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100+ Free Schleswig-Holstein Abitur Math Practice Questions

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2026 Statistics

Key Facts: Schleswig-Holstein Abitur Math Exam

300 min

Total Bearbeitungszeit for the written Mathematik Kernfach exam: HMF/Teil A max 100 min, then Komplexteil/Teil B 200 min

IQSH Fachfortbildung, Die schriftliche Abiturprüfung Mathematik im erhöhten Anforderungsniveau ab 2024 (za.schleswig-holstein.de)

06.05.2026

Written Mathematik Kernfach exam date in the 2026 main session; mündliche Prüfungen 15.-26.06.2026

za.schleswig-holstein.de Terminplan Abitur 2026 (via profiling-institut.de, stark-verlag.de)

40 / 25 / 25 BE

Sachgebiets-Gewichtung within the 90-BE Komplexteil: Analysis 40, Analytische Geometrie 25, Stochastik 25

IQSH Fachfortbildung, Die schriftliche Abiturprüfung Mathematik ab 2024

30 / 90 BE

Split between the hilfsmittelfreien Teil (HMF, 30 BE) and the Komplexteil (90 BE), 120 BE total

IQSH Fachfortbildung, Die schriftliche Abiturprüfung Mathematik ab 2024

0-15 Punkte

Grading scale for each Prüfungsfach, from Note 1 (15-13 Punkte) to Note 6 (0 Punkte)

Landesverordnung über die Gestaltung der Oberstufe und der Abiturprüfung (OAPVO), Schleswig-Holstein

200 / 100 Punkte

Minimum Gesamtqualifikation: 200+ from Block I and 100+ from Block II, out of 900 maximum

OAPVO §§31-33, Schleswig-Holstein

Free 100-question English-language MCQ study bank for Schleswig-Holstein Zentralabitur Mathematik, weighted to the confirmed 2024-reform BE structure (120 Bewertungseinheiten total: HMF Teil A 30 BE; Komplexteil Teil B 90 BE — Analysis 40, Analytische Geometrie 25, Stochastik 25) plus the Fachanforderungen Mathematik (2024) framework. Official exam: two-part written Klausur, hilfsmittelfreie Teil A (max 100 min) then calculator- and Formeldokument-supported Teil B (200 min); 300 minutes total; written date 06.05.2026. Not an official-format simulation; no fee for regular school candidates.

Sample Schleswig-Holstein Abitur Math Practice Questions

Try these sample questions to test your Schleswig-Holstein Abitur Math exam readiness. Each question includes a detailed explanation. Start the interactive quiz above for the full 100+ question experience with AI tutoring.

1Let f(x) = 4x^3 - 6x. What is f'(2)?
A.42
B.48
C.36
D.18
Explanation: By the Potenzregel, f'(x) = 12x^2 - 6. Substituting x = 2 gives f'(2) = 12(4) - 6 = 48 - 6 = 42.
2According to the Produktregel (product rule), if f(x) = u(x)*v(x), what is f'(x)?
A.u'(x)v(x) + u(x)v'(x)
B.u'(x)v'(x)
C.u'(x)v(x) - u(x)v'(x)
D.u(x)v(x)
Explanation: The Produktregel states that the derivative of a product is the derivative of the first factor times the second, plus the first factor times the derivative of the second: f'(x) = u'(x)v(x) + u(x)v'(x).
3Let f(x) = (2x + 3)^4. Using the Kettenregel, what is f'(x)?
A.8(2x + 3)^3
B.4(2x + 3)^3
C.8(2x + 3)^4
D.4x(2x + 3)^3
Explanation: The Kettenregel differentiates the outer power (4(2x+3)^3) and multiplies by the inner derivative (2), giving f'(x) = 4(2x+3)^3 * 2 = 8(2x+3)^3.
4For f(x) = u(x)/v(x) with v(x) not equal to 0, the Quotientenregel gives f'(x) as which expression?
A.[u'(x)v(x) - u(x)v'(x)] / [v(x)]^2
B.[u'(x)v(x) + u(x)v'(x)] / [v(x)]^2
C.u'(x)/v'(x)
D.[u(x)v'(x) - u'(x)v(x)] / [v(x)]^2
Explanation: The Quotientenregel is f'(x) = [u'(x)v(x) - u(x)v'(x)] / [v(x)]^2, with the numerator's subtraction order matching u before v.
5For f(x) = x^3 - 3x^2, at which x-value does f'(x) = 0 identify a candidate for a local extremum, restricting to x > 0?
A.x = 2
B.x = 0
C.x = 3
D.x = 1
Explanation: f'(x) = 3x^2 - 6x = 3x(x-2), so f'(x) = 0 at x = 0 and x = 2. Only x = 2 satisfies the restriction x > 0.
6For f(x) = x^3 - 3x^2 (critical points at x = 0 and x = 2), what does the sign of f''(x) at x = 2 indicate?
A.f''(2) = 6 > 0, so x = 2 is a local minimum
B.f''(2) = -6 < 0, so x = 2 is a local maximum
C.f''(2) = 0, so x = 2 is a saddle point
D.f''(2) = 18 > 0, so x = 2 is an inflection point
Explanation: f''(x) = 6x - 6, so f''(2) = 12 - 6 = 6, which is positive. A positive second derivative at a critical point confirms a local minimum.
7For g(x) = x^3 - 6x^2 + 9x, find the x-coordinate of the Wendepunkt (inflection point).
A.x = 2
B.x = 3
C.x = 1
D.x = 4
Explanation: g''(x) = 6x - 12. Setting g''(x) = 0 gives x = 2, which is where the concavity of g changes.
8Find the equation of the tangent line to f(x) = x^2 at x0 = 3.
A.y = 6x - 9
B.y = 6x + 9
C.y = 3x - 9
D.y = 9x - 6
Explanation: f(3) = 9 and f'(x) = 2x gives f'(3) = 6. The tangent line is y = 6(x-3) + 9 = 6x - 18 + 9 = 6x - 9.
9For h(x) = -x^2 + 4x, on which interval is h monotonically increasing?
A.x < 2
B.x > 2
C.x < 0
D.x > 4
Explanation: h'(x) = -2x + 4. Solving h'(x) > 0 gives -2x + 4 > 0, so x < 2. This is the interval where h is monotonically increasing.
10Is f(x) = x^4 - 2x^2 symmetric about the y-axis (achsensymmetrisch), the origin (punktsymmetrisch), or neither?
A.Symmetric about the y-axis, since f(x) contains only even powers of x
B.Symmetric about the origin, since f(-x) = -f(x)
C.Neither symmetric, since the function is a mixed-degree polynomial
D.Symmetric about the line y = x
Explanation: Checking f(-x) = (-x)^4 - 2(-x)^2 = x^4 - 2x^2 = f(x) confirms axis symmetry. A polynomial with only even exponents is always achsensymmetrisch.

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