IB Maths AI SL Formula Booklet — Applications & Interpretation 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 AI SL paper?

Yes. A clean copy of the formula booklet is provided in both papers. 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. AI has an SL booklet and an HL booklet. SL students get the SL booklet.

Q: Is the IB Maths AI 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 AI 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 AI SL formula booklet in both papers. 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 46 formulas you need for IB Mathematics Applications & Interpretation 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 AI SL formula booklet?

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

IB Maths AI 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
Number & algebra	Arithmetic sequence · Arithmetic series · Geometric sequence · Geometric series, $r \neq 1$ · Compound interest ( $k$ times a year, $n$ years, $r$ %) · Exponents & logs · and 1 more	Standard form · Common difference · Depreciation at $r$ % a year · Log facts · Bounds
Functions & models	Gradient; forms of a line · Quadratic	Parallel; perpendicular · Linear; quadratic models · Exponential models · Direct / inverse variation · Cubic model · Sinusoidal model (degrees) · and 2 more
Geometry & trigonometry	3D distance ( $Δ x = x_{1} - x_{2}$ , …) · 3D midpoint · Pyramid; cone · Sphere · Sine rule · Cosine rule · and 2 more	Slant height of a cone · Elevation / depression measured from the horizontal · Perpendicular bisector of $A B$ · Voronoi
Statistics & probability	Interquartile range · Mean ( $n = \sum f_{i}$ ) · Probability · Combined events · Mutually exclusive · Independent · and 4 more	Outliers · Standard deviation · Data $\times a$ then $+ b$ · Regression · $\| r \|$ near 1 · Expected number of occurrences · and 7 more
Calculus	Derivative of $x^{n}$ · Integral of $x^{n}$ , $n \neq - 1$ · Area, $y \geq 0$ · Trapezoidal rule, $h = \frac{b - a}{n}$	Constant multiples, sums · Gradient of tangent at $x = a$ · Gradient of normal · Increasing / decreasing · Stationary points; optimisation · Boundary condition

Every row is on our free one-page IB Maths AI 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: $A = π r^{2}$
Circumference of a circle: $C = 2 π r$
Volume of a cuboid: $V = l \cdot w \cdot h$
Volume of a cylinder: $V = π r^{2} h$
Volume of a prism: $V = A \cdot h (A = cross-section area)$
Area of curved surface of cylinder: $A = 2 π r h$
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: $S_{n} = \frac{u_{1} (r^{n} - 1)}{r - 1} = \frac{u_{1} (1 - r^{n})}{1 - r}, r \neq 1$
Compound interest: $F V = P V {(1 + \frac{r}{100 k})}^{k n}$
Exponents: $a^{p} \cdot a^{q} = a^{p + q}, \frac{a^{p}}{a^{q}} = a^{p - q}, (a^{p})^{q} = a^{p q}$
Logarithms — power law: $\log_{a} (x^{n}) = n \log_{a} x$
% error: $ε = | \frac{v_{A} - v_{E}}{v_{E}} | \times 100 %$

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

Using the booklet: a worked example

$2000 is invested at 3.5% a year, compounded monthly, for 5 years. Find the value at the end, to the nearest cent.

From the booklet, $F V = P V {(1 + \frac{r}{100 k})}^{k n}$ , with $P V = 2000$ , $r = 3.5$ , $k = 12$ (monthly), $n = 5$ .
$F V = 2000 {(1 + \frac{3.5}{1200})}^{60}$ .
$F V = $ 2381.89$ (the TVM solver gives the same: N = 60, I% = 3.5, PV = −2000, PMT = 0, P/Y = C/Y = 12).
Common slip: using $k = 1$ gives $$ 2375.37$ , the value with yearly compounding, which loses the mark.

Compound interest explained · Free SL AI financial maths questions with mark schemes

Topic 2 — Functions

Equation of a straight line: $y = m x + c or a x + b y + d = 0$
Gradient of a straight line: $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$
Axis of symmetry of a quadratic: $x = - \frac{b}{2 a}$

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

Topic 3 — Geometry & Trigonometry

Length of an arc: $ℓ = 2 π r \cdot \frac{θ}{360^{\circ}}$
Area of a sector: $A = π r^{2} \cdot \frac{θ}{360^{\circ}}$
Surface area of a sphere: $A = 4 π r^{2}$
Volume of a sphere: $V = \frac{4}{3} π r^{3}$
Volume of a cone: $V = \frac{1}{3} π r^{2} h$
Curved surface area of a cone: $A = π r l$
Volume of a pyramid: $V = \frac{1}{3} A_{base} \cdot h$
Right-angled triangle (SOHCAHTOA) ★ not in the booklet: $\sin θ = \frac{O}{H}, \cos θ = \frac{A}{H}, \tan θ = \frac{O}{A}$
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 (SAS): $A = \frac{1}{2} a b \sin C$

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

Topic 4 — Statistics & Probability

Interquartile range: $IQR = Q_{3} - Q_{1}$
Mean of a data set: $\bar{x} = \frac{\sum_{i = 1}^{n} f_{i} x_{i}}{n}, n = \sum f_{i}$
Probability of an event: $P (A) = \frac{n (A)}{n (U)}$
Complementary events: $P (A^{'}) = 1 - P (A)$
Combined events: $P (A \cup B) = P (A) + P (B) - P (A \cap B)$
Mutually exclusive events: $P (A \cap B) = 0$
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): $E (X) = \sum x P (X = x)$

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

Topic 5 — Calculus

Derivative of xⁿ: $f (x) = x^{n} ⟹ f^{'} (x) = n x^{n - 1}$
Integral of xⁿ: $\int x^{n} d x = \frac{x^{n + 1}}{n + 1} + C, n \neq - 1$
Area between curve and x-axis: $A = \int_{a}^{b} y d x$
Trapezoidal rule (approx. area): $A \approx \frac{h}{2} (y_{0} + y_{n} + 2 (y_{1} + y_{2} + \dots + y_{n - 1})), h = \frac{b - a}{n}$

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

Not in the AI SL booklet: 39 results to learn

The IB Maths AI 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: $a^{m} a^{n} = a^{m + n}, \frac{a^{m}}{a^{n}} = a^{m - n}, (a^{m})^{n} = a^{m n}, a^{- n} = \frac{1}{a^{n}}$

Number & algebra

Standard form: $a \times 10^{k}, 1 \leq a < 10, k \in Z$
Common difference: $d = u_{n + 1} - u_{n}$
Depreciation at $r$ % a year: $V = V_{0} {(1 - \frac{r}{100})}^{n}$
Log facts: $\log_{10} 10^{x} = x, \ln e^{x} = x, e^{\ln x} = x$
Bounds: a value rounded to the nearest $u$ lies in $[x - \frac{u}{2}, x + \frac{u}{2})$

Functions & models

Parallel; perpendicular: $m_{1} = m_{2}; m_{1} m_{2} = - 1$
Linear; quadratic models: $f (x) = m x + c; f (x) = a x^{2} + b x + c$
Exponential models: $f (x) = k a^{x} + c, f (x) = k a^{- x} + c, f (x) = k e^{r x} + c$
Direct / inverse variation: $f (x) = a x^{n}, n \in Z$
Cubic model: $f (x) = a x^{3} + b x^{2} + c x + d$
Sinusoidal model (degrees): $f (x) = a \sin (b x) + d : amplitude | a |, period \frac{360^{\circ}}{b}$
Inverse function: swap $x$ and $y$ ; graph reflects in $y = x$ ; domain of $f^{- 1}$ = range of $f$
Horizontal asymptote of $k a^{x} + c$: $y = c$

Geometry & trigonometry

Slant height of a cone: $l = \sqrt{r^{2} + h^{2}}$
Elevation / depression measured from the horizontal; bearings clockwise from north, 3 figures
Perpendicular bisector of $A B$ : through the midpoint of $A B$ , gradient $- \frac{1}{m_{A B}}$
Voronoi: cell edges lie on perpendicular bisectors of pairs of sites; the point furthest from every site ("toxic waste dump") is at a vertex or on the boundary

Statistics & probability

Outliers: $x < Q_{1} - 1.5 I Q R or x > Q_{3} + 1.5 I Q R$
Standard deviation: $σ = \sqrt{\frac{\sum f (x - \bar{x})^{2}}{n}}$
Data $\times a$ then $+ b$: $mean \to a \bar{x} + b, s.d. \to | a | σ$
Regression: $y = a x + b$ (GDC); use to predict $y$ within the data range only
$| r |$ near 1: strong linear correlation; Spearman's $r_{s}$ = PMCC of the ranks
Expected number of occurrences: $n \times P (A)$
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 $μ$
Expected frequency (independence): $f_{e} = \frac{row total \times column total}{grand total}$
Degrees of freedom: $independence: (r - 1) (c - 1); goodness of fit: classes - 1$
Test decision: reject $H_{0}$ if $p$ -value $<$ significance level (or $χ_{calc}^{2} >$ critical value)
$t$ -test (GDC): compares two population means; $H_{0} : μ_{1} = μ_{2}$

Calculus

Constant multiples, sums: $f (x) = a x^{n} + b x^{m} \Rightarrow f^{'} (x) = a n x^{n - 1} + b m x^{m - 1}$
Gradient of tangent at $x = a$: $f^{'} (a); tangent y - f (a) = f^{'} (a) (x - a)$
Gradient of normal: $- \frac{1}{f^{'} (a)}$
Increasing / decreasing: $f^{'} (x) > 0; f^{'} (x) < 0$
Stationary points; optimisation: $f^{'} (x) = 0; check the sign of f^{'} either side$
Boundary condition: find $C$ by substituting a known point into $\int f^{'} (x) d x$

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

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

Radians in an arc or sector formula. The AI SL booklet gives $l = \frac{θ}{360} \times 2 π r$ and $A = \frac{θ}{360} \times π r^{2}$ , with $θ$ in degrees. For $r = 5$ and $θ = 60^{\circ}$ , $l = \frac{5 π}{3} \approx 5.24$ .
The wrong $r$ or $k$ in compound interest. In $F V = P V {(1 + \frac{r}{100 k})}^{k n}$ , $r$ is the percentage (3.5, not 0.035) and $k$ is the number of compounding periods a year (12 for monthly).
Percentage error over the wrong value. Divide by the exact value $v_{E}$ : an estimate of 63 m for an exact 60 m is an error of $\frac{3}{60} \times 100 % = 5 %$ , not $4.76 %$ .
The $χ^{2}$ statistic without the decision. The booklet prints $χ_{c a l c}^{2}$ , not the degrees of freedom or the conclusion. For a contingency table, $df = (rows - 1) (columns - 1)$ ; reject $H_{0}$ when the $p$ -value is below the significance level.

Calculator tip: Both papers allow the GDC. Use the TVM solver for finance (money paid out is entered as negative), the $χ^{2}$ test for the statistic and $p$ -value, and regression for $r$ and the line of best fit. Write the formula or statement first, then the GDC's answer.

IB Maths AI 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 AI 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

Binomial distribution Pythagoras' theorem Standard deviation

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 AI SL paper?

Yes. A clean copy of the formula booklet is provided in both papers. 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. AI has an SL booklet and an HL booklet. SL students get the SL booklet.

Is the IB Maths AI 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 AI 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 AA SL formula booklet · IB Math AI HL formula booklet · IB Math AA HL formula booklet · Print-ready one-page booklet · SL AI revision notes · SL AI questions by topic

IB Maths AI SL Formula Booklet — Applications & Interpretation SL

What's in the IB Maths AI 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 AI SL booklet: 39 results to learn

Prior learning

Number & algebra

Functions & models

Geometry & trigonometry

Statistics & probability

Calculus

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

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

Key formulas explained, with a worked example

Questions

What else is free here