Benchmark structure

Exercise Atlas.
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Search and inspect all 60 exercises, their source material, scoring evidence and retained model responses.

21 configurations60 exercises1,260 matched cells2 subjects

Exercise Atlas scope

60 exercises1260 matched cells1344 retained runs21 model-mode configurations
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Mean score and cross-configuration SD are descriptive summaries of the selected 21-configuration panel. Lower observed mean scores do not establish intrinsic exercise difficulty. Replicas are averaged within each configuration–exercise cell, and retained runs remain available in the research record.

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60 of 60 records shown

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benchmark exercises with descriptive score and resource measurements
Exercise / topicExam recordObserved mean21-configuration distributionCross-configuration SDObserved resourcesOpen profile
Normal form, existence and uniqueness, symmetries, linear equations, and piecewise dynamics(A3-25-P1-E3)Ordinary differential equations2025First sittingAnalysis III · Exercise 358.6/100#1 of 60 by lowest mean
23.5–100.0 · 1 scoring 100
SD 24.2#4 of 60 by spread33 criteria incomplete in at least two configurations147.9s$0.131 · 13,459 tokens0.06 retries · 4 replicated cellsOpen →
RLC circuit with a switchable parallel capacitor branch(F2-26-P1-E2)Circuits and AC response2026First sittingPhysics II · Exercise 267.4/100#2 of 60 by lowest mean
50.0–89.0 · 0 scoring 100
SD 8.8#42 of 60 by spread14 criteria incomplete in at least two configurations86.2s$0.069 · 10,659 tokens0.00 retries · 0 replicated cellsOpen →
Interference of three coherent sources with unequal amplitudes(F2-25-P3-E3)Electromagnetic waves and optics2025Third sittingPhysics II · Exercise 377.5/100#3 of 60 by lowest mean
27.9–100.0 · 7 scoring 100
SD 23.6#5 of 60 by spread27 criteria incomplete in at least two configurations125.7s$0.092 · 13,401 tokens0.00 retries · 0 replicated cellsOpen →
Centroid, improper integrals, Gauss and Stokes theorems(A3-26-P2B-E2)Multiple integrals and integral theorems2026Second sitting · Theme BAnalysis III · Exercise 280.0/100#4 of 60 by lowest mean
29.5–100.0 · 11 scoring 100
SD 28.1#1 of 60 by spread30 criteria incomplete in at least two configurations328.9s$0.162 · 21,268 tokens0.14 retries · 0 replicated cellsOpen →
Centroid of a planar region, singular integrals, and Gauss theorem verification on a solid of revolution(A3-25-P2-E2)Multiple integrals, improper integrability, and Gauss theorem2025Second sittingAnalysis III · Exercise 280.4/100#5 of 60 by lowest mean
31.3–100.0 · 5 scoring 100
SD 25.7#3 of 60 by spread27 criteria incomplete in at least two configurations184.1s$0.136 · 18,309 tokens0.00 retries · 1 replicated cellsOpen →
Existence and uniqueness for an implicit equation, and Cauchy problems for alpha=1 and alpha=0(A3-25-P2-E3)First-order ordinary differential equations2025Second sittingAnalysis III · Exercise 381.2/100#6 of 60 by lowest mean
52.3–100.0 · 2 scoring 100
SD 15.2#20 of 60 by spread24 criteria incomplete in at least two configurations86.6s$0.080 · 9,142 tokens0.00 retries · 1 replicated cellsOpen →
Existence away from singular axes, integrating factor, and crossing t=0(A3-25-P5-E3)Implicit differential equations2025Fifth sittingAnalysis III · Exercise 382.9/100#7 of 60 by lowest mean
32.1–100.0 · 7 scoring 100
SD 21.8#7 of 60 by spread23 criteria incomplete in at least two configurations141.2s$0.087 · 10,699 tokens0.05 retries · 1 replicated cellsOpen →
Centroid, improper integrals, Gauss and Stokes theorems(A3-26-P2A-E2)Multiple integrals and integral theorems2026Second sitting · Theme AAnalysis III · Exercise 283.6/100#8 of 60 by lowest mean
23.5–100.0 · 11 scoring 100
SD 25.9#2 of 60 by spread30 criteria incomplete in at least two configurations413.2s$0.168 · 22,298 tokens0.05 retries · 0 replicated cellsOpen →
Existence, energy, and a forced linear ODE(A3-25-P4-E3)Second-order differential equations2025Fourth sittingAnalysis III · Exercise 384.0/100#9 of 60 by lowest mean
45.0–100.0 · 5 scoring 100
SD 15.1#21 of 60 by spread15 criteria incomplete in at least two configurations189.3s$0.095 · 10,548 tokens0.06 retries · 1 replicated cellsOpen →
Existence and uniqueness, equilibria, first integral, orbits, Cauchy problems, and time reparameterization(A3-25-P3-E3)Autonomous and linear differential systems2025Third sittingAnalysis III · Exercise 384.6/100#10 of 60 by lowest mean
15.3–100.0 · 4 scoring 100
SD 19.6#11 of 60 by spread20 criteria incomplete in at least two configurations114.2s$0.087 · 11,387 tokens0.00 retries · 1 replicated cellsOpen →
Thin-film interference and Fresnel coefficients(F2-25-P5-E3)Electromagnetic waves and optics2025Fifth sittingPhysics II · Exercise 384.7/100#11 of 60 by lowest mean
52.6–92.6 · 0 scoring 100
SD 8.3#44 of 60 by spread10 criteria incomplete in at least two configurations61.8s$0.053 · 7,533 tokens0.00 retries · 0 replicated cellsOpen →
Centroid, parametric integrability, Gauss and Stokes theorems(A3-25-P4-E2)Multiple integrals and integral theorems2025Fourth sittingAnalysis III · Exercise 285.1/100#12 of 60 by lowest mean
35.3–100.0 · 6 scoring 100
SD 19.4#12 of 60 by spread25 criteria incomplete in at least two configurations177.8s$0.121 · 16,439 tokens0.00 retries · 1 replicated cellsOpen →
Single-slit diffraction, point-source interference, and a dielectric plate(F2-25-P4-E3)Electromagnetic waves and optics2025Fourth sittingPhysics II · Exercise 385.9/100#13 of 60 by lowest mean
56.6–100.0 · 3 scoring 100
SD 10.4#33 of 60 by spread17 criteria incomplete in at least two configurations197.5s$0.115 · 15,689 tokens0.05 retries · 0 replicated cellsOpen →
Interference and diffraction from three unequal slits(F2-26-P2-E3)Electromagnetic waves and optics2026Second sittingPhysics II · Exercise 386.2/100#14 of 60 by lowest mean
51.6–100.0 · 10 scoring 100
SD 18.3#14 of 60 by spread21 criteria incomplete in at least two configurations244.3s$0.118 · 17,397 tokens0.10 retries · 0 replicated cellsOpen →
Polar centroid, integrability of singular functions, and verification of Gauss and Kelvin–Stokes(A3-25-P3-E2)Multiple integrals, improper integrability, and vector-calculus integral theorems2025Third sittingAnalysis III · Exercise 286.3/100#15 of 60 by lowest mean
32.3–100.0 · 9 scoring 100
SD 21.9#6 of 60 by spread29 criteria incomplete in at least two configurations202.6s$0.148 · 20,594 tokens0.00 retries · 1 replicated cellsOpen →
Centroid, improper integrability, Gauss and Kelvin–Stokes theorems(A3-26-P3-E2)Multiple integrals and integral theorems2026Third sittingAnalysis III · Exercise 286.4/100#16 of 60 by lowest mean
39.0–100.0 · 8 scoring 100
SD 21.4#8 of 60 by spread22 criteria incomplete in at least two configurations277.2s$0.139 · 19,288 tokens0.00 retries · 0 replicated cellsOpen →
Centroid, improper integrability, volume by slices, and fluxes(A3-26-P4-E2)Multiple integrals and Gauss theorem2026Fourth sittingAnalysis III · Exercise 287.0/100#17 of 60 by lowest mean
44.5–100.0 · 13 scoring 100
SD 20.8#9 of 60 by spread20 criteria incomplete in at least two configurations242.0s$0.106 · 14,123 tokens0.00 retries · 0 replicated cellsOpen →
Level set in R3→R2, quadratic expansion, stationary points, and absolute extrema(A3-26-P3-E1)Level curves and constrained extrema2026Third sittingAnalysis III · Exercise 187.5/100#18 of 60 by lowest mean
29.2–100.0 · 10 scoring 100
SD 19.6#10 of 60 by spread21 criteria incomplete in at least two configurations289.4s$0.122 · 14,713 tokens0.00 retries · 0 replicated cellsOpen →
Centroid and volume; Gauss and Kelvin–Stokes theorems(A3-25-P1-E2)Multiple integration and vector calculus2025First sittingAnalysis III · Exercise 288.2/100#19 of 60 by lowest mean
44.5–100.0 · 13 scoring 100
SD 17.9#15 of 60 by spread23 criteria incomplete in at least two configurations149.2s$0.085 · 11,262 tokens0.02 retries · 4 replicated cellsOpen →
Exact implicit ODE and linear Euler equation(A3-26-P1A-E3)Differential equations2026First sitting · Theme AAnalysis III · Exercise 388.4/100#20 of 60 by lowest mean
41.3–100.0 · 7 scoring 100
SD 16.9#16 of 60 by spread20 criteria incomplete in at least two configurations101.9s$0.089 · 10,944 tokens0.00 retries · 0 replicated cellsOpen →
Centroid, improper integrals, Gauss theorem verification, and lateral area(A3-25-P5-E2)Multiple integrals, Gauss theorem, and surfaces2025Fifth sittingAnalysis III · Exercise 288.7/100#21 of 60 by lowest mean
30.0–100.0 · 7 scoring 100
SD 19.4#13 of 60 by spread24 criteria incomplete in at least two configurations127.1s$0.096 · 12,383 tokens0.00 retries · 1 replicated cellsOpen →
Brewster angle and polarization in a prism(F2-26-P4-E3)Electromagnetic waves and optics2026Fourth sittingPhysics II · Exercise 389.7/100#22 of 60 by lowest mean
41.3–100.0 · 9 scoring 100
SD 16.9#16 of 60 by spread25 criteria incomplete in at least two configurations171.8s$0.123 · 17,528 tokens0.00 retries · 0 replicated cellsOpen →
Exact implicit ODE and linear Euler equation(A3-26-P1B-E3)Differential equations2026First sitting · Theme BAnalysis III · Exercise 390.0/100#23 of 60 by lowest mean
46.0–100.0 · 7 scoring 100
SD 14.7#23 of 60 by spread20 criteria incomplete in at least two configurations102.0s$0.088 · 10,705 tokens0.00 retries · 0 replicated cellsOpen →
Diffraction grating, missing orders, and resolving power(F2-25-P1-E3)Electromagnetic waves and optics2025First sittingPhysics II · Exercise 390.3/100#24 of 60 by lowest mean
66.6–100.0 · 8 scoring 100
SD 11.1#31 of 60 by spread13 criteria incomplete in at least two configurations594.6s$0.069 · 8,721 tokens0.03 retries · 3 replicated cellsOpen →
Existence, first integral, orbits, and time reparameterization(A3-26-P3-E3)Autonomous differential systems2026Third sittingAnalysis III · Exercise 390.6/100#25 of 60 by lowest mean
31.8–100.0 · 8 scoring 100
SD 15.7#19 of 60 by spread21 criteria incomplete in at least two configurations119.4s$0.099 · 11,475 tokens0.00 retries · 0 replicated cellsOpen →
Existence and uniqueness, energy integral, and linear equation(A3-26-P4-E3)Second-order differential equations2026Fourth sittingAnalysis III · Exercise 390.7/100#26 of 60 by lowest mean
82.6–100.0 · 2 scoring 100
SD 4.4#55 of 60 by spread6 criteria incomplete in at least two configurations170.1s$0.048 · 5,501 tokens0.00 retries · 0 replicated cellsOpen →
RL divider and parallel LC resonance(F2-25-P5-E2)Circuits and AC response2025Fifth sittingPhysics II · Exercise 291.4/100#27 of 60 by lowest mean
54.7–100.0 · 13 scoring 100
SD 13.6#26 of 60 by spread17 criteria incomplete in at least two configurations92.8s$0.076 · 10,625 tokens0.00 retries · 0 replicated cellsOpen →
Implicit function theorem, quadratic expansion, saddle point, and absolute extrema(A3-26-P4-E1)Level surfaces and constrained extrema2026Fourth sittingAnalysis III · Exercise 192.0/100#28 of 60 by lowest mean
51.6–100.0 · 6 scoring 100
SD 12.5#28 of 60 by spread16 criteria incomplete in at least two configurations430.9s$0.080 · 9,454 tokens0.05 retries · 0 replicated cellsOpen →
Regularity and tangent of a level curve, stationary coordinate, and absolute extrema on a quarter-annulus(A3-25-P2-E1)Level curves and constrained extrema2025Second sittingAnalysis III · Exercise 192.2/100#29 of 60 by lowest mean
43.7–100.0 · 13 scoring 100
SD 14.1#25 of 60 by spread22 criteria incomplete in at least two configurations89.0s$0.080 · 10,054 tokens0.00 retries · 1 replicated cellsOpen →
Fundamental matrix and solutions with a constant coordinate(A3-26-P2A-E3)Linear differential systems2026Second sitting · Theme AAnalysis III · Exercise 392.6/100#30 of 60 by lowest mean
34.0–100.0 · 11 scoring 100
SD 15.1#21 of 60 by spread10 criteria incomplete in at least two configurations64.3s$0.059 · 7,645 tokens0.00 retries · 0 replicated cellsOpen →
Fundamental matrix and solutions with a constant coordinate(A3-26-P2B-E3)Linear differential systems2026Second sitting · Theme BAnalysis III · Exercise 392.7/100#31 of 60 by lowest mean
36.0–100.0 · 16 scoring 100
SD 16.7#18 of 60 by spread14 criteria incomplete in at least two configurations59.0s$0.056 · 7,615 tokens0.00 retries · 0 replicated cellsOpen →
Force, work, and energy of a coil near a straight wire(F2-26-P4-E1)Magnetism and induction2026Fourth sittingPhysics II · Exercise 193.0/100#32 of 60 by lowest mean
50.0–100.0 · 10 scoring 100
SD 12.9#27 of 60 by spread23 criteria incomplete in at least two configurations107.3s$0.079 · 12,740 tokens0.00 retries · 0 replicated cellsOpen →
Moving conducting bar, magnetic braking, and ideal-inductance oscillations(F2-26-P2-E2)Magnetism and induction2026Second sittingPhysics II · Exercise 293.0/100#33 of 60 by lowest mean
46.3–100.0 · 11 scoring 100
SD 14.1#24 of 60 by spread21 criteria incomplete in at least two configurations134.8s$0.088 · 12,429 tokens0.00 retries · 0 replicated cellsOpen →
Regular level sets, implicit curves, and optimization on compact sets(A3-26-P1B-E1)Level curves and constrained extrema2026First sitting · Theme BAnalysis III · Exercise 193.2/100#34 of 60 by lowest mean
62.6–100.0 · 11 scoring 100
SD 11.4#30 of 60 by spread16 criteria incomplete in at least two configurations80.4s$0.076 · 9,219 tokens0.00 retries · 0 replicated cellsOpen →
Fields and forces in relativistic electron and positron beams(F2-25-P3-E2)Magnetism and induction2025Third sittingPhysics II · Exercise 293.6/100#35 of 60 by lowest mean
67.4–100.0 · 12 scoring 100
SD 9.8#36 of 60 by spread18 criteria incomplete in at least two configurations106.7s$0.095 · 12,233 tokens0.00 retries · 0 replicated cellsOpen →
Level sets in R3→R2, quadratic expansion, Lagrange multipliers, and absolute extrema(A3-25-P4-E1)Level curves and constrained extrema2025Fourth sittingAnalysis III · Exercise 193.6/100#36 of 60 by lowest mean
64.5–100.0 · 10 scoring 100
SD 10.5#32 of 60 by spread17 criteria incomplete in at least two configurations256.4s$0.116 · 13,665 tokens0.06 retries · 1 replicated cellsOpen →
Brewster angle, circular polarization, and Fresnel coefficients(F2-25-P2-E3)Electromagnetic waves and optics2025Second sittingPhysics II · Exercise 393.8/100#37 of 60 by lowest mean
65.5–100.0 · 11 scoring 100
SD 9.3#39 of 60 by spread9 criteria incomplete in at least two configurations470.2s$0.079 · 10,224 tokens0.02 retries · 3 replicated cellsOpen →
Improper integrals, centroid, volume, and Gauss theorem verification(A3-26-P1A-E2)Multiple integrals and the divergence theorem2026First sitting · Theme AAnalysis III · Exercise 294.4/100#38 of 60 by lowest mean
64.0–100.0 · 5 scoring 100
SD 10.1#34 of 60 by spread15 criteria incomplete in at least two configurations93.1s$0.080 · 10,310 tokens0.00 retries · 0 replicated cellsOpen →
Area, coordinate extrema, and Taylor expansion(A3-26-P2B-E1)Polar curves and local expansions2026Second sitting · Theme BAnalysis III · Exercise 195.0/100#39 of 60 by lowest mean
71.3–100.0 · 14 scoring 100
SD 10.1#35 of 60 by spread9 criteria incomplete in at least two configurations219.4s$0.101 · 13,009 tokens0.14 retries · 0 replicated cellsOpen →
Energy, potential, and forces of eight charges at a cube's vertices(F2-26-P1-E1)Electrostatics and dielectrics2026First sittingPhysics II · Exercise 195.1/100#40 of 60 by lowest mean
67.9–100.0 · 11 scoring 100
SD 9.2#40 of 60 by spread17 criteria incomplete in at least two configurations158.6s$0.091 · 11,890 tokens0.05 retries · 0 replicated cellsOpen →
Coupled solenoids, sinusoidal response, and a superconducting secondary(F2-26-P3-E2)Circuits and AC response2026Third sittingPhysics II · Exercise 295.2/100#41 of 60 by lowest mean
70.0–100.0 · 14 scoring 100
SD 9.3#38 of 60 by spread19 criteria incomplete in at least two configurations107.0s$0.092 · 12,682 tokens0.00 retries · 0 replicated cellsOpen →
Area, coordinate extrema, and Taylor expansion(A3-26-P2A-E1)Polar curves and local expansions2026Second sitting · Theme AAnalysis III · Exercise 195.3/100#42 of 60 by lowest mean
65.8–100.0 · 12 scoring 100
SD 9.6#37 of 60 by spread10 criteria incomplete in at least two configurations101.5s$0.094 · 11,724 tokens0.00 retries · 0 replicated cellsOpen →
Partially filled cylindrical capacitor, RC transient, and dielectric strength(F2-26-P2-E1)Electrostatics and dielectrics2026Second sittingPhysics II · Exercise 195.5/100#43 of 60 by lowest mean
50.8–100.0 · 10 scoring 100
SD 12.3#29 of 60 by spread14 criteria incomplete in at least two configurations73.9s$0.071 · 8,811 tokens0.00 retries · 0 replicated cellsOpen →
Polar curve: plot, length, tangent, area, and absolute extrema on a compact region(A3-25-P1-E1)Plane curves, multiple integrals, and constrained absolute extrema2025First sittingAnalysis III · Exercise 195.5/100#44 of 60 by lowest mean
71.6–100.0 · 9 scoring 100
SD 8.2#45 of 60 by spread16 criteria incomplete in at least two configurations143.9s$0.076 · 10,641 tokens0.00 retries · 4 replicated cellsOpen →
Electrostatic self-energy, polarization, and external work(F2-25-P1-E1)Electrostatics and dielectrics2025First sittingPhysics II · Exercise 195.5/100#45 of 60 by lowest mean
72.9–100.0 · 12 scoring 100
SD 6.7#49 of 60 by spread12 criteria incomplete in at least two configurations593.1s$0.083 · 11,229 tokens0.00 retries · 3 replicated cellsOpen →
Coaxial Geiger counter and alpha-particle motion(F2-25-P4-E1)Charged-particle dynamics2025Fourth sittingPhysics II · Exercise 195.6/100#46 of 60 by lowest mean
70.5–100.0 · 3 scoring 100
SD 6.3#51 of 60 by spread12 criteria incomplete in at least two configurations109.6s$0.098 · 12,186 tokens0.00 retries · 0 replicated cellsOpen →
Regular level sets, implicit curves, and optimization on compact sets(A3-26-P1A-E1)Level curves and constrained extrema2026First sitting · Theme AAnalysis III · Exercise 196.0/100#47 of 60 by lowest mean
63.2–100.0 · 13 scoring 100
SD 8.8#41 of 60 by spread11 criteria incomplete in at least two configurations79.1s$0.075 · 9,126 tokens0.00 retries · 0 replicated cellsOpen →
Improper integrals, centroid, volume, and Gauss theorem verification(A3-26-P1B-E2)Multiple integrals and the divergence theorem2026First sitting · Theme BAnalysis III · Exercise 296.2/100#48 of 60 by lowest mean
62.0–100.0 · 9 scoring 100
SD 8.7#43 of 60 by spread12 criteria incomplete in at least two configurations85.3s$0.083 · 9,866 tokens0.00 retries · 0 replicated cellsOpen →
Magnetic dipoles, helical motion, and the adiabatic invariant(F2-25-P2-E2)Charged-particle dynamics2025Second sittingPhysics II · Exercise 296.5/100#49 of 60 by lowest mean
77.1–100.0 · 10 scoring 100
SD 6.6#50 of 60 by spread12 criteria incomplete in at least two configurations554.7s$0.078 · 11,174 tokens0.03 retries · 3 replicated cellsOpen →
Moving conducting bar, motional emf, and electromechanical steady state(F2-26-P4-E2)Magnetism and induction2026Fourth sittingPhysics II · Exercise 296.7/100#50 of 60 by lowest mean
85.8–100.0 · 12 scoring 100
SD 5.0#53 of 60 by spread8 criteria incomplete in at least two configurations77.1s$0.055 · 7,895 tokens0.00 retries · 0 replicated cellsOpen →
Isolated coaxial capacitor with dielectric and polarization charges(F2-25-P5-E1)Electrostatics and dielectrics2025Fifth sittingPhysics II · Exercise 196.8/100#51 of 60 by lowest mean
77.6–100.0 · 16 scoring 100
SD 6.8#47 of 60 by spread10 criteria incomplete in at least two configurations111.5s$0.093 · 12,400 tokens0.00 retries · 0 replicated cellsOpen →
Regular level sets, implicit parametrization and tangent plane; constrained stationary points; compact-set optimization(A3-25-P3-E1)Regular surfaces, constrained extrema, and absolute extrema2025Third sittingAnalysis III · Exercise 196.9/100#52 of 60 by lowest mean
80.3–100.0 · 12 scoring 100
SD 5.3#52 of 60 by spread9 criteria incomplete in at least two configurations127.8s$0.101 · 11,955 tokens0.00 retries · 1 replicated cellsOpen →
Conducting shell with dielectric, shielding, and a dipole(F2-25-P2-E1)Electrostatics and dielectrics2025Second sittingPhysics II · Exercise 197.1/100#53 of 60 by lowest mean
74.5–100.0 · 15 scoring 100
SD 6.8#47 of 60 by spread16 criteria incomplete in at least two configurations333.8s$0.067 · 9,293 tokens0.00 retries · 3 replicated cellsOpen →
Implicit curve, constrained classification, and extrema on a truncated ellipse(A3-25-P5-E1)Level curves and extrema2025Fifth sittingAnalysis III · Exercise 197.4/100#54 of 60 by lowest mean
67.9–100.0 · 14 scoring 100
SD 7.2#46 of 60 by spread5 criteria incomplete in at least two configurations103.3s$0.083 · 9,398 tokens0.00 retries · 1 replicated cellsOpen →
Conducting sphere, dielectric strength, and Coulomb scattering of alpha particles(F2-25-P3-E1)Charged-particle dynamics2025Third sittingPhysics II · Exercise 198.6/100#55 of 60 by lowest mean
92.6–100.0 · 1 scoring 100
SD 1.4#59 of 60 by spread1 criteria incomplete in at least two configurations84.4s$0.072 · 9,205 tokens0.00 retries · 0 replicated cellsOpen →
Mutual inductance, an RL circuit, and linked fluxes(F2-25-P1-E2)Circuits and AC response2025First sittingPhysics II · Exercise 298.8/100#56 of 60 by lowest mean
77.4–100.0 · 17 scoring 100
SD 4.8#54 of 60 by spread1 criteria incomplete in at least two configurations238.2s$0.065 · 8,900 tokens0.03 retries · 3 replicated cellsOpen →
Square loop entering a uniform magnetic field(F2-25-P4-E2)Magnetism and induction2025Fourth sittingPhysics II · Exercise 299.0/100#57 of 60 by lowest mean
91.3–100.0 · 15 scoring 100
SD 2.2#56 of 60 by spread3 criteria incomplete in at least two configurations64.6s$0.057 · 7,959 tokens0.00 retries · 0 replicated cellsOpen →
Cylindrical capacitor with a resistive medium and RC discharge(F2-26-P3-E1)Circuits and AC response2026Third sittingPhysics II · Exercise 199.5/100#58 of 60 by lowest mean
94.2–100.0 · 18 scoring 100
SD 1.4#58 of 60 by spread1 criteria incomplete in at least two configurations66.8s$0.056 · 7,001 tokens0.05 retries · 0 replicated cellsOpen →
Double-slit interference with a diffraction envelope(F2-26-P3-E3)Electromagnetic waves and optics2026Third sittingPhysics II · Exercise 399.6/100#59 of 60 by lowest mean
92.6–100.0 · 19 scoring 100
SD 1.6#57 of 60 by spread0 criteria incomplete in at least two configurations50.5s$0.051 · 6,077 tokens0.00 retries · 0 replicated cellsOpen →
Young interference, diffraction, a dielectric plate, and grating resolution(F2-26-P1-E3)Electromagnetic waves and optics2026First sittingPhysics II · Exercise 399.8/100#60 of 60 by lowest mean
94.7–100.0 · 20 scoring 100
SD 1.1#60 of 60 by spread0 criteria incomplete in at least two configurations129.3s$0.059 · 7,185 tokens0.10 retries · 0 replicated cellsOpen →
Analysis III · 2025 · First sitting

Normal form, existence and uniqueness, symmetries, linear equations, and piecewise dynamics (A3-25-P1-E3)

#1

Ordinary differential equations

Observed mean
58.6
Score SD
24.2
Mean time
147.9s
Mean cost
$0.131
Mean tokens
13,459
Range / 100s
24–100 · 1
Open research profile →
Physics II · 2026 · First sitting

RLC circuit with a switchable parallel capacitor branch (F2-26-P1-E2)

#2

Circuits and AC response

Observed mean
67.4
Score SD
8.8
Mean time
86.2s
Mean cost
$0.069
Mean tokens
10,659
Range / 100s
50–89 · 0
Open research profile →
Physics II · 2025 · Third sitting

Interference of three coherent sources with unequal amplitudes (F2-25-P3-E3)

#3

Electromagnetic waves and optics

Observed mean
77.5
Score SD
23.6
Mean time
125.7s
Mean cost
$0.092
Mean tokens
13,401
Range / 100s
28–100 · 7
Open research profile →
Analysis III · 2026 · Second sitting · Theme B

Centroid, improper integrals, Gauss and Stokes theorems (A3-26-P2B-E2)

#4

Multiple integrals and integral theorems

Observed mean
80.0
Score SD
28.1
Mean time
328.9s
Mean cost
$0.162
Mean tokens
21,268
Range / 100s
30–100 · 11
Open research profile →
Analysis III · 2025 · Second sitting

Centroid of a planar region, singular integrals, and Gauss theorem verification on a solid of revolution (A3-25-P2-E2)

#5

Multiple integrals, improper integrability, and Gauss theorem

Observed mean
80.4
Score SD
25.7
Mean time
184.1s
Mean cost
$0.136
Mean tokens
18,309
Range / 100s
31–100 · 5
Open research profile →
Analysis III · 2025 · Second sitting

Existence and uniqueness for an implicit equation, and Cauchy problems for alpha=1 and alpha=0 (A3-25-P2-E3)

#6

First-order ordinary differential equations

Observed mean
81.2
Score SD
15.2
Mean time
86.6s
Mean cost
$0.080
Mean tokens
9,142
Range / 100s
52–100 · 2
Open research profile →
Analysis III · 2025 · Fifth sitting

Existence away from singular axes, integrating factor, and crossing t=0 (A3-25-P5-E3)

#7

Implicit differential equations

Observed mean
82.9
Score SD
21.8
Mean time
141.2s
Mean cost
$0.087
Mean tokens
10,699
Range / 100s
32–100 · 7
Open research profile →
Analysis III · 2026 · Second sitting · Theme A

Centroid, improper integrals, Gauss and Stokes theorems (A3-26-P2A-E2)

#8

Multiple integrals and integral theorems

Observed mean
83.6
Score SD
25.9
Mean time
413.2s
Mean cost
$0.168
Mean tokens
22,298
Range / 100s
24–100 · 11
Open research profile →
Analysis III · 2025 · Fourth sitting

Existence, energy, and a forced linear ODE (A3-25-P4-E3)

#9

Second-order differential equations

Observed mean
84.0
Score SD
15.1
Mean time
189.3s
Mean cost
$0.095
Mean tokens
10,548
Range / 100s
45–100 · 5
Open research profile →
Analysis III · 2025 · Third sitting

Existence and uniqueness, equilibria, first integral, orbits, Cauchy problems, and time reparameterization (A3-25-P3-E3)

#10

Autonomous and linear differential systems

Observed mean
84.6
Score SD
19.6
Mean time
114.2s
Mean cost
$0.087
Mean tokens
11,387
Range / 100s
15–100 · 4
Open research profile →
Physics II · 2025 · Fifth sitting

Thin-film interference and Fresnel coefficients (F2-25-P5-E3)

#11

Electromagnetic waves and optics

Observed mean
84.7
Score SD
8.3
Mean time
61.8s
Mean cost
$0.053
Mean tokens
7,533
Range / 100s
53–93 · 0
Open research profile →
Analysis III · 2025 · Fourth sitting

Centroid, parametric integrability, Gauss and Stokes theorems (A3-25-P4-E2)

#12

Multiple integrals and integral theorems

Observed mean
85.1
Score SD
19.4
Mean time
177.8s
Mean cost
$0.121
Mean tokens
16,439
Range / 100s
35–100 · 6
Open research profile →
Physics II · 2025 · Fourth sitting

Single-slit diffraction, point-source interference, and a dielectric plate (F2-25-P4-E3)

#13

Electromagnetic waves and optics

Observed mean
85.9
Score SD
10.4
Mean time
197.5s
Mean cost
$0.115
Mean tokens
15,689
Range / 100s
57–100 · 3
Open research profile →
Physics II · 2026 · Second sitting

Interference and diffraction from three unequal slits (F2-26-P2-E3)

#14

Electromagnetic waves and optics

Observed mean
86.2
Score SD
18.3
Mean time
244.3s
Mean cost
$0.118
Mean tokens
17,397
Range / 100s
52–100 · 10
Open research profile →
Analysis III · 2025 · Third sitting

Polar centroid, integrability of singular functions, and verification of Gauss and Kelvin–Stokes (A3-25-P3-E2)

#15

Multiple integrals, improper integrability, and vector-calculus integral theorems

Observed mean
86.3
Score SD
21.9
Mean time
202.6s
Mean cost
$0.148
Mean tokens
20,594
Range / 100s
32–100 · 9
Open research profile →
Analysis III · 2026 · Third sitting

Centroid, improper integrability, Gauss and Kelvin–Stokes theorems (A3-26-P3-E2)

#16

Multiple integrals and integral theorems

Observed mean
86.4
Score SD
21.4
Mean time
277.2s
Mean cost
$0.139
Mean tokens
19,288
Range / 100s
39–100 · 8
Open research profile →
Analysis III · 2026 · Fourth sitting

Centroid, improper integrability, volume by slices, and fluxes (A3-26-P4-E2)

#17

Multiple integrals and Gauss theorem

Observed mean
87.0
Score SD
20.8
Mean time
242.0s
Mean cost
$0.106
Mean tokens
14,123
Range / 100s
45–100 · 13
Open research profile →
Analysis III · 2026 · Third sitting

Level set in R3→R2, quadratic expansion, stationary points, and absolute extrema (A3-26-P3-E1)

#18

Level curves and constrained extrema

Observed mean
87.5
Score SD
19.6
Mean time
289.4s
Mean cost
$0.122
Mean tokens
14,713
Range / 100s
29–100 · 10
Open research profile →
Analysis III · 2025 · First sitting

Centroid and volume; Gauss and Kelvin–Stokes theorems (A3-25-P1-E2)

#19

Multiple integration and vector calculus

Observed mean
88.2
Score SD
17.9
Mean time
149.2s
Mean cost
$0.085
Mean tokens
11,262
Range / 100s
45–100 · 13
Open research profile →
Analysis III · 2026 · First sitting · Theme A

Exact implicit ODE and linear Euler equation (A3-26-P1A-E3)

#20

Differential equations

Observed mean
88.4
Score SD
16.9
Mean time
101.9s
Mean cost
$0.089
Mean tokens
10,944
Range / 100s
41–100 · 7
Open research profile →
Analysis III · 2025 · Fifth sitting

Centroid, improper integrals, Gauss theorem verification, and lateral area (A3-25-P5-E2)

#21

Multiple integrals, Gauss theorem, and surfaces

Observed mean
88.7
Score SD
19.4
Mean time
127.1s
Mean cost
$0.096
Mean tokens
12,383
Range / 100s
30–100 · 7
Open research profile →
Physics II · 2026 · Fourth sitting

Brewster angle and polarization in a prism (F2-26-P4-E3)

#22

Electromagnetic waves and optics

Observed mean
89.7
Score SD
16.9
Mean time
171.8s
Mean cost
$0.123
Mean tokens
17,528
Range / 100s
41–100 · 9
Open research profile →
Analysis III · 2026 · First sitting · Theme B

Exact implicit ODE and linear Euler equation (A3-26-P1B-E3)

#23

Differential equations

Observed mean
90.0
Score SD
14.7
Mean time
102.0s
Mean cost
$0.088
Mean tokens
10,705
Range / 100s
46–100 · 7
Open research profile →
Physics II · 2025 · First sitting

Diffraction grating, missing orders, and resolving power (F2-25-P1-E3)

#24

Electromagnetic waves and optics

Observed mean
90.3
Score SD
11.1
Mean time
594.6s
Mean cost
$0.069
Mean tokens
8,721
Range / 100s
67–100 · 8
Open research profile →
Analysis III · 2026 · Third sitting

Existence, first integral, orbits, and time reparameterization (A3-26-P3-E3)

#25

Autonomous differential systems

Observed mean
90.6
Score SD
15.7
Mean time
119.4s
Mean cost
$0.099
Mean tokens
11,475
Range / 100s
32–100 · 8
Open research profile →
Analysis III · 2026 · Fourth sitting

Existence and uniqueness, energy integral, and linear equation (A3-26-P4-E3)

#26

Second-order differential equations

Observed mean
90.7
Score SD
4.4
Mean time
170.1s
Mean cost
$0.048
Mean tokens
5,501
Range / 100s
83–100 · 2
Open research profile →
Physics II · 2025 · Fifth sitting

RL divider and parallel LC resonance (F2-25-P5-E2)

#27

Circuits and AC response

Observed mean
91.4
Score SD
13.6
Mean time
92.8s
Mean cost
$0.076
Mean tokens
10,625
Range / 100s
55–100 · 13
Open research profile →
Analysis III · 2026 · Fourth sitting

Implicit function theorem, quadratic expansion, saddle point, and absolute extrema (A3-26-P4-E1)

#28

Level surfaces and constrained extrema

Observed mean
92.0
Score SD
12.5
Mean time
430.9s
Mean cost
$0.080
Mean tokens
9,454
Range / 100s
52–100 · 6
Open research profile →
Analysis III · 2025 · Second sitting

Regularity and tangent of a level curve, stationary coordinate, and absolute extrema on a quarter-annulus (A3-25-P2-E1)

#29

Level curves and constrained extrema

Observed mean
92.2
Score SD
14.1
Mean time
89.0s
Mean cost
$0.080
Mean tokens
10,054
Range / 100s
44–100 · 13
Open research profile →
Analysis III · 2026 · Second sitting · Theme A

Fundamental matrix and solutions with a constant coordinate (A3-26-P2A-E3)

#30

Linear differential systems

Observed mean
92.6
Score SD
15.1
Mean time
64.3s
Mean cost
$0.059
Mean tokens
7,645
Range / 100s
34–100 · 11
Open research profile →
Analysis III · 2026 · Second sitting · Theme B

Fundamental matrix and solutions with a constant coordinate (A3-26-P2B-E3)

#31

Linear differential systems

Observed mean
92.7
Score SD
16.7
Mean time
59.0s
Mean cost
$0.056
Mean tokens
7,615
Range / 100s
36–100 · 16
Open research profile →
Physics II · 2026 · Fourth sitting

Force, work, and energy of a coil near a straight wire (F2-26-P4-E1)

#32

Magnetism and induction

Observed mean
93.0
Score SD
12.9
Mean time
107.3s
Mean cost
$0.079
Mean tokens
12,740
Range / 100s
50–100 · 10
Open research profile →
Physics II · 2026 · Second sitting

Moving conducting bar, magnetic braking, and ideal-inductance oscillations (F2-26-P2-E2)

#33

Magnetism and induction

Observed mean
93.0
Score SD
14.1
Mean time
134.8s
Mean cost
$0.088
Mean tokens
12,429
Range / 100s
46–100 · 11
Open research profile →
Analysis III · 2026 · First sitting · Theme B

Regular level sets, implicit curves, and optimization on compact sets (A3-26-P1B-E1)

#34

Level curves and constrained extrema

Observed mean
93.2
Score SD
11.4
Mean time
80.4s
Mean cost
$0.076
Mean tokens
9,219
Range / 100s
63–100 · 11
Open research profile →
Physics II · 2025 · Third sitting

Fields and forces in relativistic electron and positron beams (F2-25-P3-E2)

#35

Magnetism and induction

Observed mean
93.6
Score SD
9.8
Mean time
106.7s
Mean cost
$0.095
Mean tokens
12,233
Range / 100s
67–100 · 12
Open research profile →
Analysis III · 2025 · Fourth sitting

Level sets in R3→R2, quadratic expansion, Lagrange multipliers, and absolute extrema (A3-25-P4-E1)

#36

Level curves and constrained extrema

Observed mean
93.6
Score SD
10.5
Mean time
256.4s
Mean cost
$0.116
Mean tokens
13,665
Range / 100s
64–100 · 10
Open research profile →
Physics II · 2025 · Second sitting

Brewster angle, circular polarization, and Fresnel coefficients (F2-25-P2-E3)

#37

Electromagnetic waves and optics

Observed mean
93.8
Score SD
9.3
Mean time
470.2s
Mean cost
$0.079
Mean tokens
10,224
Range / 100s
66–100 · 11
Open research profile →
Analysis III · 2026 · First sitting · Theme A

Improper integrals, centroid, volume, and Gauss theorem verification (A3-26-P1A-E2)

#38

Multiple integrals and the divergence theorem

Observed mean
94.4
Score SD
10.1
Mean time
93.1s
Mean cost
$0.080
Mean tokens
10,310
Range / 100s
64–100 · 5
Open research profile →
Analysis III · 2026 · Second sitting · Theme B

Area, coordinate extrema, and Taylor expansion (A3-26-P2B-E1)

#39

Polar curves and local expansions

Observed mean
95.0
Score SD
10.1
Mean time
219.4s
Mean cost
$0.101
Mean tokens
13,009
Range / 100s
71–100 · 14
Open research profile →
Physics II · 2026 · First sitting

Energy, potential, and forces of eight charges at a cube's vertices (F2-26-P1-E1)

#40

Electrostatics and dielectrics

Observed mean
95.1
Score SD
9.2
Mean time
158.6s
Mean cost
$0.091
Mean tokens
11,890
Range / 100s
68–100 · 11
Open research profile →
Physics II · 2026 · Third sitting

Coupled solenoids, sinusoidal response, and a superconducting secondary (F2-26-P3-E2)

#41

Circuits and AC response

Observed mean
95.2
Score SD
9.3
Mean time
107.0s
Mean cost
$0.092
Mean tokens
12,682
Range / 100s
70–100 · 14
Open research profile →
Analysis III · 2026 · Second sitting · Theme A

Area, coordinate extrema, and Taylor expansion (A3-26-P2A-E1)

#42

Polar curves and local expansions

Observed mean
95.3
Score SD
9.6
Mean time
101.5s
Mean cost
$0.094
Mean tokens
11,724
Range / 100s
66–100 · 12
Open research profile →
Physics II · 2026 · Second sitting

Partially filled cylindrical capacitor, RC transient, and dielectric strength (F2-26-P2-E1)

#43

Electrostatics and dielectrics

Observed mean
95.5
Score SD
12.3
Mean time
73.9s
Mean cost
$0.071
Mean tokens
8,811
Range / 100s
51–100 · 10
Open research profile →
Analysis III · 2025 · First sitting

Polar curve: plot, length, tangent, area, and absolute extrema on a compact region (A3-25-P1-E1)

#44

Plane curves, multiple integrals, and constrained absolute extrema

Observed mean
95.5
Score SD
8.2
Mean time
143.9s
Mean cost
$0.076
Mean tokens
10,641
Range / 100s
72–100 · 9
Open research profile →
Physics II · 2025 · First sitting

Electrostatic self-energy, polarization, and external work (F2-25-P1-E1)

#45

Electrostatics and dielectrics

Observed mean
95.5
Score SD
6.7
Mean time
593.1s
Mean cost
$0.083
Mean tokens
11,229
Range / 100s
73–100 · 12
Open research profile →
Physics II · 2025 · Fourth sitting

Coaxial Geiger counter and alpha-particle motion (F2-25-P4-E1)

#46

Charged-particle dynamics

Observed mean
95.6
Score SD
6.3
Mean time
109.6s
Mean cost
$0.098
Mean tokens
12,186
Range / 100s
71–100 · 3
Open research profile →
Analysis III · 2026 · First sitting · Theme A

Regular level sets, implicit curves, and optimization on compact sets (A3-26-P1A-E1)

#47

Level curves and constrained extrema

Observed mean
96.0
Score SD
8.8
Mean time
79.1s
Mean cost
$0.075
Mean tokens
9,126
Range / 100s
63–100 · 13
Open research profile →
Analysis III · 2026 · First sitting · Theme B

Improper integrals, centroid, volume, and Gauss theorem verification (A3-26-P1B-E2)

#48

Multiple integrals and the divergence theorem

Observed mean
96.2
Score SD
8.7
Mean time
85.3s
Mean cost
$0.083
Mean tokens
9,866
Range / 100s
62–100 · 9
Open research profile →
Physics II · 2025 · Second sitting

Magnetic dipoles, helical motion, and the adiabatic invariant (F2-25-P2-E2)

#49

Charged-particle dynamics

Observed mean
96.5
Score SD
6.6
Mean time
554.7s
Mean cost
$0.078
Mean tokens
11,174
Range / 100s
77–100 · 10
Open research profile →
Physics II · 2026 · Fourth sitting

Moving conducting bar, motional emf, and electromechanical steady state (F2-26-P4-E2)

#50

Magnetism and induction

Observed mean
96.7
Score SD
5.0
Mean time
77.1s
Mean cost
$0.055
Mean tokens
7,895
Range / 100s
86–100 · 12
Open research profile →
Physics II · 2025 · Fifth sitting

Isolated coaxial capacitor with dielectric and polarization charges (F2-25-P5-E1)

#51

Electrostatics and dielectrics

Observed mean
96.8
Score SD
6.8
Mean time
111.5s
Mean cost
$0.093
Mean tokens
12,400
Range / 100s
78–100 · 16
Open research profile →
Analysis III · 2025 · Third sitting

Regular level sets, implicit parametrization and tangent plane; constrained stationary points; compact-set optimization (A3-25-P3-E1)

#52

Regular surfaces, constrained extrema, and absolute extrema

Observed mean
96.9
Score SD
5.3
Mean time
127.8s
Mean cost
$0.101
Mean tokens
11,955
Range / 100s
80–100 · 12
Open research profile →
Physics II · 2025 · Second sitting

Conducting shell with dielectric, shielding, and a dipole (F2-25-P2-E1)

#53

Electrostatics and dielectrics

Observed mean
97.1
Score SD
6.8
Mean time
333.8s
Mean cost
$0.067
Mean tokens
9,293
Range / 100s
74–100 · 15
Open research profile →
Analysis III · 2025 · Fifth sitting

Implicit curve, constrained classification, and extrema on a truncated ellipse (A3-25-P5-E1)

#54

Level curves and extrema

Observed mean
97.4
Score SD
7.2
Mean time
103.3s
Mean cost
$0.083
Mean tokens
9,398
Range / 100s
68–100 · 14
Open research profile →
Physics II · 2025 · Third sitting

Conducting sphere, dielectric strength, and Coulomb scattering of alpha particles (F2-25-P3-E1)

#55

Charged-particle dynamics

Observed mean
98.6
Score SD
1.4
Mean time
84.4s
Mean cost
$0.072
Mean tokens
9,205
Range / 100s
93–100 · 1
Open research profile →
Physics II · 2025 · First sitting

Mutual inductance, an RL circuit, and linked fluxes (F2-25-P1-E2)

#56

Circuits and AC response

Observed mean
98.8
Score SD
4.8
Mean time
238.2s
Mean cost
$0.065
Mean tokens
8,900
Range / 100s
77–100 · 17
Open research profile →
Physics II · 2025 · Fourth sitting

Square loop entering a uniform magnetic field (F2-25-P4-E2)

#57

Magnetism and induction

Observed mean
99.0
Score SD
2.2
Mean time
64.6s
Mean cost
$0.057
Mean tokens
7,959
Range / 100s
91–100 · 15
Open research profile →
Physics II · 2026 · Third sitting

Cylindrical capacitor with a resistive medium and RC discharge (F2-26-P3-E1)

#58

Circuits and AC response

Observed mean
99.5
Score SD
1.4
Mean time
66.8s
Mean cost
$0.056
Mean tokens
7,001
Range / 100s
94–100 · 18
Open research profile →
Physics II · 2026 · Third sitting

Double-slit interference with a diffraction envelope (F2-26-P3-E3)

#59

Electromagnetic waves and optics

Observed mean
99.6
Score SD
1.6
Mean time
50.5s
Mean cost
$0.051
Mean tokens
6,077
Range / 100s
93–100 · 19
Open research profile →
Physics II · 2026 · First sitting

Young interference, diffraction, a dielectric plate, and grating resolution (F2-26-P1-E3)

#60

Electromagnetic waves and optics

Observed mean
99.8
Score SD
1.1
Mean time
129.3s
Mean cost
$0.059
Mean tokens
7,185
Range / 100s
95–100 · 20
Open research profile →

Licensing and reuse

Rights and source material

The examination statements reproduced in the Atlas originate from University of Padua examinations.

Except where otherwise stated, original UniAIBench text, rubrics, figures and benchmark data are licensed under CC BY 4.0. Source code, when publicly released, is licensed under the MIT License. University examination statements, provider trademarks, logos and other third-party materials are excluded and remain the property of their respective rights holders. Model outputs are provided for research transparency subject to the applicable provider terms.