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Organisms respond to changes in their internal and external environments (a-level only)
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1l the quest for political stability: germany, 1871-1991
Britain & the wider world: 1745 -1901
The cold war
Inter-war germany
Medieval period: 1066 -1509
2d religious conflict and the church in england, c1529-c1570
2o democracy and nazism: germany, 1918-1945
1f industrialisation and the people: britain, c1783-1885
1c the tudors: england, 1485-1603
2m wars and welfare: britain in transition, 1906-1957
World war two & the holocaust
2n revolution and dictatorship: russia, 1917-1953
2s the making of modern britain, 1951-2007
World war one
Britain: 1509 -1745
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2,555
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28 Nov 2025
•
Grace Cherry
@gracecherry_yjow
Maths can feel overwhelming, but mastering graphs, equations, and angle... Show more
Different types of graphs have distinct shapes that you'll recognise instantly once you know what to look for. Linear graphs create straight lines - the simplest examples being y = x (a diagonal line going up) and y = -x (a diagonal line going down).
Quadratic equations produce curved graphs called parabolas, whilst exponential graphs show dramatic curves that either shoot upwards or level off. Reciprocal graphs create distinctive hyperbolas with two separate curved sections.
For circles, you've got two crucial formulas to memorise: circumference = 2πr = πd and area = πr². There's also a volume formula mentioned (⅓πr³), though this seems to be mixing up different shapes - typical maths confusion that happens to everyone!
Quick tip: Sketch these graph shapes in your notes - visual memory is your best friend for recognising them in exams.
Corresponding angles are always equal when you've got parallel lines cut by a transversal - think of them as being in matching positions. Alternate angles also equal each other, but they're on opposite sides of the transversal in a Z-pattern.
Co-interior angles work differently - they always add up to 180° instead of being equal. Vertically opposite angles are the pairs that face each other when two lines cross, and these are always identical.
The key trick is spotting these relationships quickly in diagrams. Once you can identify which type of angle pair you're dealing with, the rest becomes straightforward calculation.
Remember: When lines are parallel, corresponding and alternate angles are equal, but co-interior angles sum to 180°.
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.
App 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
Grace Cherry
@gracecherry_yjow
Maths can feel overwhelming, but mastering graphs, equations, and angle relationships is absolutely doable with the right approach. These fundamental concepts pop up everywhere in your GCSE studies and beyond, so getting them sorted now will make your life much... Show more
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Different types of graphs have distinct shapes that you'll recognise instantly once you know what to look for. Linear graphs create straight lines - the simplest examples being y = x (a diagonal line going up) and y = -x (a diagonal line going down).
Quadratic equations produce curved graphs called parabolas, whilst exponential graphs show dramatic curves that either shoot upwards or level off. Reciprocal graphs create distinctive hyperbolas with two separate curved sections.
For circles, you've got two crucial formulas to memorise: circumference = 2πr = πd and area = πr². There's also a volume formula mentioned (⅓πr³), though this seems to be mixing up different shapes - typical maths confusion that happens to everyone!
Quick tip: Sketch these graph shapes in your notes - visual memory is your best friend for recognising them in exams.
Corresponding angles are always equal when you've got parallel lines cut by a transversal - think of them as being in matching positions. Alternate angles also equal each other, but they're on opposite sides of the transversal in a Z-pattern.
Co-interior angles work differently - they always add up to 180° instead of being equal. Vertically opposite angles are the pairs that face each other when two lines cross, and these are always identical.
The key trick is spotting these relationships quickly in diagrams. Once you can identify which type of angle pair you're dealing with, the rest becomes straightforward calculation.
Remember: When lines are parallel, corresponding and alternate angles are equal, but co-interior angles sum to 180°.
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.
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Transform this note into: ✓ 50+ Practice Questions ✓ Interactive Flashcards ✓ Full Mock Exam ✓ Essay Outlines
Master key concepts in GCSE Higher Maths with this comprehensive summary covering geometry, algebra, probability, and circle theorems. Perfect for exam preparation, this resource includes essential formulas, angle facts, area calculations, and statistical measures to boost your understanding and performance. Ideal for students aiming for top grades.
MathsExplore the essential concepts of angles, including types of angles, properties of polygons, and angle relationships in geometry. This summary covers key formulas for calculating interior and exterior angles, as well as detailed characteristics of various quadrilaterals and triangles. Ideal for Year 7 students studying Module 8 on Angles.
MathsExplore the detailed mark scheme for the Edexcel GCSE Mathematics Higher Paper 3H (2020). This resource covers key concepts such as geometric transformations, probability, area under curves, and solving systems of equations. Ideal for students preparing for their exams, this document provides insights into marking criteria and essential mathematical principles.
MathsExplore the properties of interior and exterior angles in polygons. Learn how to calculate the sum of interior angles using the formula (n-2) x 180° and understand the relationship between interior and exterior angles. This summary covers triangles, quadrilaterals, pentagons, and hexagons, providing essential insights for geometry students.
MathsExplore key concepts in trigonometry and quadratic functions, including the area of triangles, sine and cosine rules, bearings, and the properties of quadratic graphs. This summary covers essential formulas and problem-solving techniques for evaluating functions and understanding the nature of quadratic equations.
MathsExplore the Sine and Cosine Rules for solving triangles in this comprehensive guide. Learn how to calculate unknown angles and side lengths using the Law of Sines and Law of Cosines, complete with worked examples and practice questions. Ideal for Edexcel and other exam boards.
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
