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Mathematik

Mathematische Grundlagen und Systeme

signifikante Ziffern

896

•

27 Jun 2025

•

8 pages

Free Nat 5 Math Notes & Fun Maths Puzzles

F

Freya McEwan

@freyamcewan_ywnx

A comprehensive guide to nat 5 mathstopics covering standard... Show more

<p>The standard deviation (S.D) formula is calculated using the square root of the sum of the squared differences between each data point a

Scientific Notation

This section covers the conversion of numbers to scientific notation format.

Definition: Scientific notation expresses numbers in the form a × 10ⁿ, where 1 ≤ a < 10 and n is an integer.

Highlight: Scientific notation and standard form are equivalent terms.

Example:

  • 2,000,000 = 2 × 10⁶
  • 0.0000002 = 2 × 10⁻⁷
<p>The standard deviation (S.D) formula is calculated using the square root of the sum of the squared differences between each data point a

Completing the Square

A detailed guide to completing the square steps and methodology.

Formula: The general form is x+ax + a² + b

Example: Converting x² + 10x + 7 to completed square form:

  1. Half the coefficient of x 10÷2=510 ÷ 2 = 5
  2. Square this number 52=255² = 25
  3. Subtract from constant 7−25=−187 - 25 = -18
  4. Final form: x+5x + 5² - 18
<p>The standard deviation (S.D) formula is calculated using the square root of the sum of the squared differences between each data point a

Significant Figures

An explanation of significant figures in numerical representation.

Definition: Significant figures are digits that carry meaningful value in a number.

Example:

  • 53,879 to 1 significant figure = 50,000
  • 0.005089 to 2 significant figures = 0.0051

Highlight: Every digit except leading and trailing zeros is significant.

<p>The standard deviation (S.D) formula is calculated using the square root of the sum of the squared differences between each data point a

Algebraic Fractions

Detailed coverage of simplifying algebraic fractions.

Definition: Algebraic fractions can be simplified by canceling common factors in numerator and denominator.

Example: Simplifying complex fractions like x−2x-2/6x = x+1x+1/2x

<p>The standard deviation (S.D) formula is calculated using the square root of the sum of the squared differences between each data point a

Adding and Subtracting Algebraic Fractions

Comprehensive guide to operations with algebraic fractions.

Highlight: The process follows the same principles as regular fraction operations.

Example: Detailed solutions for combining fractions with different denominators.

<p>The standard deviation (S.D) formula is calculated using the square root of the sum of the squared differences between each data point a

Expanding Brackets

Guide to expanding algebraic expressions.

Rule: Multiply each term inside the bracket by the term outside.

Example:

  • 73a+4b−5c3a + 4b - 5c = 21a + 28b - 35c
  • 25x−45x - 4 - 32x−12x - 1 = 10x - 8 - 6x + 3 = 4x - 5
<p>The standard deviation (S.D) formula is calculated using the square root of the sum of the squared differences between each data point a

Arcs and Sectors

Comprehensive coverage of circular geometry calculations.

Formula:

  • Arc Length = θ/360°θ/360° × πd
  • Sector Area = θ/360°θ/360° × πr²

Example: Calculating arc length for a 14° sector with diameter 8cm.

Vocabulary:

  • θ represents the angle
  • r represents the radius
  • d represents the diameter
<p>The standard deviation (S.D) formula is calculated using the square root of the sum of the squared differences between each data point a

Standard Deviation

This section introduces the fundamental concepts of variance and standard deviation.

The standard deviation formula is presented as: S.D = √(Σ(x−xˉ)2)/(n−1)(Σ(x-x̄)²)/(n-1)

Definition: Standard deviation measures the spread of data points from their mean value.

Example: A detailed calculation using school absentee data 32,29,33,33,3832, 29, 33, 33, 38 demonstrates the step-by-step process of finding standard deviation.

Vocabulary:

  • Σ represents the sum
  • x̄ represents the mean
  • n represents the number of values


We thought you’d never ask...

What is the Knowunity AI companion?

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.

Where can I download the Knowunity app?

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

Is Knowunity really free of charge?

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

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

Mathematik

Mathematische Grundlagen und Systeme

signifikante Ziffern

 

Maths

•

896

•

27 Jun 2025

•

8 pages

Free Nat 5 Math Notes & Fun Maths Puzzles

F

Freya McEwan

@freyamcewan_ywnx

A comprehensive guide to nat 5 maths topics covering standard deviation, scientific notation, and geometric concepts.

Key topics covered include:

  • Standard deviation math notes with detailed calculation examples
  • Scientific notation for large and small numbers
  • Completing the square formulaand... Show more

<p>The standard deviation (S.D) formula is calculated using the square root of the sum of the squared differences between each data point a

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

Scientific Notation

This section covers the conversion of numbers to scientific notation format.

Definition: Scientific notation expresses numbers in the form a × 10ⁿ, where 1 ≤ a < 10 and n is an integer.

Highlight: Scientific notation and standard form are equivalent terms.

Example:

  • 2,000,000 = 2 × 10⁶
  • 0.0000002 = 2 × 10⁻⁷
<p>The standard deviation (S.D) formula is calculated using the square root of the sum of the squared differences between each data point a

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

Completing the Square

A detailed guide to completing the square steps and methodology.

Formula: The general form is x+ax + a² + b

Example: Converting x² + 10x + 7 to completed square form:

  1. Half the coefficient of x 10÷2=510 ÷ 2 = 5
  2. Square this number 52=255² = 25
  3. Subtract from constant 7−25=−187 - 25 = -18
  4. Final form: x+5x + 5² - 18
<p>The standard deviation (S.D) formula is calculated using the square root of the sum of the squared differences between each data point a

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

Significant Figures

An explanation of significant figures in numerical representation.

Definition: Significant figures are digits that carry meaningful value in a number.

Example:

  • 53,879 to 1 significant figure = 50,000
  • 0.005089 to 2 significant figures = 0.0051

Highlight: Every digit except leading and trailing zeros is significant.

<p>The standard deviation (S.D) formula is calculated using the square root of the sum of the squared differences between each data point a

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

Algebraic Fractions

Detailed coverage of simplifying algebraic fractions.

Definition: Algebraic fractions can be simplified by canceling common factors in numerator and denominator.

Example: Simplifying complex fractions like x−2x-2/6x = x+1x+1/2x

<p>The standard deviation (S.D) formula is calculated using the square root of the sum of the squared differences between each data point a

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

Adding and Subtracting Algebraic Fractions

Comprehensive guide to operations with algebraic fractions.

Highlight: The process follows the same principles as regular fraction operations.

Example: Detailed solutions for combining fractions with different denominators.

<p>The standard deviation (S.D) formula is calculated using the square root of the sum of the squared differences between each data point a

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

Expanding Brackets

Guide to expanding algebraic expressions.

Rule: Multiply each term inside the bracket by the term outside.

Example:

  • 73a+4b−5c3a + 4b - 5c = 21a + 28b - 35c
  • 25x−45x - 4 - 32x−12x - 1 = 10x - 8 - 6x + 3 = 4x - 5
<p>The standard deviation (S.D) formula is calculated using the square root of the sum of the squared differences between each data point a

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

Arcs and Sectors

Comprehensive coverage of circular geometry calculations.

Formula:

  • Arc Length = θ/360°θ/360° × πd
  • Sector Area = θ/360°θ/360° × πr²

Example: Calculating arc length for a 14° sector with diameter 8cm.

Vocabulary:

  • θ represents the angle
  • r represents the radius
  • d represents the diameter
<p>The standard deviation (S.D) formula is calculated using the square root of the sum of the squared differences between each data point a

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

Standard Deviation

This section introduces the fundamental concepts of variance and standard deviation.

The standard deviation formula is presented as: S.D = √(Σ(x−xˉ)2)/(n−1)(Σ(x-x̄)²)/(n-1)

Definition: Standard deviation measures the spread of data points from their mean value.

Example: A detailed calculation using school absentee data 32,29,33,33,3832, 29, 33, 33, 38 demonstrates the step-by-step process of finding standard deviation.

Vocabulary:

  • Σ represents the sum
  • x̄ represents the mean
  • n represents the number of values

We thought you’d never ask...

What is the Knowunity AI companion?

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.

Where can I download the Knowunity app?

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

Is Knowunity really free of charge?

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

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