APS Graduate Exam study plan
APS Graduate Exam · Give each week a clear focus.
8 weeks · About 6 hours per week
General Physics Fundamentals
Derive the kinematic equations for constant acceleration from first principles and apply them to 10 projectile and relative-motion problems
State and apply conservation of energy and momentum to solve 8 collision and inclined-plane problems
Compute work, power, and efficiency for 5 mechanical systems with varying forces
Build a one-page formula sheet linking kinematics, dynamics, and energy with unit checks for each quantity
Your checkpoint
A worked problem set of 25 General Physics problems (mechanics fundamentals) with a graded self-check scoring at least 80% correct
General Physics Fundamentals & Classical Mechanics
Solve 10 rotational dynamics problems using torque, moment of inertia, and angular momentum conservation
Derive and apply the equations of motion for a rigid body rolling without slipping in 5 scenarios
Analyze 6 central-force/orbital problems using effective potential and Kepler's laws
Compare Lagrangian and Newtonian formulations by solving the same 3 problems both ways
Your checkpoint
A comparative write-up solving 3 mechanics problems via both Newtonian and Lagrangian methods, with a 10-item error log of mistakes made and corrected
Classical Mechanics
Derive the Euler-Lagrange equations for 5 systems with constraints and identify generalized coordinates
Solve 6 small-oscillation problems by linearizing the potential near equilibrium
Apply Noether's theorem to identify conserved quantities in 4 symmetric systems
Set up and solve 3 coupled-oscillator problems and interpret normal modes
Your checkpoint
A timed 90-minute mock Classical Mechanics section (20 problems) scored and reviewed, with every missed problem reworked to full solution
Electricity and Magnetism
Apply Gauss's law to compute fields for 8 symmetric charge distributions
Solve 6 boundary-value problems using separation of variables or method of images
Compute capacitance, energy density, and dielectric effects for 5 capacitor configurations
Derive and apply the Biot-Savart law and Ampere's law to 6 current configurations
Your checkpoint
A midterm checkpoint exam covering Domains 1-3 (30 problems, 2 hours) scored at or above 70%, with a remediation list for every sub-70% topic
Electricity and Magnetism & Quantum Mechanics
Apply Faraday's and Lenz's laws to 6 induction problems and compute induced EMF and current direction
Derive the Maxwell equations in differential and integral form and explain each term physically
Solve 5 AC circuit problems involving impedance, resonance, and phase
Compute electric and magnetic fields from retarded potentials for 3 simple time-dependent sources
Your checkpoint
A one-page derivation sheet for all four Maxwell equations plus 15 solved E&M problems, self-graded at 80% or better
Quantum Mechanics
Solve 8 one-dimensional Schrodinger equation problems for piecewise-constant potentials (well, step, barrier)
Compute expectation values and uncertainties for 6 wavefunctions and verify the uncertainty principle
Apply operator formalism and commutators to derive 5 conservation/uncertainty results
Solve 4 angular momentum and hydrogen-atom problems using quantum numbers and selection rules
Your checkpoint
A timed 75-minute Quantum Mechanics mock section (15 problems) scored at or above 70%, with a written correction for each error
Thermodynamics and Statistical Mechanics
Apply the first and second laws to 8 thermodynamic process problems (isothermal, adiabatic, cyclic)
Compute entropy changes for 6 reversible and irreversible processes and justify sign conventions
Derive and use the partition function for 4 canonical-ensemble systems (two-level, harmonic oscillator, ideal gas)
Relate statistical distributions (Maxwell-Boltzmann, Fermi-Dirac, Bose-Einstein) to 5 physical limits
Your checkpoint
A worked set of 20 Thermodynamics and Statistical Mechanics problems with a one-page summary table of ensembles and their thermodynamic relations
Mathematical Methods and Laboratory/Experimental Physics & General Physics Fundamentals & Classical Mechanics & Electricity and Magnetism & Quantum Mechanics & Thermodynamics and Statistical Mechanics
Solve 10 mathematical-methods problems covering linear algebra, complex analysis, and differential equations
Design and describe 3 laboratory/experimental scenarios (error propagation, data fitting, instrument limits) and compute their uncertainties
Complete two full-length timed practice exams under exam conditions
Compile a personal error log into a prioritized final-week review list of no more than 15 items
Your checkpoint
Two completed full-length practice exams with scores recorded, plus a final one-page review sheet covering only the top 15 recurring error patterns
Milestones
Week 2: Complete at least 40 cumulative practice problems across Domains 1 and 2 with an accuracy of 75% or higher
Week 4: Score 70% or higher on the 30-problem midterm checkpoint covering Domains 1-3 and produce a remediation list
Week 6: Score 70% or higher on the Quantum Mechanics mock section and confirm all Domain 3 goals are complete
Week 8: Score 75% or higher on both full-length practice exams and submit the final one-page review sheet