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Fun with Geometry: Cool Ways to Solve Inequalities and Build Triangles!

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Nila Heartin

29/06/2023

Maths

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Multiplying and dividing surds

Fun with Geometry: Cool Ways to Solve Inequalities and Build Triangles!

A comprehensive guide to advanced mathematics concepts, focusing on geometric inequalities, trigonometry, and shape constructions. This guide covers essential mathematical principles and problem-solving techniques for secondary education students.

• The material encompasses key areas including solving geometric inequalities in maths, circle theorems, and trigonometric ratios
• Detailed coverage of trigonometry and cyclic quadrilaterals explained with practical applications
• In-depth exploration of constructing triangles and calculating volumes for various 3D shapes
• Essential formulas and theorems for solving complex mathematical problems
• Comprehensive coverage of transformations, quadratic equations, and algebraic methods

...

29/06/2023

506

Inequality Emphy > dassed tre 7. Soled line X10 x70 x+y<3 find equation of line tur into inequalities Solving Inequalities solve 2x-17 2x 48

View

Page 2: Advanced Algebraic Concepts

This page delves into complex algebraic concepts including indices, transformations, and equation solving techniques. The material progresses from basic principles to more sophisticated mathematical operations.

Definition: Rational numbers are those that can be expressed as a fraction of two integers, while irrational numbers cannot be written as simple fractions.

Example: When completing the square for x² - 6x + 7, the process involves rewriting as x−3x-3² + 2.

Highlight: For perpendicular lines, the product of their gradients is always -1.

Vocabulary: Quadratic simultaneous equations involve two equations where at least one contains a squared term.

Inequality Emphy > dassed tre 7. Soled line X10 x70 x+y<3 find equation of line tur into inequalities Solving Inequalities solve 2x-17 2x 48

View

Page 3: Statistical Analysis and Line Equations

The third page covers statistical methods and linear equations, providing comprehensive techniques for data analysis and graphical representations.

Definition: Box plots are graphical representations showing the distribution of data through quartiles.

Example: When finding the equation of a line parallel to y = 3x - 6 through point 0,−60,-6, maintain the same gradient but adjust the y-intercept.

Highlight: The difference of two squares formula x2−a2x² - a² can always be factored as x+ax+ax−ax-a.

Inequality Emphy > dassed tre 7. Soled line X10 x70 x+y<3 find equation of line tur into inequalities Solving Inequalities solve 2x-17 2x 48

View

Page 4: Advanced Mathematical Applications

This final page focuses on practical applications and advanced mathematical concepts, bringing together various topics for comprehensive problem-solving.

Definition: Stem and leaf diagrams organize numerical data while preserving individual values.

Example: When calculating with standard form numbers, multiply the main numbers and add the powers of 10 separately.

Highlight: The mean of a dataset can be calculated by summing all values and dividing by the count of values.

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Subjects

Maths

Number

Surds

Multiplying and dividing surds

 

Maths

•

506

•

29 Jun 2023

•

4 pages

Fun with Geometry: Cool Ways to Solve Inequalities and Build Triangles!

user profile picture

Nila Heartin

@nilaheartin_tmsl

A comprehensive guide to advanced mathematics concepts, focusing on geometric inequalities, trigonometry, and shape constructions. This guide covers essential mathematical principles and problem-solving techniques for secondary education students.

• The material encompasses key areas including solving geometric inequalities in maths... Show more

Inequality Emphy > dassed tre 7. Soled line X10 x70 x+y<3 find equation of line tur into inequalities Solving Inequalities solve 2x-17 2x 48

Sign up to see the contentIt's free!

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Page 2: Advanced Algebraic Concepts

This page delves into complex algebraic concepts including indices, transformations, and equation solving techniques. The material progresses from basic principles to more sophisticated mathematical operations.

Definition: Rational numbers are those that can be expressed as a fraction of two integers, while irrational numbers cannot be written as simple fractions.

Example: When completing the square for x² - 6x + 7, the process involves rewriting as x−3x-3² + 2.

Highlight: For perpendicular lines, the product of their gradients is always -1.

Vocabulary: Quadratic simultaneous equations involve two equations where at least one contains a squared term.

Inequality Emphy > dassed tre 7. Soled line X10 x70 x+y<3 find equation of line tur into inequalities Solving Inequalities solve 2x-17 2x 48

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

Page 3: Statistical Analysis and Line Equations

The third page covers statistical methods and linear equations, providing comprehensive techniques for data analysis and graphical representations.

Definition: Box plots are graphical representations showing the distribution of data through quartiles.

Example: When finding the equation of a line parallel to y = 3x - 6 through point 0,−60,-6, maintain the same gradient but adjust the y-intercept.

Highlight: The difference of two squares formula x2−a2x² - a² can always be factored as x+ax+ax−ax-a.

Inequality Emphy > dassed tre 7. Soled line X10 x70 x+y<3 find equation of line tur into inequalities Solving Inequalities solve 2x-17 2x 48

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

Page 4: Advanced Mathematical Applications

This final page focuses on practical applications and advanced mathematical concepts, bringing together various topics for comprehensive problem-solving.

Definition: Stem and leaf diagrams organize numerical data while preserving individual values.

Example: When calculating with standard form numbers, multiply the main numbers and add the powers of 10 separately.

Highlight: The mean of a dataset can be calculated by summing all values and dividing by the count of values.

Inequality Emphy > dassed tre 7. Soled line X10 x70 x+y<3 find equation of line tur into inequalities Solving Inequalities solve 2x-17 2x 48

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

Page 1: Fundamental Mathematical Concepts

This page introduces core mathematical concepts focusing on inequalities, circle theorems, and trigonometry. The content builds a strong foundation for advanced mathematical understanding.

Definition: Circle theorems state that the angle at the center is twice the angle at the circumference when both angles intercept the same arc.

Highlight: In cyclic quadrilaterals, opposite angles are supplementary, meaning they add up to 180 degrees.

Example: When solving inequalities with negative numbers, the inequality sign must be reversed e.g.,ifdividingbothsidesby−2,change<to>e.g., if dividing both sides by -2, change < to >.

Vocabulary: Loci refers to the path of points that follow a specific mathematical rule or condition.

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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

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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