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Key Facts: Madrid PAU Tech & Engineering II Exam

PAU Organising Commission / UCM

Exam Body

Community of Madrid University Admissions

90 min

Duration

Madrid PAU Regulations

0–10

Scoring

PAU Spain Marking Scheme

2º Bach.

Target Level

Madrid Education Department

€93.02

Registration Fee

UCM PAU Fee Schedule

Sample Madrid PAU Tech & Engineering II Practice Questions

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

1A cylindrical steel specimen with an initial diameter of 10 mm is subjected to an axial tensile force of 50 kN. Assuming pure elastic behavior, what is the engineering stress induced in the specimen?
A.636.6 MPa
B.159.2 MPa
C.318.3 MPa
D.795.8 MPa
Explanation: Engineering stress is calculated as sigma = F / A_0. The initial cross-sectional area A_0 = pi * (d/2)^2 = pi * (0.005 m)^2 = 7.854 * 10^-5 m^2. Dividing the force of 50,000 N by 7.854 * 10^-5 m^2 yields 636.6 * 10^6 Pa = 636.6 MPa.
2During a tensile test on a metallic bar with an initial gauge length of 50 mm, an applied stress of 210 MPa produces an elastic elongation of 0.05 mm. What is the Young's Modulus (modulus of elasticity) of the material?
A.210 GPa
B.105 GPa
C.420 GPa
D.21 GPa
Explanation: Engineering strain is epsilon = delta_L / L_0 = 0.05 mm / 50 mm = 0.001. According to Hooke's Law, Young's Modulus E = sigma / epsilon = 210 MPa / 0.001 = 210,000 MPa = 210 GPa.
3In a mechanical stress-strain diagram obtained from a standard tensile test, what does the yield strength (límite elástico) represent?
A.The maximum stress the material can sustain before permanent plastic deformation occurs
B.The maximum stress achieved right at the point of physical fracture
C.The slope of the stress-strain curve in the plastic deformation region
D.The total energy absorbed per unit volume up to catastrophic failure
Explanation: Yield strength defines the transition point between elastic (reversible) deformation and plastic (permanent) deformation. Up to the yield strength, the specimen returns to its original dimensions upon unloading.
4A structural steel alloy has a yield strength of 400 MPa and a Young's Modulus of 200 GPa. What is its modulus of resilience (elastic strain energy storage capacity per unit volume)?
A.400 kJ/m³
B.800 kJ/m³
C.200 kJ/m³
D.1600 kJ/m³
Explanation: The modulus of resilience U_r is the area under the elastic region of the stress-strain curve: U_r = sigma_y^2 / (2 * E). Substituting values yields (400 * 10^6)^2 / (2 * 200 * 10^9) = 1.6 * 10^17 / 4 * 10^11 = 400,000 J/m³ = 400 kJ/m³.
5A material specimen experiences an engineering stress of 300 MPa under a tensile load with a corresponding engineering strain of 0.10. Assuming uniform deformation without necking, what is the true stress in the specimen?
A.330 MPa
B.270 MPa
C.300 MPa
D.360 MPa
Explanation: Assuming constant volume during uniform plastic deformation, true stress sigma_true = sigma_eng * (1 + epsilon_eng). Here, sigma_true = 300 * (1 + 0.10) = 330 MPa.
6In a Brinell hardness test using a steel ball indenter of diameter D = 10 mm and a standard test load P = 3000 kgf, an indentation diameter d = 4.0 mm is measured. Calculate the Brinell Hardness Number (HB).
A.228.7 HB
B.238.7 HB
C.218.7 HB
D.248.7 HB
Explanation: Brinell hardness formula is HB = (2 * P) / [pi * D * (D - sqrt(D^2 - d^2))]. Here D^2 - d^2 = 100 - 16 = 84, sqrt(84) = 9.16515 mm. Thus (D - 9.16515) = 0.83485 mm. Denominator = pi * 10 * 0.83485 = 26.227. HB = 6000 / 26.227 = 228.7 HB.
7What is the key geometric specification of the diamond pyramid indenter used in the Vickers hardness test (HV)?
A.A square-based pyramid with an apex angle of 136° between opposite faces
B.A spherical diamond ball with a 1.588 mm diameter
C.A conical diamond point with a 120° apex angle
D.A cylindrical tungsten carbide pin with a flat tip
Explanation: The Vickers hardness test uses a square-based diamond pyramid indenter with an angle of 136° between opposite faces, providing a single continuous hardness scale across soft and hard metals.
8How does the Rockwell hardness test differ fundamentally from the Brinell and Vickers hardness testing methods?
A.It directly measures the permanent depth of indentation rather than optical surface area
B.It measures the rebound kinetic energy of a falling hammer
C.It relies on ultrasonic frequency damping upon surface contact
D.It determines the scratching resistance using Mohs mineral standards
Explanation: Rockwell hardness testing measures the permanent depth of indentation produced by a minor and major load sequence, allowing direct digital or dial reading without optical measurement of impression diagonals or diameters.
9In a standard Charpy pendulum impact test, a hammer of mass m = 20 kg is released from an initial height h = 1.5 m. After fracturing the notched specimen, the hammer swings up to a final height h' = 0.6 m. Taking g = 9.81 m/s², calculate the impact energy absorbed by the specimen.
A.176.6 J
B.294.3 J
C.117.7 J
D.58.9 J
Explanation: The impact energy absorbed is equal to the change in gravitational potential energy of the pendulum: E = m * g * (h - h') = 20 kg * 9.81 m/s² * (1.5 m - 0.6 m) = 196.2 * 0.9 = 176.58 J (176.6 J).
10A binary Cu-Ni phase diagram displays complete solid solubility. An alloy containing 40 wt% Ni is slowly cooled to 1200°C. At this temperature, the liquid phase L contains 30 wt% Ni and the solid phase alpha contains 50 wt% Ni. Using the lever rule, calculate the mass fraction of the liquid phase.
A.0.50 (50%)
B.0.25 (25%)
C.0.75 (75%)
D.0.40 (40%)
Explanation: According to the lever rule, the mass fraction of liquid phase W_L = (C_alpha - C_overall) / (C_alpha - C_L) = (50 - 40) / (50 - 30) = 10 / 20 = 0.50 or 50%.

About the Madrid PAU Tech & Engineering II Exam

Comprehensive practice exam bank for Madrid PAU Technology and Engineering II (Tecnología e Ingeniería II). Features 100 high-quality practice questions in English, covering topics from the 2nd Bachillerato Technology & Engineering II curriculum and Community of Madrid PAU university entrance examination standards, covering materials science, thermodynamics, mechanics, electronics, and automatic control.

Exam sponsor: PAU Organising Commission of the Community of Madrid / Universidad Complutense de Madrid (UCM). The requirements and fees below concern the certification or admission exam, separate from our free practice resources.

Assessment

Question count not published by the exam provider

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 >= 5.0 to pass).

Exam / Certification Fees

EUR 93.02 base registration fee for compulsory Access Phase in Community of Madrid (or ~11.63 € per optional subject in voluntary phase).

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 & Testing

Atomic structure, crystal lattices, stress-strain behavior, tensile testing (engineering stress/strain, Young's modulus, yield and ultimate tensile strength, resilience, toughness), hardness tests (Brinell, Vickers, Rockwell), impact resistance (Charpy), phase diagrams, heat treatments (annealing, hardening, tempering), and material selection.

20%

Applied Thermodynamics & Thermal Engines

First and Second Laws of Thermodynamics, thermodynamic processes (isobaric, isochoric, isothermal, adiabatic), ideal gas law, heat transfer mechanisms (conduction, convection, radiation), internal combustion engines (4-stroke Otto and Diesel cycles, indicated power, brake power, specific fuel consumption), Carnot efficiency, heat pumps, and refrigeration cycles.

20%

Pneumatic, Hydraulic & Mechanical Systems

Pascal's law, hydrostatic pressure, fluid flow dynamics (continuity equation, Bernoulli's equation), pneumatic and hydraulic components (actuators, directional control valves, flow control, pressure relief), circuit design, power transmission mechanisms (gear trains, velocity ratio, torque, gear efficiency, belt drives, chain drives, lead screws, lever systems).

20%

Electrical, Electronic & Digital Systems

DC and single-phase AC circuit analysis (Ohm's law, Kirchhoff's laws, power factor, reactive/apparent power, impedance), operational amplifiers (inverting, non-inverting, summing, comparator circuits), digital logic gates, Boolean algebra simplification (Karnaugh maps), combinational circuits (decoders, multiplexers), and sequential circuits (flip-flops, counters, shift registers).

20%

Automatic Control Systems & Robotics

Open-loop and closed-loop feedback control, system modeling, block diagram algebra, Laplace transforms, transfer functions, first- and second-order system responses, step response characteristics (overshoot, settling time, rise time, steady-state error), PID controller actions (proportional, integral, derivative), stability criteria (Routh-Hurwitz stability), and industrial robotics kinematics/sensors.

Preparing for the Madrid PAU Tech & Engineering II 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 >= 5.0 to pass).
  • Assessment: Question count not published by the exam provider
  • Time limit: 90 minutes (1.5 hours)
  • Exam / certification fees: EUR 93.02 base registration fee for compulsory Access Phase in Community of Madrid (or ~11.63 € per optional subject in voluntary phase). 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

Frequently Asked Questions

What is the format of the Madrid PAU Technology and Engineering II exam?

The official Madrid PAU Technology and Engineering II (Tecnología e Ingeniería II) exam is a 90-minute written test with technical problem-solving and theoretical questions divided into structured options. This OpenExamPrep question bank adapts all curriculum competencies into 100 rigorous multiple-choice questions.

What calculators are permitted during the Technology and Engineering II exam?

Standard non-programmable, non-graphing scientific calculators without symbolic algebra capability are allowed. Tables, formulas, and constants are provided in the exam prompt where necessary.

How long is the PAU Technology and Engineering II exam in Madrid?

Students have 90 minutes (1.5 hours) to complete the examination.

Why is Technology and Engineering II valuable for Madrid university admissions?

It is a key modal/specific subject for Engineering, Architecture, Industrial Technology, Telecommunications, and Computer Science degrees in Madrid public universities (UPM, UC3M, UCM, UAH, URJC), carrying maximum weighting (0.2 coefficient) to add up to 2.0 extra points to the admission grade.

What score is required to pass the Technology and Engineering II exam?

The exam is graded on a scale from 0 to 10. In the compulsory phase, a minimum mark of 4.0 is required to average with Bachillerato. In the voluntary weight-boosting phase, a score of at least 5.0 is required for university weighting.