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Maths
4 Dec 2025
419
2 pages
๐๐๐๐๐๐๐ ๐๐ชฝ @m1kaylax
Welcome to your quick guide to key maths concepts! We'll explore index laws, surds, inequalities, sequences, and more.... Show more
Ever wondered how to simplify complex expressions? Index laws are your best friends here! When dealing with the same base, remember add powers when multiplying , subtract powers when dividing , and multiply powers when raising to another power .
Surds are simply irrational numbers that come from roots (like โ2). They can't be written as simple fractions or terminating decimals. When working with surds, remember that โa ร โb = โ(ab) and โa รท โb = โ. To rationalise a surd in the denominator, multiply both top and bottom by the same surd to eliminate it from the bottom.
Linear inequalities use symbols like < (less than), > (greater than), โค (less than or equal to), and โฅ (greater than or equal to). Solve them just like equations, but remember to flip the inequality sign if you multiply or divide by a negative number.
Pro Tip When working with sequences, identify the pattern first - is it arithmetic , geometric , or quadratic (second difference is constant)? This will determine which formula to use!
Understanding special graphs gives you powerful visual tools. Cubic graphs have distinctive S-shapes, exponential graphs curve upward rapidly, reciprocal graphs have asymptotes, and trigonometric graphs (sine, cosine, tangent) have regular wave patterns with key intercepts and turning points.
Knowing the exact trigonometric values for common angles will save you tons of time in exams! For angles 0ยฐ, 30ยฐ, 45ยฐ, 60ยฐ and 90ยฐ, there are specific values for sine, cosine and tangent that you should memorise rather than calculate each time.
The fundamental trigonometric ratios relate the sides of a right-angled triangle sine = opposite/hypotenuse, cosine = adjacent/hypotenuse, and tangent = opposite/adjacent. These are the building blocks for solving any triangle problem you'll encounter.
A clever way to remember these values is using the "finger trick" - counting from your thumb (0ยฐ) to your pinky (90ยฐ). For sin, the values start at 0 and increase (0, 1/2, โ2/2, โ3/2, 1), while for cos, they decrease from 1 to 0 (1, โ3/2, โ2/2, 1/2, 0).
Remember This Trig values appear everywhere in maths and physics! When you see sin60ยฐ, you should immediately know it equals โ3/2 without needing a calculator.
When working with angles beyond 90ยฐ, you'll need to understand how these values repeat in patterns. Sine and cosine have a period of 360ยฐ, while tangent repeats every 180ยฐ. This knowledge is crucial for sketching graphs and solving equations involving trigonometric functions.
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 โ all at your fingertips.
5
Smart Tools NEW
Transform this note into: โ 50+ Practice Questions โ Interactive Flashcards โ Full Mock Exam โ Essay Outlines
Explore key concepts in the Remainder Theorem, polynomial division, and coordinate geometry. This study note covers the factor theorem, transformations, circle equations, and tangents to circles, providing essential insights for mastering these mathematical principles.
MathsExplore the Quadratic Formula and Discriminant to solve quadratic equations and analyze their roots. Learn methods for solving simultaneous equations, including elimination and substitution, and understand how to tackle linear and quadratic inequalities. This summary provides essential techniques and examples for mastering these key algebra concepts.
MathsExplore key concepts of cubic and quartic functions, including reflections, stretches, and translations. This resource covers essential definitions and transformations of graphs, making it ideal for Year 12 Edexcel A Level Maths revision.
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 itโs 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 didnโt even know about this app three days until the exam and it has helped A LOT. Please actually trust me and use it as Iโm 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 ๐๐๐ฒ๐ค๐โจ๐๐ฎ
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 itโs 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 didnโt even know about this app three days until the exam and it has helped A LOT. Please actually trust me and use it as Iโm 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 ๐๐๐ฒ๐ค๐โจ๐๐ฎ
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
๐๐๐๐๐๐๐ ๐๐ชฝ
@m1kaylax
Welcome to your quick guide to key maths concepts! We'll explore index laws, surds, inequalities, sequences, and more. These fundamental ideas are crucial for solving complex problems and will appear in many of your exams.
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
Ever wondered how to simplify complex expressions? Index laws are your best friends here! When dealing with the same base, remember: add powers when multiplying , subtract powers when dividing , and multiply powers when raising to another power .
Surds are simply irrational numbers that come from roots (like โ2). They can't be written as simple fractions or terminating decimals. When working with surds, remember that โa ร โb = โ(ab) and โa รท โb = โ. To rationalise a surd in the denominator, multiply both top and bottom by the same surd to eliminate it from the bottom.
Linear inequalities use symbols like < (less than), > (greater than), โค (less than or equal to), and โฅ (greater than or equal to). Solve them just like equations, but remember to flip the inequality sign if you multiply or divide by a negative number.
Pro Tip: When working with sequences, identify the pattern first - is it arithmetic , geometric , or quadratic (second difference is constant)? This will determine which formula to use!
Understanding special graphs gives you powerful visual tools. Cubic graphs have distinctive S-shapes, exponential graphs curve upward rapidly, reciprocal graphs have asymptotes, and trigonometric graphs (sine, cosine, tangent) have regular wave patterns with key intercepts and turning points.
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
Knowing the exact trigonometric values for common angles will save you tons of time in exams! For angles 0ยฐ, 30ยฐ, 45ยฐ, 60ยฐ and 90ยฐ, there are specific values for sine, cosine and tangent that you should memorise rather than calculate each time.
The fundamental trigonometric ratios relate the sides of a right-angled triangle: sine = opposite/hypotenuse, cosine = adjacent/hypotenuse, and tangent = opposite/adjacent. These are the building blocks for solving any triangle problem you'll encounter.
A clever way to remember these values is using the "finger trick" - counting from your thumb (0ยฐ) to your pinky (90ยฐ). For sin, the values start at 0 and increase (0, 1/2, โ2/2, โ3/2, 1), while for cos, they decrease from 1 to 0 (1, โ3/2, โ2/2, 1/2, 0).
Remember This: Trig values appear everywhere in maths and physics! When you see sin60ยฐ, you should immediately know it equals โ3/2 without needing a calculator.
When working with angles beyond 90ยฐ, you'll need to understand how these values repeat in patterns. Sine and cosine have a period of 360ยฐ, while tangent repeats every 180ยฐ. This knowledge is crucial for sketching graphs and solving equations involving trigonometric functions.
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 โ all at your fingertips.
5
Smart Tools NEW
Transform this note into: โ 50+ Practice Questions โ Interactive Flashcards โ Full Mock Exam โ Essay Outlines
Explore key concepts in the Remainder Theorem, polynomial division, and coordinate geometry. This study note covers the factor theorem, transformations, circle equations, and tangents to circles, providing essential insights for mastering these mathematical principles.
MathsExplore the Quadratic Formula and Discriminant to solve quadratic equations and analyze their roots. Learn methods for solving simultaneous equations, including elimination and substitution, and understand how to tackle linear and quadratic inequalities. This summary provides essential techniques and examples for mastering these key algebra concepts.
MathsExplore key concepts of cubic and quartic functions, including reflections, stretches, and translations. This resource covers essential definitions and transformations of graphs, making it ideal for Year 12 Edexcel A Level Maths revision.
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 itโs 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 didnโt even know about this app three days until the exam and it has helped A LOT. Please actually trust me and use it as Iโm 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 ๐๐๐ฒ๐ค๐โจ๐๐ฎ
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 itโs 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 didnโt even know about this app three days until the exam and it has helped A LOT. Please actually trust me and use it as Iโm 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 ๐๐๐ฒ๐ค๐โจ๐๐ฎ
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