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Maths
29 Nov 2025
663
9 pages
Neo @neola_axsx
This document provides direct and inverse proportion exam practice questions with solutions PDF. It covers various types... Show more
This page presents three questions covering direct and inverse proportion problems. The questions involve calculating values based on given proportional relationships.
Example Question 1 deals with y being directly proportional to the square of x, where y = 24 when x = 2.
Vocabulary Direct proportion - a relationship where one quantity increases at the same rate as another.
Vocabulary Inverse proportion - a relationship where one quantity decreases at the same rate as another increases.
This page focuses on a more complex direct proportion problem involving the relationship between H and c, where H varies directly to the cube of c.
Example When H = 40, c = 2, students are asked to express H in terms of c, find H when c = 5, and find c when H = 5000.
Highlight The question demonstrates how to manipulate equations involving cubes in direct proportion problems.
This page presents a problem involving inverse proportion between force and distance in the context of magnetism. Students are asked to express the relationship mathematically and solve related problems.
Example The force F (newtons) exerted by a magnet is inversely proportional to the square of the distance d (cm).
Highlight The question includes an explanation of what happens to F when d is halved, reinforcing understanding of inverse proportion.
This page contains two problems involving inverse and direct proportion. The first deals with inverse proportion between A and B, while the second involves direct proportion between C and the square root of y.
Example In the first problem, A is inversely proportional to B, and students must find A when B = A.
Highlight The second problem introduces direct proportion with square roots, expanding on previous concepts.
This page presents a practical application of inverse proportion in the context of airport check-in times. It demonstrates how the time taken for check-in is inversely proportional to the square of the number of staff working.
Example Students must find an equation connecting time (t) and staff number (s), and determine the minimum number of staff needed for a specific check-in time.
Highlight This question shows how inverse proportion can be applied to real-world scenarios, enhancing students' understanding of its practical uses.
This page features a complex problem involving both direct and inverse proportion relationships. Students must navigate multiple proportional relationships to solve for the final value.
Example The problem involves variables a, w, and c, with a directly proportional to √c and w inversely proportional to a³.
Highlight This question tests students' ability to handle multiple proportion relationships simultaneously, preparing them for more advanced mathematical concepts.
This page presents a practical application of inverse proportion in the context of research planning. Students must determine the number of researchers needed to complete a project in a given time frame.
Example The number of days (D) to complete research is inversely proportional to the number of researchers (R).
Highlight This question demonstrates how inverse proportion can be used in project management and resource allocation scenarios.
The final page of the document challenges students to match different graphs to their corresponding proportional relationships. This exercise tests students' ability to visually interpret various types of proportion.
Example Students must match graphs to relationships such as y = 1/x, y = √x, and y = x².
Highlight This question helps students develop a visual understanding of how different proportional relationships appear when graphed, reinforcing their conceptual knowledge.
This page introduces the exam-style questions on direct and inverse proportion. It provides guidance for students on how to approach the questions and lists essential materials needed for the exam.
Highlight The document emphasizes the importance of showing all workings in answers.
Example Required materials include pencil, pen, ruler, protractor, pair of compasses, and eraser.
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.
You can download the app from Google Play Store and Apple App Store.
That's right! Enjoy free access to study content, connect with fellow students, and get instant help – all at your fingertips.
21
Smart Tools NEW
Transform this note into: ✓ 50+ Practice Questions ✓ Interactive Flashcards ✓ Full Mock Exam ✓ Essay Outlines
Explore the Year 9 Foundation Assessment focusing on key mathematical concepts such as ratios, proportions, similar triangles, and scale factors. This assessment includes calculator-based questions and detailed solutions to enhance understanding. Ideal for students preparing for SATS Arithmetic and improving their skills in proportional relationships and decimal calculations.
MathsExplore the concepts of direct and inverse proportion with detailed explanations and worked examples. This resource covers the constant of proportionality, equations for both types of proportion, and practical problem-solving techniques. Ideal for GCSE Maths revision.
MathsExplore key concepts of ratios and proportions in this comprehensive summary. Learn definitions, examples, and methods for simplifying ratios, sharing in ratios, and calculating percentages. Ideal for Year 7 students preparing for assessments in mathematics.
MathsExplore detailed solutions for a higher-level math exam covering key concepts such as ratios, proportions, transformations, volume calculations, and direct proportionality. This resource includes model answers for various problems, including frequency tables and geometric transformations, making it ideal for exam preparation.
MathsMaximize your exam success with this comprehensive GCSE Maths revision strategy. This guide outlines a structured approach to revising key topics, including geometry, trigonometry, and statistics. Learn effective techniques such as spaced revision, content consolidation, and exam question application to enhance your understanding and retention. Ideal for students preparing for the Edexcel Maths (Higher) exam.
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
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
Neo
@neola_axsx
This document provides direct and inverse proportion exam practice questions with solutions PDF. It covers various types of proportion problems, offering step-by-step solutions and explanations for each question. The content is suitable for GCSE and KS3 level students preparing... Show more
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This page presents three questions covering direct and inverse proportion problems. The questions involve calculating values based on given proportional relationships.
Example: Question 1 deals with y being directly proportional to the square of x, where y = 24 when x = 2.
Vocabulary: Direct proportion - a relationship where one quantity increases at the same rate as another.
Vocabulary: Inverse proportion - a relationship where one quantity decreases at the same rate as another increases.
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
This page focuses on a more complex direct proportion problem involving the relationship between H and c, where H varies directly to the cube of c.
Example: When H = 40, c = 2, students are asked to express H in terms of c, find H when c = 5, and find c when H = 5000.
Highlight: The question demonstrates how to manipulate equations involving cubes in direct proportion problems.
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
This page presents a problem involving inverse proportion between force and distance in the context of magnetism. Students are asked to express the relationship mathematically and solve related problems.
Example: The force F (newtons) exerted by a magnet is inversely proportional to the square of the distance d (cm).
Highlight: The question includes an explanation of what happens to F when d is halved, reinforcing understanding of inverse proportion.
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
This page contains two problems involving inverse and direct proportion. The first deals with inverse proportion between A and B, while the second involves direct proportion between C and the square root of y.
Example: In the first problem, A is inversely proportional to B, and students must find A when B = A.
Highlight: The second problem introduces direct proportion with square roots, expanding on previous concepts.
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
This page presents a practical application of inverse proportion in the context of airport check-in times. It demonstrates how the time taken for check-in is inversely proportional to the square of the number of staff working.
Example: Students must find an equation connecting time (t) and staff number (s), and determine the minimum number of staff needed for a specific check-in time.
Highlight: This question shows how inverse proportion can be applied to real-world scenarios, enhancing students' understanding of its practical uses.
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
This page features a complex problem involving both direct and inverse proportion relationships. Students must navigate multiple proportional relationships to solve for the final value.
Example: The problem involves variables a, w, and c, with a directly proportional to √c and w inversely proportional to a³.
Highlight: This question tests students' ability to handle multiple proportion relationships simultaneously, preparing them for more advanced mathematical concepts.
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
This page presents a practical application of inverse proportion in the context of research planning. Students must determine the number of researchers needed to complete a project in a given time frame.
Example: The number of days (D) to complete research is inversely proportional to the number of researchers (R).
Highlight: This question demonstrates how inverse proportion can be used in project management and resource allocation scenarios.
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
The final page of the document challenges students to match different graphs to their corresponding proportional relationships. This exercise tests students' ability to visually interpret various types of proportion.
Example: Students must match graphs to relationships such as y = 1/x, y = √x, and y = x².
Highlight: This question helps students develop a visual understanding of how different proportional relationships appear when graphed, reinforcing their conceptual knowledge.
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
This page introduces the exam-style questions on direct and inverse proportion. It provides guidance for students on how to approach the questions and lists essential materials needed for the exam.
Highlight: The document emphasizes the importance of showing all workings in answers.
Example: Required materials include pencil, pen, ruler, protractor, pair of compasses, and eraser.
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.
You can download the app from Google Play Store and Apple App Store.
That's right! Enjoy free access to study content, connect with fellow students, and get instant help – all at your fingertips.
21
Smart Tools NEW
Transform this note into: ✓ 50+ Practice Questions ✓ Interactive Flashcards ✓ Full Mock Exam ✓ Essay Outlines
Explore the Year 9 Foundation Assessment focusing on key mathematical concepts such as ratios, proportions, similar triangles, and scale factors. This assessment includes calculator-based questions and detailed solutions to enhance understanding. Ideal for students preparing for SATS Arithmetic and improving their skills in proportional relationships and decimal calculations.
MathsExplore the concepts of direct and inverse proportion with detailed explanations and worked examples. This resource covers the constant of proportionality, equations for both types of proportion, and practical problem-solving techniques. Ideal for GCSE Maths revision.
MathsExplore key concepts of ratios and proportions in this comprehensive summary. Learn definitions, examples, and methods for simplifying ratios, sharing in ratios, and calculating percentages. Ideal for Year 7 students preparing for assessments in mathematics.
MathsExplore detailed solutions for a higher-level math exam covering key concepts such as ratios, proportions, transformations, volume calculations, and direct proportionality. This resource includes model answers for various problems, including frequency tables and geometric transformations, making it ideal for exam preparation.
MathsMaximize your exam success with this comprehensive GCSE Maths revision strategy. This guide outlines a structured approach to revising key topics, including geometry, trigonometry, and statistics. Learn effective techniques such as spaced revision, content consolidation, and exam question application to enhance your understanding and retention. Ideal for students preparing for the Edexcel Maths (Higher) exam.
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
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
Sociology