This is a GCSE Mathematics Higher Tier non-calculator paper from... Show more
SociologySign 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
0
0
S
S Anjum
03/12/2025
Maths
AQA higher maths past paper 2022
73
•
3 Dec 2025
•
AQA Higher Maths Past Paper November 2022 - Paper 1 Non-Calculator
S
S Anjum
@sanjum_trxlm
1 / 10
Exam Information and Instructions
You've got 90 minutes to tackle 80 marks worth of questions without a calculator - so mental maths and written methods are your best friends here! The paper tests your ability to work systematically through problems whilst showing clear working.
Key requirements include using black ink, answering all questions in the spaces provided, and most importantly, showing your working clearly. Remember, even if your final answer is wrong, you can still pick up marks for correct method.
Top tip: Always show your working step by step - it's often worth more marks than just the final answer!
Basic Operations and Powers
The opening questions test your fundamental skills with negative numbers, fractions, and indices. For multiplying negative numbers, remember that negative × negative = positive, so -4 × -7/9 gives you a positive result.
When dealing with powers of surds, like (√6)⁴, think of it as (√6)² × (√6)² = 6 × 6 = 36. These questions are designed to build your confidence before tackling harder problems.
Decimal conversions require careful fraction work. To find x when 0.203 = 1/5 + x, convert 1/5 to 0.2 first, then subtract to find x = 0.003 = 3/1000.
Remember: These early questions are worth easy marks - don't rush and make silly mistakes!
Algebra and Ratio Problems
Algebraic equivalence tests whether you understand that expressions like 3x and x + 2x represent the same value. The symbol ≡ means "is equivalent to" - much stronger than just equals.
Ratio division is a crucial skill you'll use constantly. To divide 62 in the ratio 3:7, find the total parts (3 + 7 = 10), then work out what each part is worth (62 ÷ 10 = 6.2). Finally, multiply: 3 × 6.2 = 18.6 and 7 × 6.2 = 43.4.
Check your ratio answers always add up to the original number - it's a foolproof way to spot mistakes.
Quick check: Your ratio parts should always add back to the original total!
Data Analysis and Statistics
Interpreting grouped data requires careful reading of frequency tables. When data is grouped (like 2 < t ≤ 5), you can't know exact values, only which interval they fall into.
For median calculations with grouped data, you need to find which group contains the middle value. With 40 men, the median lies between the 20th and 21st values when arranged in order.
Range statements can be tricky - grouped data only shows you the spread between group boundaries, not actual minimum and maximum values. This is why some statements might be true, definitely true, or cannot be determined.
Key insight: Grouped data limits what you can say definitively about the dataset!
Vector Mathematics
Vectors represent both direction and magnitude, written as column vectors showing horizontal and vertical components. Reading from a diagram, count squares carefully to determine each component.
Scalar multiplication of vectors means multiplying each component by the same number. So 4a = 4 × (3,2) = (12,8). This changes the magnitude but keeps the same direction.
Vector addition and subtraction work component-wise. If a + c = (3,0) and a = (3,2), then c must be (0,-2) to make the vertical component zero.
Visual tip: Draw vectors on graph paper to check your answers make sense geometrically!
Complex Calculations
Mixed operations with fractions require careful order of operations. Start with brackets, convert to common denominators, then divide by multiplying by the reciprocal. Always simplify your final answer.
Solving inequalities like 12 < 4x < 25 means dividing everything by 4 to get 3 < x < 6.25. The integer values are simply 4, 5, and 6 - don't include the boundaries unless the inequality signs include equals.
Pro tip: List out integer solutions systematically to avoid missing any values!
Venn Diagrams and Set Theory
Venn diagrams organize information about overlapping sets visually. Start with the intersection (people buying both items), then work outwards to find those buying only one item.
With 120 people total and 3/4 buying neither item, that means 30 people buy at least one item. Use this constraint along with the individual totals to fill in each region systematically.
Check your work by ensuring all regions add up correctly - both the individual sets and the universal set total should match the given information.
Strategy: Always start filling Venn diagrams from the centre intersection and work outwards!
Indices, Ratios and Decimals
Index laws help simplify expressions like (3⁶ × 3⁵) ÷ 3⁷. Add indices when multiplying (6 + 5 = 11), subtract when dividing (11 - 7 = 4), giving you 3⁴ = 81.
Percentage increases create specific ratios. If a is 10% more than b, then a = 1.1b, making the ratio a:b = 11:10. Convert percentages to decimals to see the relationship clearly.
Decimal addition requires careful alignment of decimal places. Line up the decimal points and add column by column, just like with whole numbers.
Index reminder: When in doubt, write out the full multiplication to check your index law application!
Graph Analysis and Criticism
Coordinate relationships like x:y = 2:1 mean y should always be half of x. Check each plotted point against this rule to spot errors.
Graph criticism involves checking both mathematical accuracy and completeness. Look for incorrect points, missing negative values, and whether the domain is fully represented.
Common graph errors include plotting wrong coordinates, missing sections of the domain, or not maintaining the specified relationship between variables throughout.
Graph check: Always verify a few key points match the given relationship before drawing conclusions!
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.
Most popular content in Maths
Most popular content
English - inspector calls quotes and analysis
Quotes from every main character
English Literature10
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
AQA Higher Maths Past Paper November 2022 - Paper 1 Non-Calculator
S
S Anjum
@sanjum_trxlm
This is a GCSE Mathematics Higher Tier non-calculator paper from November 2022. It covers fundamental mathematical skills including fractions, algebra, vectors, ratios, and data interpretation that you'll need to master for your exams.
Exam Information and Instructions
You've got 90 minutes to tackle 80 marks worth of questions without a calculator - so mental maths and written methods are your best friends here! The paper tests your ability to work systematically through problems whilst showing clear working.
Key requirements include using black ink, answering all questions in the spaces provided, and most importantly, showing your working clearly. Remember, even if your final answer is wrong, you can still pick up marks for correct method.
Top tip: Always show your working step by step - it's often worth more marks than just the final answer!
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 Operations and Powers
The opening questions test your fundamental skills with negative numbers, fractions, and indices. For multiplying negative numbers, remember that negative × negative = positive, so -4 × -7/9 gives you a positive result.
When dealing with powers of surds, like (√6)⁴, think of it as (√6)² × (√6)² = 6 × 6 = 36. These questions are designed to build your confidence before tackling harder problems.
Decimal conversions require careful fraction work. To find x when 0.203 = 1/5 + x, convert 1/5 to 0.2 first, then subtract to find x = 0.003 = 3/1000.
Remember: These early questions are worth easy marks - don't rush and make silly mistakes!
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 Ratio Problems
Algebraic equivalence tests whether you understand that expressions like 3x and x + 2x represent the same value. The symbol ≡ means "is equivalent to" - much stronger than just equals.
Ratio division is a crucial skill you'll use constantly. To divide 62 in the ratio 3:7, find the total parts (3 + 7 = 10), then work out what each part is worth (62 ÷ 10 = 6.2). Finally, multiply: 3 × 6.2 = 18.6 and 7 × 6.2 = 43.4.
Check your ratio answers always add up to the original number - it's a foolproof way to spot mistakes.
Quick check: Your ratio parts should always add back to the original total!
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 Analysis and Statistics
Interpreting grouped data requires careful reading of frequency tables. When data is grouped (like 2 < t ≤ 5), you can't know exact values, only which interval they fall into.
For median calculations with grouped data, you need to find which group contains the middle value. With 40 men, the median lies between the 20th and 21st values when arranged in order.
Range statements can be tricky - grouped data only shows you the spread between group boundaries, not actual minimum and maximum values. This is why some statements might be true, definitely true, or cannot be determined.
Key insight: Grouped data limits what you can say definitively about the dataset!
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
Vector Mathematics
Vectors represent both direction and magnitude, written as column vectors showing horizontal and vertical components. Reading from a diagram, count squares carefully to determine each component.
Scalar multiplication of vectors means multiplying each component by the same number. So 4a = 4 × (3,2) = (12,8). This changes the magnitude but keeps the same direction.
Vector addition and subtraction work component-wise. If a + c = (3,0) and a = (3,2), then c must be (0,-2) to make the vertical component zero.
Visual tip: Draw vectors on graph paper to check your answers make sense geometrically!
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
Complex Calculations
Mixed operations with fractions require careful order of operations. Start with brackets, convert to common denominators, then divide by multiplying by the reciprocal. Always simplify your final answer.
Solving inequalities like 12 < 4x < 25 means dividing everything by 4 to get 3 < x < 6.25. The integer values are simply 4, 5, and 6 - don't include the boundaries unless the inequality signs include equals.
Pro tip: List out integer solutions systematically to avoid missing any values!
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
Venn Diagrams and Set Theory
Venn diagrams organize information about overlapping sets visually. Start with the intersection (people buying both items), then work outwards to find those buying only one item.
With 120 people total and 3/4 buying neither item, that means 30 people buy at least one item. Use this constraint along with the individual totals to fill in each region systematically.
Check your work by ensuring all regions add up correctly - both the individual sets and the universal set total should match the given information.
Strategy: Always start filling Venn diagrams from the centre intersection and work outwards!
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
Indices, Ratios and Decimals
Index laws help simplify expressions like (3⁶ × 3⁵) ÷ 3⁷. Add indices when multiplying (6 + 5 = 11), subtract when dividing (11 - 7 = 4), giving you 3⁴ = 81.
Percentage increases create specific ratios. If a is 10% more than b, then a = 1.1b, making the ratio a:b = 11:10. Convert percentages to decimals to see the relationship clearly.
Decimal addition requires careful alignment of decimal places. Line up the decimal points and add column by column, just like with whole numbers.
Index reminder: When in doubt, write out the full multiplication to check your index law application!
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
Graph Analysis and Criticism
Coordinate relationships like x:y = 2:1 mean y should always be half of x. Check each plotted point against this rule to spot errors.
Graph criticism involves checking both mathematical accuracy and completeness. Look for incorrect points, missing negative values, and whether the domain is fully represented.
Common graph errors include plotting wrong coordinates, missing sections of the domain, or not maintaining the specified relationship between variables throughout.
Graph check: Always verify a few key points match the given relationship before drawing conclusions!
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.
0
Smart Tools NEW
Transform this note into: ✓ 50+ Practice Questions ✓ Interactive Flashcards ✓ Full Mock Exam ✓ Essay Outlines
Mock Exam
Quiz
Flashcards
Essay
Most popular content in Maths
Most popular content
English - inspector calls quotes and analysis
Quotes from every main character
English Literature10
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