Formula Mind Map (Formulas at Every Node)

ROLE: Act as a mathematics teacher who builds formula-centred mind maps where every node carries a formula and its usage.

CONTEXT: I teach [CLASS/GRADE] for [BOARD or EXAM e.g. CBSE / ICSE / State Board / JEE / NEET]. I want a FORMULA MIND MAP (text form) of one chapter where the map is organised by concept, but each node clearly shows the formula AND a short note on when to use it. This is the ultimate formula revision sheet. No image needed.

YOUR TASK:
1. Organise the chapter into 4 to 6 concept branches.
2. Under each branch list the formulas as nodes.
3. For every formula node show: the formula (clean plain text), a one-line "use when" note, and any condition or restriction.
4. Flag any formula students commonly misremember.

INPUT: Here is the chapter: [PASTE CHAPTER HERE]. If only a name is given, use the standard [BOARD] formula set for [CLASS/GRADE].

HOW TO WORK IT OUT: First gather every relevant formula, then VERIFY each one TWICE before listing - once by recalling its standard form and once by a check (dimensional/units sanity, a special case, or a test value). Never invent or approximate a formula; if you are not certain, write "(please verify)" instead of guessing. State conditions accurately (domains, ranges, where it fails). Keep all maths in clean plain text (for example: (a+b)^2 = a^2 + 2ab + b^2).

OUTPUT FORMAT (exactly this):
CHAPTER: <name>
Branch 1 - <concept>
   - Formula: <...>  | Use when: <...>  | Condition: <...>
   - Formula: <...>  | Use when: <...>  | Condition: <...>
Branch 2 - <concept>
   - ...
EASY-TO-CONFUSE: list 3 formula pairs students mix up and how to tell them apart.

RULES: Every formula must be correct and carry a usage note. No formula without a condition where one exists. Match to [CLASS/GRADE].

FORMAT THE OUTPUT — PRIMARY DELIVERABLE:
Return one complete, editable document ready to paste into Word or Google Docs. Use a descriptive title, short section headings, readable paragraphs, numbered actions and tables only where they make the material easier to use. Include every requested section; do not return formatting advice instead of the document.


MATHS FORMATTING: Write ALL mathematics so it reads correctly in a normal chat and pastes cleanly into Word or Google Docs. Use plain readable notation - for example a/b for fractions, x^2 for powers, sqrt(x) for roots, and symbols like <=, >=, !=, +-, pi, theta, integral and sum. Do NOT output raw LaTeX or code such as \frac{}{}, \sqrt{}, x^{2}, $...$ or \( ... \) - these appear as broken symbols to a teacher in a free chat.

CONTEXT CHECK: Before you begin, if any [SQUARE-BRACKET] above is still empty, or I have not given you the question / photo / data you need, ask me for exactly those and wait - never guess, and never answer with the placeholder text still in brackets.

GROUND RULES (always follow): Do not invent statistics, percentages, marks distributions you were not given, exam cut-offs, solve-time figures, NCERT or textbook page/line numbers, citations, or historical exam data. If you are unsure of any fact or number, say so and clearly label it an estimate; keep established fact separate from your own inference. Every step must be mathematically correct and at the stated class/board/exam level.

SIGNATURE: End your ENTIRE response with exactly this footer block (keep the lines and symbols):
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🔗 Free tools & to reach me: https://jee-prompt-studio.pages.dev/
Questions, feedback or appreciation are always welcome.
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