A comprehensive guide to essential mathematical concepts covering cosine rule,...
Maths175 views·Updated 26 Aug 2026·12 pagesEasy Math Tricks: Using the Cosine Rule, Solving Equations, and Expanding Brackets
Harry @harry_xoxo
1 / 10
1
of 10
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
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
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
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
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$$3x+3 is expanded to 6x² + 13x + 3
6
of 10
Page 7: More Bracket Expansion
Continues with more complex bracket expansion examples.
Example: Multiple expansions including:
- x+3$$x+8 = x² + 11x + 24
- x+5$$x-3 = x² + 2x + 15
7
of 10
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
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
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
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
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Maths175 views·Updated 26 Aug 2026·12 pagesEasy Math Tricks: Using the Cosine Rule, Solving Equations, and Expanding Brackets
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
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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 10Sign 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: 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 10Sign up to see the content. It's free!
- Access to all documents
- Improve your grades
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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.
4
of 10Sign 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 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 10Sign up to see the content. It's free!
- Access to all documents
- Improve your grades
- Join milions of students
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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 10Sign up to see the content. It's free!
- Access to all documents
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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 10Sign 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 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 10Sign 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.
9
of 10Sign 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 10Sign 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
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.
That's right! Enjoy free access to study content, connect with fellow students, and get instant help – all at your fingertips.
Similar content
Most popular content: Multiplying Binomials
2MathsMastering Bracket Expansion
This comprehensive guide covers the techniques for expanding single, double, and triple brackets in mathematics. Learn methods such as FOIL and grid multiplication, and practice collecting like terms to simplify expressions. Ideal for Year 8/9 students looking to strengthen their algebra skills.
81090
MathsAlgebraic Expansion Techniques
Master the art of expanding and simplifying algebraic expressions with this comprehensive guide. Explore key concepts such as the Distributive Property and algebraic manipulation through practical examples. Ideal for students looking to enhance their understanding of algebra.
1037212
Most popular content in Maths
9MathsComprehensive Maths Concepts
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1180,3496,327
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Explore detailed solutions for the Foundation Tier Non-Calculator Maths exam. This resource covers key concepts such as probability, volume calculations, data representation, and more. Perfect for students preparing for their GCSE Maths exam, with step-by-step explanations and examples.
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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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Explore the key concepts from the 2018 GCSE Maths Paper 2, including compound interest, probability, standard form, and geometric transformations. This comprehensive summary covers essential topics such as interest rates, area calculations, and Venn diagrams, providing students with a clear understanding of the exam's requirements. Ideal for exam preparation and practice.
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Explore the Pythagorean Theorem (a² + b² = c²) with clear examples and step-by-step calculations. This summary covers key concepts such as hypotenuse and right triangles, making it essential for understanding geometry. Ideal for students preparing for exams or needing a quick reference.
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Students love us, and so will you.
4.6/5App Store
4.7/5Google Play
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 SiOS 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 KlichAndroid 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.
AnnaiOS user