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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

GCSE Maths Mindmap

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Surds

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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

498

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-3)² + 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,-6), maintain the same gradient but adjust the y-intercept.

Highlight: The difference of two squares formula (x² - a²) can always be factored as (x+a)(x-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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Can't find what you're looking for? Explore other subjects.

Knowunity is the #1 education app in five European countries

Knowunity has been named a featured story on Apple and has regularly topped the app store charts in the education category in Germany, Italy, Poland, Switzerland, and the United Kingdom. Join Knowunity today and help millions of students around the world.

Ranked #1 Education App

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Knowunity is the #1 education app in five European countries

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Pupils love Knowunity

#1

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950 K+

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iOS User

I love this app so much, I also use it daily. I recommend Knowunity to everyone!!! I went from a D to an A with it :D

Philip, iOS User

The app is very simple and well designed. So far I have always found everything I was looking for :D

Lena, iOS user

I love this app ❤️ I actually use it every time I study.

Subjects

/

Maths

/

Number

/

Surds

/

Multiplying and dividing surds

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

user profile picture

Nila Heartin

@nilaheartin_tmsl

·

39 Followers

Follow

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

498

 

10/11

 

Maths

10

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 content. It's free!

Access to all documents

Improve your grades

Join milions of students

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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-3)² + 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 content. It'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,-6), maintain the same gradient but adjust the y-intercept.

Highlight: The difference of two squares formula (x² - a²) can always be factored as (x+a)(x-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 content. It'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 content. It'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., 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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Notes on Surds and Indicies (with some additional notes /info on Rational and irrational numbers along with Recurring decimal conversions) for GCSE Maths

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simplifying surds, adding and subtracting surds, multiplying surds, dividing surds and rationalising the denominator of surds fractions.

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Know Surds - a complete note set thumbnail

Maths - Adding and Subtracting Surds

Examples and an explanation on adding and subtracting surds. With practice questions

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Know Adding and Subtracting Surds thumbnail

Can't find what you're looking for? Explore other subjects.

Knowunity is the #1 education app in five European countries

Knowunity has been named a featured story on Apple and has regularly topped the app store charts in the education category in Germany, Italy, Poland, Switzerland, and the United Kingdom. Join Knowunity today and help millions of students around the world.

Ranked #1 Education App

Download in

Google Play

Download in

App Store

Knowunity is the #1 education app in five European countries

4.9+

Average app rating

20 M

Pupils love Knowunity

#1

In education app charts in 17 countries

950 K+

Students have uploaded notes

Still not convinced? See what other students are saying...

iOS User

I love this app so much, I also use it daily. I recommend Knowunity to everyone!!! I went from a D to an A with it :D

Philip, iOS User

The app is very simple and well designed. So far I have always found everything I was looking for :D

Lena, iOS user

I love this app ❤️ I actually use it every time I study.