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MathsMaths175 views·Updated 31 Aug 2026·12 pages

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

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Harry @harry_xoxo

A comprehensive guide to essential mathematical concepts covering cosine rule,...

1
of 10
Maths Revision notes – page 1

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.

2
of 10
Maths Revision notes – page 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.

3
of 10
Maths Revision notes – page 3

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.

4
of 10
Maths Revision notes – page 4

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.

5
of 10
Maths Revision notes – page 5

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

6
of 10
Maths Revision notes – page 6

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
7
of 10
Maths Revision notes – page 7

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

8
of 10
Maths Revision notes – page 8

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.

9
of 10
Maths Revision notes – page 9

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
10
of 10
Maths Revision notes – page 10

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

We thought you’d never ask...

Our AI Companion is a student-focused AI tool that offers more than just answers. Built on millions of Knowunity resources, it provides relevant information, personalised study plans, quizzes, and content directly in the chat, adapting to your individual learning journey.

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That's right! Enjoy free access to study content, connect with fellow students, and get instant help – all at your fingertips.

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MathsMaths175 views·Updated 31 Aug 2026·12 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...
1
of 10
Maths Revision notes – page 1

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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.

2
of 10
Maths Revision notes – page 2

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  • Access to all documents
  • Improve your grades
  • Join milions of students

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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.

3
of 10
Maths Revision notes – page 3

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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.

4
of 10
Maths Revision notes – page 4

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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.

5
of 10
Maths Revision notes – page 5

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  • Access to all documents
  • Improve your grades
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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

6
of 10
Maths Revision notes – page 6

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  • Access to all documents
  • Improve your grades
  • Join milions of students

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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
7
of 10
Maths Revision notes – page 7

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  • Access to all documents
  • Improve your grades
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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

8
of 10
Maths Revision notes – page 8

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 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.

9
of 10
Maths Revision notes – page 9

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 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
10
of 10
Maths Revision notes – page 10

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:

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

We thought you’d never ask...

Our AI Companion is a student-focused AI tool that offers more than just answers. Built on millions of Knowunity resources, it provides relevant information, personalised study plans, quizzes, and content directly in the chat, adapting to your individual learning journey.

You can download the app from Google Play Store and Apple App Store.

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Explore the fundamentals of trigonometry, including the tangent, sine, and cosine functions. This summary covers key concepts such as SOH CAH TOA, trigonometric ratios, and methods for finding angles and sides in right triangles. Ideal for students preparing for exams or needing a quick reference.

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