exam-drill

Exam Drill

Workflow philosophy (critical — do not break)

The user does not type math into the CLI — it is too slow. All interactions obey:

1. Generation side (Claude → file). Problems, variants, and clean reference derivations are written as markdown files to quizzes/, twins/, chain/, derivations/. The user views them; no math dialogue in the terminal.

2. Answer side (user → PDF). The user solves on paper, scans as PDF, uploads to answers/<name>.pdf. The answer-processing skill (auto-loaded by /grade) converts the PDF to markdown and grades.

3. Strategy checks (when user is online) — when a command asks the user to verify understanding without producing a full written solution, it asks only for the strategy in 3–5 lines of prose (written in INTERFACE_LANG from .course-meta, default en): which pattern(s), which variables are fixed/expanded, what form the answer takes. Strategy matching is stronger evidence of mastery than line-by-line algebra.

Drill targeting philosophy (critical — do not break)

HW density = exam probability. The professor has already told you, through HW, where the exam points live. Every drill command must bias toward HW-emphasized sections (🔥🔥 Exam-primary > 🔥 Exam-likely > 🟡 Exam-possible). Sections with no HW (⚪ Low-risk) are not "blind spots waiting to bite" — they are the professor's signal of what is off the exam. Do not treat low-HW sections as high-risk.

Concretely:

• /twin, /blind default to the highest-HW-density problems when the user doesn't specify one.
• /chain composes patterns drawn from Exam-primary sections; avoid pulling patterns from ⚪ sections unless the user explicitly asks.
• /mock problem weighting follows HW density (see commands/mock.md).
• /quiz all samples ≥70% from 🔥🔥, ~25% from 🔥, ≤5% from 🟡, 0% from ⚪.
• If the user requests a ⚪ section drill, comply once but warn that exam probability is low.

Prerequisites

This skill assumes /ingest and /analyze have been run. If course-index/patterns.md or course-index/coverage.md don't exist, tell the user to run those first.

Files read

• course-index/patterns.md — recognition cards P1, P2, ...
• course-index/coverage.md — HW↔§ map, blind spots
• course-index/summary.md — topic tree
• converted/homework/*.md — original HW problems
• converted/solutions/*.md — HW solutions (ground truth for grading)
• errors/log.md — user's error history (append-only)

Files written

• quizzes/<topic>_<ts>.md — problem statements (answers in _answers.md sibling)
• twins/<origin>_<ts>.md — variant problems
• chain/<ts>.md — integration problems
• derivations/<topic>.md — clean reference derivations (post-success)
• errors/log.md — append error entries

Command patterns

/twin <problem-id>

1. Locate <problem-id> in converted/homework/ and converted/solutions/.
2. Identify patterns used via course-index/patterns.md.
3. Apply twin-recipe.md rules: hold pattern and topic invariant; vary system, numbers, direction, names.
4. Save problem to twins/<id>_<ts>.md and solution to twins/<id>_<ts>_sol.md. Do not reveal solution unless user either (a) uploads their answer PDF, or (b) describes a correct strategy.

/blind <problem-id>

1. Present the problem verbatim from converted/homework/.
2. Ask for strategy (3–5 lines, in $INTERFACE_LANG):
   • which pattern(s) from course-index/patterns.md
   • what variables are fixed vs. varied
   • expected form of the final answer
3. Compare against converted/solutions/. Three checks: pattern / variable-choice / end-form.
4. On success, copy the relevant solution section into derivations/<stem>-<n>.md. On failure, flag the specific axis and log to errors/log.md.

/chain <N>

1. Pick N patterns from different source problems (per course-index/coverage.md).
2. Design a problem that requires composing them sequentially in parts (a), (b), (c).
3. Bias toward user's weak zone (see course-index/coverage.md Critical column).
4. Save problem and solution; prompt for part-by-part strategy or PDF upload.

/pattern [§ or keyword or "all"]

Read-only. Filter course-index/patterns.md by the query and return compact pattern cards.

/hwmap [§ or "blind"]

Read-only. Project course-index/coverage.md by the query. blind lists all 🔴 and 🔴🔴 entries with drill recommendations.

Twin recipe (invariance rules)

Hold invariant:

• The pattern(s) required — a twin that uses a different method is not a twin, it's a new problem.
• The number of reasoning steps (±1).
• The course topic/section being tested.
• The difficulty tier (recall / calculation / derivation / analysis).

Vary:

• Numerical values.
• Variable names.
• System/model specification (if course admits multiple — ideal gas → vdW, ODE → PDE of same order, matrix 3×3 → 4×4).
• Direction of the ask: "show X = Y" ↔ "given X = Y, verify Z" ↔ "compute X".

Quality check before presenting:

1. The target pattern is clearly required (not avoidable by a shortcut).
2. The answer differs from the original (if it matches, it's not a twin).
3. No filename or wording directly references the original problem ID.
4. Final answer exists and is not pathological.

Error logging schema

When any drill reveals an error, append to errors/log.md:

- problem_id: <HW#-P#, twin-id, or chain-ts>
  pattern: <Pk from patterns.md>
  error_type: pattern-missed | wrong-variable | wrong-end-form | algebraic | sign | definition
  summary: "<one-line description>"
  date: <ISO8601>

/weakmap (top-level command) consumes this log; this skill just produces entries.

Cross-skill coordination

• /grade → loads answer-processing skill (PDF → MD → compare with converted/solutions/).
• /ingest or /analyze → loads course-builder skill.
• Any PDF read/write → loads pdf skill.
• All drill outputs (twins/, chain/, quizzes/) use plain markdown — no PDF creation inside drill commands. The user uploads answer PDFs; Claude doesn't make PDFs during drilling.

Prose conventions

• Explanations in INTERFACE_LANG (en or ko) from .course-meta. Default en if the field is absent.
• Math in LaTeX ($...$ inline, $$...$$ display).
• Pattern IDs stay Latin (P1, P2, ...) regardless of language.
• Section IDs follow the course's convention from course-index/summary.md (§, Ch., Ch 3.1, etc.) regardless of language.
• File paths, slash command names, YAML keys, and section anchors downstream tools regex on (## One-line verdict, ## Page N, # Vision-OCR transcription) stay in English regardless of language.