Graded Easy-to-Hard Worksheet (Builds Confidence)

ROLE: Act as an experienced mathematics teacher who designs graded practice worksheets.

CONTEXT: I teach [CLASS/GRADE] following [BOARD or EXAM e.g. CBSE / ICSE / State Board / JEE / NEET]. I need a worksheet on the topic [TOPIC NAME] that starts very easy and gradually becomes harder, so weak and strong students all stay engaged.

YOUR TASK:
1. Create exactly 15 questions on [TOPIC NAME], arranged in increasing difficulty.
2. Group them as: Warm-up (Q1-Q5, very easy), Practice (Q6-Q11, medium), Challenge (Q12-Q15, hard).
3. Assign marks: warm-up 1 mark each, practice 2 marks each, challenge 4 marks each. Show the total marks.
4. Make every question solvable by hand at this level. Use a variety of sub-types, not 15 copies of the same question.

INPUT: Here is the topic and any sub-points I want covered: [PASTE TOPIC AND SUB-POINTS HERE].

HOW TO WORK IT OUT: Solve every question fully in your head first. Then VERIFY each final answer by at least two independent methods (for example, re-solving a different way, or substituting the answer back into the original equation). Never invent formulas, values, or fake data. Keep all mathematics fully legible using clean LaTeX or clear plain text with proper symbols.

OUTPUT FORMAT (use these exact headings, in this order):
- TITLE BLOCK: Topic, Class, Total Marks, Time, and the line 'Compiled by [YOUR NAME]'.
- SECTION A: Warm-up (Q1-Q5) with marks shown beside each question.
- SECTION B: Practice (Q6-Q11) with marks.
- SECTION C: Challenge (Q12-Q15) with marks.
- ANSWER KEY: a clearly separated section at the very end listing the final answer to every question, plus one short line of working for the four challenge questions only.

RULES: Questions must be unambiguous and have a single correct answer unless I asked otherwise. No repeated questions. Difficulty must genuinely increase. Every answer in the key must match the worksheet exactly.

OUTPUT FILE FORMAT: present the complete result as a clean, ready-to-use document I can paste straight into Microsoft Word or Google Docs - a clear bold title, section headings, neatly numbered items, comfortable spacing, and simple tables only where helpful (avoid heavy formatting that breaks on paste). It must also print cleanly to PDF on A4 (File > Print > Save as PDF). Keep all mathematics fully readable (fractions as a/b, powers as x^2, roots as sqrt(x)).

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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