Solve, Then Suggest a Faster Route
The standard solution plus a quicker, exam-smart shortcut to the same answer.
Attach a photo of the question first · Best tool: ChatGPT or Gemini (image)
✅ How to use this effectively
- 1. Photograph the question clearly.
- 2. Attach the photo and paste this prompt.
- 3. Send and read the standard solution.
- 4. Compare it with the faster route.
- 5. Ask which shortcuts are exam-safe.
🔧 If it is not right, reply with this: If the shortcut is shaky, reply: "Show the faster route in full and prove it gives the same answer as the standard method."
THE PROMPT
ROLE: Act as an exam-smart mathematics teacher who solves a problem the standard way and then shows a faster route to the same answer.
CONTEXT: I teach [CLASS/GRADE] for [BOARD or EXAM e.g. CBSE / ICSE / State Board / JEE / NEET], topic [TOPIC]. Time matters in exams, so I want both the safe full method and a quicker shortcut.
YOUR TASK:
1. Read the question in the attached photo and restate it in clean text.
2. Solve it the standard, reliable way, step by step.
3. Then present a FASTER route to the same answer - a shortcut, a clever substitution, symmetry, elimination of options, or a known result.
4. State clearly how much time or work the faster route saves, and any conditions under which it is safe to use.
INPUT: I have attached a photo of the problem. If any part is unclear, tell me which symbol or line you cannot read, state your best assumption, and continue.
HOW TO WORK IT OUT: Solve the problem silently first by the standard method. Then VERIFY the final answer with TWO independent checks - and crucially, confirm the faster route lands on the SAME final answer as the standard method. If the two methods disagree, the shortcut is wrong - fix it or discard it. Never invent formulas or values; name standard results. Keep all mathematics fully legible in clean LaTeX or clear plain text, one step per line.
OUTPUT FORMAT (use these exact headings):
1. Question as I read it.
2. Standard method - numbered steps, one idea per line, short reasons.
3. Final answer - clearly stated.
4. Faster route - the shortcut, shown step by step, ending at the same answer.
5. Time saved and when it is safe - one or two lines.
6. Verification - Check 1 and Check 2, confirming both methods agree.
RULES: The faster route must be genuinely valid and reach the identical answer; do not present a risky trick as reliable without saying so. Use plain ASCII only with straight quotes. Be exact unless an estimate is requested.
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.
At the very end add a footer line: "Prepared by [YOUR NAME]", and put "Compiled by [YOUR NAME]" in the title or header block at the top.
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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