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Key Facts: Schleswig-Holstein MSA Math Exam

135 min

Bearbeitungszeit for the written MSA Mathematik exam (max 45 min for Heft 1), preceded by a 30-minute Einlesezeit

Durchführungsbestimmungen ESA/MSA 2025/26, Erlass MBWFK 14.11.2025 – III 334

05.05.2026

Written MSA Mathematik exam date in the 2026 main session; Nachschreibtermin 22.05.2026

Durchführungsbestimmungen ESA/MSA 2025/26, Terminübersicht 2026

4 Komplexaufgaben

Heft 2 always covers exactly four Schwerpunktbereiche: Trigonometrie, Stereometrie, Funktionen, and Statistik und Wahrscheinlichkeit

Durchführungsbestimmungen ESA/MSA 2025/26, Ziff. 10.2 Mathematik

2:1 ratio

Final subject grade combines the Vornote and the written Prüfungsnote in a 2:1 ratio

Zentrale Abschlüsse Sekundarstufe I Schleswig-Holstein (MBWFK Elterninformation)

1 Fach

The MSA is awarded when no more than one final grade is worse than 'ausreichend' and none is 'ungenügend'

Zentrale Abschlüsse Sekundarstufe I Schleswig-Holstein (MBWFK Elterninformation)

Free 100-question English-language MCQ study bank for Schleswig-Holstein's MSA Mathematik exam (Gemeinschaftsschule, end of Jahrgangsstufe 10), weighted to the confirmed Heft-2 Schwerpunktbereiche — Trigonometrie (~18%), Stereometrie (~18%), Statistik und Wahrscheinlichkeit (~17%), and Funktionen (linear/quadratic/percentage, ~34% combined) — plus Jahrgangsstufe 5-10 foundational skills (~13%). Official exam: two-Heft written paper, 135 minutes (max 45 min for Heft 1) plus a 30-minute Einlesezeit; written date 5 May 2026 (Nachschreibtermin 22 May 2026). Not an official-format simulation; no fee, since the MSA is a compulsory school exam.

Sample Schleswig-Holstein MSA Math Practice Questions

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

1Calculate: 3/4 + 1/6. Give the answer as a fully reduced fraction.

A.11/12

B.5/6

C.2/5

D.7/12

Explanation: Convert both fractions to the common denominator 12: 3/4 = 9/12 and 1/6 = 2/12. Adding gives 9/12 + 2/12 = 11/12, which is already fully reduced.

2Evaluate the term 2(x + 3) − 4x for x = 5.

A.-4

B.-7

C.36

D.4

Explanation: First substitute x = 5: 2(5 + 3) − 4(5) = 2(8) − 20 = 16 − 20 = −4. Distributing the 2 across both terms inside the parentheses before subtracting is essential.

3Simplify: 2³ · 2².

A.32

B.64

C.12

D.16

Explanation: When multiplying powers with the same base, add the exponents: 2³ · 2² = 2^(3+2) = 2⁵ = 32.

4Simplify √72 as far as possible.

A.6√2

B.36√2

C.6

D.2√6

Explanation: 72 = 36 · 2, and 36 is a perfect square, so √72 = √36 · √2 = 6√2. This is the fully simplified form since 2 has no further square factors.

5A right triangle has legs of 9 cm and 12 cm. Using the Pythagorean theorem, find the length of the hypotenuse.

A.15 cm

B.21 cm

C.225 cm

D.10.5 cm

Explanation: By the Pythagorean theorem, the hypotenuse c satisfies c² = 9² + 12² = 81 + 144 = 225, so c = √225 = 15 cm.

6A right triangle has a hypotenuse of 13 cm and one leg of 5 cm. Find the length of the other leg.

A.12 cm

B.8 cm

C.18 cm

D.144 cm

Explanation: By the Pythagorean theorem, the missing leg b satisfies b² = 13² − 5² = 169 − 25 = 144, so b = √144 = 12 cm.

7A rectangle has a length of 8 cm and a width of 5 cm. Find its area.

A.40 cm²

B.13 cm²

C.26 cm²

D.35 cm²

Explanation: The area of a rectangle is length times width: A = 8 cm · 5 cm = 40 cm².

8A square has a side length of 7 cm. Find its perimeter.

A.28 cm

B.49 cm

C.14 cm

D.21 cm

Explanation: A square has four equal sides, so its perimeter is 4 · 7 cm = 28 cm.

9A circle has a radius of 6 cm. Using π ≈ 3.14, find its area.

A.113.04 cm²

B.37.68 cm²

C.18.84 cm²

D.452.16 cm²

Explanation: The area of a circle is A = π · r². With r = 6 cm: A = 3.14 · 6² = 3.14 · 36 = 113.04 cm².

10A circle has a diameter of 10 cm. Using π ≈ 3.14, find its circumference.

A.31.4 cm

B.15.7 cm

C.78.5 cm

D.20 cm

Explanation: The circumference is C = π · d. With d = 10 cm: C = 3.14 · 10 = 31.4 cm.

About the Schleswig-Holstein MSA Math Exam

Schleswig-Holstein's Mittlerer Schulabschluss (MSA) Mathematik exam is the state's central written mathematics assessment for Gemeinschaftsschule students at the end of Jahrgangsstufe 10, administered by the MBWFK under the annually confirmed Durchführungsbestimmungen (most recently the Erlass of 14 November 2025 – III 334). It sits alongside identical central written exams in Deutsch and Englisch, plus a Projektarbeit and optional oral exams, as the components of the MSA. The written Mathematik paper has two parts: Heft 1 (Kurzformaufgaben, VERA-style short tasks drawn from the full Jahrgangsstufe 5-10 curriculum, completed without a calculator) and Heft 2 (four Komplexaufgaben covering Trigonometrie, Stereometrie, Funktionen — including linear, quadratic, and percentage/compound-interest problems — and Statistik und Wahrscheinlichkeit, each with mandatory and optional parts). This free bank of 100 original multiple-choice questions is an English-language study adaptation with fully worked calculations across those four areas, built to strengthen the same underlying algebra, geometry, trigonometry, and statistics skills. It is not a simulation of the official exam, which is a German-language written paper answered with full shown working, corrected by two teachers against centrally issued Korrekturanweisungen, and sits well below the calculus content later required for the Zentralabitur.

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 MSA examination in Mathematik, sat by all Gemeinschaftsschule students in the second half of Jahrgangsstufe 10 alongside identical central exams in Deutsch and Englisch (1. Fremdsprache), plus a Projektarbeit and optional oral exams. The written paper is split into Heft 1 (Kurzformaufgaben, capped at 45 of the 135 minutes, no calculator) and Heft 2 (four Komplexaufgaben on Trigonometrie, Stereometrie, Funktionen, and Statistik und Wahrscheinlichkeit, each with Pflicht- and Wahlteile, worked with the official Formelsammlung and a non-graphing calculator). This 100-question bank is an English-language MCQ study adaptation only — it does not reproduce the German-language two-Heft free-response format or official task wording.

Time Limit

135 minutes of Bearbeitungszeit (maximum 45 minutes for Heft 1), preceded by a 30-minute Einlesezeit during which Heft 2 is distributed for reading only. Exact scheduling is reissued annually via the Durchführungsbestimmungen; in the 2026 main session the written MSA Mathematik exam is set for Tuesday, 5 May 2026, with a Nachschreibtermin (makeup) on Friday, 22 May 2026.

Passing Score

Subject grades use the standard German 1-6 Notenskala (1 = sehr gut, 6 = ungenügend). The final Endnote for Mathematik combines the Vornote and the written Prüfungsnote in a 2:1 ratio, rounding in the student's favor at the exact midpoint. The MSA is awarded when no more than one final grade is worse than 'ausreichend' (4) and none is 'ungenügend' (6); direct promotion into the gymnasiale Oberstufe additionally requires no more than one subject worse than 'befriedigend' (3) and an average of at least 3.0 within the Deutsch/Mathematik/1. Fremdsprache Fächergruppe.

Exam / Certification Fees

No exam fee; the MSA is a compulsory central state school examination for Gemeinschaftsschule students, administered by the MBWFK. No MSA-specific candidate fee is published in the sources reviewed.

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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 ~13%

Foundational Arithmetic, Ratios & Basic Geometry

Fractions, powers and roots, rounding, unit conversion, Dreisatz, perimeter/area of 2D shapes, and the Pythagorean theorem — the Jahrgangsstufe 5-10 short-form skills tested in Heft 1.

Study emphasis ~12%

Linear Equations, Systems & Straight-Line Graphs

Solving linear equations and systems, slope and y-intercept, and linear word problems.

Study emphasis ~12%

Quadratic Functions & Equations

Factoring, the quadratic formula, completing the square, vertex form, and applied maximum/minimum problems.

Study emphasis ~10%

Percentages, Ratios & Compound Interest

Percentage change, simple interest, and Zinseszins (compound interest) calculations.

Study emphasis ~18%

Trigonometry

Sine, cosine and tangent in right triangles, angle-of-elevation/depression problems, and triangle/polygon area via ½·a·b·sin(C).

Study emphasis ~18%

Solid Geometry / Stereometry

Surface area and volume of prisms, cylinders, pyramids, cones and spheres, and 3D space-diagonal problems.

Study emphasis ~17%

Statistics & Probability

Mean, median, mode, range, Laplace probability, and tree-diagram probability with and without replacement.

Preparing for the Schleswig-Holstein MSA Math Exam

What You Need to Know

Passing score: Subject grades use the standard German 1-6 Notenskala (1 = sehr gut, 6 = ungenügend). The final Endnote for Mathematik combines the Vornote and the written Prüfungsnote in a 2:1 ratio, rounding in the student's favor at the exact midpoint. The MSA is awarded when no more than one final grade is worse than 'ausreichend' (4) and none is 'ungenügend' (6); direct promotion into the gymnasiale Oberstufe additionally requires no more than one subject worse than 'befriedigend' (3) and an average of at least 3.0 within the Deutsch/Mathematik/1. Fremdsprache Fächergruppe.
Assessment: Official written Schleswig-Holstein MSA examination in Mathematik, sat by all Gemeinschaftsschule students in the second half of Jahrgangsstufe 10 alongside identical central exams in Deutsch and Englisch (1. Fremdsprache), plus a Projektarbeit and optional oral exams. The written paper is split into Heft 1 (Kurzformaufgaben, capped at 45 of the 135 minutes, no calculator) and Heft 2 (four Komplexaufgaben on Trigonometrie, Stereometrie, Funktionen, and Statistik und Wahrscheinlichkeit, each with Pflicht- and Wahlteile, worked with the official Formelsammlung and a non-graphing calculator). This 100-question bank is an English-language MCQ study adaptation only — it does not reproduce the German-language two-Heft free-response format or official task wording.
Time limit: 135 minutes of Bearbeitungszeit (maximum 45 minutes for Heft 1), preceded by a 30-minute Einlesezeit during which Heft 2 is distributed for reading only. Exact scheduling is reissued annually via the Durchführungsbestimmungen; in the 2026 main session the written MSA Mathematik exam is set for Tuesday, 5 May 2026, with a Nachschreibtermin (makeup) on Friday, 22 May 2026.
Exam / certification fees: No exam fee; the MSA is a compulsory central state school examination for Gemeinschaftsschule students, administered by the MBWFK. No MSA-specific candidate fee is published in the sources reviewed. Official sources

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Schleswig-Holstein MSA Math: Suggested Study Strategy

1Master all three trigonometric ratios (SOH-CAH-TOA) and practice both finding a missing side and finding a missing angle with inverse trig functions, since Trigonometrie is always one of the four Heft-2 Komplexaufgaben.

2Learn the volume and surface-area formulas for prisms, cylinders, pyramids, cones and spheres side by side, since Stereometrie problems often combine several solids or ask for a 3D space diagonal via the Pythagorean theorem.

3Practice solving quadratic equations by factoring, the quadratic formula, and completing the square, since Funktionen tasks can call for any of these methods depending on the equation.

4Build speed and accuracy in percentage and compound-interest calculations, and check whether a Formel- or Dreisatz-based solution path fits the task, since both are accepted.

5Work timed Heft-1 Kurzformaufgaben without a calculator to keep mental arithmetic and basic algebra sharp, since only 45 of the 135 minutes are available for that booklet.

6Practice reading frequency tables and simple tree diagrams for Statistik und Wahrscheinlichkeit, including probability calculated with and without replacement.

Frequently Asked Questions

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

No. The official written paper consists of two Prüfungshefte: Heft 1 (short Kurzformaufgaben covering the Jahrgangsstufe 5-10 curriculum, worked without a calculator) and Heft 2 (four Komplexaufgaben with mandatory and optional parts on Trigonometrie, Stereometrie, Funktionen, and Statistik und Wahrscheinlichkeit). This bank is an English-language MCQ study adaptation for practicing the underlying calculations, not a simulation of the official two-Heft format.

Which students take the MSA Mathematik exam?

Regular participation is mandatory for all Gemeinschaftsschule students in Schleswig-Holstein in the second half of Jahrgangsstufe 10. A Gemeinschaftsschule with an Oberstufe may excuse a student on parental request if promotion into the Oberstufe already appears assured from earlier performance.

What topics does the MSA Mathematik exam cover?

Heft 1 draws short tasks from across the entire Jahrgangsstufe 5-10 Mathematik curriculum. Heft 2 always contains exactly four Komplexaufgaben, one on each of Trigonometrie, Stereometrie, Funktionen (linear, quadratic, and percentage/interest problems), and Statistik und Wahrscheinlichkeit, per the Fachanforderungen Mathematik Sekundarstufe I.

What calculator is allowed, and when?

Heft 1 (Kurzformaufgaben) is completed without a calculator. In Heft 2, candidates may use a non-graphing (nicht grafikfähiger) calculator, or an equivalent digital math tool meeting the same restrictions (non-programmable, non-graphing), alongside the official Formelsammlung, Geo-Dreieck, Zirkel, and other drawing instruments.

How long is the written exam?

135 minutes of Bearbeitungszeit, of which a maximum of 45 minutes may be used for Heft 1, preceded by a 30-minute Einlesezeit during which Heft 2 is distributed for reading only (no solving yet).

When is the exam held in 2026?

Per the Durchführungsbestimmungen ESA/MSA 2025/26 (Erlass MBWFK, 14 November 2025 – III 334), the written MSA Mathematik exam in the 2026 main session is set for Tuesday, 5 May 2026, with a Nachschreibtermin (makeup date) for students who miss it on Friday, 22 May 2026.

Is there an exam fee?

No. The MSA is a compulsory central state school examination administered by the MBWFK for Gemeinschaftsschule students, and no MSA-specific fee is published.