Free Practice Questions for Schleswig-Holstein Abitur Math

Exam-style questions and explanations by OpenExamPrep.

✓ No registration✓ No credit card

100+ Questions

100% Free

Loading practice questions...

Same family resources

Explore More Schleswig-Holstein Zentralabitur

Continue into nearby exams from the same family. Each card keeps practice questions, study guides, flashcards, videos, and articles in one place.

Exam Review

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 review concepts for the Schleswig-Holstein Abitur Math exam. 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.

About the Schleswig-Holstein Abitur Math Exam

Schleswig-Holstein Zentralabitur Mathematik is the state mathematics examination for the Allgemeine Hochschulreife, taken as a written Kernfach-Prüfung under the Landesverordnung über die Gestaltung der Oberstufe und der Abiturprüfung (OAPVO). Since the 2021/22 introduction of the Profiloberstufe, Mathematik is one of Schleswig-Holstein's three obligatorische Kernfächer (with Deutsch and a fortgeführte Fremdsprache); every student studies it at erhöhtem Anforderungsniveau across the Qualifikationsphase's four Halbjahre and may select it as one of two written Kernfach-Abiturprüfungsfächer. Content follows the Fachanforderungen Mathematik (2024): Analysis (Differential- and Integralrechnung, function families, growth and decay models), Analytische Geometrie (vectors, lines, planes, and their spatial relationships), and Stochastik (probability distributions, Erwartungswert, Normalverteilung, and hypothesis testing). Since a 2024 reform, the written exam splits into a hilfsmittelfreie Teil (HMF, Prüfungsteil A: drawing instruments only, maximum 100 minutes, 30 of 120 Bewertungseinheiten) and a Komplexteil (Prüfungsteil B: calculator- and Formeldokument-supported, 200 minutes, 90 of 120 Bewertungseinheiten split 40/25/25 across the three Sachgebiete). This free bank of 100 original multiple-choice questions is an English-language study adaptation designed to build and check genuine calculation skill and conceptual command of that content, including worked derivative, integral, vector/plane, and probability problems. It is not a simulation of the official exam, which is written in German and answered with full, structured working shown across multi-part tasks.

Exam sponsor: Ministerium für Allgemeine und Berufliche Bildung, Wissenschaft, Forschung und Kultur (MBWFK), Schleswig-Holstein, with the Institut für Qualitätsentwicklung an Schulen Schleswig-Holstein (IQSH). The requirements and fees below concern the certification or admission exam, separate from our free practice resources.

Assessment

Official written Schleswig-Holstein Zentralabitur examination in Mathematik, one of the state's three Kernfächer under the Profiloberstufe introduced in 2021/22. Every student studies Mathematik at erhöhtem Anforderungsniveau (5 Wochenstunden) across the Qualifikationsphase, and candidates choose two of the three Kernfächer (Deutsch, Mathematik, Fremdsprache) plus their Profil-giving subject as written Abiturprüfungsfächer. Since the 2024 reform, the written paper has two parts: the hilfsmittelfreie Teil (HMF, Prüfungsteil A: drawing instruments only, maximum 100 minutes, 30 of 120 BE across six student-selected tasks) and the Komplexteil (Prüfungsteil B: calculator- and Formeldokument-supported, 200 minutes, 90 of 120 BE across three tasks). Tasks are drawn from three Sachgebiete — Analysis (guaranteed at least 50 of 120 BE combined), Analytische Geometrie (guaranteed at least 30 of 120 BE), and Stochastik (guaranteed at least 30 of 120 BE), with the remaining 10 BE from the HMF's elective Aufgabengruppe-2 tasks allocated at the student's choice — following the Fachanforderungen Mathematik (2024, barrierearm), which supersedes the 2014 version and covers Primarstufe, Sekundarstufe I, and Sekundarstufe II. This 100-question bank is an English-language MCQ study adaptation only — it does not reproduce the German-language structured free-response format, is not split by Prüfungsteil, and is not a substitute for full worked-solution practice.

Time Limit

300 minutes total, per the IQSH's official Fachfortbildung guidance on the structure in force since the 2024 reform: the hilfsmittelfreie Teil (HMF, Prüfungsteil A) has a maximum Bearbeitungszeit of 100 minutes (inklusive Einlese- und Auswahlzeit) and is collected before the Komplexteil begins; the Komplexteil (Prüfungsteil B, with calculator and the official IQB Formeldokument) then runs for 200 minutes. Students receive all tasks for both parts at the start of the exam. Permitted aids in Teil B: the candidate's own WTR, GTR, or CAS calculator (whichever type was used throughout the Qualifikationsphase) and the official IQB Formeldokument, distributed only after Teil A is submitted — traditional personal Formelsammlungen are no longer permitted. Teil A permits only drawing instruments (Geodreieck/Lineal, Zirkel). Exact scheduling and any Anforderungsniveau-specific variations are re-issued annually via the Terminplan and Prüfungsregelungen on za.schleswig-holstein.de. In the 2026 main session the written Mathematik Kernfach exam was set for Wednesday, 6 May 2026; mündliche Prüfungen ran from 15 to 26 June 2026.

Passing Score

Subject performance is reported on the 0-15 Punkte scale (Note 1 = 15-13 Punkte, Note 6 = 0 Punkte). Within the written paper, the reformed structure in force since 2024 carries 120 Bewertungseinheiten total: HMF/Teil A 30 BE, Komplexteil/Teil B 90 BE (Analysis 40 BE, Analytische Geometrie 25 BE, Stochastik 25 BE). Under the OAPVO, the Gesamtqualifikation requires at least 200 of a possible 600 Punkte in Block I (Qualifikationsphase Halbjahresergebnisse) and at least 100 of a possible 300 Punkte in Block II (the Abiturprüfungen, each weighted four times), subject to further per-subject and per-Aufgabenfeld minimums and no Prüfung scored 0. The 900-point maximum converts to the Abitur-Durchschnittsnote via the nationally shared KMK table; the landesweite Abiturdurchschnittsnote in 2025 was 2.37 at Gymnasien and 2.61 at Gemeinschaftsschulen.

Exam / Certification Fees

No exam fee for regularly enrolled school candidates; the Abitur is a state school examination administered by the MBWFK. Externenprüfungen (Nichtschülerprüfungen) follow separate school-administered arrangements, and no Mathematik-specific external fee is published in the sources reviewed.

Exam sponsor website

Fees, eligibility, and exam policies can change. Confirm them with the exam sponsor before applying or paying.

Official sources

Our practice resources: topics covered

We aim to reflect publicly available exam outlines and topic information in our study resources. Coverage, format, and difficulty may differ from the actual exam, and we cannot guarantee that every detail is accurate or current. Confirm exam requirements, fees, and policies with the official exam sponsor.

Study emphasis ~18%

Differentialrechnung: Ableitungsregeln und Kurvendiskussion

Potenz-, Produkt-, Ketten- and Quotientenregel, Nullstellen, Extrempunkte, Wendepunkte, Monotonie, Symmetrie, tangent/normal lines.

Study emphasis ~14%

Integralrechnung: Flächen- und Rekonstruktionsaufgaben

Stammfunktion, bestimmtes Integral, Hauptsatz der Differential- und Integralrechnung, area between curves, function reconstruction.

Study emphasis ~7%

Exponential- und Logarithmusfunktionen, Wachstum und Zerfall

e-Funktionen, natürlicher Logarithmus, exponentielles/begrenztes Wachstum, Zerfallsprozesse and Halbwertszeit.

Study emphasis ~5%

Funktionenscharen und Extremwertprobleme

Parameter-dependent function families and applied Optimierungsaufgaben.

Study emphasis ~28%

Analytische Geometrie: Vektoren, Geraden und Ebenen

Vectors, Geraden- and Ebenengleichungen, Lagebeziehungen, distances, Schnittwinkel.

Study emphasis ~16%

Stochastik: Wahrscheinlichkeitsverteilungen und Erwartungswert

Baumdiagramme, bedingte Wahrscheinlichkeit, Bernoulli-Ketten, Binomialverteilung, Erwartungswert, Standardabweichung.

Study emphasis ~12%

Stochastik: Normalverteilung und Hypothesentests

Normal approximation, Sigma-Regeln, Signifikanztest, Fehler 1. und 2. Art.

Preparing for the Schleswig-Holstein Abitur Math Exam

What You Need to Know

Passing score: Subject performance is reported on the 0-15 Punkte scale (Note 1 = 15-13 Punkte, Note 6 = 0 Punkte). Within the written paper, the reformed structure in force since 2024 carries 120 Bewertungseinheiten total: HMF/Teil A 30 BE, Komplexteil/Teil B 90 BE (Analysis 40 BE, Analytische Geometrie 25 BE, Stochastik 25 BE). Under the OAPVO, the Gesamtqualifikation requires at least 200 of a possible 600 Punkte in Block I (Qualifikationsphase Halbjahresergebnisse) and at least 100 of a possible 300 Punkte in Block II (the Abiturprüfungen, each weighted four times), subject to further per-subject and per-Aufgabenfeld minimums and no Prüfung scored 0. The 900-point maximum converts to the Abitur-Durchschnittsnote via the nationally shared KMK table; the landesweite Abiturdurchschnittsnote in 2025 was 2.37 at Gymnasien and 2.61 at Gemeinschaftsschulen.
Assessment: Official written Schleswig-Holstein Zentralabitur examination in Mathematik, one of the state's three Kernfächer under the Profiloberstufe introduced in 2021/22. Every student studies Mathematik at erhöhtem Anforderungsniveau (5 Wochenstunden) across the Qualifikationsphase, and candidates choose two of the three Kernfächer (Deutsch, Mathematik, Fremdsprache) plus their Profil-giving subject as written Abiturprüfungsfächer. Since the 2024 reform, the written paper has two parts: the hilfsmittelfreie Teil (HMF, Prüfungsteil A: drawing instruments only, maximum 100 minutes, 30 of 120 BE across six student-selected tasks) and the Komplexteil (Prüfungsteil B: calculator- and Formeldokument-supported, 200 minutes, 90 of 120 BE across three tasks). Tasks are drawn from three Sachgebiete — Analysis (guaranteed at least 50 of 120 BE combined), Analytische Geometrie (guaranteed at least 30 of 120 BE), and Stochastik (guaranteed at least 30 of 120 BE), with the remaining 10 BE from the HMF's elective Aufgabengruppe-2 tasks allocated at the student's choice — following the Fachanforderungen Mathematik (2024, barrierearm), which supersedes the 2014 version and covers Primarstufe, Sekundarstufe I, and Sekundarstufe II. This 100-question bank is an English-language MCQ study adaptation only — it does not reproduce the German-language structured free-response format, is not split by Prüfungsteil, and is not a substitute for full worked-solution practice.
Time limit: 300 minutes total, per the IQSH's official Fachfortbildung guidance on the structure in force since the 2024 reform: the hilfsmittelfreie Teil (HMF, Prüfungsteil A) has a maximum Bearbeitungszeit of 100 minutes (inklusive Einlese- und Auswahlzeit) and is collected before the Komplexteil begins; the Komplexteil (Prüfungsteil B, with calculator and the official IQB Formeldokument) then runs for 200 minutes. Students receive all tasks for both parts at the start of the exam. Permitted aids in Teil B: the candidate's own WTR, GTR, or CAS calculator (whichever type was used throughout the Qualifikationsphase) and the official IQB Formeldokument, distributed only after Teil A is submitted — traditional personal Formelsammlungen are no longer permitted. Teil A permits only drawing instruments (Geodreieck/Lineal, Zirkel). Exact scheduling and any Anforderungsniveau-specific variations are re-issued annually via the Terminplan and Prüfungsregelungen on za.schleswig-holstein.de. In the 2026 main session the written Mathematik Kernfach exam was set for Wednesday, 6 May 2026; mündliche Prüfungen ran from 15 to 26 June 2026.
Exam / certification fees: No exam fee for regularly enrolled school candidates; the Abitur is a state school examination administered by the MBWFK. Externenprüfungen (Nichtschülerprüfungen) follow separate school-administered arrangements, and no Mathematik-specific external fee is published in the sources reviewed. Official sources

Using Our Practice Resources

Work through all 100 available questions
Review every answer and explanation
Track weak areas and revisit them
Use our AI tutor for tough concepts

Schleswig-Holstein Abitur Math: Suggested Study Strategy

1Master the four core Ableitungsregeln (Potenz-, Produkt-, Ketten-, Quotientenregel) cold, since almost every Analysis Aufgabe in both HMF and Komplexteil depends on differentiating quickly and correctly.

2Practice full Kurvendiskussionen end to end — Nullstellen, Extrempunkte, Wendepunkte, Monotonie, Symmetrie — on ganzrationale and e-Funktionen, since these recur across both Prüfungsteile.

3Drill Ebenengleichungen in all three forms (Parameter-, Normalen-, Koordinatenform) and practice converting between them, since Lagebeziehungen and Abstandsaufgaben in Analytische Geometrie almost always require a form-switch first.

4Learn the Binomialverteilung formula P(X=k) = C(n,k)·p^k·(1-p)^(n-k) alongside Erwartungswert μ=np and Standardabweichung σ=√(np(1-p)) — these underpin most Stochastik tasks including the Normalverteilung approximation.

5Work timed HMF practice sets without a calculator so mental arithmetic and algebraic manipulation stay sharp — the hilfsmittelfreie Teil tests Anforderungsbereich I/II/III fluency under a strict 100-minute cap before the Komplexteil is even distributed.

6Know your own calculator (WTR, GTR, or CAS) inside out well before exam day, since the Komplexteil assumes fluent use of whichever device you used throughout the Qualifikationsphase, alongside the official IQB Formeldokument you'll receive after Teil A.

Frequently Asked Questions

Is the official Schleswig-Holstein Mathematik Zentralabitur exam multiple-choice?

No. The official written paper is built from structured, multi-part Aufgaben worth Bewertungseinheiten (BE), where full working must be shown. Since 2024 it splits into a hilfsmittelfreier Teil (HMF, drawing instruments only, maximum 100 minutes) and a Komplexteil (calculator- and Formeldokument-supported, 200 minutes). This bank is an English-language MCQ study adaptation for learning and checking the underlying calculation skills and concepts, not a simulation of the official format or a substitute for full worked-solution practice.

Why are the questions in English when the exam is in German?

This bank is a study aid for building calculation fluency and conceptual command of the Fachanforderungen Mathematik content in English. German technical terms — Stammfunktion, Ebenengleichung, Erwartungswert, Sachgebiet, Bewertungseinheiten and so on — are preserved exactly as used in the curriculum, so you can carry the vocabulary straight into German-language revision.

Which topics does the Schleswig-Holstein Mathe-Abi cover?

Three Sachgebiete, guaranteed at least: Analysis (at least 50 of 120 BE — Differential- and Integralrechnung, function families, growth/decay models), Analytische Geometrie (at least 30 of 120 BE — vectors, lines, planes, and their spatial relationships), and Stochastik (at least 30 of 120 BE — probability distributions, Erwartungswert, Normalverteilung, hypothesis testing), with a further 10 BE allocated at the student's choice among elective HMF tasks. Analysis is the largest single share of the exam.

What calculator and formula aid are allowed, and when?

No calculator or formula aid is allowed in the hilfsmittelfreie Teil (HMF, Prüfungsteil A) — only drawing instruments (Geodreieck/Lineal, Zirkel). In the Komplexteil (Prüfungsteil B), candidates use whichever calculator type (WTR, GTR, or CAS) they used throughout their Qualifikationsphase coursework, plus a single official IQB Formeldokument distributed after Teil A is submitted. Traditional personal Formelsammlungen are no longer permitted since the 2024 reform.

Does Schleswig-Holstein still split Mathematik into Grundkurs and Leistungskurs?

Not in the way some other Länder do. Since the Profiloberstufe reform of 2021/22, Kernfächer including Mathematik are studied by every student at erhöhtem Anforderungsniveau across the Qualifikationsphase without a fixed, subject-wide Grundkurs/Leistungskurs division; students instead choose which of the three Kernfächer (Deutsch, Mathematik, Fremdsprache) become their written Abiturprüfungsfächer. This bank is built as a single, unified question set rather than split by Anforderungsniveau.

How long is the written exam?

300 minutes total: the hilfsmittelfreie Teil (HMF) has a maximum Bearbeitungszeit of 100 minutes and is collected before the Komplexteil begins, which then runs for 200 minutes. Exact scheduling is re-issued every year, so check the current Prüfungsregelungen through za.schleswig-holstein.de or your school.

Is Mathematik compulsory in the Schleswig-Holstein Abitur?

Mathematik is one of Schleswig-Holstein's three obligatorische Kernfächer (with Deutsch and a fortgeführte Fremdsprache), studied at erhöhtem Anforderungsniveau across all four Halbjahre of the Qualifikationsphase and contributing to Block I of the Gesamtqualifikation regardless of whether it is ultimately chosen as a written Abiturprüfungsfach.

When was the exam held in 2026?

The written Mathematik Kernfach exam in the 2026 main session was set for Wednesday, 6 May 2026, within a written-exam window running from late March through early May 2026 (Profilfächer from 24 March, Kernfächer and Naturwissenschaften from late April). Mündliche Prüfungen ran from 15 to 26 June 2026. Exact makeup-exam (Nachtermin) dates for illness are set centrally each year; candidates should confirm current dates through their school.

Free Practice Questions for Schleswig-Holstein Abitur Math

Explore More Schleswig-Holstein Zentralabitur

Schleswig-Holstein Zentralabitur Biology (Biologie)

Schleswig-Holstein Zentralabitur Chemistry (Chemie)

Schleswig-Holstein Zentralabitur Danish (Dänisch)

Schleswig-Holstein Zentralabitur English (Englisch)

Schleswig-Holstein Zentralabitur French (Französisch)

Schleswig-Holstein Zentralabitur German (Deutsch)