Syllabus
This year’s course structure
The course runs over roughly 60 sessions, organized into eight sections followed by a final review. Each section builds on the one before it and ends with a mock assessment in the style of the Feststellungsprüfung. From the first full-length mock onwards, dedicated sessions practice the oral examination format in small groups.
Section 1: Foundations & Algebra
Mathematical language and notation, number systems, and core algebra: fractions and percentages, manipulating terms, and working with exponents, radicals, and logarithms.
Section 2: Equations
Solving equations and systems of equations, from linear and quadratic to fractional and more complex types, together with the methods behind each.
Section 3: Functions
The function concept and the main families, including linear and quadratic functions, with transformations and inverses.
Section 4: Advanced Functions
Polynomial, power, exponential, rational, and trigonometric functions, and how to analyse their behaviour.
Section 5: Differential Calculus
Limits and derivatives through to the differentiation rules, curve sketching, and parameterised function families (Funktionsscharen).
Section 6: Integral Calculus
Antiderivatives and definite integrals, area problems, and integration by parts, with applications.
Section 7: Probability & Statistics
Descriptive statistics and probability: combinatorics, conditional probability and Bayes, contingency tables, and the binomial distribution.
Section 8: Financial Mathematics
Interest, annuities, and cost analysis in business contexts.
Final Review
Consolidation across functions, calculus, integrals, and probability, with mock-exam practice for the Feststellungsprüfung.
Attendance
Attendance is tracked with points per session: arriving on time earns 2 points, arriving late earns 1 point, and missing a session earns 0 points. The 75% requirement is measured against these points: your points divided by the maximum achievable points must be at least 75%.
Prerequisites
Students should have completed secondary-level mathematics or equivalent preparation, including arithmetic with real numbers, algebraic manipulation, elementary geometry, coordinates and graphing, and an understanding of mathematical symbols and notation. Students uncertain of their foundations are encouraged to do preparatory work before starting.
Required Materials
- Moodle course site access
- This course website
- Scientific calculator (Casio FX-991DE X; calculator use is taught inside the sessions)
- Notebook or tablet to access the course content