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Updated Mar 24, 2026
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How to Rearrange a Formula
U
Umar Kasmani
@umarkasmani
1 / 8
Getting Started with Formula Rearrangement
This is your practice paper for changing the subject of a formula - one of those essential GCSE skills that looks harder than it actually is. You've got everything from simple linear rearrangements to trickier ones involving squares and fractions.
The key thing to remember is that you're basically doing algebra in reverse. Instead of substituting numbers, you're moving terms around to isolate the letter you want.
Top Tip: Always show your working step by step - even if you make a mistake, you can still pick up marks for the right method!
Basic Linear Rearrangements
Questions 1-3 are your warm-up exercises with simple linear formulas. These follow the same pattern: get the term with your target letter on one side, then divide or multiply to isolate it.
For example, with f = 5c - 8, you'd add 8 to both sides first, then divide by 5. It's just like solving equations, but you're working with letters instead of numbers.
These questions are worth 2 marks each, so expect to show two clear steps in your working.
Multi-Variable Formulas
Questions 4-6 introduce formulas with multiple variables - don't let this throw you off! The process is exactly the same, you're just moving around more letters.
When you see something like m = 5n + 2p and need to make p the subject, treat everything else as if it were a number. Subtract 5n from both sides, then divide by 2.
The key is staying organised and taking it one step at a time - rushing leads to silly mistakes that cost you easy marks.
Stepping Up the Difficulty
Now things get more interesting with squares and physics formulas. Question 7 involves n², which means you'll need to square root both sides after rearranging.
Questions 8 and 9 use classic physics equations that you might recognise from science lessons. The v = u + at formula is particularly important - knowing how to rearrange it will help in both maths and physics exams.
Remember: When dealing with squares, don't forget the ± symbol when you take the square root (though sometimes the context tells you which sign to use).
Advanced Techniques
Question 10 brings in square roots and fractions together - this is where careful working really pays off. You'll need to square both sides first to get rid of the square root, then work with the fraction.
These questions are worth 3 marks, indicating you need to show more steps. Plan your approach before diving in, and remember that with square roots, you usually need to isolate the root first before squaring.
Fractional Coefficients
Questions 12-14 focus on formulas with fractions as coefficients. When you see something like y = ½x + 6, remember that dividing by ½ is the same as multiplying by 2.
These questions test whether you really understand how fractions work in algebra. The key is to multiply by the reciprocal (flip the fraction upside down) rather than trying to divide by fractions.
Question 14 is worth 3 marks, suggesting there might be a bit more manipulation involved than the others.
Challenge Questions
The final set brings together everything you've learned with complex rearrangements. Question 15 has everything equal to zero, Question 16 involves cubes, and Question 17 combines fractions with multiple terms.
These are the questions that separate the good students from the great ones. Take your time, work methodically, and don't panic if they look complicated at first glance.
Exam Strategy: If you're running out of time, prioritise the 2-mark questions over the 3-mark ones - they're usually quicker and give you more points per minute spent.
We thought you’d never ask...
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Where can I download the Knowunity app?
You can download the app from Google Play Store and Apple App Store.
Is Knowunity really free of charge?
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Most popular content in Maths
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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 Knowunity AI. 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 Knowunity AI. 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
How to Rearrange a Formula
U
Umar Kasmani
@umarkasmani
Changing the subject of a formula is like solving an equation backwards - instead of finding a number, you're rearranging to get a different letter on its own. This skill pops up everywhere in maths and science, so mastering it... Show more
Getting Started with Formula Rearrangement
This is your practice paper for changing the subject of a formula - one of those essential GCSE skills that looks harder than it actually is. You've got everything from simple linear rearrangements to trickier ones involving squares and fractions.
The key thing to remember is that you're basically doing algebra in reverse. Instead of substituting numbers, you're moving terms around to isolate the letter you want.
Top Tip: Always show your working step by step - even if you make a mistake, you can still pick up marks for the right method!
Sign up to see the contentIt's free!
Access to all documents
Improve your grades
Join milions of students
Basic Linear Rearrangements
Questions 1-3 are your warm-up exercises with simple linear formulas. These follow the same pattern: get the term with your target letter on one side, then divide or multiply to isolate it.
For example, with f = 5c - 8, you'd add 8 to both sides first, then divide by 5. It's just like solving equations, but you're working with letters instead of numbers.
These questions are worth 2 marks each, so expect to show two clear steps in your working.
Sign up to see the contentIt's free!
Access to all documents
Improve your grades
Join milions of students
Multi-Variable Formulas
Questions 4-6 introduce formulas with multiple variables - don't let this throw you off! The process is exactly the same, you're just moving around more letters.
When you see something like m = 5n + 2p and need to make p the subject, treat everything else as if it were a number. Subtract 5n from both sides, then divide by 2.
The key is staying organised and taking it one step at a time - rushing leads to silly mistakes that cost you easy marks.
Sign up to see the contentIt's free!
Access to all documents
Improve your grades
Join milions of students
Stepping Up the Difficulty
Now things get more interesting with squares and physics formulas. Question 7 involves n², which means you'll need to square root both sides after rearranging.
Questions 8 and 9 use classic physics equations that you might recognise from science lessons. The v = u + at formula is particularly important - knowing how to rearrange it will help in both maths and physics exams.
Remember: When dealing with squares, don't forget the ± symbol when you take the square root (though sometimes the context tells you which sign to use).
Sign up to see the contentIt's free!
Access to all documents
Improve your grades
Join milions of students
Advanced Techniques
Question 10 brings in square roots and fractions together - this is where careful working really pays off. You'll need to square both sides first to get rid of the square root, then work with the fraction.
These questions are worth 3 marks, indicating you need to show more steps. Plan your approach before diving in, and remember that with square roots, you usually need to isolate the root first before squaring.
Sign up to see the contentIt's free!
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Improve your grades
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Fractional Coefficients
Questions 12-14 focus on formulas with fractions as coefficients. When you see something like y = ½x + 6, remember that dividing by ½ is the same as multiplying by 2.
These questions test whether you really understand how fractions work in algebra. The key is to multiply by the reciprocal (flip the fraction upside down) rather than trying to divide by fractions.
Question 14 is worth 3 marks, suggesting there might be a bit more manipulation involved than the others.
Sign up to see the contentIt's free!
Access to all documents
Improve your grades
Join milions of students
Challenge Questions
The final set brings together everything you've learned with complex rearrangements. Question 15 has everything equal to zero, Question 16 involves cubes, and Question 17 combines fractions with multiple terms.
These are the questions that separate the good students from the great ones. Take your time, work methodically, and don't panic if they look complicated at first glance.
Exam Strategy: If you're running out of time, prioritise the 2-mark questions over the 3-mark ones - they're usually quicker and give you more points per minute spent.
Sign up to see the contentIt's free!
Access to all documents
Improve your grades
Join milions of students
We thought you’d never ask...
What is the Knowunity AI companion?
Our AI Companion is a student-focused AI tool that offers more than just answers. Built on millions of Knowunity resources, it provides relevant information, personalised study plans, quizzes, and content directly in the chat, adapting to your individual learning journey.
Where can I download the Knowunity app?
You can download the app from Google Play Store and Apple App Store.
Is Knowunity really free of charge?
That's right! Enjoy free access to study content, connect with fellow students, and get instant help – all at your fingertips.
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Most popular content in Maths
maths helpbook to get grade 9
material from online, not my personal advice
Maths9
Most popular content
Can't find what you're looking for? Explore other subjects.
Students love us — and so will you.
4.6/5
App Store
4.7/5
Google Play
The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
Stefan S
iOS user
This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha Klich
Android user
Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
Anna
iOS user
Best app on earth! no words because it’s too good
Thomas R
iOS user
Just amazing. Let's me revise 10x better, this app is a quick 10/10. I highly recommend it to anyone. I can watch and search for notes. I can save them in the subject folder. I can revise it any time when I come back. If you haven't tried this app, you're really missing out.
Basil
Android user
This app has made me feel so much more confident in my exam prep, not only through boosting my own self confidence through the features that allow you to connect with others and feel less alone, but also through the way the app itself is centred around making you feel better. It is easy to navigate, fun to use, and helpful to anyone struggling in absolutely any way.
David K
iOS user
The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!
Sudenaz Ocak
Android user
In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.
Greenlight Bonnie
Android user
very reliable app to help and grow your ideas of Maths, English and other related topics in your works. please use this app if your struggling in areas, this app is key for that. wish I'd of done a review before. and it's also free so don't worry about that.
Rohan U
Android user
I know a lot of apps use fake accounts to boost their reviews but this app deserves it all. Originally I was getting 4 in my English exams and this time I got a grade 7. I didn’t even know about this app three days until the exam and it has helped A LOT. Please actually trust me and use it as I’m sure you too will see developments.
Xander S
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE Knowunity AI. 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 Knowunity AI. 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