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Hamburg First General School Leaving Certificate (ESA) German

Practice Questions100 questions

Exam Review

Key Facts: Hamburg ESA Math Exam

120 min

Bearbeitungszeit for regular-school ESA Mathematik 2026 (BSFB Regelungen; school letters)

BSFB Regelungen ESA 2026 Mathematik; Hamburg school parent letters

~40 min

Guideline working time for hilfsmittelfrei Teil I before handover

BSFB Regelungen ESA 2026 Mathematik

Teil I → II

No calculator/Formelsammlung until Teil I is handed in; then aids for Teil II

BSFB Regelungen ESA 2026 Mathematik

5 Leitideen

Zahl; Größen und Messen; Raum und Form; funktionaler Zusammenhang; Daten und Zufall

Rahmenplan Mathematik Stadtteilschule 2022 / ESA Regelungen

G4 emphasis

Successful work on Zahl, Messen, and Raum und Form can support grade G4

BSFB Regelungen ESA 2026 Mathematik

BSFB

Administrator: Behörde für Schule, Familie und Berufsbildung, Hamburg

hamburg.de zentrale Prüfungen ESA 2026

180 min

External ESA Mathematik Bearbeitungszeit (not the regular-school paper)

ZSJ ESA Externe Regelungsheft 2026/2027

100

Original local English MCQ study items in this bank (not official format)

OpenExamPrep

Hamburg ESA Mathematik (BSFB 2026): 120 min school paper; Teil I hilfsmittelfrei (~40 min guideline) then Teil II with calculator + Formelsammlung. Leitideen from Rahmenplan Mathematik 2022; emphasis Zahl, Messen, Raum und Form. This free English MCQ bank is a study adaptation only—not the official German written exam.

Sample Hamburg ESA Math Practice Questions

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

1A jacket costs EUR 80. During a sale it is reduced by 25%. What is the sale price?

A.EUR 60

B.EUR 55

C.EUR 65

D.EUR 20

Explanation: 25% of EUR 80 is 0.25 × 80 = EUR 20. Sale price = 80 − 20 = EUR 60.

2Compute the sum of the fractions 3/4 + 1/8.

A.4/12

B.7/8

C.1/2

D.5/8

Explanation: Common denominator 8: 3/4 = 6/8. Then 6/8 + 1/8 = 7/8.

3Calculate 15 percent of the whole number 240.

A.24

B.30

C.36

D.40

Explanation: 0.15 × 240 = 36. The evaluated result is 36, following the arithmetic shown.

4Evaluate the expression (−8) + 3 × (−2).

A.−22

B.10

C.−2

D.−14

Explanation: Multiplication first: 3 × (−2) = −6. Then (−8) + (−6) = −14.

5Simplify the exponential expression 2 to the power of 5.

A.32

B.10

C.25

D.64

Explanation: 2^5 = 2 × 2 × 2 × 2 × 2 = 32.

6What is the principal square root of 81?

A.8

B.9

C.40.5

D.18

Explanation: 9 × 9 = 81, so √81 = 9 (principal square root).

7Round the decimal 47.652 to one decimal place.

A.47.6

B.47.65

C.47.7

D.48

Explanation: To one decimal place, look at the second decimal digit. In 47.652 that digit is 5, so school rounding rounds the first decimal up: 47.7.

8A savings account has EUR 500. Simple interest of 4% per year is paid. How much interest is earned after 1 year?

A.EUR 4

B.EUR 40

C.EUR 520

D.EUR 20

Explanation: Interest = 0.04 × 500 = EUR 20.

9Multiply the decimals 2.4 and 0.5 and choose the product.

A.1.2

B.0.12

C.12

D.2.9

Explanation: 2.4 × 0.5 = 1.2. The evaluated result is 1.2, following the arithmetic shown.

10Which of the following numbers is equal to the fraction 3/5?

A.0.35

B.0.6

C.0.53

D.1.67

Explanation: 3 ÷ 5 = 0.6. The evaluated result is 0.6, following the arithmetic shown.

About the Hamburg ESA Math Exam

Hamburg ESA Mathematik is the central written mathematics examination for the Erster allgemeinbildender Schulabschluss (first general school-leaving certificate, formerly Hauptschulabschluss), set by the Behörde für Schule, Familie und Berufsbildung (BSFB). For regular schools in 2026 the Bearbeitungszeit is 120 minutes. Teil I is hilfsmittelfrei; after handover, Teil II allows a scientific (non-programmable, non-graphing) calculator and the approved Formelsammlung. Tasks follow the Stadtteilschule Rahmenplan Mathematik (2022) Leitideen with special emphasis on Zahl und Operation, Größen und Messen, and Raum und Form. Official language and format are German. This free bank offers 100 original English MCQs—predominantly genuine calculation items—for concept and procedure practice only; it cannot replace timed German written solutions.

Exam sponsor: Behörde für Schule, Familie und Berufsbildung (BSFB), Freie und Hansestadt Hamburg. The requirements and fees below concern the certification or admission exam, separate from our free practice resources.

Assessment

Per BSFB Regelungen ESA 2026 Mathematik: Prüflinge receive Arbeitshinweise and Teil I first. Teil I is Multiple-Choice and short items across Leitideen without Taschenrechner and without Formelsammlung (guideline ~40 minutes) and is completed on the task sheets. After Teil I is handed in, candidates receive Teil II, their non-programmable non-graphing calculator, and the approved Formelsammlung for the remaining time; Teil II is generally worked on separate sheets. Aids also include Schreib- und Zeichengeräte and Rechtschreibwörterbuch. Content follows Bildungsplan Stadtteilschule Jg. 5–11, Rahmenplan Mathematik (2022). Special emphasis: Zahl und Operation, Größen und Messen, Raum und Form (successful work here can support G4); also Strukturen und funktionaler Zusammenhang and Daten und Zufall. Operators (Arbeitsaufträge) are defined in the Regelungen appendix. This OpenExamPrep bank is an English-language MCQ study adaptation—not an official translation or format simulation. Official delivery language is German (officialLanguages: de). Note: external ESA Mathematik uses 180 minutes; this page targets the regular-school 120-minute sitting.

Time Limit

120 minutes Bearbeitungszeit for regular-school ESA Mathematik (BSFB Regelungen ESA 2026; confirmed in Hamburg school letters). Guideline ~40 minutes for Teil I; remainder for Teil II. External ESA Mathematik: 180 minutes.

Passing Score

No single published raw percent cut score for the Mathematik Klausur alone. Marking follows ESA requirements; BSFB states successful work on the emphasis Leitideen can support G4. Written Prüfung is combined with the Jahresnote under APO-GrundStGy (schools commonly weight Unterricht ~80% / Prüfung ~20%).

Exam / Certification Fees

No separate statewide per-subject Mathematik fee is published for regular school ESA candidates; administration is through the school/Land pathway. External candidates follow ZSJ/Externe Prüfungsordnung registration rules.

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.

28%

Zahl und Operation

Fractions, decimals, integers, powers/roots, percent, simple interest, estimation, and result checking in context.

22%

Größen und Messen

Unit conversions and perimeter/area/volume for common figures and solids used in ESA Aufgaben.

22%

Raum und Form

Pythagoras, angles, polygons/solids, nets, transformations, similarity, and scale drawings.

15%

Strukturen und funktionaler Zusammenhang

Direct/inverse proportion, linear equations and models, rates, and map scales.

13%

Daten und Zufall + Prüfungsformat

Mean/median/mode/range, simple probability, and ESA Teil I/II timing and Hilfsmittel literacy.

Preparing for the Hamburg ESA Math Exam

What You Need to Know

Passing score: No single published raw percent cut score for the Mathematik Klausur alone. Marking follows ESA requirements; BSFB states successful work on the emphasis Leitideen can support G4. Written Prüfung is combined with the Jahresnote under APO-GrundStGy (schools commonly weight Unterricht ~80% / Prüfung ~20%).
Assessment: Per BSFB Regelungen ESA 2026 Mathematik: Prüflinge receive Arbeitshinweise and Teil I first. Teil I is Multiple-Choice and short items across Leitideen without Taschenrechner and without Formelsammlung (guideline ~40 minutes) and is completed on the task sheets. After Teil I is handed in, candidates receive Teil II, their non-programmable non-graphing calculator, and the approved Formelsammlung for the remaining time; Teil II is generally worked on separate sheets. Aids also include Schreib- und Zeichengeräte and Rechtschreibwörterbuch. Content follows Bildungsplan Stadtteilschule Jg. 5–11, Rahmenplan Mathematik (2022). Special emphasis: Zahl und Operation, Größen und Messen, Raum und Form (successful work here can support G4); also Strukturen und funktionaler Zusammenhang and Daten und Zufall. Operators (Arbeitsaufträge) are defined in the Regelungen appendix. This OpenExamPrep bank is an English-language MCQ study adaptation—not an official translation or format simulation. Official delivery language is German (officialLanguages: de). Note: external ESA Mathematik uses 180 minutes; this page targets the regular-school 120-minute sitting.
Time limit: 120 minutes Bearbeitungszeit for regular-school ESA Mathematik (BSFB Regelungen ESA 2026; confirmed in Hamburg school letters). Guideline ~40 minutes for Teil I; remainder for Teil II. External ESA Mathematik: 180 minutes.
Exam / certification fees: No separate statewide per-subject Mathematik fee is published for regular school ESA candidates; administration is through the school/Land pathway. External candidates follow ZSJ/Externe Prüfungsordnung registration rules. Official sources

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Hamburg ESA Math: Suggested Study Strategy

1Drill Teil I without calculator or Formelsammlung under a ~40-minute guideline, then switch to Teil II with aids for the remaining time inside a full 120-minute block.

2Master percent, fraction/decimal fluency, unit conversions, and Pythagoras—these recur across Zahl, Messen, and Raum und Form.

3Practice volume/surface formulas for prism, cylinder, pyramid, cone, and sphere using the ESA Formelsammlung layout.

4Distinguish direct vs inverse proportion and solve simple linear equations with equivalence transformations.

5For Daten und Zufall, compute mean/median/mode/range and simple compound probabilities from clear sample spaces.

6Learn official Operatoren from the Regelungen appendix so you know what berechnen, bestimmen, and erläutern require in German papers.

Frequently Asked Questions

Is the official Hamburg ESA Mathematics exam multiple choice only?

No. Teil I includes Multiple-Choice and short hilfsmittelfrei items; Teil II is aided constructed-response style work with calculator and Formelsammlung. This bank is an English-language MCQ study adaptation only.

How long is the school ESA Mathematics written exam in 2026?

120 minutes Bearbeitungszeit per BSFB ESA 2026 Regelungen and Hamburg school letters (Mathematik 120 min; Deutsch 135 min). External ESA Mathematik uses 180 minutes.

What aids are allowed?

Teil I: no calculator and no Formelsammlung. After Teil I handover for Teil II: non-programmable non-graphing calculator, approved Formelsammlung (in exam materials), Schreib- und Zeichengeräte, and Rechtschreibwörterbuch.

Which Leitideen are emphasized?

Tasks follow Rahmenplan Mathematik (2022). BSFB places special emphasis on Zahl und Operation, Größen und Messen, and Raum und Form (successful work can support G4), and also assesses Strukturen und funktionaler Zusammenhang and Daten und Zufall.

Who administers the exam?

Behörde für Schule, Familie und Berufsbildung (BSFB), Freie und Hansestadt Hamburg. Schools run the sitting under APO-GrundStGy; central written tasks are set per the ESA Regelungen.

Is this practice bank an official English version of the ESA paper?

No. The official exam is delivered in German. This is a free English-language MCQ study adaptation for concept practice, not an official translation or format simulation.