Photon Guidebook: Mathematics Applications and Interpretation HL for the IB Diploma
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 with the graphic display calculator, then trains every type of question until you can score on it under exam conditions.
- 2 volumes
- 24 chapters
- about 1,290 pages
- E-book: read in your browser
- 2-year access
- Print edition coming soon
An IB Maths AI HL guide built around the exam
This guide is for IB Diploma students taking Mathematics: Applications and Interpretation at Higher Level who want to go from understanding a topic to scoring on it in the exam. It covers every unit of the AI HL course across two volumes, then adds a full Paper 3 chapter on modelling investigations 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.
AI is a graphic display calculator course in every paper, so every chapter has a Using your GDC panel for the TI-Nspire CX II and the Casio fx-CG50, and the questions are set in the real-world contexts the exam uses. 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 AI HL in our IB Maths tuition. Taking AA instead? See the AA HL guide.
What’s inside the IB Maths AI HL guide: questions, mark schemes and calculator skills
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: a typical question, the idea, the steps and a fully marked worked solution, with where marks are lost.
Marked line by line
Worked examples are marked the way examiners mark, with M1, A1 and R1 on each line.
Using your GDC
A calculator panel in every chapter, with keystrokes for the TI-Nspire CX II and the Casio fx-CG50: finance solver, statistics, matrices and graphs.
Going further
Harder problems in every topic chapter, in the style of Paper 3, for students aiming at a 7.
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/aihl/.
Paper 3 and exam strategy
Volume 2 adds a full Paper 3 chapter on modelling investigations and an exam strategy chapter that ends with a timed paper.
Contents of each volume
Volume 1 covers Units 1 to 3 (Chapters 1 to 12). Volume 2 covers Units 4 and 5, then Paper 3 and exam strategy (Chapters 13 to 24).
Volume 1 Units 1–3 · Chapters 1–12 · about 668 pages
- 1Number, approximation and error
- 2Sequences, series and financial mathematics
- 3Exponents and logarithms
- 4Complex numbers
- 5Matrices, eigenvalues and Markov chains
- 6Functions and graphs
- 7Modelling with functions and regression
- 8Trigonometry and three-dimensional geometry
- 9Voronoi diagrams
- 10Vectors
- 11Matrix transformations
- 12Graph theory
Volume 2 Units 4–5 · Paper 3 · Exam strategy · Chapters 13–24 · about 622 pages
- 13Describing data
- 14Correlation and regression
- 15Probability
- 16Probability distributions
- 17Hypothesis tests and confidence intervals
- 18Differentiation
- 19Integration
- 20Kinematics
- 21Differential equations
- 22Coupled systems and phase portraits
- 23Paper 3: modelling investigations
- 24Exam strategy
Free sample chapter and sample pages
A few pages from each volume, as they appear in the reader. Select a page to enlarge it.
Read Chapter 2 free
Sequences, series and financial mathematics, the whole chapter, in the same page-turn reader the e-book uses. No sign-in needed.
Volume 1
How IB asks this: every AI HL exam question on Sequences, series and financial mathematics since 2021, counted and ranked by marks (Ch 2) A question type: a typical question, the idea, the steps and a worked solution marked line by line (Ch 2) Going further: harder problems for students aiming at a 7 (Ch 2) Practice in three steps: Basics, Tutorial and Mastery (Ch 2)
Volume 2
Chapter opener: Hypothesis tests and confidence intervals (Ch 17) A second question type, with its worked solution (Ch 17) Going further: Differential equations (Ch 21) Paper 3: modelling investigations (Ch 23)
Buy the IB Maths AI HL e-book (S$100 per volume)
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 1–12
- Chapters 1–12, about 668 pages
- Read online on phone, tablet or laptop
- 2-year access, personal licence
S$100E-book · one-time payment
Read Volume 1
Volume 2
Units 4–5 · Paper 3 · Exam strategy · Chapters 13–24
- Chapters 13–24, about 622 pages
- Read online on phone, tablet or laptop
- 2-year access, personal licence
S$100E-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 | |
About the author: Ejaz Ahmad
Ejaz Ahmad is an IB-certified teacher of Mathematics: Analysis and Approaches HL (and Applications and Interpretation) 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.
IB Maths AI HL guidebook: 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 12). Volume 2 covers Units 4 and 5 plus a Paper 3 chapter and an exam strategy chapter (Chapters 13 to 24). Each volume is S$100 as an e-book: buy either one on its own, or both.
I take AI SL or AA. Is this the right book?
Only if you take AI HL. The AI SL guide is a separate one-volume book, and the AA HL guide is for Analysis and Approaches.
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.
Which calculator does the book use?
AI is a graphic display calculator course in every paper, so each chapter has a Using your GDC panel with keystrokes for the TI-Nspire CX II and the Casio fx-CG50.
Where are the worked solutions to the practice questions?
Worked solutions for every practice question are free online at ibtuition.sg/guidebook/aihl/, 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 AI HL cheatsheets · IB Maths paper analysis · all Photon books.