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📐Group 5 — Mathematics

Mathematics: Analysis & Approaches

HL AvailableSL Available

Full IB Maths AA syllabus — algebra, functions, geometry, statistics and calculus. All formulas, proofs, and HL extensions from complex numbers to differential equations.

440
Total Cards
5
Topics Covered
260
HL Cards
180
SL Cards

Full Syllabus Coverage

Every topic in the official IB Subject Guide — nothing missed.

Topic 1 — Algebra
  • Arithmetic sequences and series: un = u1 + (n−1)d; Sn = n/2(2u1 + (n−1)d)
  • Geometric sequences and series: un = u1·rⁿ⁻¹; Sn = u1(rⁿ−1)/(r−1)
  • Infinite geometric series: S∞ = u1/(1−r) for |r| < 1
  • Sigma notation
  • Exponents and logarithms: laws, change of base, natural log
  • The binomial theorem: (a+b)ⁿ expansion, binomial coefficients
  • Proof by induction (HL)
  • Complex numbers (HL): Cartesian form, modulus-argument, De Moivre's theorem, roots of unity
  • Systems of linear equations: row reduction, Gaussian elimination (HL)
Topic 2 — Functions
  • Concept of a function: domain, range, mapping
  • Composite functions and inverse functions
  • Transformations: translation, reflection, stretch
  • Linear functions; quadratic functions; discriminant
  • Rational functions; reciprocal functions
  • Exponential and logarithmic functions; natural exponential e
  • Odd and even functions
  • Partial fractions (HL)
Topic 3 — Geometry and Trigonometry
  • Radian measure; arc length s = rθ; sector area A = ½r²θ
  • Unit circle: sin, cos, tan for all angles
  • Pythagorean identity: sin²θ + cos²θ = 1
  • Compound angle identities; double angle formulas
  • Solving trigonometric equations
  • Sine rule and cosine rule
  • Vectors in 2D and 3D: addition, scalar multiplication, dot product, angle between vectors
  • Equation of a line in vector form
  • Vector cross product (HL); equation of a plane (HL)
  • Eigenvalues and eigenvectors (HL)
Topic 4 — Statistics and Probability
  • Statistical measures: mean, median, mode, range, IQR, standard deviation
  • Data presentation: frequency tables, histograms, box-and-whisker plots, cumulative frequency
  • Correlation and regression: Pearson's r, least squares regression line
  • Set theory: union, intersection, complement, Venn diagrams
  • Probability: addition rule, conditional probability, Bayes' theorem (HL)
  • Discrete random variables: expected value E(X), variance Var(X)
  • Binomial distribution: X ~ B(n, p)
  • Normal distribution: X ~ N(μ, σ²), standard normal Z-scores
  • Hypothesis testing: null/alternative hypothesis, p-value, Type I/II errors (HL)
Topic 5 — Calculus
  • Limits and continuity: limit notation, L'Hôpital's rule (HL)
  • Differentiation from first principles
  • Standard derivatives: xⁿ, eˣ, ln x, sin x, cos x, tan x
  • Product rule, quotient rule, chain rule
  • Applications of differentiation: tangents, normals, optimisation, rates of change
  • Integration: indefinite and definite integrals
  • Standard integrals; integration by substitution
  • Integration by parts (HL)
  • Volumes of revolution (HL)
  • Differential equations: separation of variables; slope fields (HL)
  • Maclaurin series (HL): eˣ, sin x, cos x, ln(1+x)

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