Physics Competency Certification Exam (EAC-Física)

The Physics Competence Accreditation Exam (EAC-Física) is a standardized assessment instrument designed to objectively and rigorously measure a candidate's mastery of the fundamental principles and applications of the field of physics. Its purpose is to offer a reliable and valid metric that can be used for admission to graduate programs, teaching certification, and support in employment decision-making in areas requiring solid knowledge of this discipline.

This document presents the Specifications of the EAC-Física Exam, outlining the complete architecture upon which the test is built. Its objective is to provide a transparent and detailed guide for both applicants preparing for the exam and educators and institutions that will utilize its results.

The fundamental purpose of this exam is to objectively measure the level of mastery of competencies (knowledge, skills, and abilities) that a candidate possesses in the field of physics. The results obtained from this standardized instrument are designed to be used for academic, professional, or personal purposes.

Instructions for Registration and Taking the Exam

To take the Physics Competence Accreditation Exam (EAC-Física), you must follow these three steps:

1. Make the Payment

You must make a payment of RD$ 1,000.00 to the Universidad Autónoma de Santo Domingo. You can do this via bank transfer or deposit using the following details:

• Bank: Banreservas
• Account Type: Checking Account (Corriente)
• Account No.: 010-500208-9
• RNC (Tax ID): 401-004419-4
• Transaction Concept/Description: It is mandatory to write the following in the description: FIS404 EAC Firstname Lastname

2. Complete Registration

Once the payment is made, it is indispensable to formalize your registration by completing the Registration Form.

• You must upload the proof of payment (legible photo or screenshot) within the form.
• Ensure you select a date and time available in the system calendar.

3. Exam Day Presentation

To enter the exam, it is mandatory to comply with the following guidelines:

What you MUST present:

• Proof of payment:
  • If paid at the bank (teller): Present the original receipt.
  • If paid online: Present the printed receipt.
• Identity Document: Valid ID card (Cédula) or passport.
• Allowed Materials: Pencil, eraser, and a non-programmable scientific calculator (basic models that do not allow storing text, custom formulas, or executing complex algorithms).

What is NOT allowed:

• The use of mobile phones, tablets, smartwatches, or any electronic device with a camera or internet connection capabilities.
• The entry of formula sheets (math or physics) or notes in any format.

Technical Specifications of the Test

Exam Purpose

The fundamental purpose of this exam is to objectively measure the level of mastery of competencies—knowledge, skills, and abilities—that a candidate possesses in the field of physics. The results obtained from this standardized instrument are designed to be used for the following purposes:

• Admission and Diagnosis for Graduate Programs: To predict with a high degree of reliability an applicant's probability of success in physics graduate programs, such as specializations, master's degrees, or doctorates. The exam allows for the evaluation of whether the candidate possesses the conceptual foundation and analytical skills indispensable for facing the academic challenges of an advanced training program.
• Competency Certification for Teaching: To identify and certify a candidate's competencies to teach physics at different educational levels. This includes teaching at the secondary level, the university basic cycle (introductory courses), and general physics subjects at the higher level. The exam ensures the applicant masters the content they will be required to teach.
• Detailed Candidate Profile: To offer a precise description with a high degree of certainty regarding the academic profile of the examinee. Based on the evidence collected, the exam allows for clearly defining the conceptual knowledge, problem-solving skills, and analytical abilities the candidate has consolidated, providing a complete overview of their strengths and weaknesses.
• Support for Employment Decision Making: To facilitate informed decision-making for employers seeking to fill positions requiring a solid command of physics. The results offer an objective and standardized criterion to select the most suitable candidate according to the specific needs of the position, whether in academic, industrial, or research sectors.

Scope and Limitations of the Exam

To ensure a fair interpretation and appropriate use of the results, it is fundamental to understand the specific scope of the Physics Competence Accreditation Exam (EAC-Física) and recognize its inherent limitations.

• Focus on Specific Competencies: The exam is rigorously designed to measure Physical Reasoning and Modeling and Procedural and Quantitative Execution competencies, as detailed in this document. It does not intend to be a measure of general intelligence, innate aptitude, or future potential, and its results should not be interpreted as such.
• Does Not Evaluate Written Communication Skills: Given that the exam format is multiple-choice, evidence regarding candidates' ability to draft technical texts, argue in writing, or communicate complex ideas with coherence and style is not collected.
• Does Not Evaluate Practical Experimental Skills: While the syllabus includes the theoretical foundations of laboratory methods, the exam does not evaluate a candidate's practical dexterity. Skills such as instrumentation manipulation, experiment assembly, or taking measurements in a laboratory fall outside the scope of this test.
• Does Not Evaluate Creativity or Problem Formulation: The exam measures a candidate's ability to solve well-defined problems and apply known principles. It is not designed to evaluate creativity, originality of thought, or the ability to formulate new research questions—competencies that are fundamental in scientific research and development.
• Does Not Measure Computational Skills: Modern physics relies heavily on computational tools for simulation, modeling, and data analysis. This exam does not evaluate a candidate's competence in programming, use of specialized software, or the application of numerical methods to solve physical problems.
• Individual Performance Evaluation: The EAC-Física is an individual performance test. Therefore, it does not measure interpersonal competencies such as teamwork, collaboration, or leadership.
• Use as a Complementary Tool: The results of this exam should be considered as a single piece of evidence within a broader candidate profile. It is strongly recommended that admission, certification, or hiring decisions be made using the results of this test in conjunction with other sources of information, such as academic history, recommendation letters, interviews, and work portfolios.
• Point-in-Time Performance Measure: The result obtained by a candidate represents their performance on the day and under the specific conditions of the exam administration. It is important to recognize that external factors (such as health or stress) can influence performance. Therefore, the result should be interpreted as a "snapshot" of the candidate's mastery at that specific moment.

Exam Syllabus

This syllabus describes the knowledge areas and specific subtopics that will be evaluated. The assessment will focus on measuring the competencies of Physical Reasoning and Modeling and Procedural and Quantitative Execution within the following domains:

1. Classical Mechanics (20%) Analysis of principles governing the motion of bodies, from particle kinematics to advanced formalisms for complex systems.

   • Fundamentals of Kinematics and Dynamics: Description of motion (position, velocity, acceleration) and application of Newton's Laws.
   • Conservation of Energy and Momentum: Work-energy theorem, conservative forces, potential energy, conservation of linear and angular momentum in particle systems.
   • Rotational Dynamics and Oscillations: Motion of rigid bodies regarding a fixed axis (torque, moment of inertia) and simple harmonic, damped, and forced motion.
   • Gravitation and Central Forces: Law of universal gravitation and celestial mechanics (Kepler's Laws).
   • Fluids: Hydrostatics (Pascal's principle), Bernoulli's equation, and continuity equation.
   • Advanced Topics: Non-inertial reference systems and foundations of Lagrangian and Hamiltonian formalisms.

2. Electromagnetism (20%) Study of electric and magnetic phenomena, covering from static fields to electrodynamics described by Maxwell's equations.

   • Electrostatics: Coulomb's Law, electric field and potential, Gauss's Law, and behavior of dielectrics.
   • Magnetostatics: Magnetic fields in vacuum and matter (Biot-Savart Law, Ampere's Law), and Lorentz force.
   • Electric Circuits: Analysis of Direct Current (DC) and Alternating Current (AC) circuits using Ohm's Law, Kirchhoff's Laws, and impedance formalism.
   • Electrodynamics: Electromagnetic induction (Faraday's Law), Maxwell's equations in integral and differential forms, and propagation of electromagnetic waves.

3. Optics and Wave Phenomena (10%) Analysis of the behavior and properties of waves, with special emphasis on light.

   • Fundamental Principles of Waves: General properties, superposition, Doppler effect.
   • Physical Optics: Interference, diffraction, and polarization phenomena.
   • Geometric Optics: Principles of reflection and refraction applied to mirrors and thin lenses.

4. Thermodynamics and Statistical Mechanics (10%) Study of thermal energy and its transfer, connecting macroscopic properties of systems with their microscopic foundation.

   • Principles of Thermodynamics: The four laws of thermodynamics, processes, equations of state, and thermodynamic cycles.
   • Kinetic Theory and Heat Transfer: Kinetic model of ideal gases and mechanisms of conduction, convection, and radiation.
   • Foundations of Statistical Mechanics: Statistical ensembles, Boltzmann distribution, and its use to calculate thermodynamic quantities.

5. Quantum Mechanics (10%) Understanding of fundamental principles governing phenomena at atomic and subatomic scales.

   • Foundations of Quantum Mechanics: Wave-particle duality, uncertainty principle, and wave function postulate.
   • Schrödinger Equation: Applications to canonical systems such as potential wells, the harmonic oscillator, and the hydrogen atom.
   • Quantum Structure: Concepts of angular momentum and spin, and foundations of time-independent perturbation theory and variational methods.

6. Materials and Particle Physics (10%) Analysis of the structure of matter from the atomic level to the nuclear and condensed matter levels.

   • Atomic Physics: Atomic models, energy levels, spectra, selection rules, and interaction of atoms with external fields (Zeeman and Stark effects).
   • Nuclear and Particle Physics: Nucleus structure, radioactive decay, fission and fusion reactions, and classification of elementary particles.
   • Condensed Matter Physics: Crystal structures, X-ray diffraction, and basic models for thermal and electrical properties of solids.

7. Special Relativity (10%) Evaluation of the postulates of special relativity and their consequences in the description of space, time, and energy.

   • Principles and Relativistic Kinematics: Einstein's postulates, simultaneity, time dilation, and length contraction.
   • Lorentz Transformations: Transformation of space-time coordinates and velocities.
   • Relativistic Dynamics: Mass-energy relation, relativistic momentum, and energy.

8. Laboratory Methods and Data Analysis (10%) Understanding of conceptual principles behind experimental practice in physics.

   • Statistical Data Analysis: Error treatment, propagation of uncertainties, and curve fitting.
   • Instrumentation and Techniques: Principles of basic electronics, operation of key instrumentation (e.g., oscilloscope), and optical techniques (e.g., interferometers).
   • Interaction of Radiation with Matter: Foundations of particle and radiation detection.

Cognitive Competencies of the Exam

The exam is designed to evaluate two complementary and orthogonal domains of thought that are fundamental in physics:

Competency 1: Physical Reasoning and Modeling

• Weighting: 60%
• Focus: The "Why". Measures all acts of physical thinking that are independent of mathematical execution.
• General Description: This competency evaluates the candidate's ability to interpret physical situations, connect phenomena with fundamental principles, select appropriate models, and reason qualitatively about a system's behavior. It measures the depth of the candidate's conceptual scaffolding and their ability to use it as an analysis and prediction tool.

Competency 2: Procedural and Quantitative Execution

• Weighting: 40%
• Focus: The "How". Measures all algorithmic and mathematical skills necessary to solve a physics problem.
• General Description: This competency evaluates the candidate's ability to precisely and efficiently execute the steps necessary to translate a physical problem, once modeled and set up, into a quantitative solution. It focuses exclusively on the correct application of mathematical tools and the formal validation of results, assuming that conceptual understanding and strategy were already evaluated in Competency 1.

Cognitive Load Levels of Items

To ensure the exam measures a broad spectrum of the candidate's mastery, from fundamental knowledge to the ability to solve complex problems, the items (questions) are designed and classified according to four levels of cognitive load. This classification ensures a balanced distribution of difficulty throughout the test and allows for the generation of a detailed mastery report for each student.

The target distribution for the exam is as follows:

• Level 1 - Basic (Weighting: 10%)

  • Description: Items evaluating knowledge of concepts, definitions, and elementary formulas. They primarily require recognition and memory of fundamental information that is a prerequisite for any university study of physics.
  • Item Example: Identify the correct unit of angular momentum in the International System or recognize the formula for Newton's second law.

• Level 2 - Low Intermediate (Weighting: 30%)

  • Description: Items evaluating the understanding and direct application of essential principles of general physics. These correspond to the level of competence considered indispensable for any student who has satisfactorily completed basic physics courses in science or engineering programs.
  • Item Example: Solve a standard kinematics problem in one dimension or calculate the equivalent resistance of a simple series/parallel circuit.

• Level 3 - High Intermediate (Weighting: 40%)

  • Description: Items requiring a deeper understanding and the integration of multiple concepts to solve a problem. The candidate must be able to model a more complex situation, design a non-trivial solution strategy, and discriminate between various applicable principles.
  • Item Example: Analyze an inelastic collision in two dimensions where both momentum conservation and energy principles must be applied, or determine the electric field of a continuous charge distribution.

• Level 4 - Advanced (Weighting: 20%)

  • Description: Items evaluating advanced knowledge, typically covered in upper-level physics courses or introductory graduate courses. These questions may require the use of more abstract formalisms or the synthesis of ideas from different areas of physics.
  • Item Example: Set up a problem using the Lagrangian formalism, apply the Schrödinger equation to a non-trivial quantum system, or use Lorentz transformations to analyze simultaneity in a relativity problem.

Exam Specification Table

Note on difficulty distribution: The construction of the exam will be guided by the cognitive load distribution described in the previous section (10% Basic, 30% Low Intermediate, 40% High Intermediate, 20% Advanced), ensuring a global balance across all content areas.

Item Quantity and Duration

• Total Number of Items: 60
• Item Format: Multiple Choice
• Duration: 180 minutes

Results Report

Upon completing the exam, each candidate will receive a detailed and confidential results report, designed to offer a complete and constructive profile of their physics competencies. The report is structured in the following sections:

Confidentiality and Data Management Policy

The Institute of Physics is committed to protecting candidate privacy and ensuring the confidentiality of the Physics Competence Accreditation Exam (EAC-Física) results. The management of all personal information and exam results is governed by the following principles:

• Ownership and Delivery of Results: Exam results are the property of the candidate. Consequently, the results report will be delivered exclusively:

  1. To the candidate directly, via established secure communication channels.
  2. To third parties or institutions (universities, employers, etc.) only when the candidate explicitly authorizes it in writing, either on the application form or through a subsequent verified request.

• Prohibition of Public Disclosure: The Institute of Physics will not publicly disclose individual results nor share them with third parties without the prior, explicit, and written consent of the candidate.

• Protection of Personally Identifiable Information: All information that allows for the identification of a candidate (names, identity documents, contact information, etc.) will be treated as strictly confidential. Access to this data will be restricted to a minimum number of authorized personnel at the Institute of Physics, and solely for the purpose of administering the exam, processing results, and delivering reports requested by the candidate.

• Use of Data for Statistical and Improvement Purposes: The Institute of Physics reserves the right to use exam results in an anonymous and aggregated manner for statistical research, psychometric validation, and continuous improvement of the instrument. Under no circumstances will data allowing the identification of an individual candidate be published in these analyses.

Recommended Bibliography

General Physics Bibliography

These books are recommended to ensure the foundations of all areas are well covered. They are standard texts in the first years of most physics and engineering degrees. 80% of the exam items (Levels 1 to 3) can be fully prepared using the books in this section.

• Young HD, Freedman RA, Ford AL. University Physics with Modern Physics. 14th ed. Pearson Education; 2018.
• Halliday D, Resnick R, Walker J. Fundamentals of Physics. 11th ed. Wiley; 2018.
• Serway RA, Jewett JW. Physics for Scientists and Engineers. 10th ed. Cengage Learning; 2018.
• Giancoli DC. Physics for Scientists and Engineers. 4th ed. Pearson Education; 2008.

Advanced Physics Bibliography

These texts are more specialized and are suggested for preparing topics corresponding to Level 4 items (20% of the exam), which require greater depth.

1. Classical Mechanics

   • Taylor JR. Classical Mechanics. University Science Books; 2005.
   • Marion JB, Thornton ST. Classical Dynamics of Particles and Systems. 5th ed. Brooks Cole; 2003.
   • Goldstein H, Poole CP, Safko JL. Classical Mechanics. 3rd ed. Addison Wesley; 2002.

2. Electromagnetism

   • Griffiths DJ. Introduction to Electrodynamics. 4th ed. Cambridge University Press; 2017.

3. Optics and Wave Phenomena

   • Hecht E. Optics. 5th ed. Pearson; 2017.

4. Thermodynamics and Statistical Mechanics

   • Schroeder DV. An Introduction to Thermal Physics. Addison Wesley; 1999.
   • Callen HB. Thermodynamics and an Introduction to Thermostatistics. 2nd ed. John Wiley & Sons; 1985.

5. Quantum Mechanics

   • Griffiths DJ, Schroeter DF. Introduction to Quantum Mechanics. 3rd ed. Cambridge University Press; 2018.
   • Shankar R. Principles of Quantum Mechanics. 2nd ed. Springer; 1994.

6. Materials and Particle Physics

   • Kittel C. Introduction to Solid State Physics. 8th ed. John Wiley & Sons; 2005.
   • Griffiths DJ. Introduction to Elementary Particles. 2nd ed. Wiley-VCH; 2008.

7. Special Relativity

   • Taylor EF, Wheeler JA. Spacetime Physics. 2nd ed. W. H. Freeman; 1992.
   • Rindler W. Introduction to Special Relativity. 2nd ed. Oxford University Press; 1991.

8. Laboratory Methods and Data Analysis

   • Taylor JR. An Introduction to Error Analysis: The Study of Uncertainties in Physical Measurements. 2nd ed. University Science Books; 1997.