Maths
Biology
Chemistry
English Lang.
History
Responding to change (a2 only)
Energy transfers (a2 only)
Infection and response
Homeostasis and response
Cell biology
Biological molecules
Organisation
Substance exchange
The control of gene expression (a2 only)
Bioenergetics
Genetic information & variation
Inheritance, variation and evolution
Genetics & ecosystems (a2 only)
Ecology
Cells
Show all topics
Britain & the wider world: 1745 -1901
2d religious conflict and the church in england, c1529-c1570
Medieval period: 1066 -1509
1l the quest for political stability: germany, 1871-1991
1f industrialisation and the people: britain, c1783-1885
The cold war
1c the tudors: england, 1485-1603
Inter-war germany
2m wars and welfare: britain in transition, 1906-1957
2j america: a nation divided, c1845-1877
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
Show all topics
Maths
12 Oct 2025
186
5 pages
Sahal Hassan @sahalh_g
Understanding equations of a line in mathand geometric relationships between lines forms the foundation of coordinate geometry.... Show more
This page delves into midpoint calculations and more complex line properties, including perpendicular lines and distance calculations.
Definition The midpoint formula is used to find the center point between two coordinates /2, /2
Example A detailed calculation shows finding coordinates of point B(5,8) using gradient relationships.
Highlight The negative reciprocal relationship between perpendicular lines is demonstrated through practical examples.
The content focuses on finding where lines intersect with axes and calculating distances between points using the distance formula.
Definition The distance formula between two points is √² + ²)
Example Finding intersection points A and B with the axes.
Highlight The midpoint calculation is shown as an important step in solving geometric problems.
This page covers more advanced concepts involving multiple lines and their relationships, including perpendicular lines and intersection points.
Definition Perpendicular lines have gradients that are negative reciprocals of each other.
Example Solving systems of equations to find intersection points.
Highlight The transformation of equations from general form to slope-intercept form is demonstrated.
This section covers more advanced problems involving multiple lines and their relationships.
Example Solving systems of equations to find intersection points of two lines.
Definition Two lines are perpendicular if their gradients are negative reciprocals of each other.
Highlight When converting between different forms of line equations, it's crucial to maintain the same mathematical relationship while changing the presentation.
This page introduces fundamental concepts of linear equations and gradient calculations. The content focuses on working with different forms of linear equations and understanding the relationship between lines.
Definition The point-slope form of a line is y - y₁ = m, where m is the gradient and (x₁,y₁) is a point on the line.
Example A gradient calculation is shown where m = / = -3
Highlight The relationship between perpendicular lines is demonstrated through their negative reciprocal gradients.
Vocabulary Gradient (m) represents the slope or steepness of a line.
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
Master the fundamentals of straight line equations with this comprehensive guide. Learn to derive equations in the form y = mx + c, calculate gradients, and apply point-slope form. Includes practical examples, graphing techniques, and exam-style questions to enhance your understanding of linear functions.
MathsExplore the fundamentals of graphing straight lines in coordinate geometry. This study note covers key concepts such as slope-intercept form, finding equations of lines, and understanding gradients. Includes worked examples and solved GCSE exam questions relevant for all exam boards.
MathsComprehensive notes on functions for Edexcel A Level Maths Year 2, covering key concepts such as modulus functions, composite functions, inverse functions, and transformations. Includes worked examples and solutions to enhance understanding of domain, range, and function notation.
MathsExplore key topics in advanced mathematics including area between curves, integration techniques, trigonometric functions, and logarithmic properties. This comprehensive study resource covers essential concepts such as the factor theorem, permutations, combinations, and the quadratic formula, providing a solid foundation for mastering OCR FSMQ Level 3 mathematics.
MathsExplore detailed solutions for the 2023 Edexcel GCSE Maths Paper 1 (Non-Calculator). This resource covers key concepts such as solving quadratic equations, geometric constructions, probability, and statistical analysis. Ideal for students preparing for their exams, this summary provides step-by-step guidance on tackling various mathematical problems, including inequalities, graphing, and geometric formulas.
MathsMaths revision
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
Maths
12 Oct 2025
186
5 pages
Sahal Hassan @sahalh_g
Understanding equations of a line in math and geometric relationships between lines forms the foundation of coordinate geometry. This comprehensive guide covers line equations, perpendicular lines, and finding midpoints.
•... Show more
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
This page delves into midpoint calculations and more complex line properties, including perpendicular lines and distance calculations.
Definition The midpoint formula is used to find the center point between two coordinates /2, /2
Example A detailed calculation shows finding coordinates of point B(5,8) using gradient relationships.
Highlight The negative reciprocal relationship between perpendicular lines is demonstrated through practical examples.
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
The content focuses on finding where lines intersect with axes and calculating distances between points using the distance formula.
Definition The distance formula between two points is √² + ²)
Example Finding intersection points A and B with the axes.
Highlight The midpoint calculation is shown as an important step in solving geometric problems.
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
This page covers more advanced concepts involving multiple lines and their relationships, including perpendicular lines and intersection points.
Definition Perpendicular lines have gradients that are negative reciprocals of each other.
Example Solving systems of equations to find intersection points.
Highlight The transformation of equations from general form to slope-intercept form is demonstrated.
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
This section covers more advanced problems involving multiple lines and their relationships.
Example Solving systems of equations to find intersection points of two lines.
Definition Two lines are perpendicular if their gradients are negative reciprocals of each other.
Highlight When converting between different forms of line equations, it's crucial to maintain the same mathematical relationship while changing the presentation.
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
This page introduces fundamental concepts of linear equations and gradient calculations. The content focuses on working with different forms of linear equations and understanding the relationship between lines.
Definition The point-slope form of a line is y - y₁ = m, where m is the gradient and (x₁,y₁) is a point on the line.
Example A gradient calculation is shown where m = / = -3
Highlight The relationship between perpendicular lines is demonstrated through their negative reciprocal gradients.
Vocabulary Gradient (m) represents the slope or steepness of a line.
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
Master the fundamentals of straight line equations with this comprehensive guide. Learn to derive equations in the form y = mx + c, calculate gradients, and apply point-slope form. Includes practical examples, graphing techniques, and exam-style questions to enhance your understanding of linear functions.
MathsExplore the fundamentals of graphing straight lines in coordinate geometry. This study note covers key concepts such as slope-intercept form, finding equations of lines, and understanding gradients. Includes worked examples and solved GCSE exam questions relevant for all exam boards.
MathsComprehensive notes on functions for Edexcel A Level Maths Year 2, covering key concepts such as modulus functions, composite functions, inverse functions, and transformations. Includes worked examples and solutions to enhance understanding of domain, range, and function notation.
MathsExplore key topics in advanced mathematics including area between curves, integration techniques, trigonometric functions, and logarithmic properties. This comprehensive study resource covers essential concepts such as the factor theorem, permutations, combinations, and the quadratic formula, providing a solid foundation for mastering OCR FSMQ Level 3 mathematics.
MathsExplore detailed solutions for the 2023 Edexcel GCSE Maths Paper 1 (Non-Calculator). This resource covers key concepts such as solving quadratic equations, geometric constructions, probability, and statistical analysis. Ideal for students preparing for their exams, this summary provides step-by-step guidance on tackling various mathematical problems, including inequalities, graphing, and geometric formulas.
MathsMaths revision
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
