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100+ Free Abitur Mathematics Practice Questions

Pass your German Abitur Mathematics (Mathematik Allgemeine Hochschulreife) exam on the first try — instant access, no signup required.

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Solve x + y = 6 and x - y = 2. What is x?

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2026 Statistics

Key Facts: Abitur Mathematics Exam

100

Original local practice questions in this bank

OpenExamPrep

300 min / 255 min

IQB pool working time for advanced/basic Mathematics levels

IQB Beschreibung der Struktur, Stand 19.06.2024

3 core areas

Analysis, Analytic Geometry/Linear Algebra, and Stochastics

KMK Bildungsstandards and IQB Mathematics pool documents

2017

First year common Abitur task pools were available for Mathematics

KMK/IQB Abituraufgabenpools

Laender variation

The detailed design and administration are responsibility of the federal states

KMK Gymnasiale Oberstufe und Abitur

Use this 100-question original practice bank for Abitur Mathematics skills aligned to KMK/IQB themes: Analysis, Analytic Geometry/Linear Algebra, vectors, Stochastics, modeling, functions, calculus, probability, statistics, and data interpretation. The real exam varies by Land and by basic or advanced course level.

Sample Abitur Mathematics Practice Questions

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

1For f(x) = 2x^2 -2x +1, what is f'(0)?
A.-2
B.0
C.-4
D.2
Explanation: Differentiate first: f'(x) = 4x -2. Substituting x = 0 gives -2.
2Evaluate int_0^4 (3x +0) dx.
A.25
B.24
C.23
D.48
Explanation: An antiderivative is (3/2)x^2 +0x. Evaluating from 0 to 4 gives 24.
3What are the zeros of x^2 -4x +3?
A.-1 and -3
B.4 and 3
C.1 and 3
D.0 and 3
Explanation: The quadratic factors as (x - 1)(x - 3), so the zeros are 1 and 3.
4What is the slope of the line through (0, -2) and (6, 4)?
A.2
B.6
C.0
D.1
Explanation: Slope is (change in y)/(change in x) = (4 - -2)/(6 - 0) = 1.
5Compute (1, 2, 2) dot (4, 3, -2).
A.6
B.9
C.3
D.0
Explanation: The dot product is 1*4 + 2*3 + 2*-2 = 6.
6Solve x + y = 6 and x - y = 2. What is x?
A.2
B.4
C.6
D.0
Explanation: Adding the equations gives 2x = 8, so x = 4.
7For A = [[4, 2], [2, 5]], what is A(3, 2)?
A.(12, 10)
B.(17, 16)
C.(16, 16)
D.0
Explanation: Multiply rows by the vector: first entry 4*3+2*2=16; second entry 2*3+5*2=16.
8For X ~ Binomial(5, 1/3), what is P(X = 2)?
A.40/243
B.160/243
C.80/81
D.80/243
Explanation: Use C(5,2)(1/3)^2(2/3)^3 = 10*(1/9)*(8/27) = 80/243.
9If P(B) = 2/5 and P(A | B) = 3/5, what is P(A and B)?
A.6/25
B.1
C.1/5
D.3/5
Explanation: Use P(A and B)=P(B)P(A | B)=2/5*3/5=6/25.
10What is the mean of the data set 6, 4, 8, 9?
A.31/4
B.27/4
C.23/4
D.27
Explanation: The mean is (6 + 4 + 8 + 9)/4 = 27/4.

About the Abitur Mathematics Exam

German Abitur Mathematics is a state-administered upper-secondary exit examination for the Allgemeine Hochschulreife. KMK Bildungsstandards define common expectations for mathematical competencies, while the IQB coordinates common Abitur task pools used by the Laender to support comparability. Mathematics tasks emphasize Analysis, Analytic Geometry/Linear Algebra, and Stochastics, with modeling, argumentation, representation, symbolic work, and communication integrated throughout. The exam differs by federal state and by course level: grundlegendes Anforderungsniveau focuses more strongly on foundational and transfer demands, while erhoehtes Anforderungsniveau has greater complexity, abstraction, formalization, and independent reasoning.

Assessment

The German Mathematics Abitur is not one uniform national paper. The Laender administer the exam under KMK Bildungsstandards and may use IQB common task-pool material. The IQB Mathematics pool structure separates Part A without aids from Part B with approved aids and covers Analysis, Analytic Geometry/Linear Algebra, and Stochastics. It distinguishes grundlegendes Anforderungsniveau and erhoehtes Anforderungsniveau, with state-specific implementation and possible selection rules.

Time Limit

IQB pool model: 300 minutes for erhoehtes Anforderungsniveau; 255 minutes for grundlegendes Anforderungsniveau; state rules may add selection time for Part B choices.

Passing Score

Abitur success is based on the full qualification and examination rules of the Land. KMK describes the Allgemeine Hochschulreife as awarded with at least satisfactory performance; the standards-based written-exam grid maps 45% to 5 points (ausreichend).

Exam Fee

No single national Abitur Mathematics fee. Regular school candidates sit through their school and Land system; external-candidate and administrative fees, where applicable, vary by federal state. (Education ministries of the German Laender, with KMK standards and IQB-coordinated Abitur task pools)

Abitur Mathematics Exam Content Outline

Core; at least one third Analysis in KMK written-task guidance

Analysis, Functions, and Calculus

Rates of change, derivatives, tangents, monotonicity, extrema, concavity, integration, accumulated quantities, exponential and logarithmic models, and interpretation of graphs.

Core subject area

Analytic Geometry, Vectors, and Linear Algebra

Vector operations, scalar product, angles and distances, lines and planes in space, matrix and system methods, and geometric modeling.

Core subject area

Stochastics, Probability, and Statistics

Multi-stage experiments, conditional probability, independence, binomial and normal models, expected value, variance, hypothesis tests, confidence ideas, and data summaries.

Integrated competency area

Modeling, Representation, and Communication

Selecting mathematical models, interpreting residuals and graphs, translating between contexts and formulas, and communicating justified conclusions.

How to Pass the Abitur Mathematics Exam

What You Need to Know

  • Passing score: Abitur success is based on the full qualification and examination rules of the Land. KMK describes the Allgemeine Hochschulreife as awarded with at least satisfactory performance; the standards-based written-exam grid maps 45% to 5 points (ausreichend).
  • Assessment: The German Mathematics Abitur is not one uniform national paper. The Laender administer the exam under KMK Bildungsstandards and may use IQB common task-pool material. The IQB Mathematics pool structure separates Part A without aids from Part B with approved aids and covers Analysis, Analytic Geometry/Linear Algebra, and Stochastics. It distinguishes grundlegendes Anforderungsniveau and erhoehtes Anforderungsniveau, with state-specific implementation and possible selection rules.
  • Time limit: IQB pool model: 300 minutes for erhoehtes Anforderungsniveau; 255 minutes for grundlegendes Anforderungsniveau; state rules may add selection time for Part B choices.
  • Exam fee: No single national Abitur Mathematics fee. Regular school candidates sit through their school and Land system; external-candidate and administrative fees, where applicable, vary by federal state.

Keys to Passing

  • Complete 500+ practice questions
  • Score 80%+ consistently before scheduling
  • Focus on highest-weighted sections
  • Use our AI tutor for tough concepts

Abitur Mathematics Study Tips from Top Performers

1Practice both no-aid fundamentals and aided modeling tasks; the IQB pool structure explicitly separates Part A without aids from Part B with approved tools.
2Keep Analysis strong because KMK written-task guidance requires at least one third of the written requirements to address Analysis.
3Treat vectors, lines, planes, and scalar products as a connected analytic-geometry toolkit rather than isolated formulas.
4For Stochastics, write the event structure first: tree, table, binomial model, normal approximation, or hypothesis-test setup.
5When checking modeled answers, interpret units, parameters, graph behavior, and whether the conclusion fits the original context.

Frequently Asked Questions

Is Abitur Mathematics the same in every German federal state?

No. The Laender administer the Abitur and set implementation details. KMK Bildungsstandards and IQB common task pools support comparability, but timing, selection rules, course combinations, and local regulations can vary by state.

What are grundlegendes and erhoehtes Anforderungsniveau?

They are basic and advanced levels of upper-secondary requirements. The advanced level places greater emphasis on complexity, abstraction, formalization, and independent reasoning, while both levels are aligned to the KMK Mathematics standards.

What topics are central in Abitur Mathematics?

KMK and IQB materials organize Mathematics around Analysis, Analytic Geometry/Linear Algebra, and Stochastics, with modeling, argumentation, representations, symbolic work, and communication embedded across tasks.

Are official Abitur Mathematics questions multiple-choice?

Official papers commonly use multi-part constructed-response tasks with expected solution paths and scoring notes. This local bank uses MCQs for efficient practice and does not copy official IQB or state questions.

Can calculators or software be used?

The IQB pool structure has a Part A without aids and a Part B with approved aids. IQB/KMK materials distinguish no-aid tasks, simple scientific calculator (WTR) tasks, and modular mathematics system (MMS, formerly CAS) tasks.