Formula Sheets

IB Math Formula Sheets — AA and AI, SL and HL

The IB gives every student a formula booklet in the exam. A lot of students never really learn to use it properly — they either assume everything is in there (it is not) or they flip through it in a panic during the exam and waste time they do not have.

On this page I explain what is in each formula booklet, what is not in it, and how to use it as a tool during past paper practice so it becomes second nature before exam day.

What Is the IB Math Formula Booklet?

The IB Math formula booklet (officially called the Mathematics: Analysis and Approaches and Applications and Interpretation formula booklet) is a document the IB provides to all students during every IB Math exam, across all four courses. It lists key formulas, identities, and statistical tables. It is the same booklet whether you are sitting AA HL, AA SL, AI HL, or AI SL.

Here is the critical thing students miss: the formula booklet has sections. Not every formula in the booklet is relevant to every course. Some entries are HL only. Some appear in the AA section but not the AI section. Knowing which section applies to your course is itself part of exam preparation.

What Is in the IB Math Formula Booklet

The formula booklet covers the following areas (with some entries only relevant to specific courses or levels):

  • Topic 1 — Number and Algebra: Laws of logarithms, binomial theorem, sum and product of roots of quadratics, arithmetic and geometric sequence/series formulas, compound interest, Euler’s form of complex numbers (AA HL).
  • Topic 2 — Functions: Axis of symmetry for quadratics, discriminant.
  • Topic 3 — Geometry and Trigonometry: Distance formula, equation of a circle, sine rule, cosine rule, area of a triangle, radian measure, arc length and sector area, Voronoi diagrams (AI), 3D vector formulas, scalar and vector product (AA HL/AI HL).
  • Topic 4 — Statistics and Probability: Mean, variance, standard deviation formulas for grouped data, Pearson’s correlation coefficient, regression line equation, probability rules, Bayes’ theorem (HL), normal distribution, binomial distribution, Poisson distribution (AI HL).
  • Topic 5 — Calculus: Derivative rules for standard functions, integration rules for standard functions, integration by parts (AA HL), Maclaurin series (AA HL), differential equations (HL).

What Is NOT in the Formula Booklet — and Students Assume It Is

This is where students lose marks. These are formulas that students routinely expect to find in the booklet but are not there:

  • The quadratic formula — not in the booklet. You must know it.
  • Trigonometric identities such as double angle formulas — only some are given, and only for AA HL. Know which ones you need to memorise.
  • Standard derivatives and integrals beyond the basic list — chain rule, product rule, quotient rule are given as rules but not applied to every function type.
  • The laws of indices — not listed. Basic index laws must be memorised.
  • Probability formulas for combined events (e.g., P(A∪B)) — know these.

Working through past papers with the formula booklet open is the best way to learn what is and is not in it under real conditions.

Formula Booklet by Course

IB Math AA HL Formula Booklet

AA HL students use the most entries in the booklet — Maclaurin series, integration by parts, complex number forms, and proof-related identities. Knowing where these are in the booklet and how to apply them under timed conditions is essential. See the full AA HL course specifications.

IB Math AA SL Formula Booklet

AA SL students use the standard calculus, trigonometry, and statistics sections most often. The most common mistake I see is students looking up integration formulas that are not in the booklet for Paper 1, wasting time. See the AA SL course specifications.

IB Math AI HL Formula Booklet

AI HL students rely heavily on the statistics section — the normal distribution tables, chi-squared critical values, and probability formulas. The graph theory and Markov chain sections do not have dedicated formula entries, so those algorithms must be learned. See the AI HL course specifications.

IB Math AI SL Formula Booklet

AI SL students use the statistics and financial mathematics sections frequently. The financial formulas in the booklet are helpful but students must still know which formula to apply in which context — the booklet gives you the formula but not the judgment. See the AI SL course specifications.

How to Use the Formula Booklet in Exam Preparation

  1. Read it cover to cover once at the start of your exam revision. Most students have never actually read it properly.
  2. Annotate it mentally — know which sections apply to your course and level.
  3. Use it during every past paper session. Open it at the start of every paper the way you would in the real exam. This builds the habit of knowing where to look when you need it.
  4. Test yourself on what is NOT in it. Memorise the formulas that are absent — this is a small and learnable list that pays off in Paper 1.

Pair formula booklet work with the topic question banks and mock exams for complete exam preparation. If you want personalised guidance on the formula booklet and exam technique, contact Mr Ahmad to discuss tutoring options or see the tutoring packages.