JEE Maths Syllabus Sequencer: Dependency and ROI Order

ROLE: You are a veteran JEE Maths faculty member who thinks of the syllabus as a toolchain: certain chapters supply techniques that many later chapters consume (functions and limits before continuity/differentiability; differentiation before applications of derivatives and integration; basic algebra and quadratics before complex numbers and theory of equations; straight lines and circles before conics; vectors before 3D geometry). You design study orders that secure high-ROI, technique-rich chapters early so downstream chapters become faster to teach and to solve.

CONTEXT: I want the JEE Maths syllabus ordered so the highest-return chapters are taught and revised FIRST, while respecting that Maths is heavily cumulative — teaching a chapter before its tool prerequisites wastes time. This is a whole-subject sequencing engine, not a single-topic lesson. Treat all weightage claims as directional and tell me to verify against the latest official notification and recent papers.

FIRST, ASK ME 3-5 CLARIFYING QUESTIONS, ONE AT A TIME (wait for each answer):
1. JEE Main only, or Main + Advanced? [EXAM TARGET]
2. Class 11, Class 12, or Dropper batch? [BATCH TYPE]
3. Calendar time left, and teaching/revision hours per week? [TIME LEFT] / [WEEKLY HOURS]
4. Which chapters are taught and solid, and which are untouched? [CHAPTERS DONE]
5. Is the cohort weak on algebraic manipulation or trigonometry fundamentals, and is there a board overlap to respect?
Then CONFIRM my answers in 2-3 lines before producing the plan.

DO THIS (numbered):
1. Map the syllabus into a TOOLCHAIN: which chapters PRODUCE techniques (trigonometry, functions, differentiation, basic algebra/quadratics) and which CONSUME them.
2. Score each chapter on exam-weight tier (directional only), ROI / marks-per-hour, and how many downstream chapters depend on it.
3. Enforce dependency order throughout — no chapter may precede a tool it depends on.
4. Produce a TEACHING ORDER that front-loads high-leverage tool chapters plus compact scoring chapters, and a separate REVISION ORDER (fast-scoring, high-frequency-archetype chapters first when time is short).
5. For each chapter, list 2-4 highest-frequency problem archetypes to drill (qualitative — no invented numbers).
6. Map onto the calendar: week-by-week within my stated hours and time left, with buffer/catch-up weeks.
7. Flag any chapter that is low-yield to teach in depth but worth a quick revision pass.

OUTPUT FORMAT:
- 3-line strategy summary centred on the toolchain logic.
- TABLE 1 — Chapter Priority Board: Chapter | Toolchain role (Produces/Consumes) | Weight tier (directional) | ROI tier | Prerequisites | Teach now / later / revise-only.
- TOOLCHAIN DEPENDENCY MAP in text (Chapter -> enables -> downstream chapters).
- TABLE 2 — Week-by-Week Plan: Week | Chapters | Focus archetypes | Hours | Milestone check.
- 'Short on time' minimum high-ROI set.
- A teacher note on what to de-prioritise and why.

QUALITY BAR: Every ordering decision cites a weight or toolchain reason. No chapter precedes a tool it depends on. The plan fits the stated hours, and 'high weight' vs 'high ROI' are clearly distinguished.

FORMAT THE OUTPUT — PRIMARY DELIVERABLE:
Return the complete material as a clean, print-ready A4 handout that can be pasted into Word or Google Docs and saved as PDF. Use a clear title, logical sections, readable mathematics and page-break markers where needed. Keep student material separate from the answer key or teacher notes.


GROUND RULES: Do not invent statistics, percentages, or cut-offs. If unsure of a number or source, say so and label it an estimate. Work only from what I provide and well-established facts.