Easy Math Tricks: Using the Cosine Rule, Solving Equations, and Expanding Brackets

Open

Harry

04/04/2023

Maths

Maths Revision notes

Subjects

Maths

Ratio, proportion and rates of exchange

Percentages

Easy Math Tricks: Using the Cosine Rule, Solving Equations, and Expanding Brackets

A comprehensive guide to essential mathematical concepts covering cosine rule, vectors, equations, proportions, and percentages. This educational resource provides detailed explanations and practical examples for secondary school mathematics students.

Covers fundamental trigonometry with How to use the cosine rule in mathematics
Explains Solving simultaneous equations step by step with clear examples
Features Expand brackets algebra tutorial with detailed working methods
Includes key topics like compound interest, area calculations, and percentage problems
Provides practical examples and step-by-step solutions throughout

04/04/2023

Cosine rule!
b
a
а2 +2 +с? - гос
2
zbc
cos A
А с
cosine rule!
аг =b2 +c2-2bc Соз А
x2 =10.62 +13.02 + 2x10.6*
13.az cos (88)
Lo10.67413 Q2*2

Page 2: Algebraic Vectors

This page explains vector representation and addition in mathematics, showing how vectors can be equal and combined.

Vocabulary: Vectors are quantities that have both magnitude and direction.

Highlight: Vector addition is demonstrated through the relationship a + b = c, where vectors can be combined to form new vectors.

View

Page 3: Simultaneous Equations

The page demonstrates solving simultaneous equations using substitution and elimination methods.

Example: Two sets of equations are solved:

6x + 3y = 21 and 2x + 3y = 17
2x + y = 4 and 3x - y = 8

Highlight: Solutions show step-by-step working to find values for x and y.

View

Page 4: Inverse Proportion

This section explains the concept of inverse proportion and its mathematical representation.

Definition: When two quantities are inversely proportional, as one increases, the other decreases in proportion so their product remains constant.

Formula: A = k/B, where k is the constant of proportionality.

View

Page 5: Direct Proportion

The page covers direct proportion relationships between variables.

Definition: Two quantities are directly proportional when they increase or decrease in the same ratio.

Example: Using y = kx, when y = 20 and x = 5, finding k = 4 to solve for other values.

View

Page 6: Expanding Brackets

This section focuses on expanding algebraic expressions with single and squared terms.

Highlight: Special attention is given to squared terms, noting that they must be multiplied by themselves.

Example: (2x+1)(3x+3) is expanded to 6x² + 13x + 3

View

Page 7: More Bracket Expansion

Continues with more complex bracket expansion examples.

Example: Multiple expansions including:

(x+3)(x+8) = x² + 11x + 24
(x+5)(x-3) = x² + 2x + 15

View

Page 8: Compound Interest with Calculator

Explains how to calculate compound interest using a calculator.

Formula: Initial × Multiplier^Time

Example: £8000 invested at 3% for 4 years, calculating to £9004.07

View

Page 9: Compound Interest Without Calculator

Shows manual calculation method for compound interest.

Example: £3000 invested at 10% for 2 years, with step-by-step calculations.

View

Page 10: Area of Shapes

Provides formulas for calculating areas of different shapes and introduces 3D shape terminology.

Vocabulary:

Face: flat surface of a 3D shape
Edge: where two faces meet
Vertex: where two or more edges meet

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Knowunity is the #1 education app in five European countries

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Average app rating

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Pupils love Knowunity

#1

In education app charts in 17 countries

950 K+

Students have uploaded notes

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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

Ratio, proportion and rates of exchange

Percentages

Easy Math Tricks: Using the Cosine Rule, Solving Equations, and Expanding Brackets

Harry

@harry_xoxo

2 Followers

Covers fundamental trigonometry with How to use the cosine rule in mathematics
Explains Solving simultaneous equations step by step with clear examples
Features Expand brackets algebra tutorial with detailed working methods
Includes key topics like compound interest, area calculations, and percentage problems
Provides practical examples and step-by-step solutions throughout

...

04/04/2023

166

11/10

Maths

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Page 2: Algebraic Vectors

This page explains vector representation and addition in mathematics, showing how vectors can be equal and combined.

Vocabulary: Vectors are quantities that have both magnitude and direction.

Highlight: Vector addition is demonstrated through the relationship a + b = c, where vectors can be combined to form new vectors.

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Access to all documents

Improve your grades

Join milions of students

By signing up you accept Terms of Service and Privacy Policy

Page 3: Simultaneous Equations

The page demonstrates solving simultaneous equations using substitution and elimination methods.

Example: Two sets of equations are solved:

6x + 3y = 21 and 2x + 3y = 17
2x + y = 4 and 3x - y = 8

Highlight: Solutions show step-by-step working to find values for x and y.

Sign up to see the content. It's free!

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Page 4: Inverse Proportion

This section explains the concept of inverse proportion and its mathematical representation.

Definition: When two quantities are inversely proportional, as one increases, the other decreases in proportion so their product remains constant.

Formula: A = k/B, where k is the constant of proportionality.

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Page 5: Direct Proportion

The page covers direct proportion relationships between variables.

Definition: Two quantities are directly proportional when they increase or decrease in the same ratio.

Example: Using y = kx, when y = 20 and x = 5, finding k = 4 to solve for other values.

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Page 6: Expanding Brackets

This section focuses on expanding algebraic expressions with single and squared terms.

Highlight: Special attention is given to squared terms, noting that they must be multiplied by themselves.

Example: (2x+1)(3x+3) is expanded to 6x² + 13x + 3

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Page 7: More Bracket Expansion

Continues with more complex bracket expansion examples.

Example: Multiple expansions including:

(x+3)(x+8) = x² + 11x + 24
(x+5)(x-3) = x² + 2x + 15

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Join milions of students

By signing up you accept Terms of Service and Privacy Policy

Page 8: Compound Interest with Calculator

Explains how to calculate compound interest using a calculator.

Formula: Initial × Multiplier^Time

Example: £8000 invested at 3% for 4 years, calculating to £9004.07

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 9: Compound Interest Without Calculator

Shows manual calculation method for compound interest.

Example: £3000 invested at 10% for 2 years, with step-by-step calculations.

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Access to all documents

Improve your grades

Join milions of students

By signing up you accept Terms of Service and Privacy Policy

Page 10: Area of Shapes

Provides formulas for calculating areas of different shapes and introduces 3D shape terminology.

Vocabulary:

Face: flat surface of a 3D shape
Edge: where two faces meet
Vertex: where two or more edges meet

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 11: Percentage Calculations

Explains how to calculate percentages of amounts.

Method: Two-step process:

Find 1% of the amount
Multiply by the required percentage

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.

Download in

Google Play

Download in

App Store

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

Easy Math Tricks: Using the Cosine Rule, Solving Equations, and Expanding Brackets

Page 2: Algebraic Vectors

Page 3: Simultaneous Equations

Page 4: Inverse Proportion

Page 5: Direct Proportion

Page 6: Expanding Brackets

Page 7: More Bracket Expansion

Page 8: Compound Interest with Calculator

Page 9: Compound Interest Without Calculator

Page 10: Area of Shapes

Similar content

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.

4.9+

20 M

#1

950 K+

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

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

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

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

Easy Math Tricks: Using the Cosine Rule, Solving Equations, and Expanding Brackets

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Page 2: Algebraic Vectors

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Page 3: Simultaneous Equations

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Page 4: Inverse Proportion

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Page 5: Direct Proportion

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Page 6: Expanding Brackets

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Page 7: More Bracket Expansion

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Page 8: Compound Interest with Calculator

Sign up to see the content. It's free!

Page 9: Compound Interest Without Calculator

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Page 10: Area of Shapes

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Page 11: Percentage Calculations

Similar content

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.

4.9+

20 M

#1

950 K+

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

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

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

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