IB Math AA Formula Booklet: What's Included (and What's Not)

Every IB Math AA exam comes with a helper on the desk: the official IB Math AA formula booklet. It's a slim document — the content runs to just 13 numbered pages — and it holds more than 100 formulas your child can look up mid-exam. But here's what surprises most families. The booklet doesn't contain everything. Some of the most-used facts in the course, like exact trig values, aren't in it at all. Students who know the booklet inside out walk into exams calmer and faster. Students who meet it properly for the first time in May lose marks hunting for formulas that were never there. This guide walks through the booklet section by section, in plain English.

Quick answer: The IB Math AA formula booklet is the official reference document for IB Mathematics: Analysis and Approaches. One booklet covers both SL and HL. It's organised into a "Prior learning" section plus the five syllabus topics: number and algebra, functions, geometry and trigonometry, statistics and probability, and calculus. Students get a clean copy in every exam paper — including the no-calculator Paper 1. It does not include exact trig values, index laws, function transformations, or methods like integration by substitution. Those must be memorised.

What is the IB Math AA formula booklet?

The IB Math AA formula booklet is the official list of formulas that IB gives to every Mathematics: Analysis and Approaches student, for use in class and in the final exams. The full name on the cover is "Mathematics: analysis and approaches formula booklet". The IB published it in 2019 for the syllabus that was first examined in 2021, and it's still the version in use today, with only small corrections since.

Some students call it the "data booklet", borrowing the name from IB Chemistry's data booklet. Same idea, different subject: it's the sheet of facts you're allowed to consult during the exam.

Three things make this booklet different from a normal formula sheet:

• It's official. The exact same booklet sits on every AA candidate's desk worldwide. Nobody gets a better one.

• It covers SL and HL together. There is one booklet for both levels, with the HL-only material clearly labelled "AHL" (Additional Higher Level).

• It's allowed in every paper. Even Paper 1, where calculators are banned, still comes with the formula booklet.

The IB distributes it through schools. Your child's teacher will hand out copies at the start of the course, and the exam centre provides fresh, unmarked copies on exam day.

What's inside the booklet: the six sections

The booklet contains a short prior-learning section plus formulas for all five AA syllabus topics, in syllabus order. Every entry is labelled with its syllabus code (like "SL 1.2" or "AHL 5.15"), so you can match each formula to the exact part of the course it belongs to.

Here's the map of the whole booklet:

Let's open each section.

Prior learning

This first section holds the "before IB" formulas — things students met at IGCSE or MYP level. It includes the area of a parallelogram, triangle, trapezoid and circle, the circumference of a circle, and the volumes of a cuboid, cylinder and prism. It also gives the curved surface area of a cylinder, the distance between two points, and the midpoint of a line segment.

Students skip this page all the time. Don't. Exam questions quietly assume you can find the volume of a prism or the distance between two coordinates, and the formulas are sitting right there on page 2.

Topic 1: Number and algebra

The SL part gives you the nth term and sum of an arithmetic sequence, the nth term and sum of a finite geometric sequence, and the sum of an infinite geometric sequence. It also covers compound interest, the rule connecting exponents and logarithms, the three log laws plus the change-of-base rule, and the binomial theorem for positive whole-number powers, with the nCr formula.

The HL-only part adds permutations and combinations, complex numbers in the form a + bi, the polar and Euler forms of a complex number, and De Moivre's theorem.

Topic 2: Functions

This is the shortest section. SL students get the three forms of a straight line equation, the gradient formula, the axis of symmetry of a quadratic, the quadratic formula, and the discriminant. HL adds one entry: the sum and product of the roots of a polynomial.

Notice what that means. Almost everything else in the functions topic — transformations, inverse functions, composite functions, graph features — has no formula to look up. It's all technique.

Topic 3: Geometry and trigonometry

This is one of the biggest sections. At SL it covers the distance and midpoint formulas in 3D, the volumes of a pyramid, cone and sphere, the curved surface of a cone, and the surface area of a sphere. Then comes the triangle toolkit: sine rule, cosine rule (both forms), and the half-ab-sin-C area formula. Radian work is covered with arc length and sector area. For identities, you get tan as sin over cos, the Pythagorean identity, and the double angle identities for sin and cos.

The HL-only part is even richer: sec and cosec definitions, two extra Pythagorean identities, the compound angle identities, the tan double angle identity, and the full vector package — magnitude, scalar product, the angle between vectors, vector product, and the equations of lines and planes in three forms each.

Topic 4: Statistics and probability

At SL, the booklet gives the interquartile range, the mean of a frequency table, and the core probability rules: complementary events, combined events, mutually exclusive events, conditional probability, and independent events. It adds the expected value of a discrete random variable, the mean and variance of the binomial distribution, and the standardised z formula for the normal distribution.

HL adds Bayes' theorem, variance and standard deviation of a data set, the rules for linear transformations of a random variable, and the expectation and variance formulas for continuous random variables.

One catch worth knowing: for actual normal distribution probabilities, there's nothing to look up. Your child finds those with the graphic display calculator (GDC) — the calculator every IB maths student uses in Paper 2.

Topic 5: Calculus

The SL part carries the derivative and integral of x to the power n, the area under a curve, and the derivatives of sin x, cos x, e to the x, and ln x. Crucially, it also prints the chain rule, product rule and quotient rule in full — many students never notice they're there. Kinematics gets its own block, with acceleration, displacement and distance travelled. Four standard integrals round it off.

The HL-only part is the longest single stretch in the booklet: differentiation from first principles, nine extra standard derivatives (tan, sec, cosec, cot, a to the x, log base a, arcsin, arccos, arctan), three extra standard integrals, integration by parts, volumes of revolution, Euler's method, the integrating factor, and the Maclaurin series with five ready-made expansions.

SL vs HL: one booklet, two courses

SL and HL students use the exact same booklet — the difference is simply which pages they need. Every topic is split into an "SL and HL" block and an "HL only" block, and the HL entries carry the code "AHL".

For SL students, this layout is a gift. If a formula sits in an AHL block, it will never be required in an SL exam. Knowing the boundary tells you exactly what's yours and what isn't.

For HL students, the AHL blocks are a checklist of the extra machinery the course expects — and a reminder that the hardest HL techniques, like integration by substitution, aren't in the booklet at all.

Can you use the formula booklet in every paper?

Yes — every IB Math AA exam paper comes with the formula booklet, including the no-calculator paper. This is the single most misunderstood fact about it. Students mix up two separate rules: calculators are banned in Paper 1, but the formula booklet is provided in all papers.

Here's the AA exam structure with the booklet's place in it:

Two rules matter on exam day:

1. You get a clean copy. The exam centre provides fresh booklets. Your child cannot bring their own annotated copy into the exam room.

2. Every candidate must have one. IB exam rules require each student to have access to their own copy during the paper — no sharing between desks.

So the smart move is obvious: annotate a personal copy heavily during the two years of the course, but practise your final past papers with a clean printout, exactly as it will be in the real exam.

What's NOT in the formula booklet

The formula booklet leaves out a long list of facts and methods that AA exams still expect — and this list is where grades are won and lost. Educifly's IB Math specialists see the same pattern every year: students assume "it'll be in the booklet" and discover mid-exam that it isn't.

Here's what your child must carry in their head:

There's a helpful way to frame this. The booklet stores facts (what the cosine rule says). It doesn't store skills (when to use the cosine rule, or how to substitute cleverly). The IB's design is deliberate: exams reward students who can select and apply, not just recall. That's also why scoring a 7 in Math AA is about practised judgement, not memory.

The exact trig values deserve one more sentence. Paper 1 has no calculator. If a question needs cos 60° and your child doesn't know it's one half, the booklet will not save them. Learn the values table cold — it takes an afternoon.

How to use the booklet well (a study plan that works)

The booklet only speeds you up if you already know it like your own street. Here's the routine we recommend to students at Educifly, refined across hundreds of 1-on-1 lessons since 2018.

1. Get your copy in week one. Don't wait for exam season. Print the booklet the day the course starts and keep it inside your maths folder.

2. Use it for all homework. Every practice question, every time. Two years of light, constant use beats two weeks of cramming its layout.

3. Annotate your practice copy. Write next to each formula what the symbols mean and when you'd use it. You can't take this copy into the exam, but the notes move the knowledge into your head.

4. Learn locations, not just contents. In the exam, seconds matter. Knowing that the double angle identities sit in Topic 3, or that the quotient rule is printed under SL 5.6, saves real time across a whole paper.

5. Build a separate "not in the booklet" list. Take the table above, add anything your teacher flags, and turn it into flashcards. This list is your true memorisation workload — and it's much shorter than students fear.

6. Do your final mocks with a clean copy. In the last month, switch to an unmarked booklet so exam day feels identical. Pair this with timed past papers for the full effect.

A tutor can shortcut a lot of this. A specialist IB Math AA tutor will drill exactly which booklet formulas each question type needs, and which gaps your child must memorise — instead of your child discovering those gaps in May.

Common mistakes students make with the booklet

The most common mistake is never opening the booklet until exam season. The second most common is trusting it to contain things it doesn't. Here's the full list we see:

• Meeting it late. Students who first study the booklet during revision waste their exam time navigating it. Familiarity is the whole advantage.

• Assuming exact trig values are inside. They aren't. This one mistake, in a no-calculator paper, can sink several questions at once.

• Ignoring the prior learning page. Volume of a prism, midpoint formula, distance formula — all there, all forgotten.

• Reading the wrong level. SL students sometimes grab an AHL formula (like a compound angle identity) and burn time on machinery their course never requires. The AHL labels exist — check them.

• Copying formulas wrong under pressure. The booklet gives the infinite geometric sum with the condition that the common ratio sits strictly between −1 and 1. Students copy the fraction and skip the condition, then apply it where it fails.

• Expecting the GDC's job to be in the booklet. Normal distribution probabilities, solving equations numerically, statistics from data lists — that's calculator work, not booklet work.

AA vs AI: don't revise from the wrong booklet

Math AA and Math AI have different formula booklets, because they're different courses with different syllabuses. AI (Applications and Interpretation) has its own booklet with a different mix — heavier on statistics and financial maths, lighter on pure algebra and proof-flavoured content.

The booklets look similar at a glance, and plenty of students download the wrong PDF and revise from it for weeks. Check the cover: yours should say "analysis and approaches". If you're still weighing up which course fits your child, our Math AA vs AI comparison breaks down the real differences.

How to get your own copy

Your child's maths teacher or IB coordinator is the official source — schools receive the booklet through the IB's own systems. Most schools hand out printed copies at the start of the course and before mocks.

Plenty of schools also post the PDF on their public websites, so a quick search will surface a copy to print at home. Just check two things: the cover says "Mathematics: analysis and approaches", and the booklet states "first examinations 2021" — that's the current syllabus. And once your child has a predicted score in hand, our free IB score calculator shows what their maths grade means for the full 45-point diploma.

Educifly's IB Math specialists have taught Math AA 1-on-1 since 2018 — 500+ students, with an average grade-band lift of 1.4. If your child wants a study plan built around exactly what the booklet does and doesn't cover, a free trial class is an easy first step.

FAQs: IB Math AA formula booklet

Is the formula booklet allowed in IB Math AA Paper 1?

Yes. The formula booklet is provided in every AA exam paper, including Paper 1. What's banned in Paper 1 is the calculator, not the booklet. Students often mix these two rules up. Your child will sit Paper 1 with a clean copy of the booklet on their desk but no GDC.

Is the IB Math AA formula booklet the same for SL and HL?

Yes — one booklet covers both levels. Each topic is split into an "SL and HL" block and an "HL only" block, with HL material labelled "AHL". SL students can safely ignore every AHL entry; nothing in those blocks will appear in an SL exam.

How many pages is the IB Math AA formula booklet?

The content runs to 13 numbered pages, including a contents page and a prior-learning section. It's short by design — five syllabus topics, with the HL-only material folded into each topic rather than printed separately.

Can I bring my own annotated formula booklet into the exam?

No. Exam centres provide clean, unmarked copies, and those are the only ones allowed on the desk. Annotating a personal copy is still one of the best revision habits — it just stays at home on exam day. Practise your final mocks with a clean printout so nothing feels unfamiliar.

Is the quadratic formula in the IB formula booklet?

Yes. The quadratic formula and the discriminant both appear in Topic 2 (Functions), in the SL and HL section. The axis of symmetry of a quadratic is printed there too. What's not given is completing the square — that's a method your child needs to know by hand.

Are exact trig values in the formula booklet?

No — and this is the most dangerous gap in it. The values of sin, cos and tan at 0°, 30°, 45°, 60° and 90° (and their radian equivalents) must be memorised. Paper 1 has no calculator, so questions there assume your child can recall these instantly.

What's the difference between the AA and AI formula booklets?

They're separate documents for separate courses. The AA booklet follows the Analysis and Approaches syllabus, with more pure algebra, trigonometry and calculus. The AI booklet follows Applications and Interpretation, with more statistics and applied content. Revising from the wrong booklet is a surprisingly common mistake — check the cover says "analysis and approaches".

Do I need to memorise derivatives for IB Math AA?

Fewer than you'd think. The booklet prints the derivatives of x to the n, sin, cos, e to the x and ln x at SL, plus nine more at HL (including tan, arcsin and arctan). The chain, product and quotient rules are all printed too. What you must supply from memory is the skill of combining them — and, at HL, methods like implicit differentiation that have no booklet entry.

Where can I download the IB Math AA formula booklet?

Ask your school first — teachers and IB coordinators distribute the official copy. Many schools also host the PDF publicly, so searching the booklet's full name plus "PDF" will find a printable copy. Make sure it says "first examinations 2021" so you're using the current syllabus version.

Is integration by substitution in the formula booklet?

No. The booklet prints integration by parts (HL) and a set of standard integrals, but substitution is treated as a technique, not a formula. HL students should expect to choose and carry out substitutions from practice alone. This is a classic example of the booklet's rule: facts are printed, methods are not.

Does the formula booklet change from year to year?

Not meaningfully. The current booklet was published in 2019 for first exams in 2021, and the IB has only issued minor corrections since. Your child can safely use the same booklet across both years of the course — just make sure any printed copy matches the current version their school uses.

Do examiners expect you to quote formulas exactly from the booklet?

Examiners expect correct formulas, and the booklet is the safety net that makes that possible. Marks are lost when students copy a formula wrong, drop a condition (like the common ratio condition on infinite geometric series), or pick a formula that doesn't fit the question. Copy carefully, check the conditions printed beside each formula, and label which syllabus entry you're using if it helps you stay organised.