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Britain & the wider world: 1745 -1901
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5
1
Brooke Tillotson-Hurn
08/12/2025
Maths
maths gcse revision AQA
434
•
8 Dec 2025
•
Brooke Tillotson-Hurn
@brooketillotsonhurn_
Maths can seem overwhelming, but these core topics—changing formula subjects,... Show more
Changing the subject of a formula is like solving a puzzle—you just need to isolate the letter you want on one side. The subject is the letter that appears alone on the left-hand side of the equation. To change it, use inverse operations (opposite operations) to rearrange.
For example, if you have 5p - 7 = c and want to make p the subject, add 7 to both sides first , then divide by 5 . It's that simple!
Ratios help you compare quantities and can be simplified just like fractions. If you have 15:25, divide both numbers by their highest common factor (5) to get 3:5. Remember to convert units when needed—3km becomes 3000m when comparing with metres.
Quick Tip: Triangle types are easy to remember—equilateral (all equal), isosceles (two equal), scalene (all different). Angles can be acute (less than 90°), right (exactly 90°), or obtuse (more than 90°).
Inequality symbols are your friends once you remember the basics: > means "greater than" and < means "less than". Think of the symbol as a hungry mouth that always wants to eat the bigger number! The symbols ≥ and ≤ include "or equal to" in the comparison.
For example, x ≥ 3 means x can be 3 or any number larger than 3. These symbols help you describe ranges of values rather than just exact numbers.
Standard form makes huge or tiny numbers manageable by writing them as a number between 1 and 10, multiplied by a power of 10. So 723,000 becomes 7.23 × 10⁵, and 0.0000063 becomes 6.3 × 10⁻⁶. The power tells you how many places to move the decimal point.
Expanding brackets means multiplying everything inside by what's outside. With 3, multiply both x and 2 by 3 to get 3x + 6. For double brackets like , multiply each term in the first bracket by each term in the second.
Quick Tip: Prime factors are just the prime numbers that multiply together to make your original number—use factor trees to break numbers down step by step.
Standard form (also called standard index form) is brilliant for handling numbers that would otherwise be ridiculously long to write out. Scientists use it constantly because they deal with everything from the size of atoms to the distance between galaxies!
The trick is splitting any number into two parts: a number between 1 and 10, then multiply by the right power of 10. For large numbers like 50,000, you get 5 × 10⁴ . The positive power tells you it's a big number.
Small numbers use negative powers. When you see something like 4.78 × 10⁻³, the negative power means you're dealing with a decimal. 10⁻³ = 0.001, so 4.78 × 10⁻³ = 0.00478.
Converting back to ordinary numbers is straightforward—just do the multiplication. Move the decimal point right for positive powers, left for negative powers. The power tells you exactly how many places to move.
Quick Tip: Remember that 10⁰ = 1, and each time the power increases by 1, you add another zero to your number (10¹ = 10, 10² = 100, 10³ = 1000).
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
Brooke Tillotson-Hurn
@brooketillotsonhurn_
Maths can seem overwhelming, but these core topics—changing formula subjects, ratios, triangles, inequalities, and standard form—are actually quite straightforward once you break them down. These skills pop up everywhere in GCSE maths, so getting comfortable with them now will make... Show more
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Changing the subject of a formula is like solving a puzzle—you just need to isolate the letter you want on one side. The subject is the letter that appears alone on the left-hand side of the equation. To change it, use inverse operations (opposite operations) to rearrange.
For example, if you have 5p - 7 = c and want to make p the subject, add 7 to both sides first , then divide by 5 . It's that simple!
Ratios help you compare quantities and can be simplified just like fractions. If you have 15:25, divide both numbers by their highest common factor (5) to get 3:5. Remember to convert units when needed—3km becomes 3000m when comparing with metres.
Quick Tip: Triangle types are easy to remember—equilateral (all equal), isosceles (two equal), scalene (all different). Angles can be acute (less than 90°), right (exactly 90°), or obtuse (more than 90°).
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
Inequality symbols are your friends once you remember the basics: > means "greater than" and < means "less than". Think of the symbol as a hungry mouth that always wants to eat the bigger number! The symbols ≥ and ≤ include "or equal to" in the comparison.
For example, x ≥ 3 means x can be 3 or any number larger than 3. These symbols help you describe ranges of values rather than just exact numbers.
Standard form makes huge or tiny numbers manageable by writing them as a number between 1 and 10, multiplied by a power of 10. So 723,000 becomes 7.23 × 10⁵, and 0.0000063 becomes 6.3 × 10⁻⁶. The power tells you how many places to move the decimal point.
Expanding brackets means multiplying everything inside by what's outside. With 3, multiply both x and 2 by 3 to get 3x + 6. For double brackets like , multiply each term in the first bracket by each term in the second.
Quick Tip: Prime factors are just the prime numbers that multiply together to make your original number—use factor trees to break numbers down step by step.
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
Standard form (also called standard index form) is brilliant for handling numbers that would otherwise be ridiculously long to write out. Scientists use it constantly because they deal with everything from the size of atoms to the distance between galaxies!
The trick is splitting any number into two parts: a number between 1 and 10, then multiply by the right power of 10. For large numbers like 50,000, you get 5 × 10⁴ . The positive power tells you it's a big number.
Small numbers use negative powers. When you see something like 4.78 × 10⁻³, the negative power means you're dealing with a decimal. 10⁻³ = 0.001, so 4.78 × 10⁻³ = 0.00478.
Converting back to ordinary numbers is straightforward—just do the multiplication. Move the decimal point right for positive powers, left for negative powers. The power tells you exactly how many places to move.
Quick Tip: Remember that 10⁰ = 1, and each time the power increases by 1, you add another zero to your number (10¹ = 10, 10² = 100, 10³ = 1000).
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
Explore the fundamentals of Standard Form (Scientific Notation) in mathematics. This study note covers how to express large and small numbers using powers of ten, the significance of place value, and practical examples for converting between standard and ordinary forms. Ideal for students looking to master the concept of scientific notation and its applications.
MathsThis comprehensive guide covers the conversion between standard form and ordinary numbers, including key operations with scientific notation. Ideal for GCSE students, it provides step-by-step solutions and examples to enhance understanding of powers of 10 and arithmetic with scientific notation.
MathsExplore the concept of standard form (scientific notation) in mathematics. This summary covers how to express large and small numbers using powers of ten, including examples and conversion techniques. Ideal for students looking to master scientific notation and its applications.
MathsEnhance your understanding of key mathematical concepts with this comprehensive practice paper from the WJEC 2022 exam. Covering topics such as triangle congruence, Venn diagrams, trigonometric equations, and inequalities, this resource is designed to help students prepare effectively for their exams. Ideal for revision and self-assessment.
MathsExplore essential concepts in GCSE Maths, including the rules for multiplying and dividing negative numbers, understanding standard form, and the order of operations (BIDMAS). This summary provides clear explanations and examples to enhance your mathematical skills.
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