Abitur Mathematics study guide
Abitur Mathematics · Work through your exam, one topic at a time.
The Abitur is the German university entrance qualification, awarded after passing the final examinations of the gymnasiale Oberstufe. Mathematics is one of the two mandatory advanced-level subjects (Leistungsfächer) in most states, so the written Abitur examination in mathematics carries particular weight. The exam is set centrally by each state ministry and typically covers three broad content areas: Analysis (functions, derivatives, integrals, curve sketching), Analytic Geometry and Linear Algebra (vectors, lines, planes, distances, matrices), and Stochastics (probability, binomial and normal distributions, hypothesis testing), with modelling and problem-solving woven throughout. Preparation should be built around your state's official curriculum (Bildungsplan or Kerncurriculum) and the task formats used in past years. The Abitur Mathematics study guide has 4 sections and about 1,771 words.
01Analysis: functions, derivatives and integrals
Analysis is the heaviest block of the written Abitur paper. You must sketch and discuss function families (polynomial, exponential, rational, trigonometric), justify monotonicity and curvature with derivatives, and compute areas and volumes with integrals.
430 words, about 2 min02Analytic geometry and linear algebra: vectors, lines, planes, matrices
Vektorgeometrie and lineare Algebra in the Abitur: describing points, lines and planes in vector form, deciding their relative position (Lagebeziehung), computing angles and distances, and using matrices for transformations or for solving linear systems. Typical tasks ask for a proof (e.g.
458 words, about 2 min03Stochastics: binomial and normal distributions, hypothesis testing
Stochastics in the Abitur covers Bernoulli chains and the binomial distribution, expected value and standard deviation, the normal approximation, and one- or two-sided hypothesis tests on a proportion p. Contexts are quality control, surveys, medical tests and games; the arithmetic is done with the allowed calculator, so marks are lost on setting up the model, not on multiplying.
458 words, about 2 min04Mathematical modelling and problem solving in applied contexts
Modelling tasks wrap the other three domains in a real context: a tank, a population, a drug concentration, a production process. You must choose a function type, fit its parameters to given data, work with it, and - this is where the marks are - interpret every result back in the situation, including units and the limits of the model.
425 words, about 2 min