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Learn to Solve Right-Angled Triangles and Have Fun with Numbers!

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Learn to Solve Right-Angled Triangles and Have Fun with Numbers!
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MyNotes

@notesjust4you

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A comprehensive guide to mathematical problem-solving covering right-angled triangles, number systems, and algebraic expressions.

  • Learn how to solve right-angled triangle problems using Pythagoras' theorem with step-by-step examples
  • Master writing numbers in figures and words, including place value and rounding
  • Practice how to expand and simplify algebraic expressions through various mathematical operations
  • Develop skills in solving equations and working with prime numbers, multiples, and square numbers
  • Apply mathematical concepts through practical problem-solving exercises with detailed solutions

21/08/2023

75

9.2 Total for question = 2 marks) Q8. Q9. 16km X x 2=a²+b² x² = 16²+7² POR is a right-angled triangle. 7km x² =256+49 x² 305 Give your answe

View

Page 2: Triangle Measurements

This page continues with right-angled triangle problems, featuring a triangle with sides of 9m and 2m.

Example: Using Pythagoras' theorem: x² = 9² + 2² x² = 81 + 4 x² = 85 x = √85 = 9.2

Highlight: The answer is rounded to one decimal place as specified in the question.

9.2 Total for question = 2 marks) Q8. Q9. 16km X x 2=a²+b² x² = 16²+7² POR is a right-angled triangle. 7km x² =256+49 x² 305 Give your answe

View

Page 3: Number Properties

This page explores different types of numbers and their properties, using a set of numbers: 3, 5, 12, 10, 9, 26, 24.

Vocabulary:

  • Odd numbers: Numbers that cannot be divided evenly by 2
  • Multiple: A number that can be divided evenly by another number
  • Square number: The result of multiplying a number by itself
  • Prime number: A number with exactly two factors - 1 and itself

Example: From the given set:

  • Odd number: 3
  • Multiple of 12: 24
  • Square number: 9
  • Prime numbers: 3, 5
9.2 Total for question = 2 marks) Q8. Q9. 16km X x 2=a²+b² x² = 16²+7² POR is a right-angled triangle. 7km x² =256+49 x² 305 Give your answe

View

Page 4: Number Representation

This page focuses on writing numbers in figures and words and understanding place value.

Example:

  • "Five hundred and seven" written in figures: 507
  • "Forty thousand" written in figures: 40,000
  • The value of 7 in 476 is 70

Highlight: When rounding numbers to the nearest hundred, look at the tens digit to determine whether to round up or down.

9.2 Total for question = 2 marks) Q8. Q9. 16km X x 2=a²+b² x² = 16²+7² POR is a right-angled triangle. 7km x² =256+49 x² 305 Give your answe

View

Page 5: Solving Equations

This page covers solving various types of linear and algebraic equations.

Example: Solutions demonstrated:

  • 2x-14 = 3x = 12
  • 4x+4 = x-5
  • 3(x-5) = 15

Highlight: When solving equations, perform the same operation on both sides to maintain equality.

9.2 Total for question = 2 marks) Q8. Q9. 16km X x 2=a²+b² x² = 16²+7² POR is a right-angled triangle. 7km x² =256+49 x² 305 Give your answe

View

Page 6: Algebraic Expressions

This page demonstrates how to expand and simplify algebraic expressions through various operations.

Example:

  • Simplifying: 7y + 4x - 6 + 3x + 7
  • Factorising: 3x²-5x
  • Expanding: 5-2(x+2)
  • Expanding: (x-6)(2x-4)

Highlight: When expanding brackets, multiply each term inside by each term outside and combine like terms.

9.2 Total for question = 2 marks) Q8. Q9. 16km X x 2=a²+b² x² = 16²+7² POR is a right-angled triangle. 7km x² =256+49 x² 305 Give your answe

View

Page 1: Right-Angled Triangle Problems

This page introduces the application of Pythagoras' theorem in solving right-angled triangle problems. The problem demonstrates calculating the hypotenuse of a triangle with sides 16km and 7km.

Definition: Pythagoras' theorem states that in a right-angled triangle, the square of the hypotenuse equals the sum of squares of the other two sides (a²+b²=c²).

Example: For a triangle with sides 16km and 7km, the calculation is: x² = 16² + 7² x² = 256 + 49 x² = 305 x = √305 = 17.464

Highlight: When solving these problems, always remember to give answers to the specified number of significant figures.

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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.

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Knowunity is the #1 education app in five European countries

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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

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Lena, iOS user

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

Subjects

/

Maths

/

Algebra

/

Expressions & formulae

Learn to Solve Right-Angled Triangles and Have Fun with Numbers!

user profile picture

MyNotes

@notesjust4you

·

0 Follower

Follow

A comprehensive guide to mathematical problem-solving covering right-angled triangles, number systems, and algebraic expressions.

  • Learn how to solve right-angled triangle problems using Pythagoras' theorem with step-by-step examples
  • Master writing numbers in figures and words, including place value and rounding
  • Practice how to expand and simplify algebraic expressions through various mathematical operations
  • Develop skills in solving equations and working with prime numbers, multiples, and square numbers
  • Apply mathematical concepts through practical problem-solving exercises with detailed solutions

21/08/2023

75

 

8/9

 

Maths

3

9.2 Total for question = 2 marks) Q8. Q9. 16km X x 2=a²+b² x² = 16²+7² POR is a right-angled triangle. 7km x² =256+49 x² 305 Give your answe

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Join milions of students

By signing up you accept Terms of Service and Privacy Policy

Page 2: Triangle Measurements

This page continues with right-angled triangle problems, featuring a triangle with sides of 9m and 2m.

Example: Using Pythagoras' theorem: x² = 9² + 2² x² = 81 + 4 x² = 85 x = √85 = 9.2

Highlight: The answer is rounded to one decimal place as specified in the question.

9.2 Total for question = 2 marks) Q8. Q9. 16km X x 2=a²+b² x² = 16²+7² POR is a right-angled triangle. 7km x² =256+49 x² 305 Give your answe

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 3: Number Properties

This page explores different types of numbers and their properties, using a set of numbers: 3, 5, 12, 10, 9, 26, 24.

Vocabulary:

  • Odd numbers: Numbers that cannot be divided evenly by 2
  • Multiple: A number that can be divided evenly by another number
  • Square number: The result of multiplying a number by itself
  • Prime number: A number with exactly two factors - 1 and itself

Example: From the given set:

  • Odd number: 3
  • Multiple of 12: 24
  • Square number: 9
  • Prime numbers: 3, 5
9.2 Total for question = 2 marks) Q8. Q9. 16km X x 2=a²+b² x² = 16²+7² POR is a right-angled triangle. 7km x² =256+49 x² 305 Give your answe

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 4: Number Representation

This page focuses on writing numbers in figures and words and understanding place value.

Example:

  • "Five hundred and seven" written in figures: 507
  • "Forty thousand" written in figures: 40,000
  • The value of 7 in 476 is 70

Highlight: When rounding numbers to the nearest hundred, look at the tens digit to determine whether to round up or down.

9.2 Total for question = 2 marks) Q8. Q9. 16km X x 2=a²+b² x² = 16²+7² POR is a right-angled triangle. 7km x² =256+49 x² 305 Give your answe

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 5: Solving Equations

This page covers solving various types of linear and algebraic equations.

Example: Solutions demonstrated:

  • 2x-14 = 3x = 12
  • 4x+4 = x-5
  • 3(x-5) = 15

Highlight: When solving equations, perform the same operation on both sides to maintain equality.

9.2 Total for question = 2 marks) Q8. Q9. 16km X x 2=a²+b² x² = 16²+7² POR is a right-angled triangle. 7km x² =256+49 x² 305 Give your answe

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 6: Algebraic Expressions

This page demonstrates how to expand and simplify algebraic expressions through various operations.

Example:

  • Simplifying: 7y + 4x - 6 + 3x + 7
  • Factorising: 3x²-5x
  • Expanding: 5-2(x+2)
  • Expanding: (x-6)(2x-4)

Highlight: When expanding brackets, multiply each term inside by each term outside and combine like terms.

9.2 Total for question = 2 marks) Q8. Q9. 16km X x 2=a²+b² x² = 16²+7² POR is a right-angled triangle. 7km x² =256+49 x² 305 Give your answe

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 1: Right-Angled Triangle Problems

This page introduces the application of Pythagoras' theorem in solving right-angled triangle problems. The problem demonstrates calculating the hypotenuse of a triangle with sides 16km and 7km.

Definition: Pythagoras' theorem states that in a right-angled triangle, the square of the hypotenuse equals the sum of squares of the other two sides (a²+b²=c²).

Example: For a triangle with sides 16km and 7km, the calculation is: x² = 16² + 7² x² = 256 + 49 x² = 305 x = √305 = 17.464

Highlight: When solving these problems, always remember to give answers to the specified number of significant figures.

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Here are some great math questions to test yourself with before a test or just for extra revision!!

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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.

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.