IB Mathematics · AA SL
IB Math AA SL Formula Booklet — Every Formula, Explained
If you are sitting IB Mathematics: Analysis and Approaches SL, you receive the official AA formula booklet (also called the data booklet) in Paper 1 and Paper 2. SL students use only the sections without the HL label — this page lists exactly those, topic by topic, so nothing in the booklet is a surprise on exam day.
A booklet is only useful if you know what it does and does not contain. Below is every SL formula, then the list of things the booklet leaves out that you must memorise.
Check against your own copy. This page follows the IB Analysis and Approaches formula booklet for first assessment 2021 onwards. The IB occasionally reissues the booklet with small layout changes — always use the version your school gives you, and tell Mr Ahmad if you spot a difference.
What is in the AA SL formula booklet — section by section
Numbered to match the syllabus sub-topics printed in the booklet. Only the SL sections are listed — HL-only entries in the same booklet are not examined at SL.
Prior learning
Area of a parallelogram
\(\displaystyle A = bh\)
Area of a triangle
\(\displaystyle A = \tfrac{1}{2}bh\)
Area of a trapezoid
\(\displaystyle A = \tfrac{1}{2}(a+b)h\)
Area and circumference of a circle
\(\displaystyle A = \pi r^2,\quad C = 2\pi r\)
Volume of a cuboid
\(\displaystyle V = lwh\)
Volume of a cylinder
\(\displaystyle V = \pi r^2 h\)
Volume of a prism
\(\displaystyle V = Ah\)
Curved surface area of a cylinder
\(\displaystyle A = 2\pi r h\)
Distance between two points
\(\displaystyle d = \sqrt{(x_1-x_2)^2 + (y_1-y_2)^2}\)
Midpoint
\(\displaystyle \left(\dfrac{x_1+x_2}{2},\ \dfrac{y_1+y_2}{2}\right)\)
Topic 1 — Number and algebra
1.2 Arithmetic sequence, nth term
\(\displaystyle u_n = u_1 + (n-1)d\)
1.2 Sum of an arithmetic sequence
\(\displaystyle S_n = \tfrac{n}{2}\big(2u_1 + (n-1)d\big) = \tfrac{n}{2}(u_1 + u_n)\)
1.3 Geometric sequence, nth term
\(\displaystyle u_n = u_1 r^{\,n-1}\)
1.3 Sum of a geometric sequence
\(\displaystyle S_n = \dfrac{u_1(r^n - 1)}{r-1} = \dfrac{u_1(1-r^n)}{1-r},\quad r \ne 1\)
1.4 Compound interest
\(\displaystyle FV = PV\left(1 + \dfrac{r}{100k}\right)^{kn}\)
1.5 Exponents and logarithms
\(\displaystyle a^x = b \iff x = \log_a b,\quad a>0,\ b>0,\ a\ne 1\)
1.7 Laws of logarithms
\(\displaystyle \log_a xy = \log_a x + \log_a y,\quad \log_a \dfrac{x}{y} = \log_a x - \log_a y,\quad \log_a x^m = m\log_a x\)
1.7 Change of base
\(\displaystyle \log_a x = \dfrac{\log_b x}{\log_b a}\)
1.8 Sum of an infinite geometric sequence
\(\displaystyle S_\infty = \dfrac{u_1}{1-r},\quad |r|<1\)
1.9 Binomial theorem
\(\displaystyle (a+b)^n = a^n + \binom{n}{1}a^{n-1}b + \cdots + \binom{n}{r}a^{n-r}b^r + \cdots + b^n\)
1.9 Binomial coefficient
\(\displaystyle \binom{n}{r} = \dfrac{n!}{r!\,(n-r)!}\)
Topic 2 — Functions
2.1 Equations of a straight line
\(\displaystyle y = mx + c;\quad ax + by + d = 0;\quad y - y_1 = m(x - x_1)\)
2.1 Gradient
\(\displaystyle m = \dfrac{y_2 - y_1}{x_2 - x_1}\)
2.6 Axis of symmetry of a quadratic
\(\displaystyle f(x) = ax^2 + bx + c \ \Rightarrow\ x = -\dfrac{b}{2a}\)
2.7 Solutions of a quadratic equation
\(\displaystyle x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a},\quad a \ne 0\)
2.7 Discriminant
\(\displaystyle \Delta = b^2 - 4ac\)
Topic 3 — Geometry and trigonometry
3.1 Distance between two points in 3D
\(\displaystyle d = \sqrt{(x_1-x_2)^2 + (y_1-y_2)^2 + (z_1-z_2)^2}\)
3.1 Midpoint in 3D
\(\displaystyle \left(\dfrac{x_1+x_2}{2},\ \dfrac{y_1+y_2}{2},\ \dfrac{z_1+z_2}{2}\right)\)
3.1 Volume of a right pyramid
\(\displaystyle V = \tfrac{1}{3}Ah\)
3.1 Volume and curved surface of a cone
\(\displaystyle V = \tfrac{1}{3}\pi r^2 h,\qquad A = \pi r l\)
3.1 Sphere
\(\displaystyle V = \tfrac{4}{3}\pi r^3,\qquad A = 4\pi r^2\)
3.2 Sine rule
\(\displaystyle \dfrac{a}{\sin A} = \dfrac{b}{\sin B} = \dfrac{c}{\sin C}\)
3.2 Cosine rule
\(\displaystyle c^2 = a^2 + b^2 - 2ab\cos C;\qquad \cos C = \dfrac{a^2 + b^2 - c^2}{2ab}\)
3.2 Area of a triangle
\(\displaystyle A = \tfrac{1}{2}ab\sin C\)
3.4 Length of an arc (radians)
\(\displaystyle l = r\theta\)
3.4 Area of a sector (radians)
\(\displaystyle A = \tfrac{1}{2}r^2\theta\)
3.5 Identity for tan
\(\displaystyle \tan\theta = \dfrac{\sin\theta}{\cos\theta}\)
3.6 Pythagorean identity
\(\displaystyle \cos^2\theta + \sin^2\theta = 1\)
3.6 Double angle identities
\(\displaystyle \sin 2\theta = 2\sin\theta\cos\theta;\quad \cos 2\theta = \cos^2\theta - \sin^2\theta = 2\cos^2\theta - 1 = 1 - 2\sin^2\theta\)
Topic 4 — Statistics and probability
4.2 Interquartile range
\(\displaystyle IQR = Q_3 - Q_1\)
4.3 Mean of a data set
\(\displaystyle \bar{x} = \dfrac{\sum_{i=1}^{k} f_i x_i}{n},\quad n = \sum_{i=1}^{k} f_i\)
4.5 Probability of an event
\(\displaystyle P(A) = \dfrac{n(A)}{n(U)}\)
4.5 Complementary events
\(\displaystyle P(A) + P(A') = 1\)
4.6 Combined events
\(\displaystyle P(A \cup B) = P(A) + P(B) - P(A \cap B)\)
4.6 Mutually exclusive events
\(\displaystyle P(A \cup B) = P(A) + P(B)\)
4.6 Conditional probability
\(\displaystyle P(A \mid B) = \dfrac{P(A \cap B)}{P(B)}\)
4.6 Independent events
\(\displaystyle P(A \cap B) = P(A)\,P(B)\)
4.7 Expected value of a discrete random variable
\(\displaystyle E(X) = \sum x\,P(X = x)\)
4.8 Binomial distribution
\(\displaystyle X \sim B(n,p):\quad E(X) = np,\qquad \text{Var}(X) = np(1-p)\)
4.12 Standardised normal variable
\(\displaystyle z = \dfrac{x - \mu}{\sigma}\)
Topic 5 — Calculus
5.3 Derivative of a power
\(\displaystyle f(x) = x^n \ \Rightarrow\ f'(x) = nx^{n-1}\)
5.5 Integral of a power
\(\displaystyle \int x^n\,dx = \dfrac{x^{n+1}}{n+1} + C,\quad n \ne -1\)
5.5 Area between a curve and the x-axis
\(\displaystyle A = \int_a^b y\,dx\)
5.6 Standard derivatives
\(\displaystyle \dfrac{d}{dx}\sin x = \cos x;\quad \dfrac{d}{dx}\cos x = -\sin x;\quad \dfrac{d}{dx}e^x = e^x;\quad \dfrac{d}{dx}\ln x = \dfrac{1}{x}\)
5.6 Chain rule
\(\displaystyle y = g(u),\ u = f(x) \ \Rightarrow\ \dfrac{dy}{dx} = \dfrac{dy}{du}\cdot\dfrac{du}{dx}\)
5.6 Product rule
\(\displaystyle y = uv \ \Rightarrow\ \dfrac{dy}{dx} = u\dfrac{dv}{dx} + v\dfrac{du}{dx}\)
5.6 Quotient rule
\(\displaystyle y = \dfrac{u}{v} \ \Rightarrow\ \dfrac{dy}{dx} = \dfrac{v\dfrac{du}{dx} - u\dfrac{dv}{dx}}{v^2}\)
5.9 Kinematics
\(\displaystyle v = \dfrac{ds}{dt};\quad a = \dfrac{dv}{dt} = \dfrac{d^2s}{dt^2};\quad \text{distance} = \int_{t_1}^{t_2}|v|\,dt;\quad \text{displacement} = \int_{t_1}^{t_2} v\,dt\)
5.10 Standard integrals
\(\displaystyle \int \dfrac{1}{x}\,dx = \ln|x| + C;\quad \int \sin x\,dx = -\cos x + C;\quad \int \cos x\,dx = \sin x + C;\quad \int e^x\,dx = e^x + C\)
5.11 Area between curve and x-axis (general)
\(\displaystyle A = \int_a^b |y|\,dx\)
Not in the booklet — you must memorise these
Students lose marks every session looking for things that were never there. Everything below is examinable in AA SL and absent from the booklet.
- Exact trigonometric values for \(0, \tfrac{\pi}{6}, \tfrac{\pi}{4}, \tfrac{\pi}{3}, \tfrac{\pi}{2}\) and the signs of sin, cos, tan in each quadrant
- Transformations of graphs: \(y = f(x) + k\), \(y = f(x - h)\), \(y = pf(x)\), \(y = f(qx)\), reflections in the axes
- Laws of exponents, factorising, completing the square, and the graphs of \(y = \dfrac{1}{x}\), \(y = e^x\), \(y = \ln x\)
- Properties of \(\ln\) and \(e\): \(e^{\ln x} = x\), \(\ln e^x = x\), \(\ln 1 = 0\), \(\ln e = 1\)
- Composite and inverse functions: \((f\circ g)(x) = f(g(x))\), finding \(f^{-1}\) by swapping \(x\) and \(y\)
- Derivative from first principles: \(f'(x) = \lim_{h\to 0}\dfrac{f(x+h)-f(x)}{h}\)
- The second derivative test and what \(f''(x) = 0\) does and does not tell you about points of inflexion
- Integration by substitution (the method is not written out in the booklet)
- Normal distribution shape, symmetry, and using inverse normal on the GDC
- Sampling methods, the meaning of correlation vs causation, and reading a box plot
The 10 formulas AA SL students use most
From marking hundreds of practice papers: these come up in almost every exam. Know their page in the booklet and what each symbol means.
- \(\displaystyle x = \dfrac{-b \pm \sqrt{b^2-4ac}}{2a}\)Quadratic formula — and the discriminant \(b^2 - 4ac\) for 'show the equation has two real roots' questions.
- \(\displaystyle \dfrac{a}{\sin A} = \dfrac{b}{\sin B}\)Sine rule — two angles and a side, or two sides and a non-included angle.
- \(\displaystyle c^2 = a^2 + b^2 - 2ab\cos C\)Cosine rule — two sides and the included angle; rearrange to find an angle from three sides.
- \(\displaystyle \binom{n}{r}a^{n-r}b^r\)General term of the binomial expansion — the standard Paper 1 'find the coefficient' question.
- \(\displaystyle S_n = \dfrac{u_1(1-r^n)}{1-r}\)Sum of a geometric series — use with \(S_\infty\) for 'how many terms until the sum exceeds…' questions.
- \(\displaystyle \dfrac{dy}{dx} = \dfrac{dy}{du}\cdot\dfrac{du}{dx}\)Chain rule — anything composite: \(e^{3x}\), \(\sin(2x)\), \((x^2+1)^5\).
- \(\displaystyle A = \int_a^b y\,dx\)Area under a curve — set up with the correct limits, and use \(|y|\) when the curve goes below the axis.
- \(\displaystyle P(A \mid B) = \dfrac{P(A \cap B)}{P(B)}\)Conditional probability — tree diagrams and 'given that' questions.
- \(\displaystyle E(X) = np,\quad \text{Var}(X) = np(1-p)\)Binomial distribution — identify \(n\) and \(p\) from the context before touching the GDC.
- \(\displaystyle z = \dfrac{x-\mu}{\sigma}\)Standardised normal — needed whenever the mean or standard deviation is the unknown.
How to use the booklet, paper by paper
Paper 1 (no calculator)
The booklet carries the algebra and the calculus: binomial expansion, log laws, double-angle identities, standard derivatives and integrals. Tab these pages in your practice copy — you will need them under time pressure.
Paper 2 (calculator)
Statistics, probability and modelling. The formulas for expected value, binomial mean and variance, and the standardised normal are in the booklet; the GDC steps are not. Practise the GDC routines until they are automatic.
AA SL formula booklet — common questions
Is the AA SL formula booklet different from the AA HL one?
It is the same booklet. SL students use the sections without the HL label; HL students use everything. The AI courses have their own booklet.
Formula booklet or data booklet — which is right?
The IB calls it the formula booklet. Schools and students often say data booklet. Same document.
Can I take my own copy into the exam?
No — a clean copy is given out with each paper. Use an annotated copy only for practice.
Are the trig exact values in the booklet?
No. The unit-circle values for \(\tfrac{\pi}{6}, \tfrac{\pi}{4}, \tfrac{\pi}{3}\) must be memorised, and Paper 1 tests them.
Where do I get the official booklet?
From your school's IB coordinator — the IB publishes it in the Programme Resource Centre. Always use the version your school issues.
Want the booklet to feel like second nature?
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