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Maths
3 Dec 2025
360
7 pages
Kimberley @kimberley_ncyf
This guide covers key mathematical concepts including changing the subject of formulas, calculating volumes, interquartile range, standard deviation,... Show more
This page focuses on volume calculations for various 3D shapes, providing essential formulas and a practical example.
Vocabulary Volume is the amount of three-dimensional space occupied by an object.
The page lists key volume formulas
Example A complex shape consisting of a cylinder and a hemisphere is presented. The problem requires calculating the total volume to 3 significant figures.
The solution is broken down into steps
Highlight When solving complex volume problems, break the shape into simpler components and calculate their volumes separately before combining.
This page explains the concept of interquartile range (IQR) and its application in comparing data sets.
Definition The interquartile range is a measure of statistical dispersion, calculated as the difference between the upper (Q3) and lower (Q1) quartiles.
The formula for IQR is presented IQR = Q3 - Q1
Example A set of midday temperatures in Glasgow is given 3, 3, 3, 4, 4, 5, 6, 7, 9, 10. The problem requires calculating the median and IQR.
The solution demonstrates how to
Highlight The IQR is useful for comparing the spread of data between different sets, as shown in the comparison between Glasgow and Edinburgh temperatures.
This page covers the calculation of mean and standard deviation for a given data set.
Definition Standard deviation is a measure of the amount of variation or dispersion of a set of values.
The page provides a step-by-step guide to calculating standard deviation
Example A data set of 14, 17, 15, 23, 20, 19 is used to demonstrate the calculation process.
Highlight The sum of the differences between each data point and the mean should always equal zero, serving as a check for calculations.
This page focuses on the equation of a straight line and how to determine its gradient and y-intercept.
Vocabulary The general form of a straight line equation is y = mx + c, where m is the gradient and c is the y-intercept.
The page demonstrates how to
Example The equation 2x - 5y = 20 is rearranged to find the gradient and y-intercept.
Highlight The gradient formula m = / is crucial for finding the slope between two points.
This page extends the concept of straight lines, focusing on finding the equation of a line passing through two points.
Vocabulary The point-slope form of a line equation is y - y₁ = m, where (x₁, y₁) is a point on the line and m is the gradient.
The page demonstrates the process of finding a line equation
Example Find the equation of the line passing through (-1, -7) and (4, 3).
The page also introduces arc length calculations
Highlight The arc length formula can be rearranged to find unknown angles or diameters when other variables are given.
This final page covers the calculation of sector area in a circle.
Definition A sector is a part of a circular disk enclosed by two radii and an arc.
The formula for the area of a sector is presented A = θ/360° × πr², where θ is the angle in degrees and r is the radius.
Example Calculate the area of a sector with radius 3cm and angle 150°.
The page also shows how to
Highlight Sector area problems often involve rearranging the formula to solve for different variables, similar to changing the subject of a formula.
This page introduces the concept of changing the subject of a formula in mathematics. It demonstrates the process using two examples.
Definition Changing the subject of a formula involves rearranging an equation to isolate a different variable as the subject.
The first example shows how to change the subject of the formula F = C/ + 4b² to t. The process involves applying opposite operations to isolate t.
Example To change F = C/ + 4b² to make t the subject, subtract 4b² from both sides, multiply by , and then subtract 4b to isolate t.
The second example demonstrates changing the subject of P = my²/2 to v. This involves multiplying both sides by 2, dividing by m, and then taking the square root.
Highlight When changing the subject of a formula, always perform the same operation on both sides of the equation to maintain equality.
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
Maths revision
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.
MathsExplore key concepts in graphing, including the equation of a line, slope-intercept form, and how to calculate midpoints and gradients. This knowledge organizer covers essential methods for drawing straight line graphs and interpreting distance-time graphs, making it ideal for Year 10 Maths students. Enhance your understanding of graphing techniques and real-life applications.
MathsMaster 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 a comprehensive collection of mathematics revision questions covering key concepts such as Pythagorean theorem, quadratic equations, trigonometric identities, volume calculations, and statistical measures. Ideal for students preparing for exams, this resource includes practice problems on indices, surds, and inequalities, along with detailed solutions to enhance understanding. Type: Theory Guide.
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.
MathsThis is the aqa exam board for triple highwe
ChemistryApp 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
Kimberley
@kimberley_ncyf
This guide covers key mathematical concepts including changing the subject of formulas, calculating volumes, interquartile range, standard deviation, straight line equations, and arc length and sector area calculations. It provides step-by-step examples to illustrate these important topics for students.
•... Show more
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Improve your grades
Join milions of students
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This page focuses on volume calculations for various 3D shapes, providing essential formulas and a practical example.
Vocabulary: Volume is the amount of three-dimensional space occupied by an object.
The page lists key volume formulas:
Example: A complex shape consisting of a cylinder and a hemisphere is presented. The problem requires calculating the total volume to 3 significant figures.
The solution is broken down into steps:
Highlight: When solving complex volume problems, break the shape into simpler components and calculate their volumes separately before combining.
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
This page explains the concept of interquartile range (IQR) and its application in comparing data sets.
Definition: The interquartile range is a measure of statistical dispersion, calculated as the difference between the upper (Q3) and lower (Q1) quartiles.
The formula for IQR is presented: IQR = Q3 - Q1
Example: A set of midday temperatures in Glasgow is given: 3, 3, 3, 4, 4, 5, 6, 7, 9, 10. The problem requires calculating the median and IQR.
The solution demonstrates how to:
Highlight: The IQR is useful for comparing the spread of data between different sets, as shown in the comparison between Glasgow and Edinburgh temperatures.
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 the calculation of mean and standard deviation for a given data set.
Definition: Standard deviation is a measure of the amount of variation or dispersion of a set of values.
The page provides a step-by-step guide to calculating standard deviation:
Example: A data set of 14, 17, 15, 23, 20, 19 is used to demonstrate the calculation process.
Highlight: The sum of the differences between each data point and the mean should always equal zero, serving as a check for calculations.
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
This page focuses on the equation of a straight line and how to determine its gradient and y-intercept.
Vocabulary: The general form of a straight line equation is y = mx + c, where m is the gradient and c is the y-intercept.
The page demonstrates how to:
Example: The equation 2x - 5y = 20 is rearranged to find the gradient and y-intercept.
Highlight: The gradient formula m = / is crucial for finding the slope between two points.
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
This page extends the concept of straight lines, focusing on finding the equation of a line passing through two points.
Vocabulary: The point-slope form of a line equation is y - y₁ = m, where (x₁, y₁) is a point on the line and m is the gradient.
The page demonstrates the process of finding a line equation:
Example: Find the equation of the line passing through (-1, -7) and (4, 3).
The page also introduces arc length calculations:
Highlight: The arc length formula can be rearranged to find unknown angles or diameters when other variables are given.
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
This final page covers the calculation of sector area in a circle.
Definition: A sector is a part of a circular disk enclosed by two radii and an arc.
The formula for the area of a sector is presented: A = θ/360° × πr², where θ is the angle in degrees and r is the radius.
Example: Calculate the area of a sector with radius 3cm and angle 150°.
The page also shows how to:
Highlight: Sector area problems often involve rearranging the formula to solve for different variables, similar to changing the subject of a formula.
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 the concept of changing the subject of a formula in mathematics. It demonstrates the process using two examples.
Definition: Changing the subject of a formula involves rearranging an equation to isolate a different variable as the subject.
The first example shows how to change the subject of the formula F = C/ + 4b² to t. The process involves applying opposite operations to isolate t.
Example: To change F = C/ + 4b² to make t the subject, subtract 4b² from both sides, multiply by , and then subtract 4b to isolate t.
The second example demonstrates changing the subject of P = my²/2 to v. This involves multiplying both sides by 2, dividing by m, and then taking the square root.
Highlight: When changing the subject of a formula, always perform the same operation on both sides of the equation to maintain equality.
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.
10
Smart Tools NEW
Transform this note into: ✓ 50+ Practice Questions ✓ Interactive Flashcards ✓ Full Mock Exam ✓ Essay Outlines
Maths revision
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.
MathsExplore key concepts in graphing, including the equation of a line, slope-intercept form, and how to calculate midpoints and gradients. This knowledge organizer covers essential methods for drawing straight line graphs and interpreting distance-time graphs, making it ideal for Year 10 Maths students. Enhance your understanding of graphing techniques and real-life applications.
MathsMaster 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 a comprehensive collection of mathematics revision questions covering key concepts such as Pythagorean theorem, quadratic equations, trigonometric identities, volume calculations, and statistical measures. Ideal for students preparing for exams, this resource includes practice problems on indices, surds, and inequalities, along with detailed solutions to enhance understanding. Type: Theory Guide.
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.
MathsThis is the aqa exam board for triple highwe
ChemistryApp 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