Print-Ready 3-Level Differentiated Worksheet with Answer Key

Act as an expert mathematics teacher and exam-paper designer creating a print-ready differentiated worksheet.

CONTEXT: The class is [CLASS/GRADE], following [BOARD or EXAM], on the topic [TOPIC, e.g. quadratic equations]. Students range from weak to advanced, so I need three difficulty tiers on one A4 sheet plus a clean answer key.

YOUR TASK:
1. Design a single worksheet with three labelled tiers: Bronze (foundation), Silver (standard), Gold (stretch).
2. Put 6 questions in each tier, numbered B1-B6, S1-S6, G1-G6.
3. Bronze = one-step or direct recall. Silver = standard two-step exam style. Gold = multi-step, application, or a deliberate conceptual twist.
4. Keep the mathematics tightly on [TOPIC]; do not drift to other chapters.
5. After the worksheet, give a complete ANSWER KEY with the final answer for every question, plus a one-line method note for the Gold questions.

INPUT: Topic and class are above. If I paste a sample question here: [PASTE or leave blank], match its style and difficulty for the Silver tier.

HOW TO WORK IT OUT: Solve every question yourself before writing it. VERIFY each answer by two independent checks (for example, substitute the solution back, or re-solve by a second method). Never invent values or formulas; if a question would have an ugly or non-real answer, redesign it so answers are clean and classroom-appropriate. Keep all mathematics fully legible in plain text (use ^ for powers, sqrt() for roots, / for fractions, clear brackets).

OUTPUT FORMAT (exact order):
- Title block: 'Compiled by [YOUR NAME]', topic, class, and three blank lines for Name / Class / Date.
- A short instruction line: marks per tier and time suggested.
- Section BRONZE (B1-B6).
- Section SILVER (S1-S6).
- Section GOLD (G1-G6).
- Page break marker '--- ANSWER KEY (teacher copy) ---'.
- Answer key grouped by tier, with method notes for Gold only.

RULES: A4-friendly layout, generous spacing for working, no decorative clutter. Use consistent notation throughout. Do not mix topics. Make the difficulty jump between tiers visible and honest. If anything is ambiguous, state one sensible assumption and continue.

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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Questions, feedback or appreciation are always welcome.
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