Studienkolleg Math Syllabus: The Topics That Show Up Most

The Studienkolleg math syllabus is broadly consistent across institutions, even though individual Kollegs vary in emphasis and difficulty. Here's the real topic list — T-Kurs's full syllabus, and where M-Kurs's narrower one diverges.

T-Kurs: the full syllabus

• Numbers, terms and equations
• Functions
• Sequences and series
• Trigonometry
• Geometry
• Differential calculus
• Integral calculus
• Vectors and analytic geometry
• Statistics and probability
• Complex numbers (taught at some Kollegs, not tested in the centralised exams)

This is the superset most T-Kurs Aufnahmeprüfungen draw from — your specific Kolleg's exam will emphasize some of these more than others, which is why getting your target Kolleg's past papers matters once you've covered the full list.

M-Kurs: T-Kurs minus its hardest section, plus statistics

M-Kurs drops the heaviest topics — typically vectors and analytic geometry, and lighter integral calculus — while keeping statistics and probability, which matters more for medical and biological data interpretation than for engineering.

What tends to carry the most weight

Algebra (numbers, terms and equations) and functions are foundational to nearly every later topic — sequences, calculus, and trigonometry all lean on algebraic manipulation and function notation. Weakness here compounds into every topic that follows, which is why it's usually the highest-leverage place to start if your algebra is shaky.

For the centralised state exams specifically: Bayern's T-Kurs and M-Kurs exams appear to weight algebra, functions, and geometry somewhat more heavily than a generic Kolleg syllabus, based on available sample material — though this weighting is provisional pending fuller reconciliation against official past papers, and shouldn't be treated as a firm guarantee of what any single sitting will emphasize.

German runs alongside math, not after it

Every Studienkolleg entrance exam also tests German — a C-Test at minimum, sometimes grammar, reading, or listening components too, depending on the Kolleg. Treat German preparation as a parallel track from day one, not something to pick up after math is solid — a strong math score doesn't offset a weak C-Test result.

Check your own readiness

Rate yourself against the real T-Kurs or M-Kurs topic list — free readiness check, no signup — or see the full T-Kurs and M-Kurs breakdowns.

Source: studienkolleg.org's math topics guide.