IB Maths Formula Sheet
Built by Pietro Meloni, PhD in Physics · 10+ Years Teaching IGCSE
IB DP · 13 formulas · 4 sections
The essential formulas for IB Mathematics, covering both Analysis and Approaches (AA) and Applications and Interpretation (AI) at SL and HL levels.
While IB provides a formula booklet in the exam, understanding these formulas deeply saves time and reduces errors under pressure.
Download the formula booklet
Free printable PDFs, SL and HL separate, no sign-up. Updated .
Analysis and Approaches (AA)
Applications and Interpretation (AI)
Re-typeset from the official IB formula booklets, first examinations 2021, with SL and HL content separated. Not an official IB publication: in the exam you are given the official booklet. All IB formula booklets, and the errors in the official ones.
Algebra and Functions
Quadratic formula
…Given in the formula booklet. The discriminant Δ = b² − 4ac determines the nature of roots.
Binomial theorem
…Expands any binomial to a positive integer power. The coefficients come from Pascal's triangle or the nCr function.
Arithmetic series sum
…Sum of an arithmetic sequence with first term a, common difference d, and n terms.
Geometric series sum
…Sum of a geometric sequence. For |r| < 1, the infinite sum converges to a/(1−r).
Calculus
Power rule
…The foundation of differentiation. Bring the power down and reduce it by one.
Chain rule
…For differentiating composite functions. Essential for HL and AA students.
Integration (power)
…The reverse of differentiation. Don't forget the constant of integration C for indefinite integrals.
Statistics and Probability
Mean
…Sum of all values divided by the count. For grouped data, use midpoints.
Standard deviation
…Measures spread around the mean. Your GDC can calculate this, but you need to interpret it.
Conditional probability
…The probability of A given that B has occurred. Rearranges to P(A∩B) = P(A|B) × P(B).
Trigonometry and Geometry
Sine rule
…Use for non-right triangles when you have a side-angle pair.
Cosine rule
…Use for SAS or SSS triangle problems.
Volume of revolution
…HL/AA only. Rotates the curve around the x-axis to form a solid of revolution.
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