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World war two & the holocaust
2m wars and welfare: britain in transition, 1906-1957
1f industrialisation and the people: britain, c1783-1885
Medieval period: 1066 -1509
1l the quest for political stability: germany, 1871-1991
Britain & the wider world: 1745 -1901
2d religious conflict and the church in england, c1529-c1570
The cold war
1c the tudors: england, 1485-1603
Inter-war germany
2j america: a nation divided, c1845-1877
2n revolution and dictatorship: russia, 1917-1953
2s the making of modern britain, 1951-2007
World war one
Britain: 1509 -1745
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300
•
25 Feb 2023
•
Kimberley
@kimberley_ncyf
This comprehensive study guide covers key mathematical concepts including expanding... Show more
This section delves deeper into quadratic factorisation and introduces the method of completing the square.
Example: 3x² + 11x + 6 is factored as
The page provides multiple examples of factoring quadratic expressions, including those with a coefficient other than 1 for the x² term. It then transitions to completing the square, a technique used to rewrite quadratic expressions in a specific form.
Definition: Completing the square is a method used to convert a quadratic expression into the form ² + q.
Highlight: The completing the square quadratic example with solution shown is x² + 8x - 5, which is rewritten as ² - 21.
This page covers rules for indices, further examples of expanding brackets, and an introduction to surds.
Vocabulary: Indices are the powers to which a number or variable is raised.
The page provides examples of simplifying expressions with indices and expanding brackets with more complex terms. It also introduces the concept of surds and their simplification.
Example: 3a³ × 4a / 8a² is simplified to 3/2a²
Highlight: The section on surds introduces important rules for simplifying and rationalising expressions involving square roots.
This page continues with more advanced surd operations and introduces scientific notation.
Definition: A surd is a root of a number that cannot be simplified to a whole or rational number.
The page provides examples of simplifying and rationalising surds, emphasizing the importance of fully simplifying expressions. It then transitions to scientific notation, demonstrating how to represent very large or small numbers.
Example: √27 + √48 - √12 is simplified to 5√3
Highlight: The scientific notation section includes practical examples, such as calculating the surface area of Jupiter relative to Earth.
This page focuses on applying scientific notation to real-world problems, particularly in astronomy and space travel.
Vocabulary: Scientific notation is a way of expressing numbers that are too large or too small to be conveniently written in decimal form.
The page provides examples of using scientific notation to perform calculations involving very large distances and speeds. It demonstrates how to use the distance-speed-time formula in conjunction with scientific notation.
Example: A rocket traveling at 1.32 × 10⁵ miles per second for 4 minutes covers a distance of 3.168 × 10⁸ miles.
Highlight: This section emphasizes the practical applications of scientific notation in fields like astronomy and space exploration.
The final page focuses on simplifying algebraic fractions, a crucial skill in advanced algebra.
Definition: An algebraic fraction is a fraction where the numerator, denominator, or both contain algebraic expressions.
The page provides examples of simplifying complex algebraic fractions, including those involving quadratic expressions. It demonstrates techniques for factoring and canceling common terms to simplify fractions.
Example: / is simplified to /
Highlight: The simplifying algebraic fractions questions and answers provided here offer valuable practice for students preparing for advanced mathematics exams.
This page covers techniques for expanding brackets and factorising expressions. It provides several examples to illustrate these important algebraic skills.
Example: ² is expanded as 4x²-12x+9
The page demonstrates the step-by-step process of expanding squared terms and multiplying two binomials. It also covers factorising techniques, including the difference of two squares and quadratic expressions.
Highlight: Factorising quadratic expressions is a crucial skill in algebra, often used in solving equations and simplifying complex expressions.
Vocabulary: Difference of two squares - a special case in algebra where an expression can be factored into the product of two binomials.
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
Kimberley
@kimberley_ncyf
This comprehensive study guide covers key mathematical concepts including expanding brackets in mathematics, completing the square quadratic example, and simplifying algebraic fractions. It provides detailed explanations and examples for students learning these topics.
• The guide covers... Show more
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
This section delves deeper into quadratic factorisation and introduces the method of completing the square.
Example: 3x² + 11x + 6 is factored as
The page provides multiple examples of factoring quadratic expressions, including those with a coefficient other than 1 for the x² term. It then transitions to completing the square, a technique used to rewrite quadratic expressions in a specific form.
Definition: Completing the square is a method used to convert a quadratic expression into the form ² + q.
Highlight: The completing the square quadratic example with solution shown is x² + 8x - 5, which is rewritten as ² - 21.
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
This page covers rules for indices, further examples of expanding brackets, and an introduction to surds.
Vocabulary: Indices are the powers to which a number or variable is raised.
The page provides examples of simplifying expressions with indices and expanding brackets with more complex terms. It also introduces the concept of surds and their simplification.
Example: 3a³ × 4a / 8a² is simplified to 3/2a²
Highlight: The section on surds introduces important rules for simplifying and rationalising expressions involving square roots.
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
This page continues with more advanced surd operations and introduces scientific notation.
Definition: A surd is a root of a number that cannot be simplified to a whole or rational number.
The page provides examples of simplifying and rationalising surds, emphasizing the importance of fully simplifying expressions. It then transitions to scientific notation, demonstrating how to represent very large or small numbers.
Example: √27 + √48 - √12 is simplified to 5√3
Highlight: The scientific notation section includes practical examples, such as calculating the surface area of Jupiter relative to Earth.
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
This page focuses on applying scientific notation to real-world problems, particularly in astronomy and space travel.
Vocabulary: Scientific notation is a way of expressing numbers that are too large or too small to be conveniently written in decimal form.
The page provides examples of using scientific notation to perform calculations involving very large distances and speeds. It demonstrates how to use the distance-speed-time formula in conjunction with scientific notation.
Example: A rocket traveling at 1.32 × 10⁵ miles per second for 4 minutes covers a distance of 3.168 × 10⁸ miles.
Highlight: This section emphasizes the practical applications of scientific notation in fields like astronomy and space exploration.
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
The final page focuses on simplifying algebraic fractions, a crucial skill in advanced algebra.
Definition: An algebraic fraction is a fraction where the numerator, denominator, or both contain algebraic expressions.
The page provides examples of simplifying complex algebraic fractions, including those involving quadratic expressions. It demonstrates techniques for factoring and canceling common terms to simplify fractions.
Example: / is simplified to /
Highlight: The simplifying algebraic fractions questions and answers provided here offer valuable practice for students preparing for advanced mathematics exams.
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
This page covers techniques for expanding brackets and factorising expressions. It provides several examples to illustrate these important algebraic skills.
Example: ² is expanded as 4x²-12x+9
The page demonstrates the step-by-step process of expanding squared terms and multiplying two binomials. It also covers factorising techniques, including the difference of two squares and quadratic expressions.
Highlight: Factorising quadratic expressions is a crucial skill in algebra, often used in solving equations and simplifying complex expressions.
Vocabulary: Difference of two squares - a special case in algebra where an expression can be factored into the product of two binomials.
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
