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29 Nov 2025
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Comprehensive National 5 Maths Revision Guide
Lauren
@lauren_b
1 / 4
Foundation Skills: Numbers, Fractions & Basic Algebra
Scientific notation is your friend for handling massive or tiny numbers - you'll multiply and divide these values and express regular numbers in this compact form. It's surprisingly straightforward once you get the hang of it.
Fractions and percentages form the backbone of many exam questions. You'll need to confidently add, subtract, multiply and divide fractions (including mixed numbers), plus tackle percentage calculations. Reverse percentages help you work backwards to find original values, whilst compound percentages deal with things like interest rates over time.
Expanding brackets might seem tedious, but it's essential for higher-level work. You'll expand everything from simple forms like a + d to more complex expressions like . The key is systematic practice.
Top tip: Master these foundation skills first - they're the building blocks for everything else on this list!
Intermediate Algebra & Geometry
Factorising is essentially expanding in reverse - you'll use common factors, difference of two squares, and trinomials (both simple and complex forms). This skill is crucial for solving quadratic equations later.
Straight line equations pop up everywhere, so you'll need to find equations from coordinates, graphs, or real-world contexts. Surds require you to simplify expressions by breaking them down systematically.
Index laws govern how you handle powers and roots. The main rules will become second nature with practice. Don't forget that a⁻ⁿ = 1/aⁿ.
Arcs, sectors and volume calculations involve specific formulas for cylinders, cones, spheres, hemispheres, and pyramids. Completing the square transforms quadratics from x² + bx + c into the more useful form ² + q.
Remember: Pythagoras' theorem works in 2D, 3D, and circle contexts - it's one of the most versatile tools in your mathematical arsenal!
Advanced Topics: Trigonometry & Quadratics
Trigonometry extends far beyond basic SOHCAHTOA. You'll use the sine and cosine rules for non-right-angled triangles, plus the area formula. Trigonometric graphs require understanding amplitude, frequency, and period changes.
Trigonometric equations need you to find all solutions within a given range, whilst trigonometric identities like tan(x) = sin x/cos x and sin²x + cos²x = 1 help simplify complex expressions.
Angle properties cover everything from basic triangle rules to complex circle theorems. You'll identify isosceles triangles, work with triangles in semicircles, and handle tangents to circles. Polygons have their own angle rules for central and interior angles.
Algebraic fractions require the same four operations as numerical fractions, but with variables thrown in. You'll cancel terms, combine fractions, and simplify complex expressions. Simultaneous equations can be solved algebraically or interpreted from context.
Key insight: Quadratic graphs in different forms each reveal different information about turning points, roots, and intercepts.
Final Skills: Problem Solving & Precision
Quadratic equations can be solved through factorising or the quadratic formula - knowing when to use each method saves valuable exam time. The quadratic formula works for any quadratic, whilst factorising is quicker when possible.
Functions use special notation like f(x) to represent mathematical relationships. You'll evaluate expressions using functional notation, which is essentially substituting values into given formulas.
Rounding might seem basic, but precision matters in exams. You'll round to specified decimal places or significant figures - make sure you understand the difference between these two methods.
Exam strategy: Practice changing the subject of a formula involving squares and square roots - these questions often appear and can boost your confidence early in the exam!
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.
Can't find what you're looking for? Explore other subjects.
Students love us — and so will you.
4.9/5
App Store
4.8/5
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 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
Comprehensive National 5 Maths Revision Guide
Lauren
@lauren_b
Getting ready for your N5 maths exam? This comprehensive skills checklist covers all the essential topics you'll need to master, from basic algebraic manipulation to advanced trigonometry and quadratic equations. Think of this as your mathematical toolkit - once you've... Show more
Foundation Skills: Numbers, Fractions & Basic Algebra
Scientific notation is your friend for handling massive or tiny numbers - you'll multiply and divide these values and express regular numbers in this compact form. It's surprisingly straightforward once you get the hang of it.
Fractions and percentages form the backbone of many exam questions. You'll need to confidently add, subtract, multiply and divide fractions (including mixed numbers), plus tackle percentage calculations. Reverse percentages help you work backwards to find original values, whilst compound percentages deal with things like interest rates over time.
Expanding brackets might seem tedious, but it's essential for higher-level work. You'll expand everything from simple forms like a + d to more complex expressions like . The key is systematic practice.
Top tip: Master these foundation skills first - they're the building blocks for everything else on this list!
Sign up to see the contentIt's free!
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
Intermediate Algebra & Geometry
Factorising is essentially expanding in reverse - you'll use common factors, difference of two squares, and trinomials (both simple and complex forms). This skill is crucial for solving quadratic equations later.
Straight line equations pop up everywhere, so you'll need to find equations from coordinates, graphs, or real-world contexts. Surds require you to simplify expressions by breaking them down systematically.
Index laws govern how you handle powers and roots. The main rules will become second nature with practice. Don't forget that a⁻ⁿ = 1/aⁿ.
Arcs, sectors and volume calculations involve specific formulas for cylinders, cones, spheres, hemispheres, and pyramids. Completing the square transforms quadratics from x² + bx + c into the more useful form ² + q.
Remember: Pythagoras' theorem works in 2D, 3D, and circle contexts - it's one of the most versatile tools in your mathematical arsenal!
Sign up to see the contentIt's free!
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
Advanced Topics: Trigonometry & Quadratics
Trigonometry extends far beyond basic SOHCAHTOA. You'll use the sine and cosine rules for non-right-angled triangles, plus the area formula. Trigonometric graphs require understanding amplitude, frequency, and period changes.
Trigonometric equations need you to find all solutions within a given range, whilst trigonometric identities like tan(x) = sin x/cos x and sin²x + cos²x = 1 help simplify complex expressions.
Angle properties cover everything from basic triangle rules to complex circle theorems. You'll identify isosceles triangles, work with triangles in semicircles, and handle tangents to circles. Polygons have their own angle rules for central and interior angles.
Algebraic fractions require the same four operations as numerical fractions, but with variables thrown in. You'll cancel terms, combine fractions, and simplify complex expressions. Simultaneous equations can be solved algebraically or interpreted from context.
Key insight: Quadratic graphs in different forms each reveal different information about turning points, roots, and intercepts.
Sign up to see the contentIt's free!
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
Final Skills: Problem Solving & Precision
Quadratic equations can be solved through factorising or the quadratic formula - knowing when to use each method saves valuable exam time. The quadratic formula works for any quadratic, whilst factorising is quicker when possible.
Functions use special notation like f(x) to represent mathematical relationships. You'll evaluate expressions using functional notation, which is essentially substituting values into given formulas.
Rounding might seem basic, but precision matters in exams. You'll round to specified decimal places or significant figures - make sure you understand the difference between these two methods.
Exam strategy: Practice changing the subject of a formula involving squares and square roots - these questions often appear and can boost your confidence early in the exam!
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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Can't find what you're looking for? Explore other subjects.
Students love us — and so will you.
4.9/5
App Store
4.8/5
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 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