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Britain & the wider world: 1745 -1901
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2d religious conflict and the church in england, c1529-c1570
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Maths
8 Dec 2025
867
6 pages
Eren Gregg @renregg_deipnwscuzce
This collection covers essential GCSE maths topics you'll definitely encounter in your exams. From algebraic fractions to circle... Show more
Working with algebraic fractions is just like handling regular fractions, but with letters thrown into the mix. The key is spotting the highest common factor and cancelling it out to simplify.
When you're adding or subtracting algebraic fractions, you need a common denominator first. If the denominators are the same, just add or subtract the numerators and keep the denominator unchanged.
For fractions with different denominators, multiply each fraction to create matching denominators. Then combine the numerators as usual.
Quick tip Always look for common factors in brackets like – they cancel out just like numbers do!
Bounds help you understand the range of possible values when numbers are rounded. For a number rounded to the nearest 10, remember the lower bound includes the equals sign, but the upper bound doesn't.
The product rule makes counting combinations dead simple – just multiply all your options together. Restaurant menus, dice combinations, clothing choices – it works for everything.
Probability calculations often use sample space diagrams (like the dice table shown). Count your successful outcomes, divide by total possible outcomes, and you've got your answer.
Remember When finding bounds, think about what values would round to give your number – this helps you set the correct inequalities.
Simple interest stays constant each year – just calculate the percentage once and multiply by the number of years. Compound interest grows because you earn interest on your previous interest too.
Iteration is a clever method for solving equations that are too tricky for normal algebra. You use a formula repeatedly, plugging each answer back in until the values stop changing.
The iteration process continues until your answers stabilise to the required number of decimal places. It's like mathematical trial and improvement, but much more systematic.
Pro tip With compound interest, each year's calculation becomes the starting amount for the next year – that's where the "compounding" happens!
Parallel lines share identical gradients – that's literally all you need to remember. Change the y-intercept, keep the gradient the same, and you've got a parallel line.
Perpendicular lines use negative reciprocal gradients. If your original gradient is 2, the perpendicular gradient becomes -1/2. Flip the fraction and change the sign.
Bearings follow three strict rules measured from North, measured clockwise, and always written with three figures (like 045° instead of 45°).
Memory trick Perpendicular gradients multiply together to give -1, so 2 × (-1/2) = -1.
When parallel lines are cut by a transversal, you get four types of angle relationships that are absolute exam favourites. Alternate angles are equal and sit in a 'Z' pattern.
Corresponding angles are equal and sit in an 'F' pattern. Vertically opposite angles are equal where two lines cross.
Co-interior angles (also called allied angles) are different – they add up to 180° and sit in a 'C' pattern between the parallel lines.
Exam hack Learn to spot these patterns quickly – angle questions often test multiple relationships in one diagram.
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
Explore essential Nat 5 math concepts including standard deviation, scientific notation, completing the square, significant figures, algebraic fractions, expanding brackets, and arcs & sectors. This comprehensive summary provides clear examples and formulas to enhance your understanding and preparation for exams.
MathsPrepare for your Year 11 Maths Mock Exam with this comprehensive revision list for Paper 1 (non-calculator). Cover essential topics including arithmetic operations, negative numbers, fractions, percentages, graph types, and area and volume calculations. Perfect for focused study sessions and exam preparation.
MathsExplore essential topics for Edexcel GCSE Maths, including fractions, ratios, algebra, geometry, and statistics. This comprehensive overview covers non-negotiable concepts such as Pythagoras' Theorem, simultaneous equations, transformations, and probability. Perfect for revision and exam preparation.
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
Eren Gregg
@renregg_deipnwscuzce
This collection covers essential GCSE maths topics you'll definitely encounter in your exams. From algebraic fractions to circle geometry, these concepts build on each other and appear regularly in both coursework and final assessments.
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
Working with algebraic fractions is just like handling regular fractions, but with letters thrown into the mix. The key is spotting the highest common factor and cancelling it out to simplify.
When you're adding or subtracting algebraic fractions, you need a common denominator first. If the denominators are the same, just add or subtract the numerators and keep the denominator unchanged.
For fractions with different denominators, multiply each fraction to create matching denominators. Then combine the numerators as usual.
Quick tip: Always look for common factors in brackets like – they cancel out just like numbers do!
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
Bounds help you understand the range of possible values when numbers are rounded. For a number rounded to the nearest 10, remember the lower bound includes the equals sign, but the upper bound doesn't.
The product rule makes counting combinations dead simple – just multiply all your options together. Restaurant menus, dice combinations, clothing choices – it works for everything.
Probability calculations often use sample space diagrams (like the dice table shown). Count your successful outcomes, divide by total possible outcomes, and you've got your answer.
Remember: When finding bounds, think about what values would round to give your number – this helps you set the correct inequalities.
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
Simple interest stays constant each year – just calculate the percentage once and multiply by the number of years. Compound interest grows because you earn interest on your previous interest too.
Iteration is a clever method for solving equations that are too tricky for normal algebra. You use a formula repeatedly, plugging each answer back in until the values stop changing.
The iteration process continues until your answers stabilise to the required number of decimal places. It's like mathematical trial and improvement, but much more systematic.
Pro tip: With compound interest, each year's calculation becomes the starting amount for the next year – that's where the "compounding" happens!
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
Parallel lines share identical gradients – that's literally all you need to remember. Change the y-intercept, keep the gradient the same, and you've got a parallel line.
Perpendicular lines use negative reciprocal gradients. If your original gradient is 2, the perpendicular gradient becomes -1/2. Flip the fraction and change the sign.
Bearings follow three strict rules: measured from North, measured clockwise, and always written with three figures (like 045° instead of 45°).
Memory trick: Perpendicular gradients multiply together to give -1, so 2 × (-1/2) = -1.
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
When parallel lines are cut by a transversal, you get four types of angle relationships that are absolute exam favourites. Alternate angles are equal and sit in a 'Z' pattern.
Corresponding angles are equal and sit in an 'F' pattern. Vertically opposite angles are equal where two lines cross.
Co-interior angles (also called allied angles) are different – they add up to 180° and sit in a 'C' pattern between the parallel lines.
Exam hack: Learn to spot these patterns quickly – angle questions often test multiple relationships in one diagram.
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
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
Explore essential Nat 5 math concepts including standard deviation, scientific notation, completing the square, significant figures, algebraic fractions, expanding brackets, and arcs & sectors. This comprehensive summary provides clear examples and formulas to enhance your understanding and preparation for exams.
MathsPrepare for your Year 11 Maths Mock Exam with this comprehensive revision list for Paper 1 (non-calculator). Cover essential topics including arithmetic operations, negative numbers, fractions, percentages, graph types, and area and volume calculations. Perfect for focused study sessions and exam preparation.
MathsExplore essential topics for Edexcel GCSE Maths, including fractions, ratios, algebra, geometry, and statistics. This comprehensive overview covers non-negotiable concepts such as Pythagoras' Theorem, simultaneous equations, transformations, and probability. Perfect for revision and exam preparation.
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