Photon Guidebook: Mathematics HL Paper 3 for the IB Diploma
By Ejaz Ahmad with the Photon Academy team
Every Paper 3 question type. Taught, worked and practised. Paper 3 is the investigation paper of IB Maths HL. This book analyses every real Paper 3 since the 2021 specimen, teaches the arc of an investigation question, works through marked investigations step by step, then trains each type with graded practice and eight full original papers.
- One volume
- 18 chapters
- about 524 pages
- E-book: read in your browser
- 2-year access
- Print edition coming soon
An IB Maths HL Paper 3 guide built around the exam
This guide is for IB Diploma students taking Mathematics: Analysis and Approaches HL or Mathematics: Applications and Interpretation HL who want to score on Paper 3, the investigation paper. One book serves both courses: a shared opening chapter, Part A for Analysis and Approaches, Part B for Applications and Interpretation, four full practice papers for each course and a final chapter of strategy and checklists.
Paper 3 questions are unfamiliar by design, so memorising a topic is not enough. Each type chapter opens with how the IB builds this type: our count of every Paper 3 question of the kind since 2021 and the arc that such a question follows, from the first quick marks to the final stretch part. It then teaches the techniques, works through marked investigations in a three-column layout (what you write, the mark, why it earns the mark) and gives graded practice investigations of 15 to 30 marks.
Paper 3 allows a graphic display calculator in both courses, so every type chapter has a Using your GDC panel for the TI-Nspire CX II and the Casio fx-CG50. 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 Paper 3 in our IB Maths tuition. Looking for the whole course? See the AA HL guide or the AI HL guide.
What’s inside the IB Maths HL Paper 3 guide: investigations, mark schemes and calculator skills
How IB builds this type
Our analysis of every real Paper 3 since 2021, in our own words: how often each type appears, how many marks it carries and how its parts are sequenced.
The arc of a question
Every Paper 3 question moves from orient to build, explore, deduce, generalise and critique. Each chapter draws the arc for its type, so you know what the next part will ask.
Worked investigations
Whole questions marked line by line with M1, A1, R1 and AG, in three columns: what you write, the mark, and why it earns the mark.
Using your GDC
A calculator panel in every type chapter, with keystrokes for the TI-Nspire CX II and the Casio fx-CG50.
Graded practice investigations
Warm-ups, exam-standard and final-part difficulty, with short answers printed in the book.
Eight full practice papers
Four original papers for each course, with printed markschemes and a grade guide.
Free worked solutions online
Every practice investigation has a worked solution online, free, one page per chapter at ibtuition.sg/guidebook/p3/.
Final strategy
A closing chapter of checklists for time, marks and the last weeks before the exam.
Contents
Eighteen chapters in one book: an opening chapter, seven chapters for Analysis and Approaches HL (Part A), seven for Applications and Interpretation HL (Part B), then the practice papers and a final strategy chapter.
One volume Opening · Part A (AA HL) · Part B (AI HL) · Practice papers · Chapters 1–18 · about 524 pages
- 1How Paper 3 works
- 2Families of curves: explore, conjecture, justify
- 3Polynomials, roots and complex numbers
- 4Sequences, recurrences and proof by induction
- 5Limits, Maclaurin series and approximation
- 6Differential equations and their solution families
- 7Calculus of curves, surfaces and motion
- 8Probability models and generating functions
- 9Testing claims: the statistics suite
- 10One rate law, one differential equation
- 11Coupled systems, Euler and phase portraits
- 12Fitting and comparing growth models
- 13Networks and Markov chains
- 14Voronoi diagrams, vectors and optimal shapes
- 15Unfamiliar definitions and new structures
- 16Practice papers: Analysis and approaches HL
- 17Practice papers: Applications and interpretation HL
- 18Final strategy and checklists
Free sample chapter and sample pages
A few pages from the book, as they appear in the reader. Select a page to enlarge it.
Read Chapter 2 free
Families of curves: explore, conjecture, justify, the whole chapter, in the same page-turn reader the e-book uses. No sign-in needed.
How IB builds the question type: our count of every Paper 3 question on families of curves, with the arc ribbon (Ch 2) Teaching pages: short sections, key results and marked examples (Ch 2) Using your GDC: TI-Nspire CX II keystrokes first, Casio fx-CG50 second (Ch 2) A worked investigation: the question in a frame, then the solution in three columns with every mark explained (Ch 2) Practice investigations graded by difficulty, with short answers printed and full solutions online (Ch 2) Chapter opener in Part B: Testing claims: the statistics suite (Ch 9) A worked investigation for Applications and Interpretation HL (Ch 9) Final strategy and checklists for the last weeks (Ch 18)
Buy the IB Maths HL Paper 3 e-book (S$100)
One payment, the whole book. 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.
Complete book
Opening · Part A (AA HL) · Part B (AI HL) · Practice papers · Chapters 1–18
- Chapters 1–18, about 524 pages
- Read online on phone, tablet or laptop
- 2-year access, personal licence
S$100E-book · one-time payment
Read the e-bookA 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, 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 HL Paper 3 guidebook: frequently asked questions
How long can I read the e-book?
Your purchase gives you two years of access to the whole book 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.
Is this book for AA HL or AI HL?
Both. Chapter 1 and the final strategy chapter are shared. Part A (Chapters 2 to 8) teaches the question types of Analysis and Approaches HL Paper 3, Part B (Chapters 9 to 15) those of Applications and Interpretation HL Paper 3, and each course has its own four practice papers (Chapters 16 and 17). You can read the other part too.
Does it replace the AA HL or AI HL guidebook?
No. The AA HL guide and the AI HL guide teach the whole course. This book trains one skill, Paper 3: exploring an unfamiliar situation, conjecturing, proving and interpreting.
How many practice papers are there?
Eight full original papers, four for each course, each with a printed markscheme and a grade guide, plus graded practice investigations in every type chapter.
Are the questions real IB past paper questions?
No. Every question in the book is an original IB-style question written by Photon Academy, and the statistics come from our own analysis of past Paper 3 papers. The book is independent and is not endorsed by the International Baccalaureate.
Which calculator does the book use?
Paper 3 allows a graphic display calculator in both courses, so each type chapter has a Using your GDC panel with keystrokes for the TI-Nspire CX II first and the Casio fx-CG50 second.
Who can read it free?
Photon Academy students taking Mathematics AA HL or AI HL read the whole book free while they are enrolled, and so do admins. Sign in with your Photon account and the buy option is replaced by an Open the e-book button.
Where are the worked solutions to the practice investigations?
Worked solutions for every practice investigation are free online at ibtuition.sg/guidebook/p3/, 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 paper analysis · all Photon books.