One-Skill Drill (Master a Single Technique)

ROLE: Act as a drill-master mathematics teacher who builds focused single-skill practice sheets.

CONTEXT: I teach [CLASS/GRADE] under [BOARD or EXAM e.g. CBSE / ICSE / State Board / JEE / NEET]. My students need repeated practice on ONE specific skill until it becomes automatic. The skill is [NAME THE SINGLE SKILL, e.g. 'factorising quadratics by splitting the middle term' or 'differentiating using the chain rule'].

YOUR TASK:
1. Create exactly 20 questions, ALL testing only the skill [SKILL]. Do not mix in other skills.
2. Order them so the first 6 are gentle, the next 8 are standard, and the last 6 stretch the skill to its limit (still using only this skill).
3. Vary the surface details (numbers, signs, fractions, negatives) so students cannot guess by pattern.
4. Number the questions 1 to 20. Each carries 1 mark; show total 20 marks.

INPUT: Here is the exact skill and any constraints (allowed number types, what to avoid): [PASTE SKILL AND CONSTRAINTS HERE].

HOW TO WORK IT OUT: Solve each question internally first. Then VERIFY every final answer two independent ways (for example, expand back, differentiate back, or substitute). Never invent formulas or values. Keep all maths legible in clean LaTeX or clear plain text.

OUTPUT FORMAT (exact headings, in order):
- TITLE BLOCK: Skill name, Class, Total Marks 20, and 'Compiled by [YOUR NAME]'.
- DRILL QUESTIONS: Q1 to Q20, numbered, one per line.
- ANSWER KEY: final answers Q1 to Q20 in a clearly separated block at the end.
- COMMON MISTAKE NOTE: 3 short bullet points naming the typical errors students make on this skill.

RULES: Strictly one skill. No duplicate questions. Single correct answer each. Answer key must match exactly. Keep language simple and short.

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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