A-Level Further Maths Free Resources

Whether you are teaching A-level Further Maths for the first time, just wanting some extra questions for your class or a student studying A-level Further Maths, I hope you find something useful here. If you click on the link the file should automatically download or you can right click and then open in a new tab.

 

I have a complete set of notes and question booklets for the two Pure Maths modules ( AS1 and A21) and also the notes and questions booklets broken up in to individual topics, along with teachers copies for each. There are also links to the YouTube video playlist for AS1 Further Maths and A21 Further Maths where I go through the teachers notes.

 

 


Complete AS1 notes and Question Booklet

Download AS1 Pupils Notes pdf

Download AS1 Question Booklet pdf

Further Maths AS1 video playlist

Further Maths AS1 notes videos playlist

 

 

AS1 by Topic


AS1 Matrices

Download Matrices Teachers Notes pdf

Download Matrices Pupils Notes pdf

Download Matrices Question Booklet pdf

 

AS1 Roots of Polynomials

Download Roots of Polynomials Teachers Notes pdf

Download Roots of Polynomials Pupils Notes pdf

Download Roots of Polynomials Question Booklet


AS1 Vectors

Download Vectors Teachers notes pdf

Download Vectors Pupils notes pdf

Download Vectors Question Booklet pdf


AS1 Complex Numbers

Download Complex 1 Teachers Notes pdf

Download Complex 1 Pupils Notes pdf

Download Complex 1 Question Booklet pdf


Complete set of A21 notes and Question Booklet

Download A21 Pupils Notes pdf

Download A21 Question Booklet pdf

Further Maths A21 Notes Videos Playlist

Further Maths A21 Notes Videos Playlist

 



A21 by Topic

A21 Complex Numbers

Download Complex 2 Teachers notes pdf

Download Complex 2 Pupils notes pdf

Download Complex 2 Question Booklet pdf

 

A21 Partial Fractions

Download Partial Fractions Teachers notes pdf

Download Partial Fractions Pupils notes pdf

Download Partial Fractions Question Booklet pdf

 

A21 Summation of Series

Download Summation of Series Teachers notes pdf

Download Summation of Series Pupils notes pdf

Download Summation of Series Question Booklet pdf

 

A21 Induction

Download Induction Teachers notes pdf

Download Induction Pupils notes pdf

Download Induction Question Booklet pdf

 

A21 Maclaurin’s

Download Maclaurins Teachers notes pdf

Download Maclaurins  Pupils notes pdf

Download Maclaurin’s Question Booklet pdf

 

A21 Improper Integral

Download Improper Integral Teachers notes pdf

Download Improper Integral Pupils notes pdf

Download Improper Integrals Question Booklet pdf


A21 Differentiation and Integration of Inverse Trig

Download Differentiation and Integration Inverse Trig Teachers notes pdf

Download Differentiation and Integration Inverse Trig Pupils notes pdf

Download Differentiation and Integration Inverse Trig Question Booklet pdf

 

A21 Reduction Formula

Download Reduction Formula Teachers notes pdf

Download Reduction Formula Pupils notes pdf

Download Reduction Formula Question Booklet pdf

 

A21 Hyperbolic Functions

Download Hyperbolic Function Teachers notes pdf

Download Hyperbolic Functions Pupils notes pdf

Download Hyperbolic Functions Question Booklet pdf

 

A21 Differential Equations

Download Differential Equations Teachers notes pdf

Download Differential Equations Pupils notes pdf

Download Differential Equations Question Booklet pdf

 

A21 Polar Coordinates

Download Polar Coordinates Teachers notes pdf

Download Polar Coordinates Pupils notes pdf

Download Polar Coordinates Question Booklet pdf

 

 

 

How To Revise

🎯 Smart Maths Revision: A Guide for Students

Whether you're studying GCSE, AS, A-Level, or Further Maths, this guide is here to help you revise effectively — so you feel confident, prepared, and less stressed heading into your exams.

🕒 When Should You Revise?

There are two important times to focus on revision:

1. Right After Each Lesson

The best revision starts immediately after a topic is taught. This helps you lock in new concepts before they fade. Go back over the lesson, finish any worksheets or examples, and make sure everything makes sense while it’s still fresh.

It might feel like extra effort now, but it makes later revision and exam prep far easier. This is a common strategy used (quietly!) by top-performing students.

2. Past Papers – But Not Too Early

Past papers are useful, but only if you understand the material first. If you jump into full past papers too soon, it can be frustrating and even knock your confidence.

Use full exam papers once you’ve covered a full section of the course. This helps make sure you’re testing what you’ve learned — not just guessing or doing the questions you already know.

📌 What Should You Revise?

It’s tempting to just go over your weakest topics, but focusing only on those can be overwhelming. Instead, target areas where:

  • You're struggling and
  • You're "okay" — because turning an OK topic into a strength can boost your grade quickly.

Here's a quick method:

  1. Try a past paper — stop as soon as you get stuck or make a mistake.
  2. Identify the topic causing the issue — then stop working on the paper and focus fully on that topic.
  3. Avoid giant revision lists — they can feel endless and demotivating. Instead, fix one weak point at a time.

🧠 How to Revise Effectively

Once you've found what to work on, here’s how to actually learn it — not just memorise patterns.

1. Learn Your Notes Thoroughly

Before anything else, you need a deep understanding of the content. Many students feel confident just because they’ve done lots of past paper questions — but in the real exam, a slight change in how a question is asked can throw you off completely.

Don’t rely on pattern recognition alone. You need to fully understand:

  • Why each method works
  • When to use it
  • What each formula or process actually means

This kind of understanding gives you real confidence in exams — no matter how the question is worded.

2. Use Video Tutorials to Fill Gaps

If you're unsure about any part of your notes, look it up on YouTube or your course platform. Pause the video, try the questions yourself, and write down anything useful. Re-watch if needed.

➡️ Our GCSE & A-Level Revision Courses include downloadable notes booklets, with clear video links for every topic — perfect for reviewing anything you missed or didn’t fully grasp the first time.
👉 Revision Courses Main Menu

3. Textbook Practice

Textbooks still matter! Go through worked examples and then tackle the matching exercises. If you start finding these too easy or repetitive, that’s your cue to move on to exam-style questions.

4. Exam Questions by Topic

Now, practice past paper questions based only on the topic you're working on. This helps you apply your knowledge in different ways and gets you used to exam-style wording. Check your school’s Google Classroom or revision websites for topic-based question packs.

✅ Final Tips for Success

To give yourself the best chance of doing well:

  • Start revising early — especially right after each lesson
  • Understand the concepts — don’t just memorise answers
  • Practice regularly — repetition builds confidence and speed
  • Don’t leave it all to the last minute — short, consistent sessions beat cramming every time

Success in Maths = Understanding + Practice + Consistency

Stay patient with yourself. Maths rewards effort and regular revision. With the right strategies, you’ll go into your exams with the confidence you need.

Want support with your revision?
Check out our CCEA-focused revision courses for GCSE & A-Level Maths — complete with notes, video walkthroughs, and topic-specific practice questions.
👉  Revision Courses Main Menu

 

Revision Videos

Your Guide to Revision Videos

Dive into Key Stage 3 (KS3) Mathematics, GCSE Mathematics, GCSE Further Mathematics, and A-Level Mathematics with our helpful revision videos.

🌐 **KS3 Mathematics: Building the Basics**
Not just for KS3, these resources are your go-to for diving into the challenges of GCSE Mathematics. Build a strong foundation for higher levels as these videos seamlessly transition and reinforce key skills.

Key Skills Revision Videos

🚀 **GCSE Mathematics: Master the Essentials**
Conquer GCSE exams with our user-friendly revision videos. These videos not only target GCSE but also complement KS3 Mathematics, making your learning experience smooth and comprehensive.

GCSE Revision Videos

🔍 **GCSE Further Mathematics: Dive Deeper**
Ready for an extra challenge? Our GCSE Further Mathematics revision videos are here to guide you. And the best part? They seamlessly extend into A-Level Mathematics, bridging the gap and preparing you for the next academic level.

GCSE FURTHER MATHS Revision Videos

🎓 **A-Level Mathematics: Reach New Heights**
Designed for students studying AS-Level A-Level students or anyone with a keen interest in Mathematics.

A-Level Revision Videos

 

Past Papers

Ace Your Maths Exams: Dive into Video Solutions!

AQA GCSE MATHS and FURTHER MATHS PAST PAPERS:

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CCEA GCSE MATHS PAST PAPERS:  

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CCEA GCSE FURTHER MATHS PAST PAPERS: 

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CCEA AS-LEVEL MATHS PAST PAPERS:

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CCEA A-LEVEL MATHS PAST PAPERS:

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Conquer CCEA and AQA Maths exams with our video solutions!

🚀 **Why Video Solutions?**
Our videos break down complex problems step-by-step, helping you visualize solutions, grasp key concepts, and boost your confidence.

📈 **Climb the Academic Ladder**
From mastering the basics in GCSE to tackling advanced challenges in A-levels, our videos cater to every academic level.

🎯 **Targeted Learning for Your Level**
Navigate to dedicated pages for CCEA GCSE Mathematics, Further Mathematics, AS-level, and A-level Mathematics. Tailored content ensures focused learning, addressing the unique needs of each academic stage.

Meet the Tutor

 

Andrew is a distinguished UK educator with nearly two decades of experience teaching A-level Mathematics in a top Northern Ireland Grammar school. Andrew likes to stay active and has enjoying playing and coaching rugby in the past but is currently passionate about playing tennis. Andrew's expertise lies in offering online tutoring services tailored to CCEA AS-Level and A-level Mathematics. 

Educational Background:
Andrew holds a degree in Mathematics and a P.G.C.E teaching qualification from Queens University Belfast. He commenced his teaching career in 2004 at a prominent Grammar school in Northern Ireland. His expertise spans the entire spectrum of mathematics education, covering GCSE Maths, GCSE Further Maths, AS-Maths, A-Level Maths, and the PURE modules of AS and A-Level Further Maths.

Teaching and Tutoring Proficiency:
With an extensive history of teaching from year 8 to year 14, Andrew brings a nuanced understanding of various curriculum specifications. This includes a comprehensive grasp of Higher tier GCSE Maths, GCSE Further Maths (PURE, MECHANICS, and STATISTICS), and the complete AS-Level and A-Level Maths curriculum. His ability to convey mathematical concepts in diverse ways ensures a tailored approach to individual student needs.

Proven Academic Outcomes:
Andrew's students consistently achieve results that surpass the Grammar school average, demonstrating notable progress from their initial proficiency levels. Many of his students pursue STEM subjects at prestigious universities, a testament to the effectiveness of his teaching methods.

Resource Development:
Throughout his teaching career, Andrew has developed a wealth of digital resources, proving invaluable in the online tutoring environment. These resources include schemes of work for GCSE, AS, A2 Mathematics, and Further Mathematics, as well as materials created for Intensive Revision Courses and online tutorial platforms.

Enriched Learning Experience:
Andrew's commitment to personalised instruction ensures that each student comprehensively grasps mathematical principles. His diverse teaching experience allows him to adapt his approach to cater to distinct learning styles.

Educational Content:
Andrew's YouTube Channel, N.I. Maths Tutor (@n.i.mathstutor6043), serves as a reputable resource for students preparing for CCEA GCSE and A-Level examinations in Mathematics and Further Mathematics.

Experience the benefits of Andrew's online mathematics tuition, providing students with a solid foundation for academic success. 📚🎓 

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