GEAS PRE-BOARD EXAMS 2026

Prepared by Julius Ele

$$\eta = \frac{W}{Q_H} = \frac{Q_H - Q_C}{Q_H}$$

Thermal Efficiency of a Heat Engine.

Thermal efficiency represents the fraction of total heat absorbed from a high-temperature reservoir that is successfully converted into net mechanical work output. It is applied in thermodynamics to analyze and evaluate the performance of combustion engines, power cycles, and thermal energy converters

$$\text{COP}_{\text{ref}} = \frac{Q_C}{W_{\text{in}}} = \frac{Q_C}{Q_H - Q_C}$$

Coefficient of Performance of a Refrigerator.

The coefficient of performance quantifies the refrigeration effect by comparing the quantity of thermal energy removed from a refrigerated cold reservoir to the net electrical or mechanical work input required. It is applied in cooling system design, heat pumps, and data center thermal management calculations

$$\eta_{\text{Carnot}} = 1 - \frac{T_C}{T_H}$$

Carnot Engine Efficiency Limit.

Carnot efficiency defines the absolute theoretical upper limit of thermodynamic conversion efficiency achievable by any heat engine operating between two absolute temperatures $T_H$ and $T_C$. It is applied in thermodynamics to benchmark actual heat engine cycles and evaluate the thermodynamic feasibility of novel energy claims

$$\Delta U = Q - W = 0$$

First Law of Thermodynamics for a Cyclic Process.

In a closed thermodynamic cyclic process returning to its initial state, the net change in internal energy is strictly zero because internal energy is a thermodynamic state function. It is applied in power plants and refrigeration cycles to establish that net cycle work output precisely equals net heat absorbed

$$Q_V = n C_v \Delta T = \frac{3}{2} n R \Delta T$$

Isochoric Heat Transfer for a Monatomic Ideal Gas.

Constant-volume heat transfer represents the energy absorbed by a confined gas solely to increase its internal thermal energy without performing boundary expansion work. It is applied in gas-dynamic cycles and sealed chamber pressure-temperature variation calculations

$$T_1 V_1^{\gamma - 1} = T_2 V_2^{\gamma - 1}$$

Reversible Adiabatic Process Equation.

This equation governs the thermodynamic state path of an ideal gas during a reversible process wherein no thermal energy is transferred into or out of the system. It is applied in rapid gas compression calculations, internal combustion stroke modeling, and acoustics

$$W = \int_{V_1}^{V_2} P \, dV = n R T \ln\left(\frac{V_2}{V_1}\right)$$

Isothermal Work of an Ideal Gas.

Isothermal work calculates the boundary energy transferred during a quasi-static expansion or compression process maintaining an invariant operating temperature. It is applied in evaluating ideal Carnot expansion stages, pneumatic actuator power, and isothermal compressor stages

$$P V = n R T = \left(\frac{m}{M}\right) R T$$

Ideal Gas Law.

The ideal gas equation of state mathematically interrelates the absolute pressure, volume, temperature, and molar quantity of a hypothetical gas exhibiting negligible intermolecular forces. It is applied in determining molar mass, gas density, and barometric fluid pressures across environmental and chemical engineering problems

$$F_c = m a_c = \frac{m v^2}{r} = m \omega^2 r$$

Centripetal Force Equation.

Centripetal force specifies the net radial inward force required to continuously curve an object's trajectory along a circular path of radius $r$ at tangential speed $v$. It is applied in vehicular road banking, satellite orbital dynamics, and rotational machinery stress analysis

$$J = \int_{t_1}^{t_2} F(t) \, dt = \Delta p = m(v_f - v_i)$$

Impulse-Momentum Theorem.

The impulse-momentum theorem equates the time integral of an applied resultant force to the net vector change in an object's linear momentum. It is applied in analyzing vehicle collisions, ballistic impacts, and mechanical shock absorption in electronics packaging

$$m_1 v_1 + m_2 v_2 = (m_1 + m_2) v_f$$

Conservation of Momentum for a Completely Inelastic Collision.

This equation expresses the conservation of linear momentum for an isolated multi-body system wherein colliding entities coalesce and proceed at an identical final common velocity. It is applied in impact mechanics, vehicular crash analysis, and automated robotics payload docking

$$F_s = -k x$$

Hooke's Law of Elasticity.

Hooke's Law asserts that the restorative mechanical force exerted by an elastic spring is directly proportional to its displacement from equilibrium and directed oppositely. It is applied in structural sensor design, mechanical suspension tuning, and oscillatory transducers

$$T = 2\pi \sqrt{\frac{m}{k}}$$

Period of a Mass-Spring Harmonic Oscillator.

The period of oscillation represents the time duration required for a mass $m$ coupled to an elastic spring of stiffness $k$ to execute one complete simple harmonic cycle. It is applied in mechanical vibration isolation, sensor suspensions, and resonant frequency characterization

$$R = \frac{v_0^2 \sin(2\theta)}{g}$$

Ideal Projectile Range Equation.

The horizontal projectile range calculates the total distance traversed by an airborne object launched with initial velocity $v_0$ at an elevation angle $\theta$ over level terrain under uniform gravity. It is applied in ballistics, trajectory analysis, and antenna projectile deployment modeling

$$\tau_{\text{net}} = I \alpha = I \frac{d\omega}{dt}$$

Newton's Second Law for Rotational Systems.

This law establishes that the net external torque applied to a rigid body about a fixed axis is equal to the product of its moment of inertia and resulting angular acceleration. It is applied in sizing electric motor actuators, robotic joint drive selection, and flywheel energy storage systems

$$K_{\text{rot}} = \frac{1}{2} I \omega^2$$

Rotational Kinetic Energy.

Rotational kinetic energy quantifies the kinetic energy stored within a rotating rigid body as a function of its mass distribution inertia $I$ and angular velocity $\omega$. It is applied in kinetic energy recovery systems (KERS), rotating machinery design, and turbine performance calculations

$$K_{\text{total}} = \frac{1}{2} m v^2 + \frac{1}{2} I \omega^2$$

Total Kinetic Energy of Rolling Without Slipping.

Total rolling kinetic energy represents the combined scalar sum of the body's center-of-mass translational kinetic energy and its rotational kinetic energy about that center. It is applied in analyzing wheels, spherical bearings, and cylindrical rollers moving along horizontal and inclined planes

$$f_1 = \frac{v}{2L} = \frac{1}{2L}\sqrt{\frac{T}{\mu}}$$

Fundamental Frequency of a Fixed String.

This formula calculates the lowest resonant acoustic frequency supported by a tensioned flexible string of linear density $\mu$ fixed rigidly at both ends across length $L$. It is applied in acoustic transducer modeling, musical instrument physics, and structural vibration monitoring

$$\Delta P = \rho g h$$

Hydrostatic Gauge Pressure Formula.

Hydrostatic pressure defines the internal fluid pressure exerted at a designated depth $h$ resulting entirely from the gravitational weight column of an incompressible fluid of density $\rho$. It is applied in submersible equipment casing design, liquid level sensors, and barometer height calculations

$$F_B = \rho_{\text{fluid}} V_{\text{displaced}} g$$

Archimedes' Principle of Buoyancy.

Archimedes' principle states that the net upward buoyant force acting on a submerged or partially floating body strictly equals the weight of the fluid displaced by its volume. It is applied in naval architecture, hydrometer calibration, and underwater sensor buoyancy modules

$$P_1 + \frac{1}{2}\rho v_1^2 + \rho g z_1 = P_2 + \frac{1}{2}\rho v_2^2 + \rho g z_2$$

Bernoulli's Conservation of Energy Equation.

Bernoulli's equation describes the conservation of total mechanical energy along a streamline for steady, inviscid, and incompressible fluid flow. It is applied in venturi flowmeters, pitot tube velocity meters, and aerodynamic lift calculations

$$\tau = \mu \frac{du}{dy}$$

Newton's Law of Viscosity.

Newton's law of viscosity establishes that the shear stress between adjacent moving fluid layers is directly proportional to the localized perpendicular velocity gradient through dynamic viscosity $\mu$. It is applied in microfluidic channel design, lubrication engineering, and hydraulic cooling systems

$$F_e = \frac{1}{4\pi\varepsilon} \frac{|q_1 q_2|}{r^2}$$

Coulomb's Electrostatic Force Law.

Coulomb's Law defines the magnitude of the electrostatic attraction or repulsion exerted between two stationary point charges separated by distance $r$ in a dielectric medium. It is applied in electrostatics, semiconductor physics, and electron beam deflection analysis

$$\oint \vec{E} \cdot d\vec{A} = \frac{Q_{\text{enc}}}{\varepsilon_0}$$

Gauss's Law for Electrostatics.

Gauss's Law states that the total outward electric flux passing through any closed spatial Gaussian surface is directly proportional to the enclosed net electric charge. It is applied in calculating electric fields around symmetric conductors, coaxial cables, and planar capacitors

$$E_{\text{cap}} = \frac{1}{2} C V^2$$

Stored Electrostatic Energy in a Capacitor.

This formula quantifies the total electrical potential energy accumulated within the electrostatic field of a capacitor characterized by capacitance $C$ charged to terminal potential $V$. It is applied in power supply smoothing filter design, supercapacitor storage sizing, and pulsed power circuits

$$v_d = \frac{I}{n q A}$$

Electron Drift Velocity Equation.

Electron drift velocity expresses the average net axial speed of mobile charge carriers propagating through a conductive conductor of cross section $A$ under a continuous electric current $I$. It is applied in solid-state semiconductor modeling, conductor current capacity calculations, and Hall effect analyses

$$\mathcal{E} = -\frac{d\Phi_B}{dt} = -N \frac{d}{dt}(B A \cos\theta)$$

Faraday-Lenz Law of Electromagnetic Induction.

This fundamental law dictates that the magnitude of an induced electromotive force in a closed loop is directly proportional to the time rate of change of intersecting magnetic flux, opposing that change. It is applied in electric generators, inductive sensors, transformers, and wireless charging links

$$Z = \sqrt{R^2 + (X_L - X_C)^2}, \quad f_0 = \frac{1}{2\pi\sqrt{LC}}$$

Series RLC Circuit Impedance and Resonance.

This equation computes the total equivalent complex impedance magnitude of a series RLC network and defines the exact resonant frequency where inductive and capacitive reactances cancel. It is applied in RF receiver tuning, bandpass filter design, and impedance matching networks

$$n_1 \sin\theta_1 = n_2 \sin\theta_2$$

Snell's Law of Refraction.

Snell's Law defines the invariant relationship governing the angles of incidence and refraction for electromagnetic waves crossing an interface separating two media of differing refractive indices. It is applied in optical lens engineering, prism spectrometers, and optical fiber ray-tracing

$$\sin\theta_c = \frac{n_2}{n_1} \quad (n_1 > n_2)$$

Critical Angle for Total Internal Reflection.

The critical angle designates the unique angle of incidence beyond which light incident on a boundary with a lower-index medium undergoes complete internal reflection without refractive loss. It is applied in fiber optic telecommunications to calculate the acceptance angle and numerical aperture

$$\tan\theta_B = \frac{n_2}{n_1}$$

Brewster's Polarization Angle.

Brewster's angle defines the specific angle of incidence at which unpolarized light reflecting from a planar dielectric interface becomes completely linearly polarized perpendicular to the incident plane. It is applied in laser cavity window design, anti-glare filters, and optical polarization instrumentation

$$\frac{1}{f} = \frac{1}{d_o} + \frac{1}{d_i}, \quad M = -\frac{d_i}{d_o}$$

Thin Lens Equation and Linear Magnification.

The thin lens equation relates an optical element's focal length $f$ to the finite object and image distances, while magnification represents the ratio of image height to object height. It is applied in camera systems, microscopy, optical sensor alignment, and projection displays

$$a \sin\theta = m \lambda \implies y_m \approx \frac{m \lambda D}{a}$$

Single-Slit Fraunhofer Diffraction Minima.

This diffraction relationship dictates the angular positions and spatial screen coordinates where destructive wave interference generates intensity minima when light passes through an aperture of width $a$. It is applied in laser beam divergence analysis, spectrometer resolution tuning, and optical limit of resolution assessments

$$E = h f = \frac{h c}{\lambda}$$

Planck-Einstein Relation for Photon Energy.

The Planck-Einstein relation quantifies the quantized energy packet transported by an individual photon of electromagnetic radiation as a function of its operating frequency or wavelength. It is applied in optoelectronics, quantum optics, photodiode threshold analysis, and laser physics

$$\lambda_{\text{cutoff}} = \frac{h c}{E_g} = \frac{1240 \text{ eV}\cdot\text{nm}}{E_g}$$

Semiconductor Absorption Cutoff Wavelength.

The optical absorption cutoff represents the maximum permissible wavelength of an incident photon possessing sufficient quantum energy to excite an electron across the forbidden bandgap $E_g$. It is applied in designing semiconductor photodetectors, solar cells, and optical receiver transceivers

$$\text{APF} = \frac{N_{\text{atoms}} V_{\text{atom}}}{V_{\text{unit cell}}}$$

Atomic Packing Factor.

The atomic packing factor defines the fractional volume of a solid crystal unit cell that is occupied by constituent hard-sphere atoms. It is applied in materials science to classify metallic structures like FCC ($\text{APF} = 0.74$) and BCC ($\text{APF} = 0.68$) and evaluate density

$$J = -D \frac{dC}{dx}$$

Fick's First Law of Steady-State Diffusion.

Fick's First Law dictates that the net spatial diffusive mass flux of particles moves down a concentration gradient proportionally to the material diffusion coefficient $D$. It is applied in semiconductor impurity doping profiles, solid-state battery electrolytes, and gas permeation barriers

$$N(t) = N_0 \left(\frac{1}{2}\right)^{t / t_{1/2}} = N_0 e^{-\lambda t}$$

Radioactive Exponential Decay Law.

This decay equation models the time-dependent statistical reduction in the population of unstable radioactive parent nuclei as a function of half-life $t_{1/2}$ or decay constant $\lambda$. It is applied in radiometric dating, medical isotope treatment, and nuclear-powered battery lifespan estimation

$$\frac{k}{\sigma T} = L = \frac{\pi^2 k_B^2}{3 e^2}$$

Wiedemann-Franz Law.

The Wiedemann-Franz law states that the ratio of thermal conductivity to electrical conductivity in metals is directly proportional to absolute temperature through the universal Lorenz number $L$. It is applied in condensed matter physics and thermoelectric material efficiency optimization

$$i_e = \left(1 + \frac{r}{m}\right)^m - 1$$

Effective Annual Interest Rate.

The effective annual rate determines the true compounded annual financial yield or borrowing rate considering the compounding frequency $m$ of a stated nominal rate $r$. It is applied in engineering economy to rigorously compare financial project proposals and loan structures

$$P = A \left[ \frac{(1 + i)^n - 1}{i (1 + i)^n} \right] = A (P/A, i, n)$$

Uniform Series Present Worth Equation.

The uniform series present worth factor converts a sequence of equal periodic cash disbursements $A$ made over $n$ periods into a single economically equivalent lump sum today. It is applied in capital budgeting, equipment leasing evaluation, and project net present worth feasibility studies

$$A = P \left[ \frac{i (1 + i)^n}{(1 + i)^n - 1} \right] = P (A/P, i, n)$$

Capital Recovery Factor.

The capital recovery formula calculates the uniform periodic revenue or payment needed over $n$ periods at interest rate $i$ to fully amortize an initial capital asset investment $P$. It is applied in equipment justification, annualized cost analysis, and loan repayment scheduling

$$P = \frac{A}{i}$$

Capitalized Value of an Ordinary Perpetuity.

This capitalization formula computes the finite present monetary investment required to yield a perpetual, unbroken uniform cash dividend $A$ at a fixed periodic discount rate $i$. It is applied in financing perpetual endowments, municipal infrastructure maintenance funds, and capitalized cost estimations

$$D_t = \frac{B - S}{n}$$

Straight-Line Method of Depreciation.

Straight-line depreciation calculates an invariant annual asset write-down expense by dividing the unadjusted depreciable base (initial cost $B$ minus salvage $S$) equally across useful service life $n$. It is applied in corporate accounting, engineering project book-value tracking, and tax liability reduction

$$\text{Assets} = \text{Liabilities} + \text{Owner's Equity}$$

Fundamental Accounting Equation.

The fundamental accounting equation states that the aggregate economic resources owned by a commercial enterprise must precisely equal the total financial claims asserted by creditors and owners. It is applied in double-entry bookkeeping, corporate balance sheet construction, and financial audit verification

$$\text{CR} = \frac{\text{Current Assets}}{\text{Current Liabilities}}, \quad \text{QR} = \frac{\text{Current Assets} - \text{Inventory}}{\text{Current Liabilities}}$$

Current and Quick Financial Liquidity Ratios.

These financial metrics measure an organization's capacity to discharge immediate short-term debt obligations using liquid assets, with the quick ratio applying a stricter test by subtracting inventory. It is applied in evaluating startup solvency, working capital health, and enterprise credit risk

$$Q_{\text{BEP}} = \frac{\text{Fixed Costs}}{\text{Unit Selling Price} - \text{Unit Variable Cost}}$$

Break-Even Volume Analysis.

The break-even point establishes the precise sales volume threshold where total enterprise gross revenues exactly balance cumulative fixed and variable operational costs. It is applied in feasibility studies, product commercialization planning, and manufacturing capacity design

$$\text{EMV} = \sum_{i=1}^{k} P_i \cdot X_i$$

Expected Monetary Value.

Expected monetary value computes the statistical weighted average payoff of an engineering investment decision operating under probabilistic environmental states of nature. It is applied in risk analysis, decision tree evaluations, and competitive bidding strategies

$$\text{AMAT} = t_{\text{hit}} + (1 - h) \cdot t_{\text{miss}}$$

Average Memory Access Time in Computer Architecture.

AMAT calculates the effective latency of a hierarchical computer memory subsystem based on cache hit time, cache miss rate $(1-h)$, and main memory miss penalty. It is applied in processor performance profiling, embedded system benchmarking, and cache hierarchy optimization

$$T_{\text{exec}} = \frac{I \cdot \text{CPI}}{f_{\text{clk}}}$$

CPU Program Execution Time Formula.

CPU execution time quantifies total computing runtime as the product of total instruction count $I$ and cycles per instruction divided by operating system clock frequency $f_{\text{clk}}$. It is applied in computer architecture optimization, microprocessor selection, and compiler efficiency evaluation

$$\text{CO}_2 + \text{H}_2\text{O} \rightleftharpoons \text{H}_2\text{CO}_3 \rightleftharpoons \text{H}^+ + \text{HCO}_3^-$$

Seawater Carbonate and Ocean Acidification Reaction.

This chemical equilibrium chain shows how anthropogenic carbon dioxide dissolving into seawater forms carbonic acid, which dissociates into hydrogen and bicarbonate ions, directly lowering oceanic pH. It is applied in environmental monitoring, marine ecosystem impact studies, and climate mitigation assessments

$$\text{RA 9292, Section 30}$$

Code of Ethics and Technical Standards in RA 9292.

Section 30 of Republic Act No. 9292 legally directs the Electronics Engineering Regulatory Board to adopt and enforce a binding Code of Ethics and Code of Technical Standards of Practice. It is applied in regulating Philippine professional conduct, evaluating malpractice disputes, and maintaining professional board licensure standards

$$\text{RA 9292, Section 35}$$

Penal Provisions of the Electronics Engineering Law of 2004.

Section 35 specifies penal sanctions comprising fines between P50,000 to P1,000,000 and/or imprisonment from 6 months to 6 years for unauthorized practice, illegal stamping, or licensing fraud. It is applied in prosecutorial enforcement against illegal engineering practice and safeguarding public welfare in the Philippines

$$\text{RA 7925}$$

Public Telecommunications Policy Act of the Philippines.

Republic Act No. 7925 establishes the legal regulatory architecture mandating fair, non-discriminatory, and compulsory physical and logical interconnection among all authorized public telecommunications entities. It is applied in Philippine telecommunications licensing, interconnection disputes, and open market competitive regulation

$$\text{RA 8749}$$

Philippine Clean Air Act of 1999.

Republic Act No. 8749 provides a comprehensive national environmental policy framework directed toward mitigating ambient industrial air pollution and phasing out hazardous emissions. It is applied in plant emissions compliance, environmental impact assessments, and industrial HVAC scrub design

$$\text{PD 1586}$$

Philippine Environmental Impact Statement System.

Presidential Decree No. 1586 establishes the compulsory legal requirement for infrastructure developers to conduct comprehensive Environmental Impact Assessments (EIA) to obtain an Environmental Compliance Certificate. It is applied in scoping project site viability, pollution abatement, and public consultation for major technical projects

$$\text{RA 8293}$$

Intellectual Property Code of the Philippines.

Republic Act No. 8293 sets the national legal architecture governing the registration, ownership, protection, and licensing enforcement of patents, trademarks, industrial designs, and software copyrights. It is applied in securing engineering patents, software codebase licensing, and corporate innovation asset protection

$$\text{RA 11058}$$

Occupational Safety and Health Standards Act.

Republic Act No. 11058 strengthens national workplace safety compliance by mandating strict hazard controls, worker training, and punitive administrative fines for safety standard infractions. It is applied in industrial plant engineering, PPE enforcement, and electronics manufacturing safety programs

$$\text{PEC 1} \implies h \ge 5.5\text{ m } (18\text{ ft})$$

Minimum Overhead Cable Road Clearance.

The Philippine Electronics Code dictates an absolute minimum vertical clearance of 5.5 meters (18 feet) for overhead communication cables spanning roads and parking lots subject to truck traffic. It is applied in outside plant (OSP) telecommunications aerial installations and roadside distribution pole infrastructure

$$\text{EVM: } \text{CPI} = \frac{\text{EV}}{\text{AC}}, \quad \text{SPI} = \frac{\text{EV}}{\text{PV}}$$

Earned Value Management Performance Metrics.

Earned Value Management uses Cost Performance Index and Schedule Performance Index to objectively track project budget utilization and timeline adherence against an engineering project baseline. It is applied in engineering project control, milestone governance, and construction expenditure auditing

$$\mathcal{C}_{\text{subclass}} \subseteq \mathcal{C}_{\text{parent}} \implies \text{Inheritance / Polymorphism}$$

Object-Oriented Inheritance and Subtyping.

This object-oriented relationship allows a derived class to inherit operational methods and state variables from a base class while overriding interfaces to demonstrate dynamic runtime polymorphic behavior. It is applied in software architecture, GUI component design, and embedded system driver structuring