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Maths
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Jun 15, 2022
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Mathematical concepts around enlargement, gradients, and probability form core foundations... Show more
Enlarge triangle by scale factor is a fundamental geometric transformation that changes an object's size while preserving its angles. When performing enlargements, every point of the original shape moves away from or towards a fixed point called the centre of enlargement.
To perform an enlargement scale factor transformation, multiply each distance from the centre of enlargement to any point on the shape by the scale factor. For positive scale factors greater than 1, the image will be larger than the original. For scale factors between 0 and 1, the image will be smaller. When using negative scale factors like enlarge by scale factor -1/2, the image appears on the opposite side of the centre of enlargement.
Definition: The scale factor determines how much larger or smaller the enlarged shape will be compared to the original. A scale factor of 2 doubles the size, while 1/2 halves it.
When working with an enlarge triangle by scale factor example, follow these steps: First, locate the centre of enlargement. Then, draw lines from this point through each vertex of the original shape. Finally, measure the distance from the centre to each vertex and multiply by the scale factor to find the new vertices' positions.
The gradient of a line y=mx+c represents the steepness of a straight line and is a crucial concept in mathematics and physics. The formula for gradient of a line with two points is calculated by dividing the vertical change (rise) by the horizontal change (run) between any two points on the line.
When learning how to calculate gradient of a slope, remember that positive gradients indicate lines rising from left to right, while negative gradients show lines falling from left to right. The larger the gradient's absolute value, the steeper the line.
Example: To find the gradient between points (2,3) and (6,11): Gradient = / = 8/4 = 2
How to find the gradient without a graph involves using the coordinates of any two points on the line and applying the gradient formula: /. This method is particularly useful when solving real-world problems involving rates of change.
The probability scale 0-1 is a fundamental concept that helps quantify the likelihood of events occurring. On this scale, 0 represents impossible events, 1 represents certain events, and all other probabilities fall between these values.
For students learning probability scale range explanation ks3, it's important to understand that probabilities can be expressed as decimals, fractions, or percentages. A probability of 0.5 (or 1/2 or 50%) indicates an event that is equally likely to happen or not happen.
Highlight: Probabilities must always fall between 0 and 1 inclusive. Negative probabilities or probabilities greater than 1 are impossible.
When working with probability scale worksheet with answers, students practice converting between different probability representations and ordering events from least to most likely. This helps develop intuition about the relative likelihood of different events and strengthens understanding of the probability scale's practical applications.
Our AI companion is specifically built for the needs of students. Based on the millions of content pieces we have on the platform we can provide truly meaningful and relevant answers to students. But its not only about answers, the companion is even more about guiding students through their daily learning challenges, with personalised study plans, quizzes or content pieces in the chat and 100% personalisation based on the students skills and developments.
You can download the app in the Google Play Store and in the Apple App Store.
That's right! Enjoy free access to study content, connect with fellow students, and get instant help – all at your fingertips.
App Store
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
I think it’s very much worth it and you’ll end up using it a lot once you get the hang of it and even after looking at others notes you can still ask your Artificial intelligence buddy the question and ask to simplify it if you still don’t get it!!! In the end I think it’s worth it 😊👍 ⚠️Also DID I MENTION ITS FREEE YOU DON’T HAVE TO PAY FOR ANYTHING AND STILL GET YOUR GRADES IN PERFECTLY❗️❗️⚠️
Thomas R
iOS user
Knowunity is the BEST app I’ve used in a minute. This is not an ai review or anything this is genuinely coming from a 7th grade student (I know 2011 im young) but dude this app is a 10/10 i have maintained a 3.8 gpa and have plenty of time for gaming. I love it and my mom is just happy I got good grades
Brad T
Android user
Not only did it help me find the answer but it also showed me alternative ways to solve it. I was horrible in math and science but now I have an a in both subjects. Thanks for the help🤍🤍
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
I found this app a couple years ago and it has only gotten better since then. I really love it because it can help with written questions and photo questions. Also, it can find study guides that other people have made as well as flashcard sets and practice tests. The free version is also amazing for students who might not be able to afford it. Would 100% recommend
Aubrey
iOS user
Best app if you're in Highschool or Junior high. I have been using this app for 2 school years and it's the best, it's good if you don't have anyone to help you with school work.😋🩷🎀
Marco B
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 app is phenomenal down to the correct info and the various topics you can study! I greatly recommend it for people who struggle with procrastination and those who need homework help. It has been perfectly accurate for world 1 history as far as I’ve seen! Geometry too!
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
I think it’s very much worth it and you’ll end up using it a lot once you get the hang of it and even after looking at others notes you can still ask your Artificial intelligence buddy the question and ask to simplify it if you still don’t get it!!! In the end I think it’s worth it 😊👍 ⚠️Also DID I MENTION ITS FREEE YOU DON’T HAVE TO PAY FOR ANYTHING AND STILL GET YOUR GRADES IN PERFECTLY❗️❗️⚠️
Thomas R
iOS user
Knowunity is the BEST app I’ve used in a minute. This is not an ai review or anything this is genuinely coming from a 7th grade student (I know 2011 im young) but dude this app is a 10/10 i have maintained a 3.8 gpa and have plenty of time for gaming. I love it and my mom is just happy I got good grades
Brad T
Android user
Not only did it help me find the answer but it also showed me alternative ways to solve it. I was horrible in math and science but now I have an a in both subjects. Thanks for the help🤍🤍
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
I found this app a couple years ago and it has only gotten better since then. I really love it because it can help with written questions and photo questions. Also, it can find study guides that other people have made as well as flashcard sets and practice tests. The free version is also amazing for students who might not be able to afford it. Would 100% recommend
Aubrey
iOS user
Best app if you're in Highschool or Junior high. I have been using this app for 2 school years and it's the best, it's good if you don't have anyone to help you with school work.😋🩷🎀
Marco B
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 app is phenomenal down to the correct info and the various topics you can study! I greatly recommend it for people who struggle with procrastination and those who need homework help. It has been perfectly accurate for world 1 history as far as I’ve seen! Geometry too!
Paul T
iOS user
Mathematical concepts around enlargement, gradients, and probability form core foundations for geometry and statistics.
Enlargement involves changing the size of shapes while maintaining their proportions using a scale factor. When working with triangles and other shapes, the scale factor... Show more
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Join milions of students
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Enlarge triangle by scale factor is a fundamental geometric transformation that changes an object's size while preserving its angles. When performing enlargements, every point of the original shape moves away from or towards a fixed point called the centre of enlargement.
To perform an enlargement scale factor transformation, multiply each distance from the centre of enlargement to any point on the shape by the scale factor. For positive scale factors greater than 1, the image will be larger than the original. For scale factors between 0 and 1, the image will be smaller. When using negative scale factors like enlarge by scale factor -1/2, the image appears on the opposite side of the centre of enlargement.
Definition: The scale factor determines how much larger or smaller the enlarged shape will be compared to the original. A scale factor of 2 doubles the size, while 1/2 halves it.
When working with an enlarge triangle by scale factor example, follow these steps: First, locate the centre of enlargement. Then, draw lines from this point through each vertex of the original shape. Finally, measure the distance from the centre to each vertex and multiply by the scale factor to find the new vertices' positions.
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
The gradient of a line y=mx+c represents the steepness of a straight line and is a crucial concept in mathematics and physics. The formula for gradient of a line with two points is calculated by dividing the vertical change (rise) by the horizontal change (run) between any two points on the line.
When learning how to calculate gradient of a slope, remember that positive gradients indicate lines rising from left to right, while negative gradients show lines falling from left to right. The larger the gradient's absolute value, the steeper the line.
Example: To find the gradient between points (2,3) and (6,11): Gradient = / = 8/4 = 2
How to find the gradient without a graph involves using the coordinates of any two points on the line and applying the gradient formula: /. This method is particularly useful when solving real-world problems involving rates of change.
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
The probability scale 0-1 is a fundamental concept that helps quantify the likelihood of events occurring. On this scale, 0 represents impossible events, 1 represents certain events, and all other probabilities fall between these values.
For students learning probability scale range explanation ks3, it's important to understand that probabilities can be expressed as decimals, fractions, or percentages. A probability of 0.5 (or 1/2 or 50%) indicates an event that is equally likely to happen or not happen.
Highlight: Probabilities must always fall between 0 and 1 inclusive. Negative probabilities or probabilities greater than 1 are impossible.
When working with probability scale worksheet with answers, students practice converting between different probability representations and ordering events from least to most likely. This helps develop intuition about the relative likelihood of different events and strengthens understanding of the probability scale's practical applications.
Our AI companion is specifically built for the needs of students. Based on the millions of content pieces we have on the platform we can provide truly meaningful and relevant answers to students. But its not only about answers, the companion is even more about guiding students through their daily learning challenges, with personalised study plans, quizzes or content pieces in the chat and 100% personalisation based on the students skills and developments.
You can download the app in the Google Play Store and in the Apple App Store.
That's right! Enjoy free access to study content, connect with fellow students, and get instant help – all at your fingertips.
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Hol dir die App, um Zugang zu den smarten Tools mit interaktiven Karteikarten, Übungsaufgaben, Probeklausuren und Zusammenfassungen zu bekommen
Master the technique of expanding triple brackets with this concise guide tailored for GCSE students. This resource covers key concepts such as special products, the distributive property, and binomial expansion, providing clear examples and step-by-step explanations to enhance your understanding and problem-solving skills.
MathsExplore the BODMAS (Brackets, Orders, Division, Multiplication, Addition, Subtraction) rules for solving mathematical equations. This summary provides clear examples and step-by-step guidance on applying the order of operations effectively. Ideal for students looking to enhance their problem-solving skills in mathematics.
MathsComprehensive revision notes covering key concepts from GCSE Maths Units 9.1 and 9.2, including multi-step equations, LCM, HCF, significant figures, algebraic manipulation, and more. Perfect for Year 9 students preparing for exams.
MathsExplore essential algebraic concepts including graphing methods, solving equations, scientific notation, and properties of sequences. This comprehensive summary covers key topics such as inequalities, factoring, and arithmetic operations, providing a solid foundation for mastering algebra. Ideal for students preparing for exams or seeking to enhance their understanding of mathematical principles.
MathsPrepare for your Year 7 Maths exam with this comprehensive practice test covering key topics such as simplifying expressions, geometry, angles, and arithmetic operations. Ideal for students in Year 7, 8, and 9, this test includes a variety of questions on multiplication, division, and statistical averages, ensuring a well-rounded review. Perfect for exam preparation and skill reinforcement.
MathsExplore essential Year 7 algebra concepts with this comprehensive guide. Dive into function machines, algebraic notation, sequences, and inverse operations. This resource includes key vocabulary, exemplar questions, and strategies for effective teaching and learning. Perfect for educators and students aiming to strengthen their understanding of algebraic principles.
MathsApp Store
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
I think it’s very much worth it and you’ll end up using it a lot once you get the hang of it and even after looking at others notes you can still ask your Artificial intelligence buddy the question and ask to simplify it if you still don’t get it!!! In the end I think it’s worth it 😊👍 ⚠️Also DID I MENTION ITS FREEE YOU DON’T HAVE TO PAY FOR ANYTHING AND STILL GET YOUR GRADES IN PERFECTLY❗️❗️⚠️
Thomas R
iOS user
Knowunity is the BEST app I’ve used in a minute. This is not an ai review or anything this is genuinely coming from a 7th grade student (I know 2011 im young) but dude this app is a 10/10 i have maintained a 3.8 gpa and have plenty of time for gaming. I love it and my mom is just happy I got good grades
Brad T
Android user
Not only did it help me find the answer but it also showed me alternative ways to solve it. I was horrible in math and science but now I have an a in both subjects. Thanks for the help🤍🤍
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
I found this app a couple years ago and it has only gotten better since then. I really love it because it can help with written questions and photo questions. Also, it can find study guides that other people have made as well as flashcard sets and practice tests. The free version is also amazing for students who might not be able to afford it. Would 100% recommend
Aubrey
iOS user
Best app if you're in Highschool or Junior high. I have been using this app for 2 school years and it's the best, it's good if you don't have anyone to help you with school work.😋🩷🎀
Marco B
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 app is phenomenal down to the correct info and the various topics you can study! I greatly recommend it for people who struggle with procrastination and those who need homework help. It has been perfectly accurate for world 1 history as far as I’ve seen! Geometry too!
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
I think it’s very much worth it and you’ll end up using it a lot once you get the hang of it and even after looking at others notes you can still ask your Artificial intelligence buddy the question and ask to simplify it if you still don’t get it!!! In the end I think it’s worth it 😊👍 ⚠️Also DID I MENTION ITS FREEE YOU DON’T HAVE TO PAY FOR ANYTHING AND STILL GET YOUR GRADES IN PERFECTLY❗️❗️⚠️
Thomas R
iOS user
Knowunity is the BEST app I’ve used in a minute. This is not an ai review or anything this is genuinely coming from a 7th grade student (I know 2011 im young) but dude this app is a 10/10 i have maintained a 3.8 gpa and have plenty of time for gaming. I love it and my mom is just happy I got good grades
Brad T
Android user
Not only did it help me find the answer but it also showed me alternative ways to solve it. I was horrible in math and science but now I have an a in both subjects. Thanks for the help🤍🤍
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
I found this app a couple years ago and it has only gotten better since then. I really love it because it can help with written questions and photo questions. Also, it can find study guides that other people have made as well as flashcard sets and practice tests. The free version is also amazing for students who might not be able to afford it. Would 100% recommend
Aubrey
iOS user
Best app if you're in Highschool or Junior high. I have been using this app for 2 school years and it's the best, it's good if you don't have anyone to help you with school work.😋🩷🎀
Marco B
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 app is phenomenal down to the correct info and the various topics you can study! I greatly recommend it for people who struggle with procrastination and those who need homework help. It has been perfectly accurate for world 1 history as far as I’ve seen! Geometry too!
Paul T
iOS user
