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How to Change the Subject of a Formula and Calculate Volumes

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Kimberley

26/02/2023

Maths

Block 2 - National 5 Maths

How to Change the Subject of a Formula and Calculate Volumes

This guide covers key mathematical concepts including changing the subject of formulas, calculating volumes, interquartile range, standard deviation, straight line equations, and arc length and sector area calculations. It provides step-by-step examples to illustrate these important topics for students.

• Learn how to change the subject of a formula by applying opposite operations
• Practice calculating volume of a cylinder to significant figures using geometric formulas
• Understand how to calculate interquartile range of temperatures and interpret the results
• Master techniques for finding standard deviation, gradients, and equations of lines
• Apply formulas for arc length and sector area in practical examples

...

26/02/2023

355

block
Changing the Subject
1. Change the Subject of the formula
F = + + 4b₂
C
t+4b
F
t+46 CF
2
t = CF-4b
v = 2 p
to b
Opposite side
-> Oppos

View

Volume Calculations

This page focuses on volume calculations for various 3D shapes, providing essential formulas and a practical example.

Vocabulary: Volume is the amount of three-dimensional space occupied by an object.

The page lists key volume formulas:

  • Prism: V = Ah Areaofbase×heightArea of base × height
  • Cylinder: V = πr²h π×radius2×heightπ × radius² × height
  • Cuboid: V = lbh length×breadth×heightlength × breadth × height

Example: A complex shape consisting of a cylinder and a hemisphere is presented. The problem requires calculating the total volume to 3 significant figures.

The solution is broken down into steps:

  1. Calculate the volume of the cylinder V1V₁
  2. Calculate the volume of the hemisphere V2V₂
  3. Sum the two volumes and round to 3 significant figures

Highlight: When solving complex volume problems, break the shape into simpler components and calculate their volumes separately before combining.

block
Changing the Subject
1. Change the Subject of the formula
F = + + 4b₂
C
t+4b
F
t+46 CF
2
t = CF-4b
v = 2 p
to b
Opposite side
-> Oppos

View

Interquartile Range

This page explains the concept of interquartile range IQRIQR and its application in comparing data sets.

Definition: The interquartile range is a measure of statistical dispersion, calculated as the difference between the upper Q3Q3 and lower Q1Q1 quartiles.

The formula for IQR is presented: IQR = Q3 - Q1

Example: A set of midday temperatures in Glasgow is given: 3, 3, 3, 4, 4, 5, 6, 7, 9, 10. The problem requires calculating the median and IQR.

The solution demonstrates how to:

  1. Arrange the data in ascending order
  2. Find the median Q2Q2
  3. Calculate Q1 and Q3
  4. Compute the IQR

Highlight: The IQR is useful for comparing the spread of data between different sets, as shown in the comparison between Glasgow and Edinburgh temperatures.

block
Changing the Subject
1. Change the Subject of the formula
F = + + 4b₂
C
t+4b
F
t+46 CF
2
t = CF-4b
v = 2 p
to b
Opposite side
-> Oppos

View

Standard Deviation

This page covers the calculation of mean and standard deviation for a given data set.

Definition: Standard deviation is a measure of the amount of variation or dispersion of a set of values.

The page provides a step-by-step guide to calculating standard deviation:

  1. Calculate the mean of the data set
  2. Find the difference between each data point and the mean
  3. Square these differences
  4. Sum the squared differences
  5. Divide by n1n-1, where n is the number of data points
  6. Take the square root of the result

Example: A data set of 14, 17, 15, 23, 20, 19 is used to demonstrate the calculation process.

Highlight: The sum of the differences between each data point and the mean should always equal zero, serving as a check for calculations.

block
Changing the Subject
1. Change the Subject of the formula
F = + + 4b₂
C
t+4b
F
t+46 CF
2
t = CF-4b
v = 2 p
to b
Opposite side
-> Oppos

View

Straight Line Equations

This page focuses on the equation of a straight line and how to determine its gradient and y-intercept.

Vocabulary: The general form of a straight line equation is y = mx + c, where m is the gradient and c is the y-intercept.

The page demonstrates how to:

  1. Rearrange an equation into y = mx + c form
  2. Identify the gradient and y-intercept from this form
  3. Calculate the gradient using two points on the line

Example: The equation 2x - 5y = 20 is rearranged to find the gradient and y-intercept.

Highlight: The gradient formula m = y2y1y₂ - y₁ / x2x1x₂ - x₁ is crucial for finding the slope between two points.

block
Changing the Subject
1. Change the Subject of the formula
F = + + 4b₂
C
t+4b
F
t+46 CF
2
t = CF-4b
v = 2 p
to b
Opposite side
-> Oppos

View

Equation of a Line

This page extends the concept of straight lines, focusing on finding the equation of a line passing through two points.

Vocabulary: The point-slope form of a line equation is y - y₁ = mxx1x - x₁, where x1,y1x₁, y₁ is a point on the line and m is the gradient.

The page demonstrates the process of finding a line equation:

  1. Calculate the gradient using two given points
  2. Use the point-slope form to write the equation
  3. Simplify the equation to y = mx + c form

Example: Find the equation of the line passing through 1,7-1, -7 and 4,34, 3.

The page also introduces arc length calculations:

  • Formula: l = θ/360° × πd, where θ is the angle in degrees and d is the diameter

Highlight: The arc length formula can be rearranged to find unknown angles or diameters when other variables are given.

block
Changing the Subject
1. Change the Subject of the formula
F = + + 4b₂
C
t+4b
F
t+46 CF
2
t = CF-4b
v = 2 p
to b
Opposite side
-> Oppos

View

Area of a Sector

This final page covers the calculation of sector area in a circle.

Definition: A sector is a part of a circular disk enclosed by two radii and an arc.

The formula for the area of a sector is presented: A = θ/360° × πr², where θ is the angle in degrees and r is the radius.

Example: Calculate the area of a sector with radius 3cm and angle 150°.

The page also shows how to:

  • Find an unknown angle given the area and radius
  • Calculate the radius when given the area and angle

Highlight: Sector area problems often involve rearranging the formula to solve for different variables, similar to changing the subject of a formula.

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Maths

355

26 Feb 2023

7 pages

How to Change the Subject of a Formula and Calculate Volumes

user profile picture

Kimberley

@kimberley_ncyf

This guide covers key mathematical concepts including changing the subject of formulas, calculating volumes, interquartile range, standard deviation, straight line equations, and arc length and sector area calculations. It provides step-by-step examples to illustrate these important topics for students.

•... Show more

block
Changing the Subject
1. Change the Subject of the formula
F = + + 4b₂
C
t+4b
F
t+46 CF
2
t = CF-4b
v = 2 p
to b
Opposite side
-> Oppos

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Join milions of students

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Volume Calculations

This page focuses on volume calculations for various 3D shapes, providing essential formulas and a practical example.

Vocabulary: Volume is the amount of three-dimensional space occupied by an object.

The page lists key volume formulas:

  • Prism: V = Ah Areaofbase×heightArea of base × height
  • Cylinder: V = πr²h π×radius2×heightπ × radius² × height
  • Cuboid: V = lbh length×breadth×heightlength × breadth × height

Example: A complex shape consisting of a cylinder and a hemisphere is presented. The problem requires calculating the total volume to 3 significant figures.

The solution is broken down into steps:

  1. Calculate the volume of the cylinder V1V₁
  2. Calculate the volume of the hemisphere V2V₂
  3. Sum the two volumes and round to 3 significant figures

Highlight: When solving complex volume problems, break the shape into simpler components and calculate their volumes separately before combining.

Sign up to see the contentIt's free!

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Join milions of students

By signing up you accept Terms of Service and Privacy Policy

Interquartile Range

This page explains the concept of interquartile range IQRIQR and its application in comparing data sets.

Definition: The interquartile range is a measure of statistical dispersion, calculated as the difference between the upper Q3Q3 and lower Q1Q1 quartiles.

The formula for IQR is presented: IQR = Q3 - Q1

Example: A set of midday temperatures in Glasgow is given: 3, 3, 3, 4, 4, 5, 6, 7, 9, 10. The problem requires calculating the median and IQR.

The solution demonstrates how to:

  1. Arrange the data in ascending order
  2. Find the median Q2Q2
  3. Calculate Q1 and Q3
  4. Compute the IQR

Highlight: The IQR is useful for comparing the spread of data between different sets, as shown in the comparison between Glasgow and Edinburgh temperatures.

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 page covers the calculation of mean and standard deviation for a given data set.

Definition: Standard deviation is a measure of the amount of variation or dispersion of a set of values.

The page provides a step-by-step guide to calculating standard deviation:

  1. Calculate the mean of the data set
  2. Find the difference between each data point and the mean
  3. Square these differences
  4. Sum the squared differences
  5. Divide by n1n-1, where n is the number of data points
  6. Take the square root of the result

Example: A data set of 14, 17, 15, 23, 20, 19 is used to demonstrate the calculation process.

Highlight: The sum of the differences between each data point and the mean should always equal zero, serving as a check for calculations.

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

Straight Line Equations

This page focuses on the equation of a straight line and how to determine its gradient and y-intercept.

Vocabulary: The general form of a straight line equation is y = mx + c, where m is the gradient and c is the y-intercept.

The page demonstrates how to:

  1. Rearrange an equation into y = mx + c form
  2. Identify the gradient and y-intercept from this form
  3. Calculate the gradient using two points on the line

Example: The equation 2x - 5y = 20 is rearranged to find the gradient and y-intercept.

Highlight: The gradient formula m = y2y1y₂ - y₁ / x2x1x₂ - x₁ is crucial for finding the slope between two points.

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

Equation of a Line

This page extends the concept of straight lines, focusing on finding the equation of a line passing through two points.

Vocabulary: The point-slope form of a line equation is y - y₁ = mxx1x - x₁, where x1,y1x₁, y₁ is a point on the line and m is the gradient.

The page demonstrates the process of finding a line equation:

  1. Calculate the gradient using two given points
  2. Use the point-slope form to write the equation
  3. Simplify the equation to y = mx + c form

Example: Find the equation of the line passing through 1,7-1, -7 and 4,34, 3.

The page also introduces arc length calculations:

  • Formula: l = θ/360° × πd, where θ is the angle in degrees and d is the diameter

Highlight: The arc length formula can be rearranged to find unknown angles or diameters when other variables are given.

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Area of a Sector

This final page covers the calculation of sector area in a circle.

Definition: A sector is a part of a circular disk enclosed by two radii and an arc.

The formula for the area of a sector is presented: A = θ/360° × πr², where θ is the angle in degrees and r is the radius.

Example: Calculate the area of a sector with radius 3cm and angle 150°.

The page also shows how to:

  • Find an unknown angle given the area and radius
  • Calculate the radius when given the area and angle

Highlight: Sector area problems often involve rearranging the formula to solve for different variables, similar to changing the subject of a formula.

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

Changing the Subject of a Formula

This page introduces the concept of changing the subject of a formula in mathematics. It demonstrates the process using two examples.

Definition: Changing the subject of a formula involves rearranging an equation to isolate a different variable as the subject.

The first example shows how to change the subject of the formula F = C/t+4bt+4b + 4b² to t. The process involves applying opposite operations to isolate t.

Example: To change F = C/t+4bt+4b + 4b² to make t the subject, subtract 4b² from both sides, multiply by t+4bt+4b, and then subtract 4b to isolate t.

The second example demonstrates changing the subject of P = my²/2 to v. This involves multiplying both sides by 2, dividing by m, and then taking the square root.

Highlight: When changing the subject of a formula, always perform the same operation on both sides of the equation to maintain equality.

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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

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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