The Ultimate Guide for the IB: Mathematics: Analysis and Approaches HL
By Ejaz Ahmad with the Photon Academy team
From the basics to full IB exam questions. Each chapter shows how the IB asks the topic, teaches it step by step, then trains every type of question until you can score on it under exam conditions.
- 2 volumes
- 19 chapters
- about 786 pages
- E-book: read in your browser
- 2-year access
- Print edition coming soon
An IB Maths AA HL guide built around the exam
This guide is for IB Diploma students taking Mathematics: Analysis and Approaches at Higher Level who want to go from understanding a topic to scoring on it in the exam. It covers every unit of the AA HL course across two volumes, then adds a full Paper 3 chapter and an exam strategy chapter.
Most textbooks teach a topic and then set exercises. This guide starts from the exam. Each topic chapter opens with How IB asks this: our count of every exam question on the topic since 2021 and the question types that carry the marks. It then teaches the topic step by step and works through every question type one at a time: how to recognise it, the method, a fully marked worked example and where marks are lost. Practice comes in three steps, from basics to full exam-style questions.
The book is revised every year. This is the 2026 Edition, written by Ejaz Ahmad with the Photon Academy team in Singapore. It is also part of how we teach AA HL in our IB Maths tuition.
What the guide gives you
How IB asks this
Our count of every exam question on the topic since 2021, and the question types that carry the marks, so you know where to spend your time.
Every question type explained
For each type: the tell that identifies it, the method, a fully marked worked example and where marks are lost.
Marked line by line
Worked examples are marked the way examiners mark, with M1, A1 and R1 on each line, plus Examiner's pens on the points that cost marks.
Going further
Paper 3-style investigations in every topic chapter, so the extended questions feel familiar before the exam.
Practice in three steps
Basics, Tutorial and Mastery: build the skill, then apply it, then answer full exam-style questions under exam conditions.
Free worked solutions online
Every practice question has a worked solution online, free, one page per chapter at ibtuition.sg/guidebook/aahl/.
Paper 3 and exam strategy
Volume 2 adds a full Paper 3 chapter with four investigations and an exam strategy chapter that ends with a timed paper.
Contents of each volume
Volume 1 covers Units 1 to 3. Volume 2 covers Units 4 and 5, then Paper 3 and exam strategy.
Volume 1 Units 1–3 · Chapters 1–11 · about 468 pages
- 1Sequences and series
- 2Exponentials and logarithms
- 3Binomial theorem
- 4Counting principles
- 5Proof
- 6Complex numbers
- 7Systems of equations
- 8Functions
- 9Polynomials
- 10Trigonometry
- 11Vectors
Volume 2 Units 4–5 · Paper 3 · Exam strategy · Chapters 12–19 · about 318 pages
- 12Statistics
- 13Probability
- 14Differentiation
- 15Integration
- 16Differential equations
- 17Maclaurin series
- 18Paper 3
- 19Exam strategy
Sample pages
A few pages from each volume, as they appear in the reader. Select a page to enlarge it.
Read Chapter 1 free
Sequences and series, all 43 pages, in the same page-turn reader the e-book uses. No sign-in needed.
Volume 1
How IB asks this: every exam question on Functions since 2021, counted and ranked by marks (Vol. 1, Ch 8) A question type: the tell, the method and a worked example marked line by line (Vol. 1, Ch 8) Going further: a Paper 3-style investigation (Vol. 1, Ch 8) Practice, step 1: Basics (Vol. 1, Ch 8)
Volume 2
Chapter opener: Probability (Vol. 2, Ch 13) A question type: trees, total probability and Bayes (Vol. 2, Ch 13) Going further: shared birthdays and fair games (Vol. 2, Ch 13) Paper 3 chapter: Investigation 1 (Vol. 2, Ch 18)
Buy the e-book
Buy one volume or both. You read it in your browser straight after payment, on your Photon Academy account.
You will sign in with Google before paying, so the book is linked to your account.
Volume 1
Units 1–3 · Chapters 1–11
- Chapters 1–11, about 468 pages
- Read online on phone, tablet or laptop
- 2-year access, personal licence
S$50E-book · one-time payment
Read Volume 1
Volume 2
Units 4–5 · Paper 3 · Exam strategy · Chapters 12–19
- Chapters 12–19, about 318 pages
- Read online on phone, tablet or laptop
- 2-year access, personal licence
S$50E-book · one-time payment
Read Volume 2A printed edition is on the way. Its price and release date will appear here.
Secure payment by HitPay (card, Apple Pay, Google Pay, PayNow). Photon Academy never sees your card details. Already bought it? Open My e-books.
E-book and print
| E-book | ||
|---|---|---|
| Available | Now | Coming soon |
| How you read it | In your browser, with a page-turn reader, contents navigator and search | Printed book |
| Devices | Phone, tablet or laptop | – |
| Access | 2 years per volume, on your account | – |
| Download or print | No PDF download or printing; personal licence, watermarked | – |
| Worked solutions | Free online for every practice question | |
Ejaz Ahmad
Ejaz Ahmad is an IB-certified teacher of Mathematics: Analysis and Approaches HL and Physics HL, with a B.Eng. (Mechanical) from the National University of Singapore. He has taught the IB since 2015 and has worked with over 1,000 IB students in Singapore and abroad, many of whom have scored 7 in AA HL and 45 points overall.
He wrote this guide with the Photon Academy team. Meet the tutors or read about Photon Academy.
Frequently asked questions
How long can I read the e-book?
Each purchase gives you two years of access to that volume in the online reader, on your Photon Academy account. My e-books shows how long you have left.
Which devices can I read it on?
Any phone, tablet or laptop with an up-to-date web browser. Sign in with the same Google account you bought it with; there is nothing to install.
Can I download a PDF or print the book?
No. The e-book is read online in the page-turn reader and there is no PDF download or print option. It is a personal licence and each page carries your account details as a watermark.
Is there a print edition?
A print edition is coming soon. Its price and release date will be announced on this page.
Do I need both volumes?
Volume 1 covers Units 1 to 3 (Chapters 1 to 11). Volume 2 covers Units 4 and 5 plus a Paper 3 chapter and an exam strategy chapter (Chapters 12 to 19). Each volume is S$50 as an e-book: buy either one on its own, or both.
Are the questions real IB past paper questions?
No. Every question in the book is an original IB-style question written by Photon Academy. The book is independent and is not endorsed by the International Baccalaureate.
Where are the worked solutions to the practice questions?
Worked solutions for every practice question are free online at ibtuition.sg/guidebook/aahl/, one page per chapter.
What is the refund policy?
Refund terms will be published with the terms of sale. If you have a question about an order, email info@ibtuition.sg.
Can a school or tuition centre order copies?
Yes. For school or group orders, contact Photon Academy at info@ibtuition.sg or through the contact page.
The questions in this book are original IB-style questions written by Photon Academy; they are not IB past paper questions. This book is independent and is not endorsed by or affiliated with the International Baccalaureate Organization. More free help: IB Maths AA HL cheatsheets · IB Maths paper analysis · all Photon books.