Subjects

Careers

Open the App

Subjects

Easy Math Fun! Grouped Frequency and Column Vectors for Kids

Open

17

0

K

kiki chapman

31/03/2023

Maths

gcse maths notes

Subjects

/

Maths

/

Geometry & measures

/

Angles

Easy Math Fun! Grouped Frequency and Column Vectors for Kids

Hey there! Dive into grouped frequency distribution fun with our calculator and examples. Solve grouped frequency problems with solutions and learn about ungrouped distributions. Try adding and subtracting column vectors with worksheets and PDF guides. Discover solving simultaneous equations graphically, with Maths Genie and Corbettmaths helping along the way!

31/03/2023

824

O GROUPED FREQUENCY ο Class O DISCRETE) 0-10 11-20 21-30 e.g e.g CONTINUOUD: 5<h≤10 10ch ≤15 154h ≤20 o Add interval Add 20 31 o Estimated M

View

Vectors

This page covers vector notation and operations.

Key points:

  • Vectors can be represented as column vectors or with letters usuallyunderlinedusually underlined
  • Vector addition and subtraction can be visualized geometrically
  • Vector equations can be used to prove points lie on a straight line

Definition: A vector is a quantity with both magnitude and direction

Example: In the equation OB = a, AB = 2b, BD = a-b, vectors are used to describe positions and movements between points

Highlight: To show points lie on a straight line, prove that one vector is a scalar multiple of another

O GROUPED FREQUENCY ο Class O DISCRETE) 0-10 11-20 21-30 e.g e.g CONTINUOUD: 5<h≤10 10ch ≤15 154h ≤20 o Add interval Add 20 31 o Estimated M

View

Vector Problems

This page demonstrates how to solve more complex vector problems.

Key points:

  • Use parallel sides of shapes to relate vectors
  • Break down complex paths into simpler vector components
  • Ratios can be used to find positions along vectors

Example: In a parallelogram ABCD, if DE:EC = 8:1, vector DE can be expressed as 8/9 of vector DC

Highlight: When solving vector problems, break down the solution into steps: identify known vectors, use relationships between parallel sides, and combine vector components.

O GROUPED FREQUENCY ο Class O DISCRETE) 0-10 11-20 21-30 e.g e.g CONTINUOUD: 5<h≤10 10ch ≤15 154h ≤20 o Add interval Add 20 31 o Estimated M

View

Two-Way Tables

Two-way tables organize data into categories across two variables.

Key points:

  • Fill in missing information by adding and subtracting known values
  • Ensure row and column totals are consistent

Example: In a survey of 400 people 200men,200women200 men, 200 women about handedness:

  • 63 people are left-handed
  • 167 women are right-handed

Complete the two-way table using this information.

Highlight: When completing two-way tables, work systematically to fill in missing values, using row and column totals as checks.

O GROUPED FREQUENCY ο Class O DISCRETE) 0-10 11-20 21-30 e.g e.g CONTINUOUD: 5<h≤10 10ch ≤15 154h ≤20 o Add interval Add 20 31 o Estimated M

View

Similarity

This page introduces the concept of similarity in geometry.

Key points:

  • Similar shapes have the same angles and proportional sides
  • Area scales with the square of the linear scale factor
  • Volume scales with the cube of the linear scale factor

Definition: Similar shapes have the same shape but may be different sizes

Highlight: In similar shapes, corresponding angles are equal and corresponding sides are in proportion.

O GROUPED FREQUENCY ο Class O DISCRETE) 0-10 11-20 21-30 e.g e.g CONTINUOUD: 5<h≤10 10ch ≤15 154h ≤20 o Add interval Add 20 31 o Estimated M

View

Simultaneous Equations

This page covers methods for solving simultaneous equations.

Key points:

  • Rearrange equations into the form ax + by = c
  • Match coefficients of one variable
  • Add or subtract equations to eliminate one variable
  • Solve for the remaining variable and substitute back

Example: Solve the simultaneous equations: 2x + 4y = 6 4x + 3y = -3

Highlight: When solving simultaneous equations, the goal is to eliminate one variable by adding or subtracting the equations.

O GROUPED FREQUENCY ο Class O DISCRETE) 0-10 11-20 21-30 e.g e.g CONTINUOUD: 5<h≤10 10ch ≤15 154h ≤20 o Add interval Add 20 31 o Estimated M

View

Graphical Inequalities

This page explains how to represent inequalities graphically.

Key points:

  • Convert inequalities to equations for graphing
  • Use solid lines for ≥ or ≤, dotted lines for > or <
  • Shade the region that satisfies all inequalities

Example: Graph the inequalities: x + y < 5 y ≤ x + 2 y > 1

Highlight: The solution region for a system of inequalities is the area where all individual inequalities are satisfied simultaneously.

O GROUPED FREQUENCY ο Class O DISCRETE) 0-10 11-20 21-30 e.g e.g CONTINUOUD: 5<h≤10 10ch ≤15 154h ≤20 o Add interval Add 20 31 o Estimated M

View

Trigonometric Graphs

This page covers the graphs of sine, cosine, and tangent functions.

Key points:

  • Sine and cosine have a period of 360°
  • Tangent has a period of 180°
  • Key features include intercepts, peaks, and asymptotes

Vocabulary: Period - The interval after which a trigonometric function repeats

Example: Estimate the solutions for sin x = 0.7 between 0° and 360°

Highlight: Understanding the shapes and key features of trigonometric graphs is crucial for solving trigonometric equations graphically.

O GROUPED FREQUENCY ο Class O DISCRETE) 0-10 11-20 21-30 e.g e.g CONTINUOUD: 5<h≤10 10ch ≤15 154h ≤20 o Add interval Add 20 31 o Estimated M

View

Sine Rule

This page explains the sine rule and its applications.

Key points:

  • The sine rule relates sides and angles in any triangle
  • It can be used to find unknown sides or angles
  • Be cautious with the ambiguous case for angles

Definition: Sine Rule: a/sin A = b/sin B = c/sin C, where lowercase letters represent sides and uppercase letters represent opposite angles

Example: In triangle ABC, if a = 7m, A = 53°, and B = 83°, find the length of side b

Highlight: The sine rule is particularly useful when you know two angles and one side, or two sides and an angle opposite one of them.

O GROUPED FREQUENCY ο Class O DISCRETE) 0-10 11-20 21-30 e.g e.g CONTINUOUD: 5<h≤10 10ch ≤15 154h ≤20 o Add interval Add 20 31 o Estimated M

View

Cosine Rule

This page covers the cosine rule and its applications.

Key points:

  • The cosine rule relates all three sides and one angle in a triangle
  • It can be used when the sine rule is not applicable
  • There are separate formulas for finding a side and finding an angle

Definition: Cosine Rule for sides: a² = b² + c² - 2bc cos A Cosine Rule for angles: cos A = b2+c2−a2b² + c² - a² / 2bc2bc

Example: In triangle ABC, if a = 7m, b = 8m, and C = 83°, find the length of side c

Highlight: The cosine rule is particularly useful in SAS Side−Angle−SideSide-Angle-Side situations where you know two sides and the included angle.

Similar content

Know corbettmaths thumbnail

382

2353

9

corbettmaths

higher paper

Know circle theorums revision cards thumbnail

19

177

7/8

circle theorums revision cards

theorums 1-9 with key word definitions yw ;)

Know bearings thumbnail

2

129

10/11

bearings

bearing notes to help you revise

Know Bearing (Maths) thumbnail

10

439

10/11

Bearing (Maths)

Bearing maths revision note.

Know Math GCSE ; trigonometry, pythagoras and angles thumbnail

12

575

10/11

Math GCSE ; trigonometry, pythagoras and angles

Easy sum up

Know Trigonometry Revision Note thumbnail

26

1008

10/11

Trigonometry Revision Note

This revision notr is about triginimetry and SOH CAH TOA

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

21 M

Pupils love Knowunity

#1

In education app charts in 17 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.

Subjects

Maths

Geometry & measures

Angles

 

Maths

•

824

•

31 Mar 2023

•

17 pages

Easy Math Fun! Grouped Frequency and Column Vectors for Kids

K

kiki chapman

@kikichapman_nokm

Hey there! Dive into grouped frequency distribution fun with our calculator and examples. Solve grouped frequency problems with solutions and learn about ungrouped distributions. Try adding and subtracting column vectors with worksheets and PDF guides. Discover solving simultaneous equations graphically, with Maths Genie and Corbettmaths helping along the way!

O GROUPED FREQUENCY ο Class O DISCRETE) 0-10 11-20 21-30 e.g e.g CONTINUOUD: 5<h≤10 10ch ≤15 154h ≤20 o Add interval Add 20 31 o Estimated M

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

Vectors

This page covers vector notation and operations.

Key points:

  • Vectors can be represented as column vectors or with letters usuallyunderlinedusually underlined
  • Vector addition and subtraction can be visualized geometrically
  • Vector equations can be used to prove points lie on a straight line

Definition: A vector is a quantity with both magnitude and direction

Example: In the equation OB = a, AB = 2b, BD = a-b, vectors are used to describe positions and movements between points

Highlight: To show points lie on a straight line, prove that one vector is a scalar multiple of another

O GROUPED FREQUENCY ο Class O DISCRETE) 0-10 11-20 21-30 e.g e.g CONTINUOUD: 5<h≤10 10ch ≤15 154h ≤20 o Add interval Add 20 31 o Estimated M

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

Vector Problems

This page demonstrates how to solve more complex vector problems.

Key points:

  • Use parallel sides of shapes to relate vectors
  • Break down complex paths into simpler vector components
  • Ratios can be used to find positions along vectors

Example: In a parallelogram ABCD, if DE:EC = 8:1, vector DE can be expressed as 8/9 of vector DC

Highlight: When solving vector problems, break down the solution into steps: identify known vectors, use relationships between parallel sides, and combine vector components.

O GROUPED FREQUENCY ο Class O DISCRETE) 0-10 11-20 21-30 e.g e.g CONTINUOUD: 5<h≤10 10ch ≤15 154h ≤20 o Add interval Add 20 31 o Estimated M

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

Two-Way Tables

Two-way tables organize data into categories across two variables.

Key points:

  • Fill in missing information by adding and subtracting known values
  • Ensure row and column totals are consistent

Example: In a survey of 400 people 200men,200women200 men, 200 women about handedness:

  • 63 people are left-handed
  • 167 women are right-handed

Complete the two-way table using this information.

Highlight: When completing two-way tables, work systematically to fill in missing values, using row and column totals as checks.

O GROUPED FREQUENCY ο Class O DISCRETE) 0-10 11-20 21-30 e.g e.g CONTINUOUD: 5<h≤10 10ch ≤15 154h ≤20 o Add interval Add 20 31 o Estimated M

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

Similarity

This page introduces the concept of similarity in geometry.

Key points:

  • Similar shapes have the same angles and proportional sides
  • Area scales with the square of the linear scale factor
  • Volume scales with the cube of the linear scale factor

Definition: Similar shapes have the same shape but may be different sizes

Highlight: In similar shapes, corresponding angles are equal and corresponding sides are in proportion.

O GROUPED FREQUENCY ο Class O DISCRETE) 0-10 11-20 21-30 e.g e.g CONTINUOUD: 5<h≤10 10ch ≤15 154h ≤20 o Add interval Add 20 31 o Estimated M

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

Simultaneous Equations

This page covers methods for solving simultaneous equations.

Key points:

  • Rearrange equations into the form ax + by = c
  • Match coefficients of one variable
  • Add or subtract equations to eliminate one variable
  • Solve for the remaining variable and substitute back

Example: Solve the simultaneous equations: 2x + 4y = 6 4x + 3y = -3

Highlight: When solving simultaneous equations, the goal is to eliminate one variable by adding or subtracting the equations.

O GROUPED FREQUENCY ο Class O DISCRETE) 0-10 11-20 21-30 e.g e.g CONTINUOUD: 5<h≤10 10ch ≤15 154h ≤20 o Add interval Add 20 31 o Estimated M

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

Graphical Inequalities

This page explains how to represent inequalities graphically.

Key points:

  • Convert inequalities to equations for graphing
  • Use solid lines for ≥ or ≤, dotted lines for > or <
  • Shade the region that satisfies all inequalities

Example: Graph the inequalities: x + y < 5 y ≤ x + 2 y > 1

Highlight: The solution region for a system of inequalities is the area where all individual inequalities are satisfied simultaneously.

O GROUPED FREQUENCY ο Class O DISCRETE) 0-10 11-20 21-30 e.g e.g CONTINUOUD: 5<h≤10 10ch ≤15 154h ≤20 o Add interval Add 20 31 o Estimated M

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

Trigonometric Graphs

This page covers the graphs of sine, cosine, and tangent functions.

Key points:

  • Sine and cosine have a period of 360°
  • Tangent has a period of 180°
  • Key features include intercepts, peaks, and asymptotes

Vocabulary: Period - The interval after which a trigonometric function repeats

Example: Estimate the solutions for sin x = 0.7 between 0° and 360°

Highlight: Understanding the shapes and key features of trigonometric graphs is crucial for solving trigonometric equations graphically.

O GROUPED FREQUENCY ο Class O DISCRETE) 0-10 11-20 21-30 e.g e.g CONTINUOUD: 5<h≤10 10ch ≤15 154h ≤20 o Add interval Add 20 31 o Estimated M

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

Sine Rule

This page explains the sine rule and its applications.

Key points:

  • The sine rule relates sides and angles in any triangle
  • It can be used to find unknown sides or angles
  • Be cautious with the ambiguous case for angles

Definition: Sine Rule: a/sin A = b/sin B = c/sin C, where lowercase letters represent sides and uppercase letters represent opposite angles

Example: In triangle ABC, if a = 7m, A = 53°, and B = 83°, find the length of side b

Highlight: The sine rule is particularly useful when you know two angles and one side, or two sides and an angle opposite one of them.

O GROUPED FREQUENCY ο Class O DISCRETE) 0-10 11-20 21-30 e.g e.g CONTINUOUD: 5<h≤10 10ch ≤15 154h ≤20 o Add interval Add 20 31 o Estimated M

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

Cosine Rule

This page covers the cosine rule and its applications.

Key points:

  • The cosine rule relates all three sides and one angle in a triangle
  • It can be used when the sine rule is not applicable
  • There are separate formulas for finding a side and finding an angle

Definition: Cosine Rule for sides: a² = b² + c² - 2bc cos A Cosine Rule for angles: cos A = b2+c2−a2b² + c² - a² / 2bc2bc

Example: In triangle ABC, if a = 7m, b = 8m, and C = 83°, find the length of side c

Highlight: The cosine rule is particularly useful in SAS Side−Angle−SideSide-Angle-Side situations where you know two sides and the included angle.

O GROUPED FREQUENCY ο Class O DISCRETE) 0-10 11-20 21-30 e.g e.g CONTINUOUD: 5<h≤10 10ch ≤15 154h ≤20 o Add interval Add 20 31 o Estimated M

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

Scatter Graphs

This page discusses scatter graphs and correlation.

Key points:

  • Scatter graphs show relationships between two variables
  • Correlation can be positive, negative, or none
  • The line of best fit helps estimate values and identify trends

Vocabulary: Correlation - The strength and direction of the relationship between two variables

Example: A scatter graph showing the relationship between temperature and number of visitors to a beach

Highlight: Outliers are points that don't fit the general trend and should be considered carefully when interpreting scatter graphs.

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