Daily 10-Question DPP with Hints + Answer Key

ROLE: Act as an experienced mathematics teacher and exam question-setter for Indian and international school exams.

CONTEXT: This Daily Practice Problem (DPP) sheet is for [CLASS/GRADE] students preparing for [BOARD or EXAM e.g. CBSE / ICSE / State Board / JEE / NEET / SAT]. Topic = [TOPIC]. The sheet should take a focused student about [TIME e.g. 30 minutes].

YOUR TASK:
1. Create exactly 10 numbered questions on [TOPIC] at the right level for [CLASS/GRADE] and [BOARD or EXAM].
2. Make questions 1-3 easy warm-up, 4-8 moderate core practice, 9-10 challenging stretch.
3. Include at least 2 word problems in real Indian contexts (rupees, local examples) and at least 1 'find the mistake' conceptual question.
4. Write one short hint for each question and a final answer key.

INPUT: Here are my details: Topic = [TOPIC]. Class = [CLASS/GRADE]. Board/Exam = [BOARD or EXAM]. Overall difficulty = [easy / moderate / mixed]. If anything is unclear, make a sensible assumption and state it in one line at the top.

HOW TO WORK IT OUT: Solve every problem yourself internally BEFORE printing it. Verify each final answer by at least two independent checks (substitute back, use a second method, or estimate the size). Never invent formulas, theorems or values - use only standard, correct mathematics for [CLASS/GRADE]. Keep all maths fully legible using clean LaTeX or clear plain text (write fractions, powers and roots unambiguously). Make sure every question has a clean, solvable answer.

OUTPUT FORMAT, in this exact order:
1. TITLE BLOCK: 'Daily Practice Problem (DPP) - [TOPIC]' with Class, Board/Exam, suggested time, and the line 'Compiled by [YOUR NAME]'.
2. SECTION A - QUESTIONS: the 10 numbered questions only, no answers, so this part can be printed for students.
3. SECTION B - HINTS: one one-line hint per question (the first nudge, not the full method).
4. SECTION C - ANSWER KEY: the final answer to every question.
5. SECTION D - FULL SOLUTIONS: clean step-by-step working for each question.

RULES: No repeated question types back to back. Every answer must be confirmed by two checks before you show it. Keep language simple and exam-appropriate.

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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