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Topics

The structure the problems are ordered by. It does not say which topic is examinable in which German state — that is stated on each product.

§019 topics

Calculus

The behaviour of functions: how they change, where they reach extremes, and what area or volume lies beneath them.

  • Functions and their properties
  • Limits and continuity
  • DerivativesRules of differentiation, higher derivatives, implicit differentiation
  • Curve analysisRoots, monotonicity, extrema, concavity, inflection points, asymptotes
  • IntegrationAntiderivatives, definite integrals, substitution, integration by parts
  • Areas and volumes of revolution
  • Applied problemsOptimisation, growth and decay, quantity and rate of change
  • Families of functions
  • Differential equationsPart of some syllabuses only. Each product states its curriculum reference.

§0211 topics

Analytic geometry

Lines, planes and solids in space described by vectors — and how they are positioned relative to one another.

  • Vectors and vector arithmetic
  • Lines in space
  • PlanesParametric, normal and coordinate form, and converting between them
  • Relative positionPoint, line, plane — parallel, intersecting, skew, coincident
  • Systems of linear equations
  • Dot productOrthogonality, angles between vectors
  • Cross productPart of some syllabuses only. Each product states its curriculum reference.
  • DistancesPoint–line, point–plane, line–line, line–plane
  • Angles
  • Areas and volumes of solids
  • SpheresPart of some syllabuses only. Each product states its curriculum reference.

§037 topics

Probability and statistics

How likely an outcome is, how outcomes are distributed, and when an observation counts as evidence against an assumption.

  • ProbabilityEqually likely outcomes, tree diagrams, two-way tables, conditional probability
  • Counting methods
  • Random variables, expectation, variance
  • Binomial distribution
  • Normal distributionPart of some syllabuses only. Each product states its curriculum reference.
  • Hypothesis testingOne- and two-tailed tests, type I and type II errors
  • Confidence intervalsPart of some syllabuses only. Each product states its curriculum reference.