IB Maths AA SL Formula Booklet — Analysis & Approaches SL

Q: Is this the IB's own formula booklet?

No. It is our own page, written in the same notation as the IB formula booklet so you get used to it. In the exam you are given a clean copy of the IB booklet.

Q: Can I take this sheet into the exam?

No. Only the clean copy of the IB formula booklet that the exam provides is allowed. Use this page and the PDF to revise.

Q: Which formulas do I have to learn by heart?

Some results you need are not printed in the booklet. They are listed on this page under "Not in the booklet", and the one-page formula sheet marks each of them with a star.

Q: Do you get the formula booklet in every IB Maths AA SL paper?

Yes. A clean copy of the formula booklet is provided in every paper, including calculator-free Paper 1. You cannot bring your own copy or any notes.

Q: How do I get quick at using the formula booklet?

Practise past-style questions with the booklet open beside you, so you know which topic each formula sits under and what each letter means. Then learn the results it leaves out (our formulas-to-memorise page lists them with worked examples).

Q: Is there a separate formula booklet for SL and HL?

Yes. AA has an SL booklet and an HL booklet. SL students get the SL booklet.

Q: Is the IB Maths AA SL data booklet the same as the formula booklet?

Yes. For maths the IB calls it the formula booklet; "data booklet" is the name of the IB Chemistry and Physics booklets, so many students use either name. Everything on this page is in the IB Maths AA SL formula booklet, apart from the results marked as not in the booklet.

Q: Which formula booklet is used for the 2026 exams?

The current editions, for first assessment 2021. They are used for every exam on the current courses, up to the last ones in November 2028. The revised courses are first examined in May 2029.

Q: Is the PDF free?

Yes. The PDFs (A4, A3 poster, black and white, and the formulas to memorise) and this page are free, with no sign-up.

Quick answer: yes, you get a clean copy of the IB Maths AA SL formula booklet in every paper, including calculator-free Paper 1. SL and HL have separate booklets; the 2026 exams use the current editions (first assessment 2021). Your school can give you a copy to revise with: the IB publishes it only to schools on its Programme Resource Centre, and there is no public copy on ibo.org (we don't host it either; the course is on the IB DP Mathematics page). It does not have everything, so also learn the 39 results it leaves out.

All 51 formulas you need for IB Mathematics Analysis & Approaches SL, grouped by syllabus topic and written in the same notation as the IB formula booklet. Use it to revise which formulas are given in the exam, and which you still need to understand how to apply.

Download the free PDF Practise these formulas: free questions

Updated November 2026

What's in the IB Maths AA SL formula booklet?

There is a separate SL booklet and HL booklet for AA. This table is for the AA SL booklet. Topic by topic, this is what it prints and the main results it leaves out (★), which you must learn.

IB Maths AA SL formula booklet by topic: printed, and ★ not printed
Topic	Printed in the booklet	★ Not printed: learn these
Prior learning	Area · Circle · Volume · Curved surface of a cylinder · Distance; midpoint	Pythagoras · Right-angled trig · Laws of indices · Standard form
Number & algebra	Arithmetic sequence · Arithmetic series · Geometric sequence · Geometric series, $r \neq 1$ · Sum to infinity, $\| r \| < 1$ · Compound interest ( $k$ times a year, $n$ years, $r$ %) · and 5 more	Special values · General term
Functions	Gradient; forms of a line · Quadratic · Quadratic formula; discriminant	Parallel; perpendicular lines · Roots · Vertex form, vertex $(h, k)$ ; intercept form · Composite; inverse · Graph of $f^{- 1}$ · Translations · and 4 more
Geometry & trigonometry	3D distance · 3D midpoint · Pyramid; cone · Sphere · Sine rule · Cosine rule · and 4 more	Ambiguous case · Radians · Exact values at $0, \frac{π}{6}, \frac{π}{4}, \frac{π}{3}, \frac{π}{2}$ · Symmetry · $y = a \sin (b (x - c)) + d$ , $b > 0$ · $\sin x = k$
Statistics & probability	Interquartile range · Mean ( $n = \sum f_{i}$ ) · Probability · Combined events · Mutually exclusive · Independent · and 4 more	Outliers · Variance (s.d. $σ$ ) · Data $\times a$ then $+ b$ · Regression · Valid distribution; fair game · Binomial $X \sim B (n, p)$ · and 1 more
Calculus	Power rule · Standard derivatives · Chain rule · Product rule · Quotient rule · Integral of $x^{n}$ , $n \neq - 1$ · and 4 more	Linear inside · Tangent; normal gradient at $x = a$ · Increasing / decreasing · Stationary points · Concave up $f^{″} > 0$ ; point of inflexion · Reverse chain rule · and 3 more

Every row is on our free one-page IB Maths AA SL formula sheet (PDF), with ★ on the ones to learn.

Prior learning

Area of a parallelogram: $A = b \cdot h$
Area of a triangle: $A = \frac{1}{2} (b \cdot h)$
Area of a trapezium: $A = \frac{1}{2} (a + b) h$
Area of a circle: $A = π r^{2}$
Volume of a cuboid: $V = l w h$
Volume of a cylinder: $V = π r^{2} h$
Distance between two points: $d = \sqrt{(x_{1} - x_{2})^{2} + (y_{1} - y_{2})^{2}}$
Midpoint of two points: $(\frac{x_{1} + x_{2}}{2}, \frac{y_{1} + y_{2}}{2})$

Topic 1 — Number & Algebra

The n-th term of an arithmetic sequence: $u_{n} = u_{1} + (n - 1) d$
Sum of n terms of an arithmetic sequence: $S_{n} = \frac{n}{2} (2 u_{1} + (n - 1) d) = \frac{n}{2} (u_{1} + u_{n})$
The n-th term of a geometric sequence: $u_{n} = u_{1} \cdot r^{n - 1}$
Sum of n terms of a geometric sequence: $S_{n} = \frac{u_{1} (r^{n} - 1)}{r - 1}, r \neq 1$
Infinite geometric series: $S_{\infty} = \frac{u_{1}}{1 - r}, | r | < 1$
Compound interest: $F V = P V {(1 + \frac{r}{100 k})}^{k n}$
Exponents & logs (change of base): $\log_{a} x = \frac{\log_{b} x}{\log_{b} a}$
Product / quotient / power laws: $\log_{a} (x y) = \log_{a} x + \log_{a} y, \log_{a} \frac{x}{y} = \log_{a} x - \log_{a} y, \log_{a} (x^{n}) = n \log_{a} x$
Binomial theorem: $(a + b)^{n} = \sum_{k = 0}^{n} (\binom{n}{k}) a^{n - k} b^{k}, (\binom{n}{k}) = \frac{n!}{k! (n - k)!}$

Practise Topic 1: free SL AA questions with mark schemes →

Using the booklet: a worked example

A geometric sequence has $u_{1} = 24$ and $r = 0.5$ . Find $S_{\infty}$ , then the smallest $n$ for which $S_{n} > 47.9$ .

From the booklet, $S_{\infty} = \frac{u_{1}}{1 - r}$ (valid because $| r | < 1$ ): $S_{\infty} = \frac{24}{0.5} = 48$ .
Also from the booklet, $S_{n} = \frac{u_{1} (1 - r^{n})}{1 - r} = 48 (1 - {0.5}^{n})$ .
Solve $48 (1 - {0.5}^{n}) > 47.9$ : ${0.5}^{n} < \frac{0.1}{48}$ , so $n > 8.91$ (use logs or a table of values).
Check: $S_{8} = 47.8125$ and $S_{9} = 47.906 \dots$ , so the smallest is $n = 9$ .

Infinite geometric series and sum of n terms explained · Free SL AA sequences and series questions with mark schemes

Topic 2 — Functions

Equation of a straight line: $y - y_{1} = m (x - x_{1})$
Gradient: $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$
Axis of symmetry of a quadratic: $x = - \frac{b}{2 a}$
Quadratic formula: $x = \frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a}$
Discriminant: $Δ = b^{2} - 4 a c$

Practise Topic 2: free SL AA questions with mark schemes →

Topic 3 — Geometry & Trigonometry

Arc length (radians): $ℓ = r θ$
Area of a sector (radians): $A = \frac{1}{2} r^{2} θ$
Sine rule: $\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}$
Cosine rule: $c^{2} = a^{2} + b^{2} - 2 a b \cos C$
Area of a triangle: $A = \frac{1}{2} a b \sin C$
Pythagorean identity: $\sin^{2} θ + \cos^{2} θ = 1$
Double-angle: sine: $\sin 2 θ = 2 \sin θ \cos θ$
Double-angle: cosine: $\cos 2 θ = \cos^{2} θ - \sin^{2} θ = 2 \cos^{2} θ - 1 = 1 - 2 \sin^{2} θ$
Tangent from sine & cosine: $\tan θ = \frac{\sin θ}{\cos θ}$

Practise Topic 3: free SL AA questions with mark schemes →

Topic 4 — Statistics & Probability

Interquartile range: $IQR = Q_{3} - Q_{1}$
Mean of a data set: $\bar{x} = \frac{\sum f_{i} x_{i}}{n}, n = \sum f_{i}$
Probability of an event: $P (A) = \frac{n (A)}{n (U)}$
Complementary events: $P (A^{'}) = 1 - P (A)$
Combined events: $P (A \cup B) = P (A) + P (B) - P (A \cap B)$
Conditional probability: $P (A ∣ B) = \frac{P (A \cap B)}{P (B)}$
Independent events: $P (A \cap B) = P (A) P (B)$
Expected value (discrete): $E (X) = \sum x P (X = x)$
Binomial distribution: $X \sim B (n, p) ⟹ P (X = r) = (\binom{n}{r}) p^{r} (1 - p)^{n - r}$
Mean & variance of a binomial: $E (X) = n p, Var (X) = n p (1 - p)$
Standardising a normal variable: $Z = \frac{X - μ}{σ}$

Practise Topic 4: free SL AA questions with mark schemes →

Topic 5 — Calculus

Derivative of xⁿ: $\frac{d}{d x} (x^{n}) = n x^{n - 1}$
Chain rule: $\frac{d y}{d x} = \frac{d y}{d u} \cdot \frac{d u}{d x}$
Product rule: $(u v)^{'} = u^{'} v + u v^{'}$
Quotient rule: ${(\frac{u}{v})}^{'} = \frac{u^{'} v - u v^{'}}{v^{2}}$
Derivatives of standard functions: $\frac{d}{d x} (\sin x) = \cos x, \frac{d}{d x} (\cos x) = - \sin x$
Exponential & log derivatives: $\frac{d}{d x} (e^{x}) = e^{x}, \frac{d}{d x} (\ln x) = \frac{1}{x}$
Integral of xⁿ: $\int x^{n} d x = \frac{x^{n + 1}}{n + 1} + C, n \neq - 1$
Standard integrals: $\int \sin x d x = - \cos x + C, \int \cos x d x = \sin x + C, \int e^{x} d x = e^{x} + C, \int \frac{1}{x} d x = \ln | x | + C$
Area between a curve and the x-axis: $A = \int_{a}^{b} y d x$

Practise Topic 5: free SL AA questions with mark schemes →

Not in the AA SL booklet: 39 results to learn

The IB Maths AA SL formula booklet does not print these, but questions expect you to know them. Learn them by heart; every formula above without a ★ is given in the exam.

Prior learning

Pythagoras: $a^{2} + b^{2} = c^{2}$
Right-angled trig: $\sin θ = \frac{opp}{hyp}, \cos θ = \frac{adj}{hyp}, \tan θ = \frac{opp}{adj}$
Laws of indices: $a^{m} a^{n} = a^{m + n}, \frac{a^{m}}{a^{n}} = a^{m - n}, (a^{m})^{n} = a^{m n}, a^{- n} = \frac{1}{a^{n}}, a^{\frac{m}{n}} = \sqrt[n]{a^{m}}$
Standard form: $a \times 10^{k}, 1 \leq a < 10, k \in Z$

Number & algebra

Special values: $\log_{a} 1 = 0, \log_{a} a = 1, \ln e = 1, e^{\ln x} = x$
General term: $T_{r + 1} = (\binom{n}{r}) a^{n - r} b^{r}$

Functions

Parallel; perpendicular lines: $m_{1} = m_{2}; m_{1} m_{2} = - 1$
Roots: $Δ > 0$ two distinct real, $Δ = 0$ one repeated, $Δ < 0$ no real roots
Vertex form, vertex $(h, k)$ ; intercept form: $y = a (x - h)^{2} + k; y = a (x - p) (x - q)$
Composite; inverse: $(f \circ g) (x) = f (g (x)); f (f^{- 1} (x)) = x$
Graph of $f^{- 1}$ : reflect $y = f (x)$ in $y = x$ ; domain of $f^{- 1}$ = range of $f$
Translations: $f (x) + b$ up $b$ ; $f (x - a)$ right $a$
Stretches: $p f (x)$ vertical × $p$ ; $f (q x)$ horizontal × $\frac{1}{q}$
Reflections: $- f (x)$ in the $x$ -axis; $f (- x)$ in the $y$ -axis
$y = \frac{a x + b}{c x + d}$ asymptotes: $x = - \frac{d}{c}, y = \frac{a}{c}$
Exponential ↔ log: $y = a^{x} ⟺ x = \log_{a} y; e^{x} and \ln x are inverses$

Geometry & trigonometry

Ambiguous case: given $a, b, A$ with $A$ acute, two triangles if $b \sin A < a < b$
Radians: $π rad = 180^{\circ}$
Exact values at $0, \frac{π}{6}, \frac{π}{4}, \frac{π}{3}, \frac{π}{2}$: $\sin : 0, \frac{1}{2}, \frac{\sqrt{2}}{2}, \frac{\sqrt{3}}{2}, 1; \cos : reverse order; \tan : 0, \frac{1}{\sqrt{3}}, 1, \sqrt{3}, undefined$
Symmetry: $\sin (π - θ) = \sin θ, \cos (π - θ) = - \cos θ, \cos (- θ) = \cos θ, \sin (- θ) = - \sin θ$
$y = a \sin (b (x - c)) + d$ , $b > 0$: $amplitude | a |, period \frac{2 π}{b}, principal axis y = d$
$\sin x = k$ : $x = \arcsin k$ or $π - \arcsin k$ , then add $2 π n$ ; keep solutions in the interval

Statistics & probability

Outliers: $x < Q_{1} - 1.5 I Q R or x > Q_{3} + 1.5 I Q R$
Variance (s.d. $σ$ ): $σ^{2} = \frac{\sum f (x - μ)^{2}}{n} = \frac{\sum f x^{2}}{n} - μ^{2}$
Data $\times a$ then $+ b$: $mean \to a \bar{x} + b, s.d. \to | a | σ$
Regression: use $y$ on $x$ to predict $y$ , $x$ on $y$ to predict $x$ ; interpolate, don't extrapolate
Valid distribution; fair game: $\sum P (X = x) = 1; E (gain) = 0$
Binomial $X \sim B (n, p)$: $P (X = r) = (\binom{n}{r}) p^{r} (1 - p)^{n - r}$
Normal: about 68%, 95%, 99.7% of values lie within 1, 2, 3 s.d. of $μ$

Calculus

Linear inside: $\frac{d}{d x} e^{k x} = k e^{k x}, \frac{d}{d x} \sin k x = k \cos k x, \frac{d}{d x} \ln (k x) = \frac{1}{x}$
Tangent; normal gradient at $x = a$: $y - f (a) = f^{'} (a) (x - a); m_{normal} = - \frac{1}{f^{'} (a)}$
Increasing / decreasing: $f^{'} (x) > 0; f^{'} (x) < 0$
Stationary points: $f^{'} (x) = 0 : f^{″} < 0 max, f^{″} > 0 min$
Concave up $f^{″} > 0$ ; point of inflexion: $f^{″} = 0$ and $f^{″}$ changes sign
Linear inside: $\int f (a x + b) d x = \frac{1}{a} F (a x + b) + C$
Reverse chain rule: $\int f^{'} (g (x)) g^{'} (x) d x = f (g (x)) + C$
Definite integral: $\int_{a}^{b} f^{'} (x) d x = f (b) - f (a)$
Area between two curves: $A = \int_{a}^{b} | f (x) - g (x) | d x$
Displacement $t_{1} \to t_{2}$: $\int_{t_{1}}^{t_{2}} v (t) d t$

Each of these with a worked example · Tick them off on the interactive sheet · One-page PDF of just these

Using the IB Maths AA SL formula booklet: mistakes that cost marks

Degrees in an arc or sector formula. The booklet's $l = r θ$ and $A = \frac{1}{2} r^{2} θ$ need $θ$ in radians. For $r = 5$ cm and $θ = 60^{\circ} = \frac{π}{3}$ , $l = \frac{5 π}{3} \approx 5.24$ cm; typing 60 gives 300 cm.
Variance in place of standard deviation. $X \sim N (50, 64)$ means $σ = 8$ , and $z = \frac{x - μ}{σ}$ uses $σ$ . $P (X < 60) = 0.894$ ; entering 64 as the standard deviation gives 0.562.
A sum to infinity that does not exist. $S_{\infty} = \frac{u_{1}}{1 - r}$ holds only for $| r | < 1$ . With $r = 1.5$ there is no sum to infinity, so say so rather than writing a number.
Expanding without the general term. The booklet gives $(a + b)^{n}$ and $(\binom{n}{r})$ , not the term in $x^{r}$ . The coefficient of $x^{3}$ in $(2 + x)^{5}$ is $(\binom{5}{3}) \times 2^{2} = 40$ .

Calculator tip: Paper 1 has no calculator, and the booklet does not print the exact values of sin, cos and tan at $0, \frac{π}{6}, \frac{π}{4}, \frac{π}{3}, \frac{π}{2}$ , so learn them. In Paper 2, let the GDC do binomial and normal probabilities, inverse normal and regression, and write the probability statement, such as $P (X < 60)$ , before the number.

IB Maths AA SL formula sheet PDF: download it your way

Our own one-page sheets (not the IB's booklet), free to print, no sign-up.

Preview of our free one-page IB Maths AA SL formula sheet: every formula on one A4 page, colour-coded by topic, with a star on each one the booklet leaves out — The A4 sheet (PDF)

Key formulas explained, with a worked example

Derivative of sin x nCr formula (combinations) Pythagoras' theorem SOH CAH TOA (right-angled trigonometry) Standard deviation Volume of a cone Volume of a sphere

Questions

Is this the IB's own formula booklet?

No. It is our own page, written in the same notation as the IB formula booklet so you get used to it. In the exam you are given a clean copy of the IB booklet.

Can I take this sheet into the exam?

No. Only the clean copy of the IB formula booklet that the exam provides is allowed. Use this page and the PDF to revise.

Which formulas do I have to learn by heart?

Some results you need are not printed in the booklet. They are listed on this page under "Not in the booklet", and the one-page formula sheet marks each of them with a star.

Do you get the formula booklet in every IB Maths AA SL paper?

Yes. A clean copy of the formula booklet is provided in every paper, including calculator-free Paper 1. You cannot bring your own copy or any notes.

How do I get quick at using the formula booklet?

Practise past-style questions with the booklet open beside you, so you know which topic each formula sits under and what each letter means. Then learn the results it leaves out (our formulas-to-memorise page lists them with worked examples).

Is there a separate formula booklet for SL and HL?

Yes. AA has an SL booklet and an HL booklet. SL students get the SL booklet.

Is the IB Maths AA SL data booklet the same as the formula booklet?

Yes. For maths the IB calls it the formula booklet; "data booklet" is the name of the IB Chemistry and Physics booklets, so many students use either name. Everything on this page is in the IB Maths AA SL formula booklet, apart from the results marked as not in the booklet.

Which formula booklet is used for the 2026 exams?

The current editions, for first assessment 2021. They are used for every exam on the current courses, up to the last ones in November 2028. The revised courses are first examined in May 2029.

Is the PDF free?

Yes. The PDFs (A4, A3 poster, black and white, and the formulas to memorise) and this page are free, with no sign-up.

What else is free here

Make a free account: no card needed5 more practice questions on every topic with instant feedback, full worked answers on free questions, 3 AI-marked answers a week, free, and your streak and progress on any device.

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Other courses: IB Math AI SL formula sheet · IB Math AI HL formula booklet · IB Math AA HL formula booklet · Print-ready one-page booklet · SL AA revision notes · SL AA questions by topic

IB Maths AA SL Formula Booklet — Analysis & Approaches SL

What's in the IB Maths AA SL formula booklet?

Prior learning

Topic 1 — Number & Algebra

Using the booklet: a worked example

Topic 2 — Functions

Topic 3 — Geometry & Trigonometry

Topic 4 — Statistics & Probability

Topic 5 — Calculus

Try it now

Not in the AA SL booklet: 39 results to learn

Prior learning

Number & algebra

Functions

Geometry & trigonometry

Statistics & probability

Calculus

Using the IB Maths AA SL formula booklet: mistakes that cost marks

IB Maths AA SL formula sheet PDF: download it your way

Key formulas explained, with a worked example

Questions

What else is free here