Reasoning diagnostics for AP Physics, F=ma & USAPhO mechanics
Find the physics model behind each miss.
Practice sites tell you what you missed. This maps why.
FirstPrinciples maps each diagnostic choice to a named reasoning trap, then routes you to the Atlas entry and ladder rung written to repair it.
- answer
Q04 · B - trap
circular-direction - atlas
NL-05 - rung
R7
Live example: one diagnostic item, routed
A car rounds a flat curve at constant speed. The direction of the net force on the car is:
Pick any answer, right or wrong. Nothing is scored or saved.
- 01 Answer —
- 02 Reasoning pattern the model behind the choice
- 03 Misconception code one of 12 trap families
- 04 Explanation · Error Atlas the entry that explains the trap
- 05 Repair · ladder rung the problem that rebuilds the idea
The full diagnostic runs this on 48 items, then ranks the traps that recur.
Run the 48-item diagnostic →01 The correction loop
Every miss runs through the same six steps.
The same coding rules power the report, the Atlas links, and the recommendations — shown here for the miss above.
- 01Answer patternWhich choice, on which item.
Q04 · chose B - 02Misconception codeEvery distractor carries a trap code.
circular-direction - 03Diagnostic reportCodes are tallied; traps that recur rank first.
ranked by recurrence - 04Error Atlas entryWhy the wrong model felt right, and what replaces it.
NL-05 - 05Recommended rungOne problem that adds the missing idea.
R7 - 06Progress dataA held-out follow-up checks whether the trap recurs.
recurring / resolved
02 Three surfaces
Diagnosis, atlas, ladder — wired together.
Practice alone rehearses mistakes. Here, each attempt decides what you read next and which problem you work next.
Trap detected across items
Circular-motion direction error
- Q04A car rounds a flat curve at constant speed. The direction of the net force on the car is:
- Q05A ball on a string swings in a vertical circle of radius r. The minimum speed at the top for the string to stay taut satisfies:
- Q41A car rounds a banked curve without friction. Which force provides the necessary centripetal acceleration?
- Q42A ball swings on a string in a vertical circle. At the bottom of the loop, the tension is:
Each wrong choice is tallied by trap, so a pattern that recurs across items outranks a one-off slip.
NL-05 · one of 66 entries
Centripetal acceleration points inward
- feels right
- You feel flung outward in a turning car, so it seems a force pushes out.
- first principle
- The net force is centripetal — inward — supplying a = v²/r.
One new idea per rung
- R5Pulley constraintAP C
- R6Two-block system: choosing the systemAP C
- R7Circular motion: force directionF=ma
- R8Wedge/block constraintF=ma
- R9Non-inertial frame, introUSAPhO
R7 adds: Uniform circular motion has inward acceleration even at constant speed.
03 Verified reach
Where the numbers come from.
65 of 19,185 reached the verified cohort; 45 have matched pre/post pairs. Each figure is drawn to scale, with the claim it can support.
Full methodology →- 19,185prep users
Broad reach. Supports reach. It does not prove learning gain.
- 2,102diagnostics completed
Platform adoption. Supports product usage and diagnostic adoption.
- 65verified cohort
Research sample. Supports cohort-scale analysis.
- 45paired pre/post
Learning evidence. The layer used for learning-impact claims. Pre/post evidence, not a controlled trial.
04 The open question
Does knowing which reasoning step broke actually help more than doing another practice set?
Baseline diagnostic, targeted ladder work, held-out follow-up, paired comparison. Results get published with the denominator attached.