From One Problem to a General Formula
A method that solves the case and then generalises into a reusable formula.
Works on any free AI · Best tool: Any AI chat (ChatGPT/Gemini/Claude/Copilot)
✅ How to use this effectively
- 1. Paste the prompt into any AI chat.
- 2. Fill class and exam brackets.
- 3. Paste your specific question.
- 4. Send and read the derived formula.
- 5. Test the formula on a second example.
🔧 If it is not right, reply with this: If the formula seems wrong, reply: 'Test the general formula on two more numbers and show it matches a direct solution each time.'
THE PROMPT
ROLE: Act as a mathematics teacher who solves a specific problem and then generalises the method into a reusable formula.
CONTEXT: For a [CLASS/GRADE] student in [BOARD or EXAM e.g. CBSE / ICSE / State Board / JEE / NEET]. The teacher wants students to see that this one problem is an instance of a general pattern, and to walk away with a formula they can reuse.
YOUR TASK:
1. Find the correct final answer to the specific question below (the SPECIFIC CASE).
2. Solve the specific case with a clear method (numbered steps).
3. GENERALISE: replace the specific numbers with symbols/parameters and derive a GENERAL FORMULA using the same method.
4. VERIFY the formula by plugging the original numbers back in to recover the specific answer, and by testing one more example.
INPUT: Here is the question: [PASTE THE QUESTION HERE]
HOW TO WORK IT OUT: Solve privately, lock the specific answer, then derive the formula carefully. The formula must reproduce the specific answer exactly. Verify the specific answer with two independent checks, and verify the formula with at least two substitutions. Never invent formulas; derive yours and show the derivation. Keep all maths legible in clean LaTeX or plain text.
OUTPUT FORMAT (exact order):
SPECIFIC FINAL ANSWER (once)
SPECIFIC SOLUTION (numbered steps)
GENERAL DERIVATION (replace numbers with symbols; numbered steps)
GENERAL FORMULA (state it clearly, with what each symbol means)
FORMULA CHECK (plug original numbers back; test one more example)
VERIFICATION (two independent checks of the specific answer)
RULES: The general formula must collapse to the specific answer when the original values are inserted. Show the derivation, do not just assert the formula. Use exact values where possible.
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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