Maths
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Responding to change (a2 only)
Infection and response
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Organisms respond to changes in their internal and external environments (a-level only)
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Britain & the wider world: 1745 -1901
1l the quest for political stability: germany, 1871-1991
The cold war
Inter-war germany
Medieval period: 1066 -1509
2d religious conflict and the church in england, c1529-c1570
2o democracy and nazism: germany, 1918-1945
1f industrialisation and the people: britain, c1783-1885
1c the tudors: england, 1485-1603
2m wars and welfare: britain in transition, 1906-1957
World war two & the holocaust
2n revolution and dictatorship: russia, 1917-1953
2s the making of modern britain, 1951-2007
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324
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30 Nov 2025
•
Olamide
@olamide_26
Ratio and proportion might sound intimidating, but they're actually everywhere... Show more
Ratios compare one part to another part using the ':' symbol, whilst proportions compare one part to the whole and are written as fractions. Think of it this way: if there are 3 boys and 2 girls in your group, the ratio is 3:2, but the proportion of boys is 3/5 of the total.
Simplifying ratios works just like simplifying fractions - divide both sides by their common factor. For example, 10:15 becomes 2:3 when you divide both by 5. Sometimes you'll need ratios in the form 1:n or n:1, which means making one side equal to 1 by dividing through.
When sharing amounts in ratios, add up all the parts first, then divide your total by this number to find what one part is worth. If you're sharing £90 in the ratio 2:3:4, that's 9 parts total, so each part is worth £10.
Quick Tip: Always check your ratio sharing adds up to the original total!
Proportional reasoning and the unitary method are your go-to tools for solving trickier problems. The unitary method means finding the value of one unit first, then scaling up. If 3 cakes need 450g sugar, then 1 cake needs 150g, so 5 cakes need 750g.
Sometimes you'll have ratios that are already shared and need to work backwards. If money was split 3:2:5 and you know one person got £16 for their '2 parts', then each part is worth £8, making the total £80.
Best buys are dead simple once you know the trick - divide the price by the quantity to get the cost per item. The cheapest per item wins! This skill will save you money when shopping.
Real-world Tip: Use the unitary method for anything involving rates - cooking recipes, currency exchange, or working out how long tasks will take.
Percentages are just another way of writing proportions, but out of 100 instead of the actual total. The key building blocks are finding 1% (divide by 100) and 10% (divide by 10) - everything else builds from these.
Percentage change uses the formula: difference ÷ original × 100%. For increasing or decreasing by percentages, you can either find the percentage amount and add/subtract it, or use percentage multipliers (like 1.12 for a 12% increase or 0.88 for a 12% decrease).
Reverse percentages trip up loads of students, but remember to identify what percentage you actually have first. If something costs £45 after a 10% discount, that £45 represents 90% of the original price, not 100%.
The module wraps up with simple interest (just percentage of the original amount each year) and the essential speed, distance, time triangle - speed equals distance divided by time.
Exam Hack: For reverse percentages, look for words like 'after', 'following', or 'reduced to' - these tell you the given amount isn't 100%.
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
Olamide
@olamide_26
Ratio and proportion might sound intimidating, but they're actually everywhere in your daily life - from splitting a pizza fairly among mates to working out the best deal at the shops. This module breaks down all the essential skills you... Show more
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Ratios compare one part to another part using the ':' symbol, whilst proportions compare one part to the whole and are written as fractions. Think of it this way: if there are 3 boys and 2 girls in your group, the ratio is 3:2, but the proportion of boys is 3/5 of the total.
Simplifying ratios works just like simplifying fractions - divide both sides by their common factor. For example, 10:15 becomes 2:3 when you divide both by 5. Sometimes you'll need ratios in the form 1:n or n:1, which means making one side equal to 1 by dividing through.
When sharing amounts in ratios, add up all the parts first, then divide your total by this number to find what one part is worth. If you're sharing £90 in the ratio 2:3:4, that's 9 parts total, so each part is worth £10.
Quick Tip: Always check your ratio sharing adds up to the original total!
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
Proportional reasoning and the unitary method are your go-to tools for solving trickier problems. The unitary method means finding the value of one unit first, then scaling up. If 3 cakes need 450g sugar, then 1 cake needs 150g, so 5 cakes need 750g.
Sometimes you'll have ratios that are already shared and need to work backwards. If money was split 3:2:5 and you know one person got £16 for their '2 parts', then each part is worth £8, making the total £80.
Best buys are dead simple once you know the trick - divide the price by the quantity to get the cost per item. The cheapest per item wins! This skill will save you money when shopping.
Real-world Tip: Use the unitary method for anything involving rates - cooking recipes, currency exchange, or working out how long tasks will take.
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
Percentages are just another way of writing proportions, but out of 100 instead of the actual total. The key building blocks are finding 1% (divide by 100) and 10% (divide by 10) - everything else builds from these.
Percentage change uses the formula: difference ÷ original × 100%. For increasing or decreasing by percentages, you can either find the percentage amount and add/subtract it, or use percentage multipliers (like 1.12 for a 12% increase or 0.88 for a 12% decrease).
Reverse percentages trip up loads of students, but remember to identify what percentage you actually have first. If something costs £45 after a 10% discount, that £45 represents 90% of the original price, not 100%.
The module wraps up with simple interest (just percentage of the original amount each year) and the essential speed, distance, time triangle - speed equals distance divided by time.
Exam Hack: For reverse percentages, look for words like 'after', 'following', or 'reduced to' - these tell you the given amount isn't 100%.
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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Explore the Year 9 Foundation Assessment focusing on key mathematical concepts such as ratios, proportions, similar triangles, and scale factors. This assessment includes calculator-based questions and detailed solutions to enhance understanding. Ideal for students preparing for SATS Arithmetic and improving their skills in proportional relationships and decimal calculations.
MathsExplore the concepts of direct and inverse proportion with detailed explanations and worked examples. This resource covers the constant of proportionality, equations for both types of proportion, and practical problem-solving techniques. Ideal for GCSE Maths revision.
MathsExplore direct and inverse proportionality through a series of exam-style questions. This resource covers key concepts such as proportional relationships, constants of proportionality, and multi-step problem-solving techniques. Ideal for students preparing for exams in mathematics.
MathsExplore detailed solutions for a higher-level math exam covering key concepts such as ratios, proportions, transformations, volume calculations, and direct proportionality. This resource includes model answers for various problems, including frequency tables and geometric transformations, making it ideal for exam preparation.
MathsMaximize your exam success with this comprehensive GCSE Maths revision strategy. This guide outlines a structured approach to revising key topics, including geometry, trigonometry, and statistics. Learn effective techniques such as spaced revision, content consolidation, and exam question application to enhance your understanding and retention. Ideal for students preparing for the Edexcel Maths (Higher) exam.
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