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Maths
8 Dec 2025
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This GCSE Mathematics mark scheme shows you exactly how examiners award marks for Higher Tier Paper 6 questions.... Show more
You're looking at the mark scheme for GCSE Mathematics Higher Tier Paper 6 from June 2018. This is the document that shows examiners exactly how to mark your answers and award points.
OCR (Oxford Cambridge and RSA) is one of the main exam boards in the UK that creates your GCSE qualifications. They're a not-for-profit organisation, which means any money they make goes back into improving qualifications and support for students like you.
Remember Mark schemes help you understand what examiners are looking for, but they don't show you every possible correct answer - examiners are trained to give credit for alternative methods too!
Examiners use special symbols and codes to show how they've marked your work. The tick (✓) means you're correct, whilst the cross (×) shows an error.
Method marks (M1, M2) are awarded for using the right approach, even if your final answer is wrong due to a simple calculation error. Accuracy marks (A1) depend on getting the right answer after using a correct method.
Independent marks (B1, B2) are given for correct answers or key steps, regardless of your method. Special abbreviations like 'cao' (correct answer only) and 'nfww' (not from wrong working) tell examiners when to be strict about answers.
Top Tip Show all your working clearly - you can still earn method marks even if your final answer is incorrect!
Follow through marking means you can earn marks for correct working based on a previous wrong answer. If you make an error early on but use the wrong number correctly in later steps, you won't be penalised twice.
When you misread data consistently (like reading 37 instead of 73), examiners will follow your work and only deduct one mark. This is fairer than penalising you for every subsequent error.
If you give two different answers, examiners will mark the weaker one. Always cross out work you don't want marked, and make sure your final answer is clear on the answer line.
Exam Strategy If you spot an error partway through, don't panic - you can still earn follow-through marks for the rest of your solution!
Looking at Question 1, you needed four numbers where at least two are 8, the range is 7, and the total is 44. The answer 8, 8, 13, 15 gets full marks, but partial credit is available for meeting some conditions.
Question 2 involves ratio calculations. You get marks for identifying the correct ratios (like 5936) and then calculating percentages. The key is showing that 9 out of 50 total parts equals 18%.
For algebraic estimation in Question 4, you need to substitute values and show your calculation clearly. Getting 20 and explaining it's close to 19.5 earns full marks.
Working Smart Even if you can't complete a question fully, you can still earn valuable partial marks by showing relevant working!
Coordinate geometry questions test multiple skills. For finding equations of lines, you need the correct gradient (like 0.75) and y-intercept. Show your gradient calculation clearly using the change in y over change in x.
Quadratic substitution problems require careful algebra. When substituting into y = -x² + kx + 8, make sure you handle negative signs correctly. The mark scheme shows common sign errors that lose marks.
Triangle proofs can be solved using different methods - symmetry, Pythagoras, or trigonometry. All approaches can earn full marks if properly executed. The key is showing that two sides are equal (making it isosceles).
Multiple Methods Don't worry if your method differs from friends - there are often several correct approaches to geometry problems!
Inverse proportion and algebraic manipulation appear in the final questions. For inverse proportion, set up the relationship correctly and solve systematically.
Substitution problems with sequences require you to find the correct value first, then substitute into given formulas. Show each step clearly - you can earn marks for finding intermediate values like u = 14.
The mark scheme shows that accuracy matters but isn't everything. Method marks mean you're rewarded for understanding the process, even when small errors creep in.
Confidence Builder Remember that GCSE marking is designed to reward what you know - focus on showing your mathematical thinking clearly!
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.
12
Smart Tools NEW
Transform this note into: ✓ 50+ Practice Questions ✓ Interactive Flashcards ✓ Full Mock Exam ✓ Essay Outlines
Explore the methods for calculating the area of various quadrilaterals, including squares, rectangles, and parallelograms. This summary covers essential formulas, properties, and examples to enhance your understanding of area and perimeter in geometry.
MathsExplore essential trigonometry concepts including formulas for sine, cosine, and tangent. Learn how to find angles and side lengths in right triangles using trigonometric ratios and inverse functions. This summary is perfect for students preparing for exams or needing a quick reference on trigonometric principles.
MathsExplore the fundamentals of bearings in geometry, including angle measurement, relationships, and rules. This summary covers key concepts such as calculating bearings, angle pairs, and the total angles in triangles. Ideal for students preparing for exams or seeking to enhance their understanding of geometry.
MathsPrepare for your GCSE exams with this comprehensive non-calculator practice paper. Covering key concepts such as area of triangles, ratios, statistical averages, and more, this resource includes 22 questions with varying marks to help you master essential mathematical skills. Ideal for students aiming for higher grades, this practice paper is designed to enhance your problem-solving abilities and exam readiness.
MathsExplore essential circle theorems, including properties of inscribed quadrilaterals, central angles, and angle bisectors. This summary covers key concepts such as congruent chords, angles subtended by arcs, and the relationship between tangents and radii. Ideal for quick revision and understanding of circle geometry.
MathsExplore the fundamentals of bearings in geometry, including how to measure angles accurately and the importance of using three digits. This summary covers key concepts such as angle relationships and measurement techniques, essential for mastering this topic in your studies.
MathsQuotes from every main character
English LiteratureApp 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
This GCSE Mathematics mark scheme shows you exactly how examiners award marks for Higher Tier Paper 6 questions. Understanding these marking criteria can help you maximise your exam performance and avoid common mistakes.
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
You're looking at the mark scheme for GCSE Mathematics Higher Tier Paper 6 from June 2018. This is the document that shows examiners exactly how to mark your answers and award points.
OCR (Oxford Cambridge and RSA) is one of the main exam boards in the UK that creates your GCSE qualifications. They're a not-for-profit organisation, which means any money they make goes back into improving qualifications and support for students like you.
Remember: Mark schemes help you understand what examiners are looking for, but they don't show you every possible correct answer - examiners are trained to give credit for alternative methods too!
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
Examiners use special symbols and codes to show how they've marked your work. The tick (✓) means you're correct, whilst the cross (×) shows an error.
Method marks (M1, M2) are awarded for using the right approach, even if your final answer is wrong due to a simple calculation error. Accuracy marks (A1) depend on getting the right answer after using a correct method.
Independent marks (B1, B2) are given for correct answers or key steps, regardless of your method. Special abbreviations like 'cao' (correct answer only) and 'nfww' (not from wrong working) tell examiners when to be strict about answers.
Top Tip: Show all your working clearly - you can still earn method marks even if your final answer is incorrect!
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
Follow through marking means you can earn marks for correct working based on a previous wrong answer. If you make an error early on but use the wrong number correctly in later steps, you won't be penalised twice.
When you misread data consistently (like reading 37 instead of 73), examiners will follow your work and only deduct one mark. This is fairer than penalising you for every subsequent error.
If you give two different answers, examiners will mark the weaker one. Always cross out work you don't want marked, and make sure your final answer is clear on the answer line.
Exam Strategy: If you spot an error partway through, don't panic - you can still earn follow-through marks for the rest of your solution!
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
Looking at Question 1, you needed four numbers where at least two are 8, the range is 7, and the total is 44. The answer 8, 8, 13, 15 gets full marks, but partial credit is available for meeting some conditions.
Question 2 involves ratio calculations. You get marks for identifying the correct ratios (like 5:9:36) and then calculating percentages. The key is showing that 9 out of 50 total parts equals 18%.
For algebraic estimation in Question 4, you need to substitute values and show your calculation clearly. Getting 20 and explaining it's close to 19.5 earns full marks.
Working Smart: Even if you can't complete a question fully, you can still earn valuable partial marks by showing relevant working!
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
Coordinate geometry questions test multiple skills. For finding equations of lines, you need the correct gradient (like 0.75) and y-intercept. Show your gradient calculation clearly using the change in y over change in x.
Quadratic substitution problems require careful algebra. When substituting into y = -x² + kx + 8, make sure you handle negative signs correctly. The mark scheme shows common sign errors that lose marks.
Triangle proofs can be solved using different methods - symmetry, Pythagoras, or trigonometry. All approaches can earn full marks if properly executed. The key is showing that two sides are equal (making it isosceles).
Multiple Methods: Don't worry if your method differs from friends - there are often several correct approaches to geometry problems!
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
Inverse proportion and algebraic manipulation appear in the final questions. For inverse proportion, set up the relationship correctly and solve systematically.
Substitution problems with sequences require you to find the correct value first, then substitute into given formulas. Show each step clearly - you can earn marks for finding intermediate values like u = 14.
The mark scheme shows that accuracy matters but isn't everything. Method marks mean you're rewarded for understanding the process, even when small errors creep in.
Confidence Builder: Remember that GCSE marking is designed to reward what you know - focus on showing your mathematical thinking clearly!
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
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.
12
Smart Tools NEW
Transform this note into: ✓ 50+ Practice Questions ✓ Interactive Flashcards ✓ Full Mock Exam ✓ Essay Outlines
Explore the methods for calculating the area of various quadrilaterals, including squares, rectangles, and parallelograms. This summary covers essential formulas, properties, and examples to enhance your understanding of area and perimeter in geometry.
MathsExplore essential trigonometry concepts including formulas for sine, cosine, and tangent. Learn how to find angles and side lengths in right triangles using trigonometric ratios and inverse functions. This summary is perfect for students preparing for exams or needing a quick reference on trigonometric principles.
MathsExplore the fundamentals of bearings in geometry, including angle measurement, relationships, and rules. This summary covers key concepts such as calculating bearings, angle pairs, and the total angles in triangles. Ideal for students preparing for exams or seeking to enhance their understanding of geometry.
MathsPrepare for your GCSE exams with this comprehensive non-calculator practice paper. Covering key concepts such as area of triangles, ratios, statistical averages, and more, this resource includes 22 questions with varying marks to help you master essential mathematical skills. Ideal for students aiming for higher grades, this practice paper is designed to enhance your problem-solving abilities and exam readiness.
MathsExplore essential circle theorems, including properties of inscribed quadrilaterals, central angles, and angle bisectors. This summary covers key concepts such as congruent chords, angles subtended by arcs, and the relationship between tangents and radii. Ideal for quick revision and understanding of circle geometry.
MathsExplore the fundamentals of bearings in geometry, including how to measure angles accurately and the importance of using three digits. This summary covers key concepts such as angle relationships and measurement techniques, essential for mastering this topic in your studies.
MathsQuotes from every main character
English LiteratureApp 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