IB Math AI SL — Formula Booklet
Every formula printed in your official IB formula booklet, organised by topic. Knowing which formulas you're given frees up mental space to memorise what isn't here.
★ Must memorise — NOT in the booklet
- • Rounding & significant figures rules
- • Laws of logarithms (log(ab) = log a + log b; log(aⁿ) = n log a; etc.)
- • Domain and range reasoning
- • Increasing / decreasing function tests from derivatives
- • Interpolation vs extrapolation distinction
- • Spearman's rank correlation formula — not in the booklet despite being assessed
- • Voronoi diagram construction steps
GDC workflows (Chi-squared, Finance Solver, linear regression) do not require you to recall a formula — your calculator computes them.
Prior Learning
Distance between two points (2D)
3.1
Straight-line distance between two points in the coordinate plane
Midpoint of a line segment
3.1
Coordinates of the midpoint between two points
Area of a triangle
3.2
Area = ½ × base × perpendicular height
Area of a parallelogram
Area = base × perpendicular height
Area of a trapezoid
Area = ½ × (sum of parallel sides) × height
Circumference of a circle
Perimeter of a circle
Area of a circle
Area enclosed by a circle of radius r
Volume of a cuboid
Volume = length × width × height
Volume of a cylinder
Volume of a right circular cylinder
Volume of a prism
Volume = cross-sectional area × length/height
Area of curved surface of a cylinder
Lateral surface area of a cylinder with radius r and height h
Topic 1: Number & Algebra
Arithmetic sequence — nth term
1.2
The nth term of an arithmetic sequence with first term u₁ and common difference d
Arithmetic series — sum of n terms
1.2
Sum of the first n terms of an arithmetic series
Geometric sequence — nth term
1.3
The nth term of a geometric sequence with first term u₁ and common ratio r
Geometric series — sum of n terms
1.3
Sum of the first n terms of a geometric series (r ≠ 1)
Compound interest
1.4, 1.7
Future value of an investment with annual interest rate r%, compounded k times per year for n years
Logarithm definition
1.5
Definition connecting exponential and logarithm forms
Percentage error
1.6
Percentage error where vA is approximate value and vE is exact value
Topic 2: Functions
Equations of a straight line
2.1
Standard forms of a straight line
Gradient between two points
2.1
Gradient (slope) of the line through two points
Equation of a line (point-slope)
2.1
Line through point (x₁, y₁) with gradient m
Axis of symmetry of a quadratic
2.5
x-coordinate of the vertex of y = ax² + bx + c
Topic 3: Geometry & Trigonometry
Distance between two points (3D)
3.1
Straight-line distance between two points in 3D space
Midpoint in 3D
3.1
Midpoint of a line segment in 3D space
Volume of a right pyramid
3.1
Volume of a right pyramid with base area A and height h
Volume of a right cone
3.1
Volume of a right cone with radius r and height h
Area of curved surface of a cone
3.1
Lateral surface area of a cone with radius r and slant height l
Volume of a sphere
3.1
Volume of a sphere with radius r
Surface area of a sphere
3.1
Total surface area of a sphere with radius r
Sine rule
3.2
Relates each side of a triangle to the sine of the opposite angle
Cosine rule — finding a side
3.2
Finds side c given sides a, b and included angle C
Cosine rule — finding an angle
3.2
Finds angle C given all three sides a, b, c
Area of a triangle (trig)
3.2
Area of a triangle given two sides and the included angle
Arc length
3.4
Length of an arc with central angle θ° in a circle of radius r
Area of a sector
3.4
Area of a sector with central angle θ° in a circle of radius r
Topic 4: Statistics & Probability
Interquartile range
4.2
Spread of the middle 50% of data
Mean of a frequency distribution
4.3
Weighted mean where fᵢ is the frequency of value xᵢ
Probability of an event
4.5
Probability = (favourable outcomes) / (total outcomes) in a uniform sample space
Complementary events
4.5
The probabilities of an event and its complement sum to 1
Addition rule
4.6
Probability of A or B (or both)
Mutually exclusive events
4.6
When A and B cannot both occur
Conditional probability
4.6
Probability of A given that B has already occurred
Independent events
4.6
If A and B are independent, their joint probability is the product of their probabilities
Expected value of a discrete distribution
4.7
Long-run average value of a discrete random variable
Binomial distribution — mean
4.8
Expected value of X ~ B(n, p)
Binomial distribution — variance
4.8
Variance of X ~ B(n, p)
Topic 5: Calculus
Power rule (differentiation)
5.1, 5.3
Derivative of a power function
Integration of a power function
5.5
Indefinite integral of xⁿ (n ≠ −1)
Area under a curve (definite integral)
5.5
Signed area between f(x) and the x-axis from a to b
Trapezoidal rule
5.8
Numerical approximation of a definite integral using trapezoids
Source: IB Diploma Programme Mathematics: applications and interpretation — Formula booklet (first examinations 2021). Always verify against your official IB materials.