Search and inspect all 60 exercises, their source material, scoring evidence and retained model responses.
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.
Research index
33 of 33 records shown
| Exercise / topic | Exam record | Observed mean | 21-configuration distribution | Cross-configuration SD | Observed resources | Open profile |
|---|---|---|---|---|---|---|
| Normal form, existence and uniqueness, symmetries, linear equations, and piecewise dynamics(A3-25-P1-E3)Ordinary differential equations | 2025First sittingExercise 3 | 58.6/100#1 of 33 by lowest mean | 23.5–100.0 · 1 scoring 100 | SD 24.2#4 of 33 by spread33 criteria incomplete in at least two configurations | 147.9s$0.131 · 13,459 tokens0.06 retries · 4 replicated cells | Open → |
| Centroid, improper integrals, Gauss and Stokes theorems(A3-26-P2B-E2)Multiple integrals and integral theorems | 2026Second sitting · Theme BExercise 2 | 80.0/100#2 of 33 by lowest mean | 29.5–100.0 · 11 scoring 100 | SD 28.1#1 of 33 by spread30 criteria incomplete in at least two configurations | 328.9s$0.162 · 21,268 tokens0.14 retries · 0 replicated cells | Open → |
| 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 theorem | 2025Second sittingExercise 2 | 80.4/100#3 of 33 by lowest mean | 31.3–100.0 · 5 scoring 100 | SD 25.7#3 of 33 by spread27 criteria incomplete in at least two configurations | 184.1s$0.136 · 18,309 tokens0.00 retries · 1 replicated cells | Open → |
| Existence and uniqueness for an implicit equation, and Cauchy problems for alpha=1 and alpha=0(A3-25-P2-E3)First-order ordinary differential equations | 2025Second sittingExercise 3 | 81.2/100#4 of 33 by lowest mean | 52.3–100.0 · 2 scoring 100 | SD 15.2#17 of 33 by spread24 criteria incomplete in at least two configurations | 86.6s$0.080 · 9,142 tokens0.00 retries · 1 replicated cells | Open → |
| Existence away from singular axes, integrating factor, and crossing t=0(A3-25-P5-E3)Implicit differential equations | 2025Fifth sittingExercise 3 | 82.9/100#5 of 33 by lowest mean | 32.1–100.0 · 7 scoring 100 | SD 21.8#6 of 33 by spread23 criteria incomplete in at least two configurations | 141.2s$0.087 · 10,699 tokens0.05 retries · 1 replicated cells | Open → |
| Centroid, improper integrals, Gauss and Stokes theorems(A3-26-P2A-E2)Multiple integrals and integral theorems | 2026Second sitting · Theme AExercise 2 | 83.6/100#6 of 33 by lowest mean | 23.5–100.0 · 11 scoring 100 | SD 25.9#2 of 33 by spread30 criteria incomplete in at least two configurations | 413.2s$0.168 · 22,298 tokens0.05 retries · 0 replicated cells | Open → |
| Existence, energy, and a forced linear ODE(A3-25-P4-E3)Second-order differential equations | 2025Fourth sittingExercise 3 | 84.0/100#7 of 33 by lowest mean | 45.0–100.0 · 5 scoring 100 | SD 15.1#18 of 33 by spread15 criteria incomplete in at least two configurations | 189.3s$0.095 · 10,548 tokens0.06 retries · 1 replicated cells | Open → |
| Existence and uniqueness, equilibria, first integral, orbits, Cauchy problems, and time reparameterization(A3-25-P3-E3)Autonomous and linear differential systems | 2025Third sittingExercise 3 | 84.6/100#8 of 33 by lowest mean | 15.3–100.0 · 4 scoring 100 | SD 19.6#10 of 33 by spread20 criteria incomplete in at least two configurations | 114.2s$0.087 · 11,387 tokens0.00 retries · 1 replicated cells | Open → |
| Centroid, parametric integrability, Gauss and Stokes theorems(A3-25-P4-E2)Multiple integrals and integral theorems | 2025Fourth sittingExercise 2 | 85.1/100#9 of 33 by lowest mean | 35.3–100.0 · 6 scoring 100 | SD 19.4#11 of 33 by spread25 criteria incomplete in at least two configurations | 177.8s$0.121 · 16,439 tokens0.00 retries · 1 replicated cells | Open → |
| 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 theorems | 2025Third sittingExercise 2 | 86.3/100#10 of 33 by lowest mean | 32.3–100.0 · 9 scoring 100 | SD 21.9#5 of 33 by spread29 criteria incomplete in at least two configurations | 202.6s$0.148 · 20,594 tokens0.00 retries · 1 replicated cells | Open → |
| Centroid, improper integrability, Gauss and Kelvin–Stokes theorems(A3-26-P3-E2)Multiple integrals and integral theorems | 2026Third sittingExercise 2 | 86.4/100#11 of 33 by lowest mean | 39.0–100.0 · 8 scoring 100 | SD 21.4#7 of 33 by spread22 criteria incomplete in at least two configurations | 277.2s$0.139 · 19,288 tokens0.00 retries · 0 replicated cells | Open → |
| Centroid, improper integrability, volume by slices, and fluxes(A3-26-P4-E2)Multiple integrals and Gauss theorem | 2026Fourth sittingExercise 2 | 87.0/100#12 of 33 by lowest mean | 44.5–100.0 · 13 scoring 100 | SD 20.8#8 of 33 by spread20 criteria incomplete in at least two configurations | 242.0s$0.106 · 14,123 tokens0.00 retries · 0 replicated cells | Open → |
| Level set in R3→R2, quadratic expansion, stationary points, and absolute extrema(A3-26-P3-E1)Level curves and constrained extrema | 2026Third sittingExercise 1 | 87.5/100#13 of 33 by lowest mean | 29.2–100.0 · 10 scoring 100 | SD 19.6#9 of 33 by spread21 criteria incomplete in at least two configurations | 289.4s$0.122 · 14,713 tokens0.00 retries · 0 replicated cells | Open → |
| Centroid and volume; Gauss and Kelvin–Stokes theorems(A3-25-P1-E2)Multiple integration and vector calculus | 2025First sittingExercise 2 | 88.2/100#14 of 33 by lowest mean | 44.5–100.0 · 13 scoring 100 | SD 17.9#13 of 33 by spread23 criteria incomplete in at least two configurations | 149.2s$0.085 · 11,262 tokens0.02 retries · 4 replicated cells | Open → |
| Exact implicit ODE and linear Euler equation(A3-26-P1A-E3)Differential equations | 2026First sitting · Theme AExercise 3 | 88.4/100#15 of 33 by lowest mean | 41.3–100.0 · 7 scoring 100 | SD 16.9#14 of 33 by spread20 criteria incomplete in at least two configurations | 101.9s$0.089 · 10,944 tokens0.00 retries · 0 replicated cells | Open → |
| Centroid, improper integrals, Gauss theorem verification, and lateral area(A3-25-P5-E2)Multiple integrals, Gauss theorem, and surfaces | 2025Fifth sittingExercise 2 | 88.7/100#16 of 33 by lowest mean | 30.0–100.0 · 7 scoring 100 | SD 19.4#12 of 33 by spread24 criteria incomplete in at least two configurations | 127.1s$0.096 · 12,383 tokens0.00 retries · 1 replicated cells | Open → |
| Exact implicit ODE and linear Euler equation(A3-26-P1B-E3)Differential equations | 2026First sitting · Theme BExercise 3 | 90.0/100#17 of 33 by lowest mean | 46.0–100.0 · 7 scoring 100 | SD 14.7#20 of 33 by spread20 criteria incomplete in at least two configurations | 102.0s$0.088 · 10,705 tokens0.00 retries · 0 replicated cells | Open → |
| Existence, first integral, orbits, and time reparameterization(A3-26-P3-E3)Autonomous differential systems | 2026Third sittingExercise 3 | 90.6/100#18 of 33 by lowest mean | 31.8–100.0 · 8 scoring 100 | SD 15.7#16 of 33 by spread21 criteria incomplete in at least two configurations | 119.4s$0.099 · 11,475 tokens0.00 retries · 0 replicated cells | Open → |
| Existence and uniqueness, energy integral, and linear equation(A3-26-P4-E3)Second-order differential equations | 2026Fourth sittingExercise 3 | 90.7/100#19 of 33 by lowest mean | 82.6–100.0 · 2 scoring 100 | SD 4.4#33 of 33 by spread6 criteria incomplete in at least two configurations | 170.1s$0.048 · 5,501 tokens0.00 retries · 0 replicated cells | Open → |
| Implicit function theorem, quadratic expansion, saddle point, and absolute extrema(A3-26-P4-E1)Level surfaces and constrained extrema | 2026Fourth sittingExercise 1 | 92.0/100#20 of 33 by lowest mean | 51.6–100.0 · 6 scoring 100 | SD 12.5#22 of 33 by spread16 criteria incomplete in at least two configurations | 430.9s$0.080 · 9,454 tokens0.05 retries · 0 replicated cells | Open → |
| Regularity and tangent of a level curve, stationary coordinate, and absolute extrema on a quarter-annulus(A3-25-P2-E1)Level curves and constrained extrema | 2025Second sittingExercise 1 | 92.2/100#21 of 33 by lowest mean | 43.7–100.0 · 13 scoring 100 | SD 14.1#21 of 33 by spread22 criteria incomplete in at least two configurations | 89.0s$0.080 · 10,054 tokens0.00 retries · 1 replicated cells | Open → |
| Fundamental matrix and solutions with a constant coordinate(A3-26-P2A-E3)Linear differential systems | 2026Second sitting · Theme AExercise 3 | 92.6/100#22 of 33 by lowest mean | 34.0–100.0 · 11 scoring 100 | SD 15.1#18 of 33 by spread10 criteria incomplete in at least two configurations | 64.3s$0.059 · 7,645 tokens0.00 retries · 0 replicated cells | Open → |
| Fundamental matrix and solutions with a constant coordinate(A3-26-P2B-E3)Linear differential systems | 2026Second sitting · Theme BExercise 3 | 92.7/100#23 of 33 by lowest mean | 36.0–100.0 · 16 scoring 100 | SD 16.7#15 of 33 by spread14 criteria incomplete in at least two configurations | 59.0s$0.056 · 7,615 tokens0.00 retries · 0 replicated cells | Open → |
| Regular level sets, implicit curves, and optimization on compact sets(A3-26-P1B-E1)Level curves and constrained extrema | 2026First sitting · Theme BExercise 1 | 93.2/100#24 of 33 by lowest mean | 62.6–100.0 · 11 scoring 100 | SD 11.4#23 of 33 by spread16 criteria incomplete in at least two configurations | 80.4s$0.076 · 9,219 tokens0.00 retries · 0 replicated cells | Open → |
| Level sets in R3→R2, quadratic expansion, Lagrange multipliers, and absolute extrema(A3-25-P4-E1)Level curves and constrained extrema | 2025Fourth sittingExercise 1 | 93.6/100#25 of 33 by lowest mean | 64.5–100.0 · 10 scoring 100 | SD 10.5#24 of 33 by spread17 criteria incomplete in at least two configurations | 256.4s$0.116 · 13,665 tokens0.06 retries · 1 replicated cells | Open → |
| Improper integrals, centroid, volume, and Gauss theorem verification(A3-26-P1A-E2)Multiple integrals and the divergence theorem | 2026First sitting · Theme AExercise 2 | 94.4/100#26 of 33 by lowest mean | 64.0–100.0 · 5 scoring 100 | SD 10.1#25 of 33 by spread15 criteria incomplete in at least two configurations | 93.1s$0.080 · 10,310 tokens0.00 retries · 0 replicated cells | Open → |
| Area, coordinate extrema, and Taylor expansion(A3-26-P2B-E1)Polar curves and local expansions | 2026Second sitting · Theme BExercise 1 | 95.0/100#27 of 33 by lowest mean | 71.3–100.0 · 14 scoring 100 | SD 10.1#26 of 33 by spread9 criteria incomplete in at least two configurations | 219.4s$0.101 · 13,009 tokens0.14 retries · 0 replicated cells | Open → |
| Area, coordinate extrema, and Taylor expansion(A3-26-P2A-E1)Polar curves and local expansions | 2026Second sitting · Theme AExercise 1 | 95.3/100#28 of 33 by lowest mean | 65.8–100.0 · 12 scoring 100 | SD 9.6#27 of 33 by spread10 criteria incomplete in at least two configurations | 101.5s$0.094 · 11,724 tokens0.00 retries · 0 replicated cells | Open → |
| Polar curve: plot, length, tangent, area, and absolute extrema on a compact region(A3-25-P1-E1)Plane curves, multiple integrals, and constrained absolute extrema | 2025First sittingExercise 1 | 95.5/100#29 of 33 by lowest mean | 71.6–100.0 · 9 scoring 100 | SD 8.2#30 of 33 by spread16 criteria incomplete in at least two configurations | 143.9s$0.076 · 10,641 tokens0.00 retries · 4 replicated cells | Open → |
| Regular level sets, implicit curves, and optimization on compact sets(A3-26-P1A-E1)Level curves and constrained extrema | 2026First sitting · Theme AExercise 1 | 96.0/100#30 of 33 by lowest mean | 63.2–100.0 · 13 scoring 100 | SD 8.8#28 of 33 by spread11 criteria incomplete in at least two configurations | 79.1s$0.075 · 9,126 tokens0.00 retries · 0 replicated cells | Open → |
| Improper integrals, centroid, volume, and Gauss theorem verification(A3-26-P1B-E2)Multiple integrals and the divergence theorem | 2026First sitting · Theme BExercise 2 | 96.2/100#31 of 33 by lowest mean | 62.0–100.0 · 9 scoring 100 | SD 8.7#29 of 33 by spread12 criteria incomplete in at least two configurations | 85.3s$0.083 · 9,866 tokens0.00 retries · 0 replicated cells | Open → |
| Regular level sets, implicit parametrization and tangent plane; constrained stationary points; compact-set optimization(A3-25-P3-E1)Regular surfaces, constrained extrema, and absolute extrema | 2025Third sittingExercise 1 | 96.9/100#32 of 33 by lowest mean | 80.3–100.0 · 12 scoring 100 | SD 5.3#32 of 33 by spread9 criteria incomplete in at least two configurations | 127.8s$0.101 · 11,955 tokens0.00 retries · 1 replicated cells | Open → |
| Implicit curve, constrained classification, and extrema on a truncated ellipse(A3-25-P5-E1)Level curves and extrema | 2025Fifth sittingExercise 1 | 97.4/100#33 of 33 by lowest mean | 67.9–100.0 · 14 scoring 100 | SD 7.2#31 of 33 by spread5 criteria incomplete in at least two configurations | 103.3s$0.083 · 9,398 tokens0.00 retries · 1 replicated cells | Open → |
(A3-25-P1-E3)Ordinary differential equations
(A3-26-P2B-E2)Multiple integrals and integral theorems
(A3-25-P2-E2)Multiple integrals, improper integrability, and Gauss theorem
(A3-25-P2-E3)First-order ordinary differential equations
(A3-25-P5-E3)Implicit differential equations
(A3-26-P2A-E2)Multiple integrals and integral theorems
(A3-25-P4-E3)Second-order differential equations
(A3-25-P3-E3)Autonomous and linear differential systems
(A3-25-P4-E2)Multiple integrals and integral theorems
(A3-25-P3-E2)Multiple integrals, improper integrability, and vector-calculus integral theorems
(A3-26-P3-E2)Multiple integrals and integral theorems
(A3-26-P4-E2)Multiple integrals and Gauss theorem
(A3-26-P3-E1)Level curves and constrained extrema
(A3-25-P1-E2)Multiple integration and vector calculus
(A3-26-P1A-E3)Differential equations
(A3-25-P5-E2)Multiple integrals, Gauss theorem, and surfaces
(A3-26-P1B-E3)Differential equations
(A3-26-P3-E3)Autonomous differential systems
(A3-26-P4-E3)Second-order differential equations
(A3-26-P4-E1)Level surfaces and constrained extrema
(A3-25-P2-E1)Level curves and constrained extrema
(A3-26-P2A-E3)Linear differential systems
(A3-26-P2B-E3)Linear differential systems
(A3-26-P1B-E1)Level curves and constrained extrema
(A3-25-P4-E1)Level curves and constrained extrema
(A3-26-P1A-E2)Multiple integrals and the divergence theorem
(A3-26-P2B-E1)Polar curves and local expansions
(A3-26-P2A-E1)Polar curves and local expansions
(A3-25-P1-E1)Plane curves, multiple integrals, and constrained absolute extrema
(A3-26-P1A-E1)Level curves and constrained extrema
(A3-26-P1B-E2)Multiple integrals and the divergence theorem
(A3-25-P3-E1)Regular surfaces, constrained extrema, and absolute extrema
(A3-25-P5-E1)Level curves and extrema
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