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

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Harry

04/04/2023

Maths

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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

168

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

View

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.

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

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.

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

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.

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

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.

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

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+12x+13x+33x+3 is expanded to 6x² + 13x + 3

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

View

Page 7: More Bracket Expansion

Continues with more complex bracket expansion examples.

Example: Multiple expansions including:

  • x+3x+3x+8x+8 = x² + 11x + 24
  • x+5x+5x3x-3 = x² + 2x + 15
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

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

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

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.

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

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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Maths

168

4 Apr 2023

12 pages

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

user profile picture

Harry

@harry_xoxo

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... Show more

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

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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.

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

Sign up to see the contentIt's free!

Access to all documents

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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.

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

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: 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.

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

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 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.

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

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 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+12x+13x+33x+3 is expanded to 6x² + 13x + 3

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

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Page 7: More Bracket Expansion

Continues with more complex bracket expansion examples.

Example: Multiple expansions including:

  • x+3x+3x+8x+8 = x² + 11x + 24
  • x+5x+5x3x-3 = x² + 2x + 15
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

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 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

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

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 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.

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

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 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
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

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 11: Percentage Calculations

Explains how to calculate percentages of amounts.

Method: Two-step process:

  1. Find 1% of the amount
  2. Multiply by the required percentage

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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.

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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.

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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