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4 Dec 2025
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Understanding Algebra: A Fundamental Part of Math
B
Bob Lemon
@boblemon_etrw
1 / 5
Assessment Overview
This comprehensive algebra assessment tests 14 key areas that are absolutely crucial for your maths success. The topics range from basic simplification through to more complex quadratic graphs and sequences.
The assessment is worth 100 marks total and covers everything from combining like terms to finding nth terms of sequences. Each section builds on the previous one, so mastering the early topics makes the later ones much easier.
Top Tip: Focus extra attention on simplifying expressions and expanding brackets - these skills appear in nearly every other algebra topic!
Simplifying Expressions
Adding and subtracting like terms is all about combining terms that have exactly the same variables. Think of it like collecting similar objects - you can add 2 apples + 5 apples, but you can't directly combine apples and oranges.
For multiplication, remember that x × x = x², and when multiplying powers you add the indices: x² × x³ = x⁵. When you see 3x² × 2x⁵, multiply the numbers (3 × 2 = 6) and add the powers (2 + 5 = 7) to get 6x⁷.
Division with algebra follows the opposite rule - you subtract the powers instead of adding them. So x⁵ ÷ x³ = x². This is because you're essentially cancelling out matching factors.
Remember: You can only combine terms that have identical variable parts - 3x and 5x can be added, but 3x and 5y cannot!
Function Machines, Brackets and Factorisation
Function machines show you step-by-step operations applied to input values. If you put 1 into a machine that multiplies by 3 then adds 2, you get 1 × 3 + 2 = 5. Work backwards from the output to find unknown inputs.
Expanding brackets means multiplying everything inside the bracket by what's outside. For 2, multiply both 4x and -3 by 2 to get 8x - 6. With expressions like x, you get x² + 7x.
Factorisation is the reverse of expanding - you're looking for common factors to take outside a bracket. For 6x + 9, both terms divide by 3, so you get 3.
Quick Check: After expanding or factorising, substitute a simple number like x = 2 to verify your answer matches the original expression!
Substitution and Linear Graphs
Substitution means replacing letters with actual numbers and calculating the result. When x = 6, the expression 3x - 20 becomes 3(6) - 20 = 18 - 20 = -2. Always follow the order of operations (BIDMAS).
For straight line graphs, you'll often work with equations like y = 2x - 1. Create a table of values by choosing x-values and calculating the corresponding y-values. Then plot these coordinate pairs and draw a straight line through them.
Gradient tells you how steep a line is. Count how many units you go up (or down) for every unit you go across. A line that rises 2 units for every 1 unit across has a gradient of 2.
Pro Tip: When finding gradient, remember "change in y divided by change in x" - pick two clear points on the line to make your calculation easier!
Quadratic Graphs and Sequences
Quadratic graphs have x² terms and create U-shaped curves called parabolas. Complete a table of values for equations like y = x² - 4x + 3, plot the points, and draw a smooth curve through them. These graphs can help you solve equations graphically.
Sequences follow patterns that you can describe with formulas. For the nth term like 5n - 3, substitute the position number to find any term. The 7th term would be 5(7) - 3 = 32.
Arithmetic sequences increase by the same amount each time. To find the nth term, identify the common difference and the pattern. Special sequences like triangular numbers have their own unique formulas.
Memory Aid: For arithmetic sequences, if the common difference is 4 and the first term is 7, the nth term is 4n + 3 (always one less than the first term added to the difference × n)!
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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 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
Understanding Algebra: A Fundamental Part of Math
B
Bob Lemon
@boblemon_etrw
This Algebra 1H assessment covers the essential building blocks of higher-level maths that you'll use throughout your GCSE studies. From simplifying expressions to drawing graphs, these skills form the foundation for more advanced topics you'll tackle later.
Assessment Overview
This comprehensive algebra assessment tests 14 key areas that are absolutely crucial for your maths success. The topics range from basic simplification through to more complex quadratic graphs and sequences.
The assessment is worth 100 marks total and covers everything from combining like terms to finding nth terms of sequences. Each section builds on the previous one, so mastering the early topics makes the later ones much easier.
Top Tip: Focus extra attention on simplifying expressions and expanding brackets - these skills appear in nearly every other algebra topic!
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
Simplifying Expressions
Adding and subtracting like terms is all about combining terms that have exactly the same variables. Think of it like collecting similar objects - you can add 2 apples + 5 apples, but you can't directly combine apples and oranges.
For multiplication, remember that x × x = x², and when multiplying powers you add the indices: x² × x³ = x⁵. When you see 3x² × 2x⁵, multiply the numbers (3 × 2 = 6) and add the powers (2 + 5 = 7) to get 6x⁷.
Division with algebra follows the opposite rule - you subtract the powers instead of adding them. So x⁵ ÷ x³ = x². This is because you're essentially cancelling out matching factors.
Remember: You can only combine terms that have identical variable parts - 3x and 5x can be added, but 3x and 5y cannot!
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
Function Machines, Brackets and Factorisation
Function machines show you step-by-step operations applied to input values. If you put 1 into a machine that multiplies by 3 then adds 2, you get 1 × 3 + 2 = 5. Work backwards from the output to find unknown inputs.
Expanding brackets means multiplying everything inside the bracket by what's outside. For 2, multiply both 4x and -3 by 2 to get 8x - 6. With expressions like x, you get x² + 7x.
Factorisation is the reverse of expanding - you're looking for common factors to take outside a bracket. For 6x + 9, both terms divide by 3, so you get 3.
Quick Check: After expanding or factorising, substitute a simple number like x = 2 to verify your answer matches the original expression!
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
Substitution and Linear Graphs
Substitution means replacing letters with actual numbers and calculating the result. When x = 6, the expression 3x - 20 becomes 3(6) - 20 = 18 - 20 = -2. Always follow the order of operations (BIDMAS).
For straight line graphs, you'll often work with equations like y = 2x - 1. Create a table of values by choosing x-values and calculating the corresponding y-values. Then plot these coordinate pairs and draw a straight line through them.
Gradient tells you how steep a line is. Count how many units you go up (or down) for every unit you go across. A line that rises 2 units for every 1 unit across has a gradient of 2.
Pro Tip: When finding gradient, remember "change in y divided by change in x" - pick two clear points on the line to make your calculation easier!
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
Quadratic Graphs and Sequences
Quadratic graphs have x² terms and create U-shaped curves called parabolas. Complete a table of values for equations like y = x² - 4x + 3, plot the points, and draw a smooth curve through them. These graphs can help you solve equations graphically.
Sequences follow patterns that you can describe with formulas. For the nth term like 5n - 3, substitute the position number to find any term. The 7th term would be 5(7) - 3 = 32.
Arithmetic sequences increase by the same amount each time. To find the nth term, identify the common difference and the pattern. Special sequences like triangular numbers have their own unique formulas.
Memory Aid: For arithmetic sequences, if the common difference is 4 and the first term is 7, the nth term is 4n + 3 (always one less than the first term added to the difference × n)!
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