These are fundamental for solving problems involving right-angled triangles and have numerous applications in geometry and physics.
Vocabulary: Trigonometry is the study of relationships between the sides and angles of triangles.
Graph transformations are also covered, explaining how functions can be shifted, stretched, or reflected. For instance, y = f(x) + 2 adds 2 to all y-values, shifting the graph up by 2 units.
The equation of a circle is presented as (x - a)² + (y - b)² = r², where (a, b) is the center and r is the radius. This formula is essential for problems involving circular geometry.
Example: The equation (x - 3)² + (y + 1)² = 25 represents a circle with center (3, -1) and radius 5.
The discriminant of a quadratic equation is explained, showing how it determines the number of roots:
- When b² - 4ac > 0, there are two distinct roots
- When b² - 4ac = 0, there is one repeated root
- When b² - 4ac < 0, there are no real roots
Coordinate geometry concepts are also included, such as finding the gradient between two points and the distance formula.
Formula: The distance between two points (x₁, y₁) and (x₂, y₂) is given by √((x₂ - x₁)² + (y₂ - y₁)²).
The page concludes with advanced topics like the factor theorem, remainder theorem, circle theorems, and trigonometric identities. It also touches on the binomial expansion, which is crucial for higher-level mathematics.
This comprehensive overview serves as an excellent revision tool for students preparing for their CCEA GCSE Maths exams, covering a wide range of topics from basic algebra to advanced geometry and trigonometry.
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.
Can't find what you're looking for? Explore other subjects.
Students love us — and so will you.
4.9/5
App Store
4.8/5
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