This is an OCR GCSE Mathematics Higher Tier practice paper... Show more
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
7
0
F
Fie /Fi
28/11/2025
Maths
Higher OCR maths
841
•
28 Nov 2025
•
Higher OCR Maths - Non-Calculator Paper
F
Fie /Fi
@iei_jr9djat5ckxaywaq
1 / 10
Exam Overview
This OCR GCSE Higher Tier maths paper is your chance to show off what you know without a calculator! You've got 90 minutes to tackle 100 marks worth of questions.
The paper tests loads of different topics, so you'll need to switch between different types of maths quickly. From fractions and percentages to coordinate geometry and trigonometry - it's all here.
Top tip: The marks in brackets tell you how much time to spend on each question, so a 4-mark question deserves more attention than a 1-mark quickie!
Remember: You must show all your working - even if you get the wrong answer, you can still pick up method marks!
Basic Number Skills (Questions 1-2)
These opening questions test your fraction arithmetic and estimation skills - the building blocks you absolutely need to nail first.
For fractions, you'll need to find common denominators to subtract properly. With estimation, round everything to 1 significant figure to make the mental maths manageable.
Highest common factors pop up regularly, so practise your factor trees and division methods. These questions are designed to build your confidence before the trickier stuff kicks in.
Quick win: Questions 1 and 2 are only worth 7 marks total, but getting them right sets you up mentally for the rest of the paper!
Data and Geometry (Questions 3-4)
Pie charts aren't just about angles - this question combines them with real-world calculations involving weight. You'll need to work out how many marbles of each size, then multiply by their individual weights.
The coordinate geometry question tests whether you understand parallel lines and rectangle properties. When AD is parallel to the x-axis, that's a massive hint about the coordinates you're looking for.
These questions are worth 7 marks combined, so they're testing your ability to work through multi-step problems methodically.
Pro tip: Draw diagrams clearly and label everything - it prevents silly mistakes when you're working with coordinates!
Percentages and Profit (Questions 5-7)
Real-world percentage problems are exam favourites because they test whether you can actually use maths in everyday situations. The disco question combines offers, profit margins, and reverse percentages.
For the "buy 2, get 1 free" offer, work out how much Rachel actually pays first. Then add 25% for her profit margin. With reverse percentages, remember that £64 represents 80% of the original price.
Standard form questions test your understanding of powers of 10. Make sure you know the difference between ordinary numbers and proper standard form.
Money matters: These percentage questions are worth 9 marks total - they're testing skills you'll actually use in real life!
Algebra and Probability (Questions 6-8)
Linear equations with multiple variables might look scary, but spot the connection: if 2a + 3b = 0.35, then 4a + 6b is just double that value.
The probability game combines theoretical probability with expected outcomes. Prime numbers from 1 to 10 are: 2, 3, 5, 7 - that's your probability sorted.
For the money calculation, work out how many people you expect to win, then subtract prize money from total income. Expected value calculations like this appear regularly in GCSE papers.
Think smart: Look for patterns and connections between different parts of questions - they're often related!
Trigonometry and Powers (Questions 9-11)
Exact trigonometric values are crucial knowledge - sin 30° = 1/2, and you need to memorise this alongside cos 60° and others.
The kite area calculation combines trigonometry with shape properties. Split the kite into triangles and use the sine rule for area: ½ab sin C.
Index laws are tested through various power calculations. Remember: anything to the power 0 equals 1, fractional powers mean roots, and negative powers mean "one over".
Recurring decimals test your understanding of fraction-decimal conversions. Look for patterns when you do the long division.
Memory bank: Learn your exact trig values and index laws by heart - they're worth easy marks if you know them!
We thought you’d never ask...
What is the Knowunity AI companion?
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.
Where can I download the Knowunity app?
You can download the app from Google Play Store and Apple App Store.
Is Knowunity really free of charge?
That's right! Enjoy free access to study content, connect with fellow students, and get instant help – all at your fingertips.
Can't find what you're looking for? Explore other subjects.
Students love us — and so will you.
4.9/5
App Store
4.8/5
Google Play
The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
Stefan S
iOS user
This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha Klich
Android user
Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
Anna
iOS user
Best app on earth! no words because it’s too good
Thomas R
iOS user
Just amazing. Let's me revise 10x better, this app is a quick 10/10. I highly recommend it to anyone. I can watch and search for notes. I can save them in the subject folder. I can revise it any time when I come back. If you haven't tried this app, you're really missing out.
Basil
Android user
This app has made me feel so much more confident in my exam prep, not only through boosting my own self confidence through the features that allow you to connect with others and feel less alone, but also through the way the app itself is centred around making you feel better. It is easy to navigate, fun to use, and helpful to anyone struggling in absolutely any way.
David K
iOS user
The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!
Sudenaz Ocak
Android user
In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.
Greenlight Bonnie
Android user
very reliable app to help and grow your ideas of Maths, English and other related topics in your works. please use this app if your struggling in areas, this app is key for that. wish I'd of done a review before. and it's also free so don't worry about that.
Rohan U
Android user
I know a lot of apps use fake accounts to boost their reviews but this app deserves it all. Originally I was getting 4 in my English exams and this time I got a grade 7. I didn’t even know about this app three days until the exam and it has helped A LOT. Please actually trust me and use it as I’m sure you too will see developments.
Xander S
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE THE SCHOOLGPT. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮
Elisha
iOS user
This apps acc the goat. I find revision so boring but this app makes it so easy to organize it all and then you can ask the freeeee ai to test yourself so good and you can easily upload your own stuff. highly recommend as someone taking mocks now
Paul T
iOS user
The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
Stefan S
iOS user
This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha Klich
Android user
Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
Anna
iOS user
Best app on earth! no words because it’s too good
Thomas R
iOS user
Just amazing. Let's me revise 10x better, this app is a quick 10/10. I highly recommend it to anyone. I can watch and search for notes. I can save them in the subject folder. I can revise it any time when I come back. If you haven't tried this app, you're really missing out.
Basil
Android user
This app has made me feel so much more confident in my exam prep, not only through boosting my own self confidence through the features that allow you to connect with others and feel less alone, but also through the way the app itself is centred around making you feel better. It is easy to navigate, fun to use, and helpful to anyone struggling in absolutely any way.
David K
iOS user
The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!
Sudenaz Ocak
Android user
In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.
Greenlight Bonnie
Android user
very reliable app to help and grow your ideas of Maths, English and other related topics in your works. please use this app if your struggling in areas, this app is key for that. wish I'd of done a review before. and it's also free so don't worry about that.
Rohan U
Android user
I know a lot of apps use fake accounts to boost their reviews but this app deserves it all. Originally I was getting 4 in my English exams and this time I got a grade 7. I didn’t even know about this app three days until the exam and it has helped A LOT. Please actually trust me and use it as I’m sure you too will see developments.
Xander S
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE THE SCHOOLGPT. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮
Elisha
iOS user
This apps acc the goat. I find revision so boring but this app makes it so easy to organize it all and then you can ask the freeeee ai to test yourself so good and you can easily upload your own stuff. highly recommend as someone taking mocks now
Paul T
iOS user
Higher OCR Maths - Non-Calculator Paper
F
Fie /Fi
@iei_jr9djat5ckxaywaq
This is an OCR GCSE Mathematics Higher Tier practice paper designed to test your non-calculator skills across key maths topics. It's worth 100 marks and covers everything from basic fractions to trigonometry and probability.
Exam Overview
This OCR GCSE Higher Tier maths paper is your chance to show off what you know without a calculator! You've got 90 minutes to tackle 100 marks worth of questions.
The paper tests loads of different topics, so you'll need to switch between different types of maths quickly. From fractions and percentages to coordinate geometry and trigonometry - it's all here.
Top tip: The marks in brackets tell you how much time to spend on each question, so a 4-mark question deserves more attention than a 1-mark quickie!
Remember: You must show all your working - even if you get the wrong answer, you can still pick up method marks!
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
Basic Number Skills (Questions 1-2)
These opening questions test your fraction arithmetic and estimation skills - the building blocks you absolutely need to nail first.
For fractions, you'll need to find common denominators to subtract properly. With estimation, round everything to 1 significant figure to make the mental maths manageable.
Highest common factors pop up regularly, so practise your factor trees and division methods. These questions are designed to build your confidence before the trickier stuff kicks in.
Quick win: Questions 1 and 2 are only worth 7 marks total, but getting them right sets you up mentally for the rest of the paper!
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
Data and Geometry (Questions 3-4)
Pie charts aren't just about angles - this question combines them with real-world calculations involving weight. You'll need to work out how many marbles of each size, then multiply by their individual weights.
The coordinate geometry question tests whether you understand parallel lines and rectangle properties. When AD is parallel to the x-axis, that's a massive hint about the coordinates you're looking for.
These questions are worth 7 marks combined, so they're testing your ability to work through multi-step problems methodically.
Pro tip: Draw diagrams clearly and label everything - it prevents silly mistakes when you're working with coordinates!
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
Percentages and Profit (Questions 5-7)
Real-world percentage problems are exam favourites because they test whether you can actually use maths in everyday situations. The disco question combines offers, profit margins, and reverse percentages.
For the "buy 2, get 1 free" offer, work out how much Rachel actually pays first. Then add 25% for her profit margin. With reverse percentages, remember that £64 represents 80% of the original price.
Standard form questions test your understanding of powers of 10. Make sure you know the difference between ordinary numbers and proper standard form.
Money matters: These percentage questions are worth 9 marks total - they're testing skills you'll actually use in real life!
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
Algebra and Probability (Questions 6-8)
Linear equations with multiple variables might look scary, but spot the connection: if 2a + 3b = 0.35, then 4a + 6b is just double that value.
The probability game combines theoretical probability with expected outcomes. Prime numbers from 1 to 10 are: 2, 3, 5, 7 - that's your probability sorted.
For the money calculation, work out how many people you expect to win, then subtract prize money from total income. Expected value calculations like this appear regularly in GCSE papers.
Think smart: Look for patterns and connections between different parts of questions - they're often related!
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
Trigonometry and Powers (Questions 9-11)
Exact trigonometric values are crucial knowledge - sin 30° = 1/2, and you need to memorise this alongside cos 60° and others.
The kite area calculation combines trigonometry with shape properties. Split the kite into triangles and use the sine rule for area: ½ab sin C.
Index laws are tested through various power calculations. Remember: anything to the power 0 equals 1, fractional powers mean roots, and negative powers mean "one over".
Recurring decimals test your understanding of fraction-decimal conversions. Look for patterns when you do the long division.
Memory bank: Learn your exact trig values and index laws by heart - they're worth easy marks if you know them!
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
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
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
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
We thought you’d never ask...
What is the Knowunity AI companion?
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.
Where can I download the Knowunity app?
You can download the app from Google Play Store and Apple App Store.
Is Knowunity really free of charge?
That's right! Enjoy free access to study content, connect with fellow students, and get instant help – all at your fingertips.
7
Smart Tools NEW
Transform this note into: ✓ 50+ Practice Questions ✓ Interactive Flashcards ✓ Full Mock Exam ✓ Essay Outlines
Mock Exam
Quiz
Flashcards
Essay
Similar content
Understanding Histograms & Frequency
Explore the fundamentals of histograms and frequency tables, essential for iGCSE Maths. This resource covers key concepts such as cumulative frequency, frequency density, and step-by-step instructions for drawing histograms and cumulative frequency graphs. Ideal for students preparing for exams.
Maths10
Key Statistics Concepts
Comprehensive study material covering essential GCSE statistics topics including normal distribution, measures of central tendency, probability models, and data visualization techniques. Ideal for Edexcel Paper 2 revision, this resource includes detailed explanations of box plots, histograms, and the 68-95-99.7 rule, ensuring a solid understanding for achieving top grades.
Maths10
Cumulative Frequency Analysis
Explore key concepts of cumulative frequency, including how to construct cumulative frequency tables and graphs. This resource provides worked examples, including finding medians and estimating interquartile ranges, essential for mastering GCSE Maths. Ideal for students preparing for exams.
Maths10
Understanding Histograms
Explore the fundamentals of histograms, including their structure, frequency density calculations, and practical examples. This summary covers key concepts such as continuous data representation, bar spacing, and how to interpret histograms through provided tables and graphs. Ideal for exam preparation and enhancing your understanding of data visualization.
Maths10
Geometric Transformations Explained
Explore the fundamentals of geometric transformations including translations, reflections, rotations, and enlargements. This summary covers key concepts such as translation vectors, reflection lines, rotation directions, and scale factors, providing clear examples and explanations for each transformation type.
Maths9
Data Analysis Techniques
Explore essential data analysis techniques including two-way tables, box plots, correlation, and various data representations. This summary covers key concepts such as measures of location, statistical averages, and graphical representations like bar charts and pie charts. Ideal for Year 7 students looking to enhance their understanding of data in mathematics.
Maths11
Can't find what you're looking for? Explore other subjects.
Students love us — and so will you.
4.9/5
App Store
4.8/5
Google Play
The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
Stefan S
iOS user
This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha Klich
Android user
Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
Anna
iOS user
Best app on earth! no words because it’s too good
Thomas R
iOS user
Just amazing. Let's me revise 10x better, this app is a quick 10/10. I highly recommend it to anyone. I can watch and search for notes. I can save them in the subject folder. I can revise it any time when I come back. If you haven't tried this app, you're really missing out.
Basil
Android user
This app has made me feel so much more confident in my exam prep, not only through boosting my own self confidence through the features that allow you to connect with others and feel less alone, but also through the way the app itself is centred around making you feel better. It is easy to navigate, fun to use, and helpful to anyone struggling in absolutely any way.
David K
iOS user
The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!
Sudenaz Ocak
Android user
In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.
Greenlight Bonnie
Android user
very reliable app to help and grow your ideas of Maths, English and other related topics in your works. please use this app if your struggling in areas, this app is key for that. wish I'd of done a review before. and it's also free so don't worry about that.
Rohan U
Android user
I know a lot of apps use fake accounts to boost their reviews but this app deserves it all. Originally I was getting 4 in my English exams and this time I got a grade 7. I didn’t even know about this app three days until the exam and it has helped A LOT. Please actually trust me and use it as I’m sure you too will see developments.
Xander S
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE THE SCHOOLGPT. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮
Elisha
iOS user
This apps acc the goat. I find revision so boring but this app makes it so easy to organize it all and then you can ask the freeeee ai to test yourself so good and you can easily upload your own stuff. highly recommend as someone taking mocks now
Paul T
iOS user
The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
Stefan S
iOS user
This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha Klich
Android user
Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
Anna
iOS user
Best app on earth! no words because it’s too good
Thomas R
iOS user
Just amazing. Let's me revise 10x better, this app is a quick 10/10. I highly recommend it to anyone. I can watch and search for notes. I can save them in the subject folder. I can revise it any time when I come back. If you haven't tried this app, you're really missing out.
Basil
Android user
This app has made me feel so much more confident in my exam prep, not only through boosting my own self confidence through the features that allow you to connect with others and feel less alone, but also through the way the app itself is centred around making you feel better. It is easy to navigate, fun to use, and helpful to anyone struggling in absolutely any way.
David K
iOS user
The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!
Sudenaz Ocak
Android user
In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.
Greenlight Bonnie
Android user
very reliable app to help and grow your ideas of Maths, English and other related topics in your works. please use this app if your struggling in areas, this app is key for that. wish I'd of done a review before. and it's also free so don't worry about that.
Rohan U
Android user
I know a lot of apps use fake accounts to boost their reviews but this app deserves it all. Originally I was getting 4 in my English exams and this time I got a grade 7. I didn’t even know about this app three days until the exam and it has helped A LOT. Please actually trust me and use it as I’m sure you too will see developments.
Xander S
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE THE SCHOOLGPT. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮
Elisha
iOS user
This apps acc the goat. I find revision so boring but this app makes it so easy to organize it all and then you can ask the freeeee ai to test yourself so good and you can easily upload your own stuff. highly recommend as someone taking mocks now
Paul T
iOS user