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

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

@harry_xoxo

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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

136

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+1)(3x+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+3)(x+8) = x² + 11x + 24
  • (x+5)(x-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
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 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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Subjects

/

Maths

/

Ratio, proportion and rates of exchange

/

Percentages

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

user profile picture

Harry

@harry_xoxo

·

2 Followers

Follow

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

136

 

11/10

 

Maths

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

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

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

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

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

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

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 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
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 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

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

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

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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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

15 M

Pupils love Knowunity

#1

In education app charts in 12 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.