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100+ Free BHS-Matura Practice Questions

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Austria AHS-Reifeprüfung (Matura)

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Austria Berufsreifeprüfung (BRP)

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2026 Statistics

Key Facts: BHS-Matura Exam

Free (0 €)

Exam Fee

BMB

Grade 4

Minimum Passing Grade

BMB / SchUG

Dual Title

Credential Conferred

Prüfungsordnung BMHS

42 Points

Applied Math Max Points

matura.gv.at (BMB)

5 Years

Curriculum Duration

Schulorganisationsgesetz

3 Pillars

Examination Structure

matura.gv.at

The Austrian BHS-Matura (Reife- und Diplomprüfung) is the 5-year vocational secondary exit exam administered by the Bundesministerium für Bildung (BMB) across HTL, HAK and HUM schools, awarding both general university access and certified professional qualification.

Sample BHS-Matura Practice Questions

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

1A production machine is purchased for €120,000 and depreciates linearly over an expected useful life of 8 years to a salvage value of €24,000. What is the annual depreciation expense, and what is the book value after 5 years?
A.Annual depreciation = €12,000; Book value after 5 years = €60,000
B.Annual depreciation = €15,000; Book value after 5 years = €45,000
C.Annual depreciation = €12,000; Book value after 5 years = €48,000
D.Annual depreciation = €9,600; Book value after 5 years = €72,000
Explanation: Annual linear depreciation is (Initial Cost - Salvage Value) / Useful Life = (€120,000 - €24,000) / 8 = €96,000 / 8 = €12,000 per year. After 5 years, accumulated depreciation is 5 · €12,000 = €60,000. The book value is €120,000 - €60,000 = €60,000.
2The temperature T(t) (in °C) of an industrial component cooling in ambient air (20°C) is modeled by Newton's Law of Cooling: T(t) = 20 + 80 · e^(-0.05t), where t is time in minutes. What is the component's temperature at t = 0 and after t = 20 minutes? (Use e^(-1) ≈ 0.3679).
A.T(0) = 100°C; T(20) ≈ 49.43°C
B.T(0) = 80°C; T(20) ≈ 49.43°C
C.T(0) = 100°C; T(20) ≈ 29.43°C
D.T(0) = 120°C; T(20) ≈ 59.43°C
Explanation: At t = 0: T(0) = 20 + 80 · e^0 = 20 + 80(1) = 100°C. At t = 20: T(20) = 20 + 80 · e^(-0.05 · 20) = 20 + 80 · e^(-1) = 20 + 80(0.36788) = 20 + 29.43 = 49.43°C.
3A company models its total revenue as R(x) = -0.5x^2 + 80x and total cost as C(x) = 20x + 450 (where x is output in units, R and C in €). For what production quantity x is the profit P(x) = R(x) - C(x) maximized?
A.x = 60 units
B.x = 80 units
C.x = 40 units
D.x = 100 units
Explanation: Profit function P(x) = R(x) - C(x) = -0.5x^2 + 80x - (20x + 450) = -0.5x^2 + 60x - 450. Take derivative: P'(x) = -x + 60. Setting P'(x) = 0 yields x = 60. Since P''(x) = -1 < 0, this represents a maximum.
4What is the economic interpretation of the marginal cost function K'(x) in business mathematics?
A.The approximate additional cost incurred by producing one additional unit of output at production level x
B.The total fixed cost of the manufacturing plant divided by total employees
C.The selling price per unit at which total revenue equals zero
D.The historical average cost of all previously produced batches
Explanation: In calculus and economics, marginal cost K'(x) is the instantaneous rate of change of total cost K(x) with respect to output x, approximating the cost to produce the (x+1)-th unit.
5Evaluate the definite integral representing total accumulated energy (in Joules) over the first 4 seconds for a power function P(t) = 3t^2 + 4t + 10 (t in seconds, P in Watts):
A.136 J
B.96 J
C.74 J
D.120 J
Explanation: Energy is W = ∫_{0}^{4} (3t^2 + 4t + 10) dt = [t^3 + 2t^2 + 10t]_{0}^{4} = (4^3 + 2(4^2) + 10(4)) - 0 = (64 + 2(16) + 40) = 64 + 32 + 40 = 136 J.
6A quality control test shows that 5% of manufactured components are defective (p = 0.05). In a random sample of n = 100 components, what are the expected value μ and standard deviation σ of defective items?
A.μ = 5, σ ≈ 2.18
B.μ = 5, σ = 5.00
C.μ = 0.05, σ = 0.0475
D.μ = 10, σ ≈ 3.16
Explanation: For a binomial distribution: expected value μ = n·p = 100 · 0.05 = 5. Standard deviation σ = √(n·p·(1 - p)) = √(100 · 0.05 · 0.95) = √4.75 ≈ 2.1794 ≈ 2.18.
7The diameter of manufactured metal rods is normally distributed with mean μ = 25.0 mm and standard deviation σ = 0.2 mm. What proportion of rods have a diameter between 24.6 mm and 25.4 mm?
A.Approximately 95.45% (within μ ± 2σ)
B.Approximately 68.27% (within μ ± 1σ)
C.Approximately 99.73% (within μ ± 3σ)
D.Approximately 50.00%
Explanation: The interval [24.6, 25.4] corresponds to [25.0 - 2(0.2), 25.0 + 2(0.2)] = [μ - 2σ, μ + 2σ]. For a standard normal distribution, P(μ - 2σ ≤ X ≤ μ + 2σ) = 2·Φ(2) - 1 = 2(0.9772) - 1 = 0.9545 = 95.45%.
8An investor deposits €10,000 into an account paying 4% annual interest compounded annually. What will be the account balance after 5 years? (Use (1.04)^5 ≈ 1.21665).
A.€12,166.53
B.€12,000.00
C.€12,500.00
D.€14,000.00
Explanation: Using the compound interest formula K_n = K_0 · (1 + i)^n: K_5 = €10,000 · (1.04)^5 = €10,000 · 1.2166529 = €12,166.53.
9Find the general solution to the first-order linear differential equation y'(t) + 3y(t) = 0.
A.y(t) = C · e^(-3t)
B.y(t) = C · e^(3t)
C.y(t) = -3t + C
D.y(t) = C · sin(3t)
Explanation: Separating variables: dy/dt = -3y => (1/y) dy = -3 dt => ln|y| = -3t + c => y(t) = C · e^(-3t), where C = ±e^c.
10A dataset of 7 monthly sales figures (in thousands of €) is: 12, 15, 18, 22, 28, 30, 45. What are the median and the interquartile range (IQR)?
A.Median = 22; IQR = 15 (Q3 = 30, Q1 = 15)
B.Median = 24.29; IQR = 33
C.Median = 22; IQR = 33
D.Median = 28; IQR = 15
Explanation: With n = 7 ordered values (12, 15, 18, 22, 28, 30, 45), the median (4th value) is 22. Lower quartile Q1 (median of lower half 12, 15, 18) is 15. Upper quartile Q3 (median of upper half 28, 30, 45) is 30. IQR = Q3 - Q1 = 30 - 15 = 15.

About the BHS-Matura Exam

The BHS-Reife- und Diplomprüfung is Austria's comprehensive school-leaving examination for colleges of higher vocational education (Berufsbildende Höhere Schulen, including HTL, HAK, HLW, and BMKS). Concluding a 5-year curriculum (grades 9–13), the qualification confers a dual entitlement: the Reifeprüfung (Allgemeine Hochschulreife) for unrestricted university entry, and the Diplomprüfung certifying professional vocational qualification and occupational title. The standardized sRDP format comprises a team Diplomarbeit with presentation, 3–4 written Klausuren (featuring Angewandte Mathematik with cluster-specific Part B applications, German, and Foreign Language), and 2–3 oral examinations. This practice question bank provides an English-language MCQ study adaptation focused on applied mathematical modeling, technical and business text analysis, and vocational reasoning aligned with official BMB standards for the BMHS sector.

Assessment

Three-pillar model: Pillar 1 (Diplomarbeit team project with defense), Pillar 2 (3–4 written Klausuren with cluster-specific Part B), Pillar 3 (2–3 oral exams in general and vocational subjects).

Time Limit

Angewandte Mathematik 270 minutes; Deutsch and the lebende Fremdsprache 300 minutes each at BHS; oral exams 10–15 minutes; Diplomarbeit presentation and discussion up to 25 minutes per candidate.

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))

BHS-Matura Exam Content Outline

35%

Applied Mathematics (Angewandte Mathematik)

Core competencies in Teil A (24 points) and cluster-specific applications in Teil B (18 points) across the five clusters HTL 1, HTL 2, W 1 (HLFS/HUM), W 2 (HAK) and P (BAfEP/BASOP, BRP).

25%

German & Professional Text Competencies (Deutsch)

The seven standardized text types (Erörterung, Kommentar, Leserbrief, Meinungsrede, Textanalyse, Textinterpretation, Zusammenfassung) and professional communication.

20%

Business & Technical Foreign Language (English B2)

CEFR B2 reading comprehension, professional vocabulary, business correspondence, and technical comprehension.

20%

Vocational Specialization & Diplomarbeit

Discipline-specific engineering/business theory, project management lifecycle, empirical research, and presentation methods.

How to Pass the BHS-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 (Diplomarbeit team project with defense), Pillar 2 (3–4 written Klausuren with cluster-specific Part B), Pillar 3 (2–3 oral exams in general and vocational subjects).
  • Time limit: Angewandte Mathematik 270 minutes; Deutsch and the lebende Fremdsprache 300 minutes each at BHS; oral exams 10–15 minutes; Diplomarbeit presentation and discussion up to 25 minutes per candidate.
  • 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

BHS-Matura Study Tips from Top Performers

1Master the Part A core competencies in Applied Mathematics, which constitute 24 out of 42 points across all BHS clusters.
2In Part B, practice cluster-specific problem contexts such as cost accounting and financial math for HAK, or physics and engineering modeling for HTL.
3Learn all seven text types in the official Textsortenkatalog — Erörterung, Kommentar, Leserbrief, Meinungsrede, Textanalyse, Textinterpretation and Zusammenfassung — focusing on concise synthesis in the Zusammenfassung and logical rebuttal in the Erörterung.
4Review CEFR B2 business and technical English terminology, especially idioms, register shifts, and formal correspondence conventions.
5Practice multi-step applied calculus questions involving marginal cost, revenue optimization, velocity, and decay rates.
6Consult official past exam collections on matura.gv.at to review scoring keys and grading rubrics.

Frequently Asked Questions

What is the BHS-Reife- und Diplomprüfung?

It is the terminal examination for 5-year vocational secondary colleges (BHS) in Austria—such as HTL (technical), HAK (commercial), and HLW (economic/service)—granting both general university access (Reifeprüfung) and professional qualification (Diplomprüfung).

How does BHS Applied Mathematics differ from AHS Mathematics?

BHS Angewandte Mathematik runs 270 minutes for a maximum of 42 points: Teil A (24 points, at least four independent tasks) covers the common core, while Teil B (18 points, at least two tasks) is cluster-specific. There are five clusters — HTL 1, HTL 2, W 1 (HLFS/HUM), W 2 (HAK) and P (BAfEP/BASOP together with the Berufsreifeprüfung). The grading key is 37–42 Sehr gut, 31–36.5 Gut, 25–30.5 Befriedigend, 20–24.5 Genügend, 0–19.5 Nicht genügend, and at least 13 points are needed before the final-year mark may be taken into account. AHS Mathematik by contrast has 36 points and no cluster split.

What is the Diplomarbeit in the BHS Matura?

The Diplomarbeit is a collaborative project conducted in teams of 2 to 5 students during the 5th school year. It involves practical research on an authentic technical or business problem, followed by a formal written report and an oral defense before the examination board.

What qualification and legal rights does a BHS graduate obtain?

Graduates earn full university and Fachhochschule entrance rights across all disciplines, exemptions from trade licensing exams, and professional titles such as Ingenieur (for HTL after qualifying professional experience) or commercial specialist designations.

Does the BHS-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 Angewandte Mathematik, Deutsch, the Fremdsprache and the Diplomarbeit. 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 BHS Matura?

The official examination is conducted in German, uses open-response and calculation-based written tasks, and includes a team Diplomarbeit with an oral defence. This bank is an English-language multiple-choice study adaptation, not an official translation and not a simulation of the exam format. It trains problem-solving in applied calculus, financial mathematics and statistics, German text-type conventions and professional English, but it cannot substitute for the written Klausur work, the oral examinations or the Diplomarbeit.