Studienkolleg
The Feststellungsprüfung (FSP, assessment test) is the final exam of the Studienkolleg. Passing it gives you access to the degrees that match your course anywhere in Germany, at universities or universities of applied sciences depending on the Kolleg. It usually comes after two semesters.
Each Kolleg sets its subjects. At Studienkolleg Frankfurt they are:
Saxony's FSP regulations give one state's example: three subjects are written, each written exam takes 180 minutes (German can differ), and at least one subject is oral, for up to 30 minutes. Grades run from 1 (very good) to 5 (not sufficient), and you pass when every subject is at least 4 (sufficient).
Under Saxony's rules you can repeat the FSP once, as a whole, at the same Kolleg after at least one more semester; a second fail is final. The DAAD notes that you can also prepare privately and sit the FSP as an external candidate, but places for external candidates are often limited. Studienkolleg Frankfurt holds the FSP twice a year.
Maths is examined in the T, M and W courses, and it goes far beyond the entrance test. The units below are the course syllabus Kollego teaches for each course. Every Kolleg sets its own syllabus, so check yours.
FSP subjects at Studienkolleg Frankfurt: German, Mathematics, Computer science, Chemistry, Physics
Sample tasks at course level
1. Evaluate the limit (the expression is 0/0 at x = 5, so factor and cancel first): lim(x→5) (x² − 2x − 15) / (x − 5)
Answer: 8
Factor the numerator into (x − a)(x − b); the (x − a) factor cancels with the denominator, removing the singularity.
x² − 2x − 15 = (x − 5)(x + 3). Cancel (x − 5): lim = 5 + 3 = 8.
2. a = (5, 1, 5) b = (2, 2, 0) What is the y-component of a + b?
Answer: 3
Vectors are added or subtracted component by component: (a + b)_y = a_y + b_y.
1 + 2 = 3.
3. Evaluate ∫₀¹ 4x·eˣ dx
Answer: 4
By parts with u = x, dv = eˣ dx: ∫x·eˣ dx = (x − 1)eˣ + C. At x = 1 the bracket is 0; at x = 0 it is −1.
[4(x − 1)eˣ]₀¹ = 4·0 − 4·(−1) = 4.
FSP subjects at Studienkolleg Frankfurt: German, Mathematics, Biology, Chemistry, Physics
Sample tasks at course level
1. A fruit stand recorded sales by type: Grapes: 36 Dates: 2 Cherries: 9 Pears: 3 What percentage of all sales were Pears?
Answer: 6%
Percentage of a category = (category count ÷ total count) × 100.
3 / 50 × 100 = 6%.
2. f(x) = 3·2ˣ. What is f(2)?
Answer: 12
Exponential growth: raise the base to the power, then multiply by the front coefficient.
3·2² = 3·4 = 12.
3. f(x) = (x + 1)² What is f′(3)?
Answer: 8
Chain rule: d/dx[u(x)ⁿ] = n·u(x)ⁿ⁻¹·u′(x). Here u(x) = mx + c, so u′(x) = m.
u(3) = 4. f′(x) = 2·u(x)¹·1. f′(3) = 2·4¹·1 = 8.
FSP subjects at Studienkolleg Frankfurt: German, Mathematics, Economics, Sociology or geography
Sample tasks at course level
1. A geometric sequence starts 1, 2, 4, … What is the 6th term?
Answer: 32
aₙ = a₁ · rⁿ⁻¹.
1·2⁶⁻¹ = 1·32 = 32.
2. f(x) = x² − 2x + 5. What is the x-coordinate of the vertex?
Answer: 1
For x² + bx + c the vertex is at x = −b / 2.
x = −(-2) / 2 = 1.
3. Find the median of: 9, 23, 11, 10, 5, 7, 11
Answer: 10
Sort the values; the median is the middle one (for an odd count).
Sorted: 5, 7, 9, 10, 11, 11, 23. The middle value is 10.
G-Kurs: FSP subjects at Studienkolleg Frankfurt are German, History, German literature, Sociology or geography. G-Kurs guide
Feststellungsprüfung, the assessment test at the end of the Studienkolleg.
According to the DAAD, passing it allows access to studies throughout Germany in the subject area of your course. Check that your target university accepts the FSP of your Kolleg.
Yes, as an external candidate at some Kollegs, but places are often limited.
Rules differ by state. Under Saxony's regulations you can repeat it once; a second fail is final.
One diagnostic, a projected score, and your first unit. No card, no time limit on the free tier.
Start free, no card needed