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23 Nov 2025
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GCSE Maths Higher Tier Paper 3 Calculator Practice
S
Sam Turnbull
@samturnbull
1 / 10
Exam Instructions and Setup
Before you dive into any GCSE maths exam, you'll need to sort out the basics first. This Higher Tier paper is worth 80 marks total and you've got 90 minutes to smash it.
Make sure you've got all your kit ready: calculator, ruler, protractor, compasses, and the formulae sheet that comes with the paper. The examiners want to see all your working - even if you get the wrong answer, you can still pick up method marks.
Top Tip: The marks in brackets tell you how much time to spend on each question - roughly one mark per minute!
Remember that diagrams aren't drawn to scale unless they tell you otherwise, so don't try measuring them with your ruler.
Algebra Basics - Indices and Expanding
Question 1 tests your algebra fundamentals with indices and expanding brackets. These are bread-and-butter skills you'll use throughout the paper.
For part (a), you're simplifying (m²)³ - remember that when you raise a power to another power, you multiply the indices. Part (b) asks you to simplify x⁵ × x⁸, where you add the powers when multiplying terms with the same base.
Remember: When expanding brackets like 4p, multiply everything inside by what's outside!
Part (c) is about expanding brackets - multiply 4p by each term inside the brackets separately. These skills pop up everywhere in GCSE maths, so nail them early.
Real-Life Percentages and Problem Solving
This percentage problem shows how maths applies to real situations - Jonny's planning coffee for 800 people at a meeting. You'll need to work through multiple steps carefully.
First, calculate how many people will drink coffee using 68% of 800. Then work out total cups needed (2 per person) and multiply by 10.6g per cup. Don't forget to round to the nearest gram!
Watch Out: Part (b) asks how the answer changes if 72% drink coffee instead - you might not need to recalculate everything!
This type of multi-step percentage problem is classic GCSE material. Break it down into smaller chunks and you'll find it much more manageable.
Angle Geometry and Proof
This geometry proof combines parallel lines, angles, and triangle properties. You need to prove triangle ACD is isosceles by showing two sides are equal or two angles are equal.
Use the given angles (125° and 110°) along with parallel line rules and angles on a straight line. Look for alternate angles, corresponding angles, and co-interior angles where the parallel lines are cut by the straight lines.
Proof Tip: Write down the reason for each step - "alternate angles are equal" or "angles on a straight line sum to 180°"
An isosceles triangle has two equal angles opposite the equal sides. Once you've found the angles in triangle ACD, you can show which two are equal.
Inverse Proportion - Pump Problem
This is a classic inverse proportion problem about pumps filling tanks. When you have fewer pumps, it takes longer - that's the inverse relationship you need to work with.
Start by finding how much work one pump does. If 5 pumps take 14 hours, that's 5 × 14 = 70 pump-hours of total work needed. Now you can work out how long 4 pumps would take.
Think About It: More workers = less time, fewer workers = more time. That's inverse proportion!
Set up the calculation: if the total work is 70 pump-hours, then 4 pumps will take 70 ÷ 4 hours to complete the same job.
Prime Factorisation - HCF and LCM
Working with prime factors makes finding HCF and LCM much easier than other methods. You've got A = 2² × 3⁴ × 7 and B = 3² × 7² already broken down for you.
For the HCF (Highest Common Factor), take the lowest power of each prime that appears in both numbers. For the LCM (Lowest Common Multiple), take the highest power of each prime that appears in either number.
Quick Check: HCF × LCM should equal A × B when you multiply it out!
Look at each prime factor: 2 only appears in A, 3 appears as 3⁴ and 3², and 7 appears as 7¹ and 7². Pick the right powers for each calculation.
Unit Conversion and Rate Problems
This rate calculation combines unit conversions with time. Lava flows at 11.9 m³/s and you need to find how many days for 67,205,600 m³ to flow.
First, work out how many seconds it takes: total volume ÷ rate per second. Then convert seconds to days by dividing by the number of seconds in a day (60 × 60 × 24 = 86,400).
Unit Reminder: Always check your units match up - seconds to days needs two conversion steps!
Remember to round to the nearest day as requested. These multi-step unit problems are common in GCSE - take them one conversion at a time.
Quadratic Graphs and Roots
Reading information from quadratic graphs is a key GCSE skill. The graph shows y = x² - 2x - 2 and you need to identify key features.
The turning point is the lowest point on this u-shaped curve - read the coordinates directly from the graph. For the roots, you're looking for where the curve crosses the x-axis .
Graph Reading: Always state coordinates as (x, y) and estimate roots to 1 decimal place from the graph.
Roots of the equation x² - 2x - 2 = 0 are the x-values where the graph crosses the x-axis. The graph should cross twice for a quadratic.
Density and Percentage of Percentages
Question 8 uses the density formula: density = mass ÷ volume, so mass = density × volume. With density 9 g/cm³ and volume 72 cm³, this is straightforward multiplication.
Question 9 is trickier - it's a percentage of a percentage problem. 70% said yes to a new TV, and 80% of those wanted a large screen. You need 80% of 70% of the total people.
Double Percentages: Calculate 70% × 80% = 56% want a large screen TV.
Remember that "80% of the people who said yes" means you're taking 80% of the 70%, not 80% of everyone who was asked.
Trigonometry in Triangles
This trigonometry problem needs the sine rule to find length DC. You've got triangle ABD with some angles and one side length (6.8 cm).
First, work out all the angles in triangle ABD using the fact that angles in a triangle sum to 180°. Then apply the sine rule: a/sin A = b/sin B = c/sin C.
Sine Rule Reminder: Make sure you match each side with the angle opposite to it!
You'll need to find angle ADB first , then use the sine rule to find BD, and finally work out what fraction DC is of the whole length BD.
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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
GCSE Maths Higher Tier Paper 3 Calculator Practice
S
Sam Turnbull
@samturnbull
This is a GCSE Mathematics Higher Tier Paper 3 from June 2023, where you'll use a calculator for 1 hour 30 minutes. The paper covers key maths topics including algebra, geometry, percentages, and trigonometry that you need to master for... Show more
Exam Instructions and Setup
Before you dive into any GCSE maths exam, you'll need to sort out the basics first. This Higher Tier paper is worth 80 marks total and you've got 90 minutes to smash it.
Make sure you've got all your kit ready: calculator, ruler, protractor, compasses, and the formulae sheet that comes with the paper. The examiners want to see all your working - even if you get the wrong answer, you can still pick up method marks.
Top Tip: The marks in brackets tell you how much time to spend on each question - roughly one mark per minute!
Remember that diagrams aren't drawn to scale unless they tell you otherwise, so don't try measuring them with your ruler.
Sign up to see the contentIt's free!
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Join milions of students
By signing up you accept Terms of Service and Privacy Policy
Algebra Basics - Indices and Expanding
Question 1 tests your algebra fundamentals with indices and expanding brackets. These are bread-and-butter skills you'll use throughout the paper.
For part (a), you're simplifying (m²)³ - remember that when you raise a power to another power, you multiply the indices. Part (b) asks you to simplify x⁵ × x⁸, where you add the powers when multiplying terms with the same base.
Remember: When expanding brackets like 4p, multiply everything inside by what's outside!
Part (c) is about expanding brackets - multiply 4p by each term inside the brackets separately. These skills pop up everywhere in GCSE maths, so nail them early.
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Real-Life Percentages and Problem Solving
This percentage problem shows how maths applies to real situations - Jonny's planning coffee for 800 people at a meeting. You'll need to work through multiple steps carefully.
First, calculate how many people will drink coffee using 68% of 800. Then work out total cups needed (2 per person) and multiply by 10.6g per cup. Don't forget to round to the nearest gram!
Watch Out: Part (b) asks how the answer changes if 72% drink coffee instead - you might not need to recalculate everything!
This type of multi-step percentage problem is classic GCSE material. Break it down into smaller chunks and you'll find it much more manageable.
Sign up to see the contentIt's free!
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Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
Angle Geometry and Proof
This geometry proof combines parallel lines, angles, and triangle properties. You need to prove triangle ACD is isosceles by showing two sides are equal or two angles are equal.
Use the given angles (125° and 110°) along with parallel line rules and angles on a straight line. Look for alternate angles, corresponding angles, and co-interior angles where the parallel lines are cut by the straight lines.
Proof Tip: Write down the reason for each step - "alternate angles are equal" or "angles on a straight line sum to 180°"
An isosceles triangle has two equal angles opposite the equal sides. Once you've found the angles in triangle ACD, you can show which two are equal.
Sign up to see the contentIt's free!
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Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
Inverse Proportion - Pump Problem
This is a classic inverse proportion problem about pumps filling tanks. When you have fewer pumps, it takes longer - that's the inverse relationship you need to work with.
Start by finding how much work one pump does. If 5 pumps take 14 hours, that's 5 × 14 = 70 pump-hours of total work needed. Now you can work out how long 4 pumps would take.
Think About It: More workers = less time, fewer workers = more time. That's inverse proportion!
Set up the calculation: if the total work is 70 pump-hours, then 4 pumps will take 70 ÷ 4 hours to complete the same job.
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Improve your grades
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By signing up you accept Terms of Service and Privacy Policy
Prime Factorisation - HCF and LCM
Working with prime factors makes finding HCF and LCM much easier than other methods. You've got A = 2² × 3⁴ × 7 and B = 3² × 7² already broken down for you.
For the HCF (Highest Common Factor), take the lowest power of each prime that appears in both numbers. For the LCM (Lowest Common Multiple), take the highest power of each prime that appears in either number.
Quick Check: HCF × LCM should equal A × B when you multiply it out!
Look at each prime factor: 2 only appears in A, 3 appears as 3⁴ and 3², and 7 appears as 7¹ and 7². Pick the right powers for each calculation.
Sign up to see the contentIt's free!
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Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
Unit Conversion and Rate Problems
This rate calculation combines unit conversions with time. Lava flows at 11.9 m³/s and you need to find how many days for 67,205,600 m³ to flow.
First, work out how many seconds it takes: total volume ÷ rate per second. Then convert seconds to days by dividing by the number of seconds in a day (60 × 60 × 24 = 86,400).
Unit Reminder: Always check your units match up - seconds to days needs two conversion steps!
Remember to round to the nearest day as requested. These multi-step unit problems are common in GCSE - take them one conversion at a time.
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Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
Quadratic Graphs and Roots
Reading information from quadratic graphs is a key GCSE skill. The graph shows y = x² - 2x - 2 and you need to identify key features.
The turning point is the lowest point on this u-shaped curve - read the coordinates directly from the graph. For the roots, you're looking for where the curve crosses the x-axis .
Graph Reading: Always state coordinates as (x, y) and estimate roots to 1 decimal place from the graph.
Roots of the equation x² - 2x - 2 = 0 are the x-values where the graph crosses the x-axis. The graph should cross twice for a quadratic.
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Density and Percentage of Percentages
Question 8 uses the density formula: density = mass ÷ volume, so mass = density × volume. With density 9 g/cm³ and volume 72 cm³, this is straightforward multiplication.
Question 9 is trickier - it's a percentage of a percentage problem. 70% said yes to a new TV, and 80% of those wanted a large screen. You need 80% of 70% of the total people.
Double Percentages: Calculate 70% × 80% = 56% want a large screen TV.
Remember that "80% of the people who said yes" means you're taking 80% of the 70%, not 80% of everyone who was asked.
Sign up to see the contentIt's free!
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Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
Trigonometry in Triangles
This trigonometry problem needs the sine rule to find length DC. You've got triangle ABD with some angles and one side length (6.8 cm).
First, work out all the angles in triangle ABD using the fact that angles in a triangle sum to 180°. Then apply the sine rule: a/sin A = b/sin B = c/sin C.
Sine Rule Reminder: Make sure you match each side with the angle opposite to it!
You'll need to find angle ADB first , then use the sine rule to find BD, and finally work out what fraction DC is of the whole length BD.
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?
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Is Knowunity really free of charge?
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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