TurtleMaths

Free IB Maths formula sheets

IB Maths Formula Booklet: Free AA & AI Formula Sheets

Download free formula summaries for AA HL, AA SL, AI HL and AI SL, designed for faster revision and easier recall.

Built by a Mathematics coach with a proven track record. IB Examiner & IBEN.

AA HLAA SLAI HLAI SL

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5,112verified formula-sheet downloads
counted from 2 September 2026

These TurtleMaths PDFs are free revision companions created independently by Amit Raj. They are not official IB publications and do not replace the current clean formula booklet supplied through your school.

A proven track record

Coaching That Moves the Grade

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+2.5MAA SL grade increase after coaching
+1.7MAI HL/SL average grade improvement

What students say

Trusted by Ambitious IB Students

“Tutoring with Mr. Raj completely changed my experience. I scored a 7 in IB Maths AA HL and performed very well in my final exam.”
David M.IB Maths AA HL
“My grades have almost doubled since doing sessions with him. The support he gave me with my IA and throughout the whole IBDP journey was outstanding. I am incredibly thankful.”
Sarah D.IB Maths AA SL
“His patience and encouragement made a huge difference in my confidence with maths. I achieved a 7 in IB Maths AA HL and my grades improved rapidly.”
Peter S.IB Maths AA HL

Beyond the formula sheet

High-Ability Students Need a Coach, Not Just a Tutor

The formula booklet can remind you of a relationship, but it cannot tell you which method to choose, how to structure your working or where you repeatedly lose marks. Reaching your next milestone, whether that is a 6 to a 7 or a good grade to an outstanding one, takes a coach who diagnoses exactly where marks are lost and builds the judgement a formula sheet can’t teach.

AA HL · AA SL · AI HL · AI SL

Your paid first lesson includes an additional 20-minute diagnostic at no extra charge, making the first session 80 minutes.

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The official reference

What Is the IB Maths Formula Booklet?

The official IB Mathematics formula booklet is the clean examination reference supplied through a student’s school. It collects selected relationships and notation for Diploma Programme Mathematics. Students should practise with the current version used by their school so that finding a topic during an examination becomes quick and familiar.

The booklet supports recall; it does not replace understanding. A student still has to recognise the question type, choose a valid method, manage algebra, use technology appropriately and communicate a result.

Five shared topic areas

What’s Included in the IB Maths Formula Booklet?

Number and Algebra

Selected relationships support sequences, series and algebraic work. Students must still rearrange expressions, recognise patterns and choose exact or approximate forms.

Functions

Function relationships can support modelling and graph work, but domains, transformations and the meaning of parameters still require understanding.

Geometry and Trigonometry

Measurement and trigonometric relationships assist calculation. Diagram interpretation, identities and accurate substitution remain essential.

Statistics and Probability

Distribution and statistical references support recall. They cannot decide which model applies, check conditions or interpret output in context.

Calculus

Derivative and integral forms can prompt a method. Students must still connect change to the question, manage algebra and interpret solutions.

Choose the right companion

IB Maths AA and AI Formula Sheets

IB Maths AA HL Formula Sheet

AA HL is the most algebraically and analytically demanding pathway. The companion brings together high-use relationships across proof, advanced functions, trigonometry, probability and calculus. Use it to audit recall, then practise selecting and deriving methods in unfamiliar problems.

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IB Maths AA SL Formula Sheet

AA SL retains a strong focus on symbolic reasoning and mathematical argument within a narrower range. This sheet helps organise core relationships without obscuring the algebraic fluency and clean written method needed in examination questions.

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IB Maths AI HL Formula Sheet

AI HL combines sophisticated modelling and statistics with substantial function and calculus work. The companion is designed to sit beside calculator practice: it prompts relationships while students learn to choose models, test assumptions and interpret technology output.

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IB Maths AI SL Formula Sheet

AI SL emphasises contextual problem solving, statistics, financial mathematics and technology. The sheet is most useful when paired with practice translating a situation into mathematics and explaining what a result means in the original context.

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Course and level differences

IB Maths AA vs AI Formula Booklets

Analysis and Approaches

AA gives greater weight to symbolic algebra, mathematical reasoning, functions, trigonometry and calculus. Higher Level extends both the range and sophistication of these ideas; Standard Level is narrower but still requires confident manipulation and explanation.

Applications and Interpretation

AI gives greater weight to modelling, statistics, technology and interpretation. AI HL develops these areas in considerably greater depth than AI SL. At both levels, selecting a model and explaining output matters as much as finding a formula.

What isn’t in the booklet?

The Most Important Things Aren’t Written in the Formula Booklet

Exact content depends on the current course and guide, but no formula page can supply mathematical judgement.

  • Which formula or method applies
  • Whether a calculator method is appropriate
  • How much working to show
  • Why a model is appropriate
  • Whether an answer is reasonable
  • How to interpret a result
  • How to recognise a disguised question type

Those are exactly the skills a Mathematics coach builds through deliberate, personalised practice, not generic tutoring.

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Exam technique

How to Use the IB Maths Formula Booklet Effectively

  1. Learn the layout. Practise finding each topic before the examination.
  2. Identify the mathematics first. Decide whether the question involves a distribution, model, trigonometric relationship or calculus idea before searching.
  3. Check notation and conditions. Match every symbol to the question and confirm that a method is valid.
  4. Show the method. Substitute clearly, keep sufficient working and interpret answers when context requires it.
  5. Practise with realistic questions. Familiarity grows from using the booklet during timed exam-style work.

Meet your coach

A Coach for Students Reaching Their Next Milestone

Amit Raj is a Mathematics coach with more than 17 years’ international-school experience, working with high-achieving students aiming for the top grades. IB Examiner · IA Moderator · IBEN

These companion sheets were created to make revision more focused without pretending that formula recall alone produces strong examination performance.

Read about Amit Raj’s experience

Teachers and schools are welcome to share this page with students for personal educational use.

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Questions students ask

IB Maths Formula Booklet FAQ

Is there a formula booklet for IB Maths?

Yes. Schools provide students with the current clean official formula booklet under the arrangements for the relevant IB Mathematics examination. The TurtleMaths PDFs on this page are revision companions, not official IB publications.

Is the IB Maths formula booklet allowed in Paper 1?

Students are normally provided with the relevant clean formula booklet for applicable external mathematics papers, including Paper 1. Always follow the instructions on the current examination paper and the arrangements confirmed by your school.

Do you get the formula booklet in Paper 2?

Students are normally provided with the relevant clean formula booklet for applicable external mathematics papers, including Paper 2. Your school is responsible for supplying the correct current version.

Does IB Maths AA have a formula booklet?

Yes. Mathematics: Analysis and Approaches students use the formula reference relevant to their course and level. AA places particular emphasis on algebraic reasoning, functions, trigonometry and calculus.

Does IB Maths AI have a formula booklet?

Yes. Mathematics: Applications and Interpretation students use formula reference material relevant to their course and level, with strong emphasis on modelling, statistics, technology and interpretation.

Is the AA HL formula requirement different from AA SL?

AA HL covers a greater range and depth than AA SL. Both require fluent algebra, method recognition and clear working; the formula booklet does not replace these skills.

Is the AI HL formula requirement different from AI SL?

AI HL extends the depth and range of modelling, statistics, functions and calculus beyond AI SL. Students at both levels must know when a relationship applies and how to interpret technology output.

Do I need to memorise formulas for IB Maths?

You should know foundational facts, notation and techniques that are not supplied, and become familiar with the booklet layout. More importantly, you must recognise methods, manipulate expressions and explain results.

What formulas are not included in the IB Maths formula booklet?

The booklet is not a complete record of every identity, algebraic step or calculator procedure a student may need. Exact requirements vary by course and current guide, so use the booklet with your teacher’s materials and syllabus.

Can I use the TurtleMaths formula sheet in the actual IB exam?

The TurtleMaths sheet is a revision companion. In the examination, use the clean current official formula booklet supplied under your school’s examination arrangements, not a personal annotated or companion sheet.

Formula recall is only the start

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