SL AA Formula Booklet — Analysis & Approaches SL
All 53 formulas you need for IB Mathematics Analysis & Approaches SL, grouped by syllabus topic and written in the same notation as the official IB formula booklet. Use it to revise which formulas are given in the exam, and which you still need to understand how to apply.
Open the print-ready one-page booklet → Practise SL AA questionsPrior learning · Topic 1 — Number & Algebra · Topic 2 — Functions · Topic 3 — Geometry & Trigonometry · Topic 4 — Statistics & Probability · Topic 5 — Calculus
Prior learning
- Area of a parallelogram
- \(A = b \cdot h\)
- Area of a triangle
- \(A = \tfrac{1}{2}(b \cdot h)\)
- Area of a trapezium
- \(A = \tfrac{1}{2}(a+b) h\)
- Area of a circle
- \(A = \pi r^2\)
- Volume of a cuboid
- \(V = l w h\)
- Volume of a cylinder
- \(V = \pi r^2 h\)
- Distance between two points
- \(d = \sqrt{(x_1-x_2)^2 + (y_1-y_2)^2}\)
- Midpoint of two points
- \(\left(\tfrac{x_1+x_2}{2},\ \tfrac{y_1+y_2}{2}\right)\)
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
- \(S_n = \tfrac{n}{2}\bigl(2u_1 + (n-1)d\bigr) = \tfrac{n}{2}(u_1 + u_n)\)
- The n-th term of a geometric sequence
- \(u_n = u_1 \cdot r^{\,n-1}\)
- Sum of n terms of a geometric sequence
- \(S_n = \frac{u_1(r^n - 1)}{r - 1},\ r \ne 1\)
- Infinite geometric series
- \(S_\infty = \dfrac{u_1}{1 - r},\ |r| < 1\)
- Compound interest
- \(FV = PV\left(1 + \frac{r}{100k}\right)^{kn}\)
- Exponents & logs (change of base)
- \(\log_a x = \dfrac{\log_b x}{\log_b a}\)
- Product / quotient / power laws
- \(\log_a(xy) = \log_a x + \log_a y,\ \log_a\!\tfrac{x}{y} = \log_a x - \log_a y,\ \log_a(x^n) = n\log_a x\)
- Binomial theorem
- \((a+b)^n = \sum_{k=0}^{n}\binom{n}{k} a^{n-k} b^{k},\quad \binom{n}{k} = \dfrac{n!}{k!(n-k)!}\)
Topic 2 — Functions
- Equation of a straight line
- \(y - y_1 = m(x - x_1)\)
- Gradient
- \(m = \dfrac{y_2 - y_1}{x_2 - x_1}\)
- Axis of symmetry of a quadratic
- \(x = -\dfrac{b}{2a}\)
- Quadratic formula
- \(x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}\)
- Discriminant
- \(\Delta = b^2 - 4ac\)
- Sum & product of roots (quadratic)
- \(\text{sum} = -\tfrac{b}{a},\quad \text{product} = \tfrac{c}{a}\)
Topic 3 — Geometry & Trigonometry
- Arc length (radians)
- \(\ell = r\theta\)
- Area of a sector (radians)
- \(A = \tfrac{1}{2} r^2 \theta\)
- Sine rule
- \(\dfrac{a}{\sin A} = \dfrac{b}{\sin B} = \dfrac{c}{\sin C}\)
- Cosine rule
- \(c^2 = a^2 + b^2 - 2ab\cos C\)
- Area of a triangle
- \(A = \tfrac{1}{2}ab\sin C\)
- Pythagorean identity
- \(\sin^2\theta + \cos^2\theta = 1\)
- Double-angle: sine
- \(\sin 2\theta = 2\sin\theta\cos\theta\)
- Double-angle: cosine
- \(\cos 2\theta = \cos^2\theta - \sin^2\theta = 2\cos^2\theta - 1 = 1 - 2\sin^2\theta\)
- Tangent from sine & cosine
- \(\tan\theta = \dfrac{\sin\theta}{\cos\theta}\)
Topic 4 — Statistics & Probability
- Interquartile range
- \(\mathrm{IQR} = Q_3 - Q_1\)
- Mean of a data set
- \(\bar{x} = \dfrac{\sum f_i x_i}{n},\ n = \sum f_i\)
- Probability of an event
- \(P(A) = \dfrac{n(A)}{n(U)}\)
- Complementary events
- \(P(A') = 1 - P(A)\)
- Combined events
- \(P(A \cup B) = P(A) + P(B) - P(A \cap B)\)
- Conditional probability
- \(P(A \mid B) = \dfrac{P(A \cap B)}{P(B)}\)
- Independent events
- \(P(A \cap B) = P(A)P(B)\)
- Expected value (discrete)
- \(E(X) = \sum x P(X=x)\)
- Binomial distribution
- \(X \sim B(n,p) \implies P(X=r) = \binom{n}{r} p^r (1-p)^{n-r}\)
- Mean & variance of a binomial
- \(E(X) = np,\quad \mathrm{Var}(X) = np(1-p)\)
- Standardising a normal variable
- \(Z = \dfrac{X - \mu}{\sigma}\)
Topic 5 — Calculus
- Derivative of x^n
- \(\dfrac{d}{dx}\bigl(x^n\bigr) = n x^{\,n-1}\)
- Chain rule
- \(\dfrac{dy}{dx} = \dfrac{dy}{du} \cdot \dfrac{du}{dx}\)
- Product rule
- \((uv)' = u'v + uv'\)
- Quotient rule
- \(\left(\dfrac{u}{v}\right)' = \dfrac{u'v - uv'}{v^2}\)
- Derivatives of standard functions
- \(\dfrac{d}{dx}(\sin x) = \cos x,\ \dfrac{d}{dx}(\cos x) = -\sin x,\ \dfrac{d}{dx}(\tan x) = \sec^2 x\)
- Exponential & log derivatives
- \(\dfrac{d}{dx}(e^x) = e^x,\ \dfrac{d}{dx}(\ln x) = \dfrac{1}{x}\)
- Integral of x^n
- \(\int x^n\, dx = \dfrac{x^{n+1}}{n+1} + C,\ n \ne -1\)
- Standard integrals
- \(\int \sin x\, dx = -\cos x + C,\ \int \cos x\, dx = \sin x + C,\ \int e^x\, dx = e^x + C,\ \int \dfrac{1}{x}\, dx = \ln|x| + C\)
- Area between a curve and the x-axis
- \(A = \int_a^b y\, dx\)
- Volume of revolution (about x-axis)
- \(V = \pi \int_a^b y^2\, dx\)
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