auditing-question-bank-accuracy

name	auditing_question_bank_accuracy
description	Audit math question bank files for answer-key and explanation accuracy. Use when asked to check, verify, review, or audit answers, correct answers, explanations, or calculations in test question bank files (bank 1 or bank 2). Covers locating source files, verifying every \correctAnswer and \explanation, fixing errors, and compiling to validate.

Auditing Question Bank Accuracy

Overview

This skill guides you through a rigorous chapter-by-chapter accuracy audit of the Grade 7 math question bank LaTeX files. The goal is to catch wrong answer keys (\correctAnswer) and incorrect math in explanations (\explanation), then fix them with minimal changes.

When to Use

• User asks to "check", "verify", "audit", or "review" question bank answers or explanations
• User mentions "calculations", "accuracy", "correct answer", or "miscalculations" in the context of test questions
• User references a specific chapter's question bank

Question Bank Structure

There are two independent question bank sets:

Bank	Source directory	Assembled review docs	Books that use it
Bank 1	tests_questions_bank/	tests/grade7_test_questions_bank_ch{N}.tex	3, 5, 7, 10 practice tests
Bank 2	tests_questions_bank_2/	tests/grade7_test_questions_bank_2_ch{N}.tex	6, 9, 12 practice tests

Within each bank directory, source files live in three subdirectories:

tests_questions_bank_2/
    topics/              # Core CCSS topic question files
    topics_additional/   # Additional state-specific topic questions
    topics_modified/     # Modified topic questions

Each source file contains 27 questions: 15 multiple choice (mc), 6 short answer (sa), and 6 graphical (gmc/gsa).

Procedure

Step 1: Identify the Exact Source Files

First, run the chapter-facts Python script to discover the topic IDs and relative file paths for that chapter:

p scripts/get_chapter_topic_facts.py --chapter {N}

This prints the chapter's:

• core topic files under topics/
• additional topic files under topics_additional/
• modified topic files under topics_modified/

Use that output to build the exact bank-specific source file list:

• For bank 1, prepend tests_questions_bank/ to each printed file path.
• For bank 2, prepend tests_questions_bank_2/ to each printed file path.

Then read the assembled chapter review document to confirm the exact \input{} lines:

tests/grade7_test_questions_bank_2_ch{N}.tex   # for bank 2
tests/grade7_test_questions_bank_ch{N}.tex      # for bank 1

The script tells you what topic files exist for the chapter, and the assembled review file confirms which ones are actually included in that bank/chapter build. Do not guess.

Step 2: Read Every Source File

Read each source file in full. Do not skim or sample. Every question must be checked.

Step 3: Verify Each Question

For every question, perform these checks:

Multiple Choice (mc and gmc)

1. Independently compute the correct answer first. Solve the problem yourself before looking at any choices. This prevents anchoring bias.
2. Expand / evaluate EVERY choice. Do not just check the keyed answer — work out what each choice (A, B, C, D) actually equals. For factoring questions, expand each factored form by distributing. For scientific notation, convert each choice to standard form. For equations, substitute each proposed answer back in. This is the single most important step: many bugs are only visible when you verify that the wrong choices really are wrong.
3. Confirm the keyed answer is correct. Verify that \correctAnswer{X} matches the only choice that equals the right value.
4. Check the explanation math step by step. Walk through the arithmetic or algebra in \explanation{} and confirm every intermediate step is correct. Watch for sign errors, exponent mistakes, and wrong arithmetic.
5. Check for contradictions. Does the explanation arrive at the same answer as \correctAnswer? If the explanation derives one answer but the key says another, that's a bug.

Short Answer (sa and gsa)

1. Solve the problem independently and compare your result with \correctAnswer{}.
2. Walk through the explanation to verify each step matches the stated answer.

Graphical Questions

1. Read the TikZ code carefully to understand what the graphic actually shows (coordinates, labels, plotted points).
2. Verify the answer matches the graphic, not just the text description. A common bug is the explanation describing one thing while the TikZ code draws another.

Step 4: Classify What You Find

Only flag issues where:

• The \correctAnswer is objectively wrong
• The \explanation contains a calculation error, wrong intermediate result, or a factually false statement
• The explanation contradicts the keyed answer

Do NOT flag or change (unless the user explicitly requests it):

• Distractor choices that happen to be equivalent to each other or to the correct answer — do not rewrite distractors
• Style or wording preferences
• Missing context that doesn't affect correctness

Hard rule — \correctAnswer changes:

• Only change \correctAnswer when the current value is objectively, mathematically wrong. If the existing answer is correct, leave it alone — even if you think additional words or context could be added.
• For multiple-choice questions the correct answer must be a single letter (A, B, C, or D). Never expand it into words or a phrase.
• For short-answer / graphical questions the correct answer should be the shortest correct response — typically one or two numbers, a single expression, or at most a few words. Do not pad a correct short answer with extra explanation, qualifiers, or reworded phrasing. If the existing text is mathematically correct and answers the question, it is good enough.
• Never modify \choiceA / \choiceB / \choiceC / \choiceD text. If a distractor is identical to the keyed answer, change only the key and explanation to point to the right choice — do not rewrite the choice text.

Step 5: Fix with Minimal Changes

For each confirmed issue:

1. Change only what is necessary. If the answer key is wrong but the explanation is right, change only \correctAnswer. If both are wrong, fix both.
2. Do not rewrite surrounding questions that are correct.
3. Do not restructure distractors unless the user specifically asks for it.
4. Preserve the original phrasing wherever possible — change numbers and math, not prose.

Step 6: Validate with Audit Review PDF

After editing, build a review PDF containing only the changed questions so the user can visually verify the corrections. Use the build_audit_review.py script, which has two subcommands: add to accumulate changed questions, and open to compile and display the PDF.

6a. Add changed questions (call after each fix)

Each time you fix a question, immediately register it with the script. Pass the chapter title on the first call via --chapter; subsequent calls inherit it.

# First call — include --chapter
python3 scripts/build_audit_review.py add \
    --chapter "Ratios and Proportional Relationships" \
    tests_questions_bank_2/topics/ch01-02-recognizing-proportional-relationships.tex 1-2-q03 1-2-q15

# Later calls — chapter is inherited
python3 scripts/build_audit_review.py add \
    tests_questions_bank_2/topics_additional/ch01-07-proportional-reasoning-with-scale-models.tex 1-7-q12

The positional arguments are: a .tex file path (relative to workspace root) followed by the question IDs you changed in that file. Multiple files can be passed in one call. If you re-edit a question, just add it again — the script replaces the earlier version.

The grade is read automatically from config.py.

6b. Open the review PDF (call once at the end)

After all fixes are done:

python3 scripts/build_audit_review.py open

This generates tests/audit_review.tex, compiles it into build/audit_review.pdf, opens the PDF, and clears the accumulated data for the next audit.

Each page shows one question with its ID and source file in the header, rendered with inline answer/explanation boxes.

If compilation fails, check editor diagnostics on every changed file and fix any LaTeX syntax errors before retrying.

6c. Report what you fixed

List each question ID, the file it lives in, what was wrong, and what you changed.

Common Error Patterns

These are the most frequent bugs found in past audits:

Pattern	Example	Where to look
Sign error in factoring	−4x(x + 2) claimed to equal −4x² + 8x but actually gives −4x² − 8x (caught in 3-8-q15: key said "Both A and B" but expanding A shows it's wrong)	Factoring and expanding questions
Explanation contradicts key	Explanation derives answer A but \correctAnswer{B}	Any question type
Wrong graph interpretation	TikZ plots point at (3, 4) but explanation says "the point is at (3, 5)"	Graphical questions (gmc, gsa)
Arithmetic slip in explanation	"5 × 8 = 45" or "$3^{-2} = \frac{1}{6}$"	Scientific notation, exponents
Financial formula error	Interest calculated as $P \times r$ instead of $P \times r \times t$	Financial literacy topics

Reporting Format

After completing the audit, summarize:

1. How many source files were audited (and list them).
2. Issues found and fixed — one bullet per fix with question ID, file, what was wrong, and what you changed.
3. Compilation result — confirm the chapter review document compiled successfully.
4. Clean bill of health — explicitly state if no other issues were found, so the user knows the audit is complete rather than abandoned.