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80

•

21 Aug 2023

•

6 pages

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

user profile picture

MyNotes

@notesjust4you

A comprehensive guide to mathematical problem-solving covering right-angled triangles, number... Show more

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

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

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

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

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
  • 3x−5x-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

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: 5-2x+2x+2
  • Expanding: x−6x-62x−42x-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

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=c2a²+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.



Can't find what you're looking for? Explore other subjects.

Students love us — and so will you.

4.9/5

App Store

4.8/5

Google 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 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

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

Subjects

Maths

Algebra

Expressions & formulae

 

Maths

•

80

•

21 Aug 2023

•

6 pages

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

user profile picture

MyNotes

@notesjust4you

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... Show more

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 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 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 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 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 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: 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 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: Solving Equations

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

Example: Solutions demonstrated:

  • 2x-14 = 3x = 12
  • 4x+4 = x-5
  • 3x−5x-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 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: 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: 5-2x+2x+2
  • Expanding: x−6x-62x−42x-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 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 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=c2a²+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.

Can't find what you're looking for? Explore other subjects.

Students love us — and so will you.

4.9/5

App Store

4.8/5

Google 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 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

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