SL AI Formula Booklet — Applications & Interpretation SL

All 46 formulas you need for IB Mathematics Applications & Interpretation 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 AI questions
Prior 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
\(A = \pi r^2\)
Circumference of a circle
\(C = 2\pi r\)
Volume of a cuboid
\(V = l \cdot w \cdot h\)
Volume of a cylinder
\(V = \pi r^2 h\)
Volume of a prism
\(V = A \cdot h \quad (A = \text{cross-section area})\)
Area of curved surface of cylinder
\(A = 2\pi r h\)
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
\(S_n = \frac{u_1(r^n - 1)}{r - 1} = \frac{u_1(1 - r^n)}{1 - r},\ r \ne 1\)
Compound interest
\(FV = PV\left(1 + \frac{r}{100k}\right)^{kn}\)
Exponents
\(a^p \cdot a^q = a^{p+q},\quad \frac{a^p}{a^q} = a^{p-q},\quad (a^p)^q = a^{pq}\)
Logarithms — power law
\(\log_a(x^n) = n \log_a x\)
% error
\(\varepsilon = \left|\frac{v_A - v_E}{v_E}\right| \times 100\%\)

Topic 2 — Functions

Equation of a straight line
\(y = mx + c \quad\text{or}\quad ax + by + d = 0\)
Gradient of a straight line
\(m = \dfrac{y_2 - y_1}{x_2 - x_1}\)
Axis of symmetry of a quadratic
\(x = -\dfrac{b}{2a}\)

Topic 3 — Geometry & Trigonometry

Length of an arc
\(\ell = 2\pi r \cdot \dfrac{\theta}{360^\circ}\)
Area of a sector
\(A = \pi r^2 \cdot \dfrac{\theta}{360^\circ}\)
Surface area of a sphere
\(A = 4\pi r^2\)
Volume of a sphere
\(V = \tfrac{4}{3}\pi r^3\)
Volume of a cone
\(V = \tfrac{1}{3}\pi r^2 h\)
Curved surface area of a cone
\(A = \pi r l\)
Volume of a pyramid
\(V = \tfrac{1}{3} A_{\text{base}} \cdot h\)
Right-angled triangle (SOHCAHTOA)
\(\sin\theta = \tfrac{O}{H},\ \cos\theta = \tfrac{A}{H},\ \tan\theta = \tfrac{O}{A}\)
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 (SAS)
\(A = \tfrac{1}{2}ab\sin C\)

Topic 4 — Statistics & Probability

Interquartile range
\(\mathrm{IQR} = Q_3 - Q_1\)
Mean of a data set
\(\bar{x} = \dfrac{\sum_{i=1}^{n} f_i x_i}{n}, \quad n = \sum f_i\)
Probability of an event
\(P(A) = \dfrac{n(A)}{n(U)}\)
Complementary events
\(P(A') = 1 - P(A)\)
Combined events
\(P(A \cup B) = P(A) + P(B) - P(A \cap B)\)
Mutually exclusive events
\(P(A \cap B) = 0\)
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)
\(E(X) = \sum x \, P(X=x)\)

Topic 5 — Calculus

Derivative of x^n
\(f(x) = x^n \implies f'(x) = n x^{\,n-1}\)
Integral of x^n
\(\int x^n \, dx = \dfrac{x^{n+1}}{n+1} + C, \quad n \ne -1\)
Area between curve and x-axis
\(A = \int_a^b y\, dx\)
Trapezoidal rule (approx. area)
\(A \approx \tfrac{h}{2}\bigl(y_0 + y_n + 2(y_1 + y_2 + \cdots + y_{n-1})\bigr),\ h = \dfrac{b-a}{n}\)

Other courses: SL AA formulas · HL AI formulas · HL AA formulas · SL AI revision notes · SL AI questions by topic