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4 Dec 2025

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WJEC Maths Unit 1 Practice Paper 2022

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Alfie @alfie_revisionguides

This is a comprehensive GCSE Mathematics Higher Tier exam paper from WJEC, covering essential non-calculator maths skills. You'll... Show more

Surname

First name(s)

GCSE
wjec
свас
3300U50-1

Centre
Number

A22-3300U50-1

MONDAY, 14 NOVEMBER 2022 - MORNING

MATHEMATICS
UNIT 1: NON-

Exam Overview

This GCSE Higher Tier mathematics exam lasts 1 hour 45 minutes and is worth 80 marks total. You'll tackle 21 questions without a calculator, so mental maths and written methods are crucial.

The paper covers a brilliant mix of topics that regularly appear in GCSE exams. You'll need basic equipment like a ruler, protractor, and compass for construction work. Remember to use black ink and show all your working clearly.

Top Tip Each question shows its mark value in brackets – use this to gauge how much detail and time to spend on each part!

The marking scheme ranges from quick 2-mark questions to more complex 6-mark problems. Question 10 specifically assesses your mathematical communication skills, so clear explanations matter.

Surname

First name(s)

GCSE
wjec
свас
3300U50-1

Centre
Number

A22-3300U50-1

MONDAY, 14 NOVEMBER 2022 - MORNING

MATHEMATICS
UNIT 1: NON-

Essential Formulae

You're given a formula sheet with all the key equations you'll need. The area of a trapezium uses ½a+ba + bh, whilst volume calculations include spheres (⁴⁄₃πr³) and cones (¹⁄₃πr²h).

Trigonometry features heavily with the sine rule, cosine rule, and triangle area formula (½ab sin C). These are absolute lifesavers for triangle problems! The quadratic formula is also provided – memorising the layout helps you substitute values quickly.

Remember You'll use π = 3.14 throughout this paper, not the calculator value!

The Annual Equivalent Rate formula might seem scary, but it's just compound interest in disguise. Focus on substituting values correctly rather than understanding the complex financial theory.

Surname

First name(s)

GCSE
wjec
свас
3300U50-1

Centre
Number

A22-3300U50-1

MONDAY, 14 NOVEMBER 2022 - MORNING

MATHEMATICS
UNIT 1: NON-

Probability and Venn Diagrams

Question 1 tests your Venn diagram skills with a real-world scenario about hair colour and glasses. With 200 people total, you need to work systematically through the given information to fill each section correctly.

Start with the intersection peoplewithblackhairANDglasses=20people with black hair AND glasses = 20. Then use the fact that 70 people have black hair total to find those with black hair but no glasses. The key is working step-by-step rather than guessing.

Smart Strategy Always check your Venn diagram adds up to the total number given!

Part (b) asks for a probability calculation. Once your Venn diagram is complete, simply count everyone wearing glasses and divide by 200. Converting to a fraction in its simplest form usually scores full marks.

Surname

First name(s)

GCSE
wjec
свас
3300U50-1

Centre
Number

A22-3300U50-1

MONDAY, 14 NOVEMBER 2022 - MORNING

MATHEMATICS
UNIT 1: NON-

Geometric Construction

Question 2 requires accurate geometric construction using only ruler and compass – no protractor allowed! You're constructing triangle ABC where side AC is already drawn, with angles of 60° and 45°.

For the 60° angle, you'll need to construct an equilateral triangle using compass arcs. The 45° angle is trickier – you'll likely need to bisect a 90° angle that you've constructed using perpendicular lines.

Essential Rule Keep all construction arcs and lines visible – examiners need to see your method!

Remember that construction questions test your geometric skills, not your measuring ability. Accuracy comes from proper compass technique, not trying to estimate angles by eye.

Surname

First name(s)

GCSE
wjec
свас
3300U50-1

Centre
Number

A22-3300U50-1

MONDAY, 14 NOVEMBER 2022 - MORNING

MATHEMATICS
UNIT 1: NON-

Prime Factorisation and Algebra

Question 3 asks you to express 1575 as a product of prime factors in index form. Start by dividing by small primes (2, 3, 5, 7...) until you're left with 1. Write your answer using powers like 3² × 5³.

The algebra questions test your manipulation skills. For 2p³q × 3p⁴q⁷, multiply the numbers (2 × 3 = 6) then add the indices for like terms p3+4=p7p³⁺⁴ = p⁷.

Index Law Reminder When multiplying powers of the same base, add the indices!

The expansion 7aa+5a+5 - 23a2+6a73a²+6a-7 requires careful bracket expansion followed by collecting like terms. Watch your signs – the minus before the second bracket affects every term inside.

Surname

First name(s)

GCSE
wjec
свас
3300U50-1

Centre
Number

A22-3300U50-1

MONDAY, 14 NOVEMBER 2022 - MORNING

MATHEMATICS
UNIT 1: NON-

Linear Graphs and Gradients

Question 5 focuses on straight line graphs and their equations. Reading the gradient from a graph means finding how much y increases for every 1 unit increase in x. Count squares carefully or use two clear points.

The y-intercept is where your line crosses the y-axis whenx=0when x = 0. Once you have the gradient (m) and y-intercept (c), you can write the equation as y = mx + c.

Graph Reading Tip Choose points on grid intersections to avoid reading errors!

This question type appears frequently in GCSE mathematics, so practising graph interpretation is time well spent. Always double-check your equation by substituting a point from the line.

Surname

First name(s)

GCSE
wjec
свас
3300U50-1

Centre
Number

A22-3300U50-1

MONDAY, 14 NOVEMBER 2022 - MORNING

MATHEMATICS
UNIT 1: NON-

Parallel Lines

Part (b) asks you to prove that y = 3x - 8 and 2y - 6x = 23 are parallel lines. Parallel lines have identical gradients, so rearrange both equations into y = mx + c form.

The first equation already shows gradient = 3. For the second equation, rearrange 2y = 6x + 23, so y = 3x + 11.5. Both have gradient 3, proving they're parallel.

Parallel Line Rule Same gradient = parallel lines, regardless of the y-intercept!

This algebraic proof technique is essential for higher-tier questions. Show each step clearly to demonstrate your understanding of linear equations.

Surname

First name(s)

GCSE
wjec
свас
3300U50-1

Centre
Number

A22-3300U50-1

MONDAY, 14 NOVEMBER 2022 - MORNING

MATHEMATICS
UNIT 1: NON-

Dimensional Analysis

Question 6 tests your understanding of dimensional analysis – working out whether formulae represent length, area, volume, or none. Each letter represents a length measurement.

For area, you need dimensions that multiply to give length² (like ab or a²). For volume, you need length³ (like abc or a³). When terms are added or subtracted, they must have the same dimensions.

Key Rule You can only add or subtract quantities with the same dimensions!

Look at each term separately, then check if they're compatible. For example, 5abc - 6bc + b² mixes volume and area terms, so it represents "none of these". This mathematical reasoning skill becomes crucial in advanced mathematics.

Surname

First name(s)

GCSE
wjec
свас
3300U50-1

Centre
Number

A22-3300U50-1

MONDAY, 14 NOVEMBER 2022 - MORNING

MATHEMATICS
UNIT 1: NON-

Standard Form Calculations

Question 7 tests standard form arithmetic without a calculator. For (3×10⁴) ÷ (6×10⁻³), divide the numbers (3÷6 = 0.5) and subtract the powers (4-(-3) = 7).

Your answer becomes 0.5×10⁷, which converts to 5×10⁶ in proper standard form. Remember that the first number must be between 1 and 10.

Standard Form Rule When dividing powers of 10, subtract the indices!

For addition like (4.78×10⁴) + (1.5×10²), convert to the same power of 10 first. This gives (4.78×10⁴) + (0.015×10⁴) = 4.795×10⁴. Standard form questions are common in GCSE papers, so master these techniques.

Surname

First name(s)

GCSE
wjec
свас
3300U50-1

Centre
Number

A22-3300U50-1

MONDAY, 14 NOVEMBER 2022 - MORNING

MATHEMATICS
UNIT 1: NON-

Pythagoras and Trigonometry

Question 8 tests your understanding of when to use Pythagoras's theorem versus trigonometry. For finding the hypotenuse x, you need x = √(25² + 10²) since you're adding the squares of the two shorter sides.

For the trigonometry part, you have the hypotenuse (25 cm) and need the opposite side y to a 40° angle. Use sin 40° = y/25 because sine relates opposite to hypotenuse.

SOHCAHTOA Reminder Sin = Opposite/Hypotenuse, Cos = Adjacent/Hypotenuse, Tan = Opposite/Adjacent

Recognising which method to use is crucial for GCSE success. Pythagoras works with right-angled triangles when you know two sides, whilst trigonometry needs an angle and one side.

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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.

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Maths

250

4 Dec 2025

24 pages

WJEC Maths Unit 1 Practice Paper 2022

user profile picture

Alfie

@alfie_revisionguides

This is a comprehensive GCSE Mathematics Higher Tier exam paper from WJEC, covering essential non-calculator maths skills. You'll find everything from Venn diagrams and prime factorisation to trigonometry and standard form – all the core topics you need to master... Show more

Surname

First name(s)

GCSE
wjec
свас
3300U50-1

Centre
Number

A22-3300U50-1

MONDAY, 14 NOVEMBER 2022 - MORNING

MATHEMATICS
UNIT 1: NON-

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Exam Overview

This GCSE Higher Tier mathematics exam lasts 1 hour 45 minutes and is worth 80 marks total. You'll tackle 21 questions without a calculator, so mental maths and written methods are crucial.

The paper covers a brilliant mix of topics that regularly appear in GCSE exams. You'll need basic equipment like a ruler, protractor, and compass for construction work. Remember to use black ink and show all your working clearly.

Top Tip: Each question shows its mark value in brackets – use this to gauge how much detail and time to spend on each part!

The marking scheme ranges from quick 2-mark questions to more complex 6-mark problems. Question 10 specifically assesses your mathematical communication skills, so clear explanations matter.

Surname

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GCSE
wjec
свас
3300U50-1

Centre
Number

A22-3300U50-1

MONDAY, 14 NOVEMBER 2022 - MORNING

MATHEMATICS
UNIT 1: NON-

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Essential Formulae

You're given a formula sheet with all the key equations you'll need. The area of a trapezium uses ½a+ba + bh, whilst volume calculations include spheres (⁴⁄₃πr³) and cones (¹⁄₃πr²h).

Trigonometry features heavily with the sine rule, cosine rule, and triangle area formula (½ab sin C). These are absolute lifesavers for triangle problems! The quadratic formula is also provided – memorising the layout helps you substitute values quickly.

Remember: You'll use π = 3.14 throughout this paper, not the calculator value!

The Annual Equivalent Rate formula might seem scary, but it's just compound interest in disguise. Focus on substituting values correctly rather than understanding the complex financial theory.

Surname

First name(s)

GCSE
wjec
свас
3300U50-1

Centre
Number

A22-3300U50-1

MONDAY, 14 NOVEMBER 2022 - MORNING

MATHEMATICS
UNIT 1: NON-

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Probability and Venn Diagrams

Question 1 tests your Venn diagram skills with a real-world scenario about hair colour and glasses. With 200 people total, you need to work systematically through the given information to fill each section correctly.

Start with the intersection peoplewithblackhairANDglasses=20people with black hair AND glasses = 20. Then use the fact that 70 people have black hair total to find those with black hair but no glasses. The key is working step-by-step rather than guessing.

Smart Strategy: Always check your Venn diagram adds up to the total number given!

Part (b) asks for a probability calculation. Once your Venn diagram is complete, simply count everyone wearing glasses and divide by 200. Converting to a fraction in its simplest form usually scores full marks.

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GCSE
wjec
свас
3300U50-1

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Number

A22-3300U50-1

MONDAY, 14 NOVEMBER 2022 - MORNING

MATHEMATICS
UNIT 1: NON-

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Geometric Construction

Question 2 requires accurate geometric construction using only ruler and compass – no protractor allowed! You're constructing triangle ABC where side AC is already drawn, with angles of 60° and 45°.

For the 60° angle, you'll need to construct an equilateral triangle using compass arcs. The 45° angle is trickier – you'll likely need to bisect a 90° angle that you've constructed using perpendicular lines.

Essential Rule: Keep all construction arcs and lines visible – examiners need to see your method!

Remember that construction questions test your geometric skills, not your measuring ability. Accuracy comes from proper compass technique, not trying to estimate angles by eye.

Surname

First name(s)

GCSE
wjec
свас
3300U50-1

Centre
Number

A22-3300U50-1

MONDAY, 14 NOVEMBER 2022 - MORNING

MATHEMATICS
UNIT 1: NON-

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Prime Factorisation and Algebra

Question 3 asks you to express 1575 as a product of prime factors in index form. Start by dividing by small primes (2, 3, 5, 7...) until you're left with 1. Write your answer using powers like 3² × 5³.

The algebra questions test your manipulation skills. For 2p³q × 3p⁴q⁷, multiply the numbers (2 × 3 = 6) then add the indices for like terms p3+4=p7p³⁺⁴ = p⁷.

Index Law Reminder: When multiplying powers of the same base, add the indices!

The expansion 7aa+5a+5 - 23a2+6a73a²+6a-7 requires careful bracket expansion followed by collecting like terms. Watch your signs – the minus before the second bracket affects every term inside.

Surname

First name(s)

GCSE
wjec
свас
3300U50-1

Centre
Number

A22-3300U50-1

MONDAY, 14 NOVEMBER 2022 - MORNING

MATHEMATICS
UNIT 1: NON-

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Linear Graphs and Gradients

Question 5 focuses on straight line graphs and their equations. Reading the gradient from a graph means finding how much y increases for every 1 unit increase in x. Count squares carefully or use two clear points.

The y-intercept is where your line crosses the y-axis whenx=0when x = 0. Once you have the gradient (m) and y-intercept (c), you can write the equation as y = mx + c.

Graph Reading Tip: Choose points on grid intersections to avoid reading errors!

This question type appears frequently in GCSE mathematics, so practising graph interpretation is time well spent. Always double-check your equation by substituting a point from the line.

Surname

First name(s)

GCSE
wjec
свас
3300U50-1

Centre
Number

A22-3300U50-1

MONDAY, 14 NOVEMBER 2022 - MORNING

MATHEMATICS
UNIT 1: NON-

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Parallel Lines

Part (b) asks you to prove that y = 3x - 8 and 2y - 6x = 23 are parallel lines. Parallel lines have identical gradients, so rearrange both equations into y = mx + c form.

The first equation already shows gradient = 3. For the second equation, rearrange: 2y = 6x + 23, so y = 3x + 11.5. Both have gradient 3, proving they're parallel.

Parallel Line Rule: Same gradient = parallel lines, regardless of the y-intercept!

This algebraic proof technique is essential for higher-tier questions. Show each step clearly to demonstrate your understanding of linear equations.

Surname

First name(s)

GCSE
wjec
свас
3300U50-1

Centre
Number

A22-3300U50-1

MONDAY, 14 NOVEMBER 2022 - MORNING

MATHEMATICS
UNIT 1: NON-

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Dimensional Analysis

Question 6 tests your understanding of dimensional analysis – working out whether formulae represent length, area, volume, or none. Each letter represents a length measurement.

For area, you need dimensions that multiply to give length² (like ab or a²). For volume, you need length³ (like abc or a³). When terms are added or subtracted, they must have the same dimensions.

Key Rule: You can only add or subtract quantities with the same dimensions!

Look at each term separately, then check if they're compatible. For example, 5abc - 6bc + b² mixes volume and area terms, so it represents "none of these". This mathematical reasoning skill becomes crucial in advanced mathematics.

Surname

First name(s)

GCSE
wjec
свас
3300U50-1

Centre
Number

A22-3300U50-1

MONDAY, 14 NOVEMBER 2022 - MORNING

MATHEMATICS
UNIT 1: NON-

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Standard Form Calculations

Question 7 tests standard form arithmetic without a calculator. For (3×10⁴) ÷ (6×10⁻³), divide the numbers (3÷6 = 0.5) and subtract the powers (4-(-3) = 7).

Your answer becomes 0.5×10⁷, which converts to 5×10⁶ in proper standard form. Remember that the first number must be between 1 and 10.

Standard Form Rule: When dividing powers of 10, subtract the indices!

For addition like (4.78×10⁴) + (1.5×10²), convert to the same power of 10 first. This gives (4.78×10⁴) + (0.015×10⁴) = 4.795×10⁴. Standard form questions are common in GCSE papers, so master these techniques.

Surname

First name(s)

GCSE
wjec
свас
3300U50-1

Centre
Number

A22-3300U50-1

MONDAY, 14 NOVEMBER 2022 - MORNING

MATHEMATICS
UNIT 1: NON-

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Pythagoras and Trigonometry

Question 8 tests your understanding of when to use Pythagoras's theorem versus trigonometry. For finding the hypotenuse x, you need x = √(25² + 10²) since you're adding the squares of the two shorter sides.

For the trigonometry part, you have the hypotenuse (25 cm) and need the opposite side y to a 40° angle. Use sin 40° = y/25 because sine relates opposite to hypotenuse.

SOHCAHTOA Reminder: Sin = Opposite/Hypotenuse, Cos = Adjacent/Hypotenuse, Tan = Opposite/Adjacent

Recognising which method to use is crucial for GCSE success. Pythagoras works with right-angled triangles when you know two sides, whilst trigonometry needs an angle and one side.

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?

That's right! Enjoy free access to study content, connect with fellow students, and get instant help – all at your fingertips.

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Transform this note into: ✓ 50+ Practice Questions ✓ Interactive Flashcards ✓ Full Mock Exam ✓ Essay Outlines

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Similar content

Understanding Standard Form

Explore the fundamentals of Standard Form (Scientific Notation) in mathematics. This study note covers how to express large and small numbers using powers of ten, the significance of place value, and practical examples for converting between standard and ordinary forms. Ideal for students looking to master the concept of scientific notation and its applications.

MathsMaths
8

Mastering Standard Form

This concise study note covers the essentials of Standard Form, including conversion between standard and ordinary numbers, powers of 10, and practical examples. Ideal for GCSE Maths revision, it also touches on related concepts like formula manipulation and inequalities. Perfect for students preparing for exams.

MathsMaths
11

Mastering Standard Form

This comprehensive guide covers the conversion between standard form and ordinary numbers, including key operations with scientific notation. Ideal for GCSE students, it provides step-by-step solutions and examples to enhance understanding of powers of 10 and arithmetic with scientific notation.

MathsMaths
11

Understanding Standard Form

Explore the concept of standard form (scientific notation) in mathematics. This summary covers how to express large and small numbers using powers of ten, including examples and conversion techniques. Ideal for students looking to master scientific notation and its applications.

MathsMaths
10

Mastering Negative Numbers

Explore essential concepts in GCSE Maths, including the rules for multiplying and dividing negative numbers, understanding standard form, and the order of operations (BIDMAS). This summary provides clear explanations and examples to enhance your mathematical skills.

MathsMaths
10

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Anna

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Best app on earth! no words because it’s too good

Thomas R

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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

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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

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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