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Exam Review

Key Facts: PAU Technology & Engineering II (Cantabria) Exam

90 min

Exam duration for the PAU Technology and Engineering II paper

University of Cantabria (UNICAN) PAU Organising Commission

0–10 scale

Scoring scale (minimum 4.0 required in Access Phase)

Cantabria PAU Regulations

0.2 Weight

Maximum admission weighting parameter for engineering degrees in Spain

UNICAN Degree Admission Weighting Table

5 Blocks

Core content areas (Materials, Thermodynamics, Electrical, Control/Pneumatics, Digital/Programming)

2º Bachillerato Curriculum (RD 243/2022)

100

High-quality practice questions in this OpenExamPrep subject bank

OpenExamPrep

Master the 2026 Cantabria PAU Technology and Engineering II exam with 100 practice questions covering materials science, mechanical testing, thermodynamics, electrical circuits, control systems, pneumatics, and digital electronics.

Sample PAU Technology & Engineering II (Cantabria) Practice Questions

Try these sample questions to review concepts for the PAU Technology & Engineering II (Cantabria) exam. Each question includes a detailed explanation. Start the interactive quiz above for the full 100+ question experience with AI tutoring.

1A cylindrical metal specimen with an initial cross-sectional area of 100 mm² is subjected to an axial tensile force of 50 kN. What is the engineering stress induced in the specimen?
A.500 MPa
B.50 MPa
C.5000 MPa
D.0.5 MPa
Explanation: Engineering stress (σ) is defined as force divided by the initial cross-sectional area: σ = F / A₀. Converting force to Newtons gives F = 50,000 N, so σ = 50,000 N / 100 mm² = 500 N/mm² = 500 MPa.
2A steel tie rod of original gauge length L₀ = 200 mm elongates by ΔL = 0.4 mm under tension. What is the engineering strain (ε) of the rod?
A.0.02 (2.0%)
B.0.002 (0.2%)
C.0.0002 (0.02%)
D.0.004 (0.4%)
Explanation: Engineering strain is defined as unit elongation: ε = ΔL / L₀. Substituting the values gives ε = 0.4 mm / 200 mm = 0.002, which corresponds to 0.2%.
3An elastic structural component experiences an engineering stress of σ = 210 MPa at a strain of ε = 0.001. What is the Young's modulus (E) of the material?
A.2.1 GPa
B.21 GPa
C.210 GPa
D.2100 GPa
Explanation: According to Hooke's Law in the elastic regime, E = σ / ε. Substituting σ = 210 × 10⁶ Pa and ε = 0.001 yields E = 210 × 10⁹ Pa = 210 GPa, typical for structural steel.
4Which indenter geometry and material are standardized for performing a Brinell hardness test (HB)?
A.A square-based diamond pyramid with a 136° face angle
B.A 120° diamond cone with a spherical tip
C.A 1/16-inch steel ball indenter for soft metals
D.A hardened steel or tungsten carbide spherical ball
Explanation: The Brinell hardness test utilizes a hardened steel or tungsten carbide spherical ball indenter (typically 10 mm in diameter) pressed into the test piece under a specified load.
5What fundamental material property is measured by the Charpy impact test?
A.Impact energy absorbed during dynamic fracture (toughness/resilience)
B.Yield strength under static loading
C.Resistance to localized plastic surface deformation
D.Fatigue limit under cyclic loading
Explanation: The Charpy pendulum impact test measures impact energy absorbed (in Joules or J/cm²) when a notched specimen is fractured under high-strain-rate impact, evaluating material resilience and toughness.
6Why can thermoplastic polymers be repeatedly melted, reshaped, and recycled, whereas thermosetting polymers cannot?
A.Thermoplastics possess cross-linked covalent network bonds between chains.
B.Thermoplastics consist of linear or branched polymer chains joined by weak secondary van der Waals bonds.
C.Thermosets have no covalent bonds in their molecular structure.
D.Thermoplastics expand irreversibly when heated due to chemical degradation.
Explanation: Thermoplastics consist of linear or branched macromolecular chains held together by weak secondary forces (van der Waals or hydrogen bonds) that break easily upon heating, allowing remelting. Thermosets contain permanent, highly cross-linked covalent network bonds that decompose rather than melt when heated.
7A solid cylindrical alloy rod with diameter d = 10 mm is subjected to a tensile force F = 15.71 kN. Calculate the tensile stress σ in the rod.
A.100 MPa
B.157 MPa
C.200 MPa
D.400 MPa
Explanation: First calculate the cross-sectional area: A₀ = (π/4) × d² = (π/4) × (10 mm)² ≈ 78.54 mm². Then calculate stress: σ = F / A₀ = 15,710 N / 78.54 mm² = 200 N/mm² = 200 MPa.
8In a Brinell hardness test, a load P = 3000 kgf applied with a D = 10 mm diameter ball indenter produces an indentation diameter d = 4 mm. Calculate the Brinell Hardness Number (HB).
A.143 kgf/mm²
B.352 kgf/mm²
C.475 kgf/mm²
D.229 kgf/mm²
Explanation: The Brinell hardness formula is HB = 2P / [π D (D - √(D² - d²))]. Substituting values: √(D² - d²) = √(100 - 16) = √84 ≈ 9.165 mm. Indentation area A = π × 10 × (10 - 9.165) / 2 = 5π × 0.835 ≈ 13.116 mm². Thus HB = 3000 / 13.116 ≈ 228.7 ≈ 229 kgf/mm².
9A Charpy test uses a pendulum of mass m = 20 kg released from height h₁ = 1.5 m. After fracturing a specimen with cross-section S₀ = 80 mm² (0.8 cm²), the pendulum rises to height h₂ = 0.6 m. Taking g = 9.8 m/s², calculate the resilience K (absorbed energy per unit area) in J/cm².
A.220.5 J/cm²
B.110.25 J/cm²
C.176.4 J/cm²
D.275.6 J/cm²
Explanation: Absorbed energy ΔE = m·g·(h₁ - h₂) = 20 kg × 9.8 m/s² × (1.5 m - 0.6 m) = 196 N × 0.9 m = 176.4 J. Resilience K is absorbed energy per unit cross-sectional area: K = ΔE / S₀ = 176.4 J / 0.8 cm² = 220.5 J/cm².
10In materials fatigue analysis, what does the 'fatigue limit' (or endurance limit) on a Wöhler S-N curve represent?
A.The maximum stress a material can withstand for a single load cycle
B.The stress level below which the material can endure an infinite number of cyclic loads without failing
C.The stress at which necking initiates during a fatigue test
D.The energy required to propagate a fatigue crack to catastrophic failure
Explanation: The fatigue limit (endurance limit) is the horizontal asymptote on a Wöhler (S-N) diagram; for stress amplitudes below this limit, ferrous alloys can theoretically withstand infinite loading cycles without fatigue failure.

About the PAU Technology & Engineering II (Cantabria) Exam

Comprehensive 100-question practice test bank for the Cantabria (Universidad de Cantabria / UNICAN) PAU exam in Technology and Engineering II (Tecnología e Ingeniería II). Covers materials science, mechanical testing, thermodynamics, heat engines, AC/DC circuit analysis, electrical machines, control systems, fluid power, and digital electronics.

Exam sponsor: University of Cantabria (UNICAN) PAU Organising Commission. The requirements and fees below concern the certification or admission exam, separate from our free practice resources.

Assessment

The Cantabria PAU exam in Technology and Engineering II (UNICAN) runs 90 minutes and is a key modality paper sat by Science & Technology Bachillerato students. It evaluates engineering principles across five blocks: materials science and mechanical testing, thermodynamics and thermal machines, electrical circuits and machines, automated control and pneumatics/hydraulics, and digital electronics and programming.

Time Limit

90 minutes (1.5 hours)

Passing Score

Marked on a 0–10 scale. Minimum 4.0 required in Access Phase to combine with Bachillerato GPA (60% Bachillerato + 40% PAU Access Phase >= 5.0 to pass).

Exam / Certification Fees

EUR 71.09 base registration fee for PAU Access Phase (ordinary sitting, set by Universidad de Cantabria).

Exam sponsor website

Fees, eligibility, and exam policies can change. Confirm them with the exam sponsor before applying or paying.

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.

20%

Materials Science, Mechanical Properties & Testing (Ciencia y Propiedades de Materiales)

Mechanical testing (tensile, hardness, impact/resilience), stress-strain diagrams, thermal and chemical properties, material selection, oxidation, corrosion, and recycling.

20%

Thermodynamics, Thermal Machines & Energy Systems (Termodinámica y Máquinas Térmicas)

First and second laws of thermodynamics, thermal efficiency, Carnot cycle, internal combustion engines (Otto/Diesel), heat pumps, refrigeration, and energy efficiency.

20%

Circuit Analysis, Power Electronics & Electrical Machines (Circuitos y Máquinas Eléctricas)

DC and AC single/three-phase circuit analysis, active/reactive/apparent power, transformers, DC motors, AC induction motors, slip, and power semiconductor devices (diodes, SCRs, BJTs, MOSFETs).

20%

Automated Systems, Control Theory & Pneumatics/Hydraulics (Sistemas Automáticos y Neumática/Hidráulica)

Open/closed-loop control systems, block diagrams, transfer functions, sensors, PID actions, Pascal's law, pneumatic/hydraulic cylinder force calculations, valves, and fluid power logic circuits.

20%

Digital Electronics, Logic Gates & Programming (Electrónica Digital, Puertas Lógicas y Programación)

Binary/hexadecimal number systems, Boolean algebra, Karnaugh map minimization, combinational logic (decoders, multiplexers), sequential logic (flip-flops, counters), PLCs, and microcontroller programming fundamentals.

Preparing for the PAU Technology & Engineering II (Cantabria) Exam

What You Need to Know

  • Passing score: Marked on a 0–10 scale. Minimum 4.0 required in Access Phase to combine with Bachillerato GPA (60% Bachillerato + 40% PAU Access Phase >= 5.0 to pass).
  • Assessment: The Cantabria PAU exam in Technology and Engineering II (UNICAN) runs 90 minutes and is a key modality paper sat by Science & Technology Bachillerato students. It evaluates engineering principles across five blocks: materials science and mechanical testing, thermodynamics and thermal machines, electrical circuits and machines, automated control and pneumatics/hydraulics, and digital electronics and programming.
  • Time limit: 90 minutes (1.5 hours)
  • Exam / certification fees: EUR 71.09 base registration fee for PAU Access Phase (ordinary sitting, set by Universidad de Cantabria). Official sources

Using Our Practice Resources

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

PAU Technology & Engineering II (Cantabria): Suggested Study Strategy

1Master mechanical testing formulas: stress σ = F/A, strain ε = ΔL/L₀, Young's modulus E = σ/ε, Charpy resilience K = ΔE/S₀, and Brinell hardness HB = 2P / [π D (D - √(D² - d²))].
2Memorize thermodynamic laws and heat engine efficiency: Carnot efficiency η_C = 1 - T_C/T_H (with temperatures in Kelvin!), heat pump COP_HP = Q_H / W, and cylinder displacement V_d = N · (π/4) · d² · s.
3Practice AC and three-phase circuit calculations: active power P = √3 V_L I_L cos φ, impedance Z = √(R² + X²), power factor correction Q_C = P (tan φ₁ - tan φ₂), and induction motor slip s = (n_s - n) / n_s.
4Understand fluid power systems: Pascal's law F₂ = F₁ (A₂/A₁), pneumatic cylinder advancing force F = P · (π/4) D² · η, retraction force F_r = P · (π/4) (D² - d²) · η, and valve function (5/2, OR shuttle, AND dual-pressure).
5Brush up on digital logic and control theory: Boolean reduction, 3- and 4-variable Karnaugh maps, closed-loop transfer functions T(s) = G(s) / [1 + G(s)H(s)], and PID control action roles.

Frequently Asked Questions

Is this practice bank in the same format as the real Cantabria PAU Technology and Engineering II exam?

No. The official Cantabria PAU paper for Tecnología e Ingeniería II is a 90-minute written examination sat in Spanish, consisting of numerical calculation problems and open-ended engineering questions requiring step-by-step mathematical work and justified explanations. This bank is an English-language multiple-choice study adaptation of the official 2º Bachillerato syllabus (materials science, thermodynamics, electrical circuits, control theory, pneumatics/hydraulics, and digital electronics) designed to test conceptual understanding and calculation mastery.

What is the official subject title for this PAU exam in Cantabria?

The official subject title is Tecnología e Ingeniería II, a 2º Bachillerato modality subject in the Science and Technology track established under Real Decreto 243/2022 (LOMLOE), examined by the University of Cantabria (UNICAN) PAU Organising Commission.

Which students take Technology and Engineering II in Cantabria?

It is an elective modality subject for students in the Science and Technology Bachillerato track (modalidad de Ciencias y Tecnología). Students can select it as one of their modality papers in either the compulsory Access Phase or the voluntary Admission Phase to boost their university admission grade for engineering degrees.

How is the PAU grade calculated for university entry in Cantabria?

The Access Phase grade is calculated as 60% Bachillerato GPA + 40% PAU Access Phase mark (combining Lengua Castellana y Literatura, Historia/Filosofía, Foreign Language, and the Modality Subject). An overall mark of at least 5.0 is required to pass. Candidates can gain up to 4 extra points in the Admission Phase, where engineering faculties heavily weight Tecnología e Ingeniería II (weighting parameter 0.2).

What calculation topics are tested on the Cantabria Tecnología e Ingeniería II exam?

Key calculation topics include tensile stress/strain and Young's modulus, Brinell/Charpy hardness and resilience tests, thermal expansion, Carnot heat engine efficiency and heat pump COP, internal combustion engine displacement, single/three-phase AC power and impedance, induction motor slip, pneumatic cylinder thrust and retraction forces, hydraulic press amplification, block diagram transfer functions, Boolean algebra/Karnaugh maps, and microcontroller PWM/ADC values.

In what language is the Cantabria PAU examination conducted?

Official PAU examination papers in Cantabria are written and answered in Spanish.

When is the Cantabria PAU 2026 Tecnología e Ingeniería II exam scheduled?

The 2026 ordinary convocation takes place June 2–4, 2026, with the extraordinary convocation scheduled for June 30–July 2, 2026. Exact session timetables are published by the University of Cantabria PAU Organising Commission.