academic-notes-exercise-writer

name	academic-notes-exercise-writer
description	Create a single LaTeX worksheet for Singapore secondary school math with concise notes, aligned new questions based on a named reference exercise, and very concise end-of-document solutions.

Academic Notes Exercise Writer

Use this skill when a user provides lecture material and a named reference exercise and wants one worksheet that:

• teaches the topic with short, student-friendly notes
• includes basic examples taken from the taught ideas
• creates exactly {user_designated_number} new questions unless the user overrides the count
• matches the style and pedagogy of Exercise {user_specified_exercise} as closely as practical
• stays within secondary-school scope and within the provided material
• ends with very concise solutions in a separate compact format

Treat the following as default constraints unless the user explicitly overrides them:

• audience: Singapore secondary school students
• notes: concise, clear, precise, and easy to follow
• terminology and notation: simplest correct wording and notation, adhering as closely as possible to the lecture material
• questions difficulty level: middle-level to hard unless specified by user
• multipart questions: multipart questions are allowed and encouraged (each multipart question counts as ONE question)
• output: one .tex file in math_curriculum/
• layout: notes and questions stay in the normal worksheet font and normal single-column layout
• solutions: begin on a fresh page at the end of the document and switch into the bundled compact solutions format only from that point onward

Workflow

1. Inspect the source material before writing.

   • Read the lecture notes and the named exercise set.
   • If the user names a section and an exercise, use that exact pair.
   • If the files are PDFs, try normal text extraction first.
   • If extraction fails because a PDF is scanned, use OCR or page rendering plus OCR.
   • Do not draft notes or questions until the actual source content has been inspected.

2. Build a scope map.

   • List the concepts explicitly taught in the lecture notes.
   • List the worked examples or recurring solution patterns in the notes.
   • List the major question types and difficulty spread in Exercise {user_specified_exercise}.
   • Note any terminology, notation, or methods that do not appear in the source and should stay out of the new worksheet.

3. Draft the notes.

   • Keep the notes concise, clear, and student-facing.
   • Follow the source order unless a small reordering makes the teaching sequence clearer.
   • Explain each key idea in simple language.
   • Add short basic examples that directly illustrate the taught ideas.
   • Do not add content that goes beyond the lecture notes or the reference exercise.

4. Draft the new questions.

   • Create exactly {user_designated_number} questions unless the user overrides the count.
   • Match the command verbs, answer expectations, scaffolding, and pacing of Exercise {user_specified_exercise}.
   • Cover the main skill range of the reference exercise as best as possible.
   • Keep the questions genuinely new rather than trivial edits of the source problems.
   • Keep every question solvable using only the taught material.
   • Default to middle-level to hard difficulty unless the user overrides it.
   • Treat each multipart question as one question.

5. Draft the solutions.

   • Keep the solutions very concise.
   • Include brief working only when it is needed for clarity.
   • Do not introduce extra methods that were not taught in the notes.
   • Read references/math-solution-presentation-format.md before drafting the solutions section.
   • Apply that format only to the solutions section.
   • Start the solutions on a fresh page at the end of the document.
   • Box every final numerical answer in the solutions.

6. Write the worksheet to disk.

   • Output one .tex file unless the user explicitly asks for another format.
   • Default output location: math_curriculum/.
   • If the user specifies another path, follow that instruction.
   • Use a file name that clearly identifies the topic or chapter.

Source Rules

• Read both the lecture notes and the exercise set if both are referenced.
• If the user says "use Exercise X" and "the lecture notes associated with it", identify the matching notes section rather than using the whole chapter blindly.
• Extract the real topic coverage from the source; do not rely on the chapter title alone.
• Treat the lecture notes as the source of truth for explanations, examples, notation, and allowed methods.
• Treat the exercise set as the source of truth for question style, pacing, and expected answer form.
• If the source material is incomplete, say so and work only from what is available.
• If OCR is noisy, cross-check key formulas, headings, and prompts before using them.

Writing Rules

Notes

• Write simple, easy-to-understand notes.
• Keep explanations short and direct.
• Prefer phrasing such as "To find...", "Use...", and "This means..." over formal academic prose.
• Keep notation simple and consistent with the source.
• Avoid jargon beyond secondary-school scope.
• Do not import later-topic methods, notation, or theorems.

Questions

• Match the reference set's questioning style as closely as practical.
• Stay within the requested difficulty band.
• Avoid unfamiliar notation, technical vocabulary, representations, or question types that were not modelled or clearly implied by the source.
• Mirror the source pedagogy where relevant:
  • if the source starts with direct practice before mixed questions, do the same
  • if the source uses multipart scaffolding, preserve that pattern
  • if the source mixes routine and challenging items, preserve that balance as far as practical

Solutions

• Keep the wording simple enough for Singapore secondary school students unless the user asks for another audience.
• Use references/math-solution-presentation-format.md as the source of truth for the solutions section layout.
• Keep notes and questions in the document's normal worksheet font and normal single-column layout.
• After \newpage, switch into the compact solutions format and keep it confined to that section only.
• In the solutions section, keep these defaults unless the user overrides them:
  • \small
  • exactly two columns via multicols
  • default LaTeX serif and math fonts
  • a restrained bold solutions heading
  • compact subpart lists
  • boxed final numerical answers
• Keep the solutions telegraphic and computation-first.

Output Shape

Default output is one LaTeX worksheet file with this structure:

\documentclass[10pt]{article}
...
\begin{document}

\section*{Notes}
...

\section*{Questions}
...

\newpage

{%
\small
\begin{center}
{\bfseries Very Concise Solutions}
\end{center}
\begin{multicols}{2}
\raggedcolumns
...
\[
\boxed{42}
\]
...
\end{multicols}
}

\end{document}

Notes and questions stay in the normal worksheet font and normal single-column layout. Only the solutions section switches into the compact bundled format. Write the .tex file into math_curriculum/ unless the user explicitly asks for another location.

Final Checks

Before finishing, verify all of the following:

• The notes are clearly based on the named lecture material.
• The questions are clearly based on Exercise {user_specified_exercise}.
• The new questions cover the main skill range of Exercise {user_specified_exercise} as best as possible.
• No mathematical concept appears unless it is taught or clearly assumed by the source.
• The wording fits Singapore secondary school students unless the user asked for another audience.
• The solutions are correct and very concise.
• Every final numerical answer in the solutions is boxed.
• The output is a single .tex file unless the user explicitly requested another format.
• The solutions section begins on a fresh page at the end of the document.
• The notes and questions stay in the normal worksheet font and normal single-column layout.
• The compact two-column format is used only for the solutions section.
• The output file exists in math_curriculum/ unless the user requested another location.

Use references/quality-checklist.md as a compact audit list when the output is substantial or the source set is large.