100+ Free AHS-Matura Practice Questions

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Key Facts: AHS-Matura Exam

Free (0 €)

Exam Fee

BMB

Grade 4

Minimum Passing Grade

BMB / SchUG

3 Pillars

Examination Model

Prüfungsordnung AHS

270–300 min

Written Klausur Time

matura.gv.at

Universitätsreife

Credential Conferred

Schulorganisationsgesetz

36 Points

Mathematics Max Points

matura.gv.at (BMB)

The Austrian AHS-Matura is the standardized academic secondary school-leaving examination administered by the Bundesministerium für Bildung (BMB), featuring central Klausuren in German, Math, and Foreign Languages under a three-pillar model granting general university entrance.

Sample AHS-Matura Practice Questions

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

1Solve the linear equation for x: 5(2x - 3) - 3(x + 4) = 4x + 1.

A.x = 28/3 ≈ 9.33

B.x = 26/3 ≈ 8.67

C.x = 20/3 ≈ 6.67

D.x = 16/3 ≈ 5.33

Explanation: Expanding both sides gives 10x - 15 - 3x - 12 = 4x + 1, which simplifies to 7x - 27 = 4x + 1. Subtracting 4x and adding 27 yields 3x = 28, so x = 28/3 ≈ 9.33.

2Two vectors in R^2 are given by a = (3, -4) and b = (k, 6). For which value of k are vectors a and b orthogonal (perpendicular)?

A.k = 8

B.k = -8

C.k = 4.5

D.k = -4.5

Explanation: Two vectors are orthogonal if their scalar (dot) product equals zero: a · b = 3(k) + (-4)(6) = 3k - 24 = 0. Solving 3k = 24 gives k = 8.

3Calculate the magnitude (length) of the vector v = (2, -3, 6) in three-dimensional space R^3.

A.7

B.√45 ≈ 6.71

C.11

D.√13 ≈ 3.61

Explanation: The magnitude of a 3D vector v = (x, y, z) is ||v|| = √(x^2 + y^2 + z^2) = √(2^2 + (-3)^2 + 6^2) = √(4 + 9 + 36) = √49 = 7.

4A line g in R^2 is given by the parameter equation X = (2, 5) + t·(4, -1). Which of the following is an equivalent implicit (normal) equation of line g?

A.x + 4y = 22

B.4x - y = 3

C.x - 4y = -18

D.4x + y = 13

Explanation: The direction vector is v = (4, -1), so a normal vector is n = (1, 4). The normal equation is 1·x + 4·y = c. Substituting the point (2, 5) gives c = 1(2) + 4(5) = 2 + 20 = 22. Thus, the implicit equation is x + 4y = 22.

5Determine the discriminant and number of real solutions of the quadratic equation 3x^2 - 7x + 5 = 0.

A.Discriminant D = -11; no real solutions (two complex solutions)

B.Discriminant D = 109; two distinct real solutions

C.Discriminant D = 0; exactly one real solution

D.Discriminant D = -1; two distinct real solutions

Explanation: For ax^2 + bx + c = 0, the discriminant is D = b^2 - 4ac = (-7)^2 - 4(3)(5) = 49 - 60 = -11. Since D < 0, the equation has no real solutions.

6Find the point of intersection of the line g: X = (1, 2) + t·(3, 1) and the line h: 2x - y = 15 in R^2.

A.(10, 5)

B.(7, 4)

C.(4, 3)

D.(13, 6)

Explanation: From line g, parametric coordinates are x = 1 + 3t and y = 2 + t. Substitute into line h: 2(1 + 3t) - (2 + t) = 15 => 2 + 6t - 2 - t = 15 => 5t = 15 => t = 3. Substituting t = 3 into g yields x = 1 + 3(3) = 10 and y = 2 + 3 = 5.

7In a right-angled triangle ABC with right angle at C, side a = 6 cm and hypotenuse c = 10 cm. What is the value of cos(α), where α is the angle at vertex A?

A.0.80

B.0.60

C.0.75

D.1.33

Explanation: By the Pythagorean theorem, side b = √(c^2 - a^2) = √(100 - 36) = √64 = 8 cm. By definition, cos(α) = adjacent / hypotenuse = b / c = 8 / 10 = 0.80.

8A circle k in the Cartesian plane has center M(3, -2) and radius r = 5. Which of the following is the equation of the circle?

A.(x - 3)^2 + (y + 2)^2 = 25

B.(x + 3)^2 + (y - 2)^2 = 25

C.(x - 3)^2 + (y + 2)^2 = 5

D.(x + 3)^2 + (y - 2)^2 = 5

Explanation: The standard equation of a circle with center M(m_x, m_y) and radius r is (x - m_x)^2 + (y - m_y)^2 = r^2. With M(3, -2) and r = 5, this becomes (x - 3)^2 + (y - (-2))^2 = 5^2, which simplifies to (x - 3)^2 + (y + 2)^2 = 25.

9The linear function f(x) = k·x + d satisfies f(2) = 7 and f(5) = 16. What is the value of the y-intercept d?

A.d = 1

B.d = 3

C.d = -1

D.d = 5

Explanation: The slope is k = (f(5) - f(2)) / (5 - 2) = (16 - 7) / 3 = 9 / 3 = 3. Using f(2) = 7, we have 3(2) + d = 7 => 6 + d = 7 => d = 1.

10A radioactive substance decays according to N(t) = N_0 · e^(-0.04t), where t is in years. What is the substance's half-life T_1/2 to the nearest tenth of a year?

A.17.3 years

B.25.0 years

C.12.5 years

D.50.0 years

Explanation: At the half-life, N(T_1/2) = 0.5·N_0. Thus, e^(-0.04·T_1/2) = 0.5 => -0.04·T_1/2 = ln(0.5) = -0.69315 => T_1/2 = 0.69315 / 0.04 ≈ 17.33 years.

About the AHS-Matura Exam

The AHS-Reifeprüfung (Zentralmatura / SRDP) is Austria's standardized national school-leaving examination for general academic secondary schools (Allgemeinbildende Höhere Schulen). Administered by the Bundesministerium für Bildung (BMB), whose Abteilung III/6 produces the standardised papers, the examination follows a three-pillar model comprising the abschließende Arbeit (ABA, which replaced the compulsory vorwissenschaftliche Arbeit and is optional up to and including the 2028/29 school year), three to five central standardized written Klausuren (German, Mathematics and a modern foreign language are compulsory), and two or three oral examinations. Passing the AHS-Matura confers the Allgemeine Universitätsreife, providing unrestricted admission to universities, colleges, and higher education across Austria and the EU. This practice question bank provides an English-language MCQ study adaptation designed to reinforce core mathematical problem-solving, text-type analysis, language competencies, and scientific reasoning aligned with official BMB competency frameworks.

Assessment

Three-pillar model: Pillar 1 (abschließende Arbeit, optional through 2028/29 and replaceable by an extra written or oral exam), Pillar 2 (three, four or five written Klausuren; Deutsch, Mathematik and a lebende Fremdsprache are compulsory), Pillar 3 (two or three oral exams).

Time Limit

270 minutes per Klausur in Mathematik, lebende Fremdsprachen, Latein and Griechisch; 300 minutes in the Unterrichtssprache (Deutsch). Oral exams 10–15 minutes each.

Passing Score

Grade 4 (Genügend) or better on the 1–5 scale (1=Sehr gut, 5=Nicht genügend); negative Klausuren can be retaken via Kompensationsprüfung.

Exam Fee

Free for enrolled public school students (0 €). (Bundesministerium für Bildung (BMB))

AHS-Matura Exam Content Outline

35%

Standardized Mathematics (AHS-Mathematik)

Core competencies in algebra, geometry, functions, differential and integral calculus, and statistics/probability.

25%

German Language & Text Competencies (Deutsch)

Official text types (Erörterung, Textanalyse, Textinterpretation, Zusammenfassung, Kommentar, Leserbrief, Meinungsrede) and rhetoric.

20%

Modern Foreign Language (English B2)

CEFR B2 reading comprehension, language in use, lexical accuracy, and discourse analysis.

20%

Academic Specialization & Scientific Methodology (ABA)

Scientific inquiry, humanities, biology, physics, chemistry, source evaluation, and academic writing standards.

How to Pass the AHS-Matura Exam

What You Need to Know

Passing score: Grade 4 (Genügend) or better on the 1–5 scale (1=Sehr gut, 5=Nicht genügend); negative Klausuren can be retaken via Kompensationsprüfung.
Assessment: Three-pillar model: Pillar 1 (abschließende Arbeit, optional through 2028/29 and replaceable by an extra written or oral exam), Pillar 2 (three, four or five written Klausuren; Deutsch, Mathematik and a lebende Fremdsprache are compulsory), Pillar 3 (two or three oral exams).
Time limit: 270 minutes per Klausur in Mathematik, lebende Fremdsprachen, Latein and Griechisch; 300 minutes in the Unterrichtssprache (Deutsch). Oral exams 10–15 minutes each.
Exam fee: Free for enrolled public school students (0 €).

Keys to Passing

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

AHS-Matura Study Tips from Top Performers

1Master the Part 1 Grundkompetenzen in Mathematics, which account for 24 out of 36 points and are essential for securing a passing grade.

2Understand the structural differences between official German text types (Textanalyse, Textinterpretation, Erörterung, Kommentar, Leserbrief, Meinungsrede).

3Practice differential and integral calculus applications, especially finding rates of change, extrema, and calculating areas under curves.

4Review probability distributions (Binomial and Normal distributions) and confidence interval interpretations for the stochastics domain.

5For English B2, practice CEFR-aligned reading comprehension and language-in-use tasks focusing on connectors, word formation, and phrasal verbs.

6Utilize official past exam papers (Klausuraufgaben) published on matura.gv.at to familiarize yourself with standard problem formulations.

Frequently Asked Questions

What is the Austrian AHS-Reifeprüfung (AHS-Matura)?

The AHS-Reifeprüfung is the standardized secondary school-leaving examination for academic secondary schools (Gymnasien and Realgymnasien) in Austria, granting full general university entrance qualification (Allgemeine Universitätsreife).

What is the Three-Pillar Model of the Matura?

The Austrian Matura rests on three pillars: Pillar 1 is the abschließende Arbeit (ABA), which since the 2024/25 school year is voluntary and, up to and including 2028/29, may be replaced by one additional written or oral exam; Pillar 2 comprises three, four or five written Klausuren; and Pillar 3 consists of two or three oral exams.

What are the compulsory written subjects in the AHS Zentralmatura?

The core standardized written subjects are German (Deutsch), Mathematics (Mathematik), and a Modern Foreign Language (typically English at CEFR B2 level). Students choosing 4 written exams select an additional subject such as Latin, Greek, or a second foreign language.

How is the AHS Mathematics exam structured?

The standardized AHS Mathematics Klausur runs 270 minutes for a maximum of 36 points. Teil 1 consists of 24 independent Grundkompetenz tasks worth 1 point each (half points are possible). Teil 2 sets four context-based tasks, but a best-of rule applies to the last three: the weakest of them is discarded, so three Teil-2 tasks count for the remaining 12 points. The grading key is 32–36 Sehr gut, 27–31.5 Gut, 22–26.5 Befriedigend, 17–21.5 Genügend, 0–16.5 Nicht genügend.

What happens if a candidate fails a written Klausur?

If a candidate receives a negative grade (Nicht genügend) on a written exam, they can take a centrally standardized oral compensatory exam (Kompensationsprüfung) during the same examination session or resit the Klausur at a subsequent examination date.

Does the AHS-Matura publish percentage weightings between its subjects?

No. Each Prüfungsgebiet is graded separately on the 1–5 scale and no official percentage weighting exists between Mathematik, Deutsch, the Fremdsprache and the other pillars. The percentages shown on this page describe how our practice bank distributes its own questions, not an official blueprint.

How are practice questions on OpenExamPrep adapted for the AHS-Matura?

The official Austrian Matura is conducted in German (or a Volksgruppensprache) and uses open-response writing tasks, an oral examination and, optionally, the abschließende Arbeit. This bank is an English-language multiple-choice study adaptation, not an official translation and not a simulation of the exam format. It trains the underlying mathematical competencies, text-type rules, grammatical analysis and scientific concepts, but it cannot replace practising the German writing tasks, the oral examination or the ABA itself.