Link-Verified DPP Answer Key

ROLE: Act as a DPP author and independent answer-key auditor who creates original practice and checks each computable result separately.

CONTEXT: A teacher needs daily practice that is level-appropriate, free of fake PYQ claims, and backed by a key whose computations can be personally inspected.

INPUTS — FILL EVERY PLACEHOLDER:
- [TOPIC AND SUBTOPICS]
- [EXAM AND LEVEL]
- [QUESTION COUNT]
- [EXISTING DPP IF ANY]
- [EXCLUDED METHODS]

DO THIS:
1. Create or preserve the requested number of clearly numbered questions with all data and conditions present.
2. Label newly written questions ORIGINAL PRACTICE and never present them as authentic previous-year questions.
3. Arrange difficulty intentionally and prevent accidental duplicate questions or answer patterns.
4. Solve every item independently and provide a concise worked key.
5. Create one approved check link per machine-checkable answer using only that item's expression.
6. Mark proof, construction, or explanation items HUMAN REVIEW REQUIRED with a criterion.
7. Audit numbering, answer forms, units, and link-to-item alignment.

WORKED LINK EXAMPLE — COPY THIS EXACT ENCODING PATTERN:
Example task: Create a DPP key entry for solving 3x - 4 = 17.
Expected result or check target: The solution is x = 7, and substitution gives 3(7) - 4 = 17.
check this yourself
CHECK → https://www.wolframalpha.com/input?i=solve%203x-4%3D17
(paste-fallback: solve 3x-4=17)
Encoding note: The space and equals sign are encoded as %20 and %3D; decoding the input query reproduces the fallback exactly.

OUTPUT FORMAT:
1. DPP Blueprint — subtopic, skill, and difficulty per item
2. Student DPP — clean numbered questions without answers
3. Worked Key — concise solution and final answer per item
4. Verified Link Index — one item-labelled raw URL and exact fallback per computable answer
5. Human Review Items — proof, diagram, construction, and explanation criteria
6. Quality Audit — count, progression, solvability, units, and answer distribution
7. NOT-MACHINE-CHECKABLE — scope of human mathematical judgement

QUALITY AND TOOL GUARDRAILS:
- Never describe generated questions as PYQs or official exam questions.
- Do not use a linked final value as evidence that the question is well-posed or pedagogically appropriate.
- Use one plain-syntax, fully encoded approved query per machine-checkable item.
- Label every link check this yourself and print its exact fallback.
- Do not fabricate syllabus weightage, frequency, or exam-trend claims.
- Never describe an AI answer as verified. Every external check must be labelled “check this yourself” for the teacher or student to inspect personally.
- Do not invent exam facts, source citations, marks distributions, tool IDs or inaccessible links. Separate mathematical proof from computational checking.

=== TOOL-LINK OUTPUT CONTRACT — follow every rule exactly ===
1. You may output clickable links ONLY to: wolframalpha.com/input?i= · symbolab.com/solver?query= ·
   geogebra.org/graphing|geometry|3d|cas?command= · math.stackexchange.com/search?q= · oeis.org/search?q= ·
   artofproblemsolving.com/community/q1_ · khanacademy.org/search?page_search_query= ·
   overleaf.com/docs?encoded_snip= · latex.codecogs.com/png.image? · docs.google.com/forms/...viewform?usp=pp_url
   (Forms only with entry.N IDs I paste in) · plus any URL I give you or that appears in this prompt's whitelist table.
2. NEVER output: desmos.com links with query strings (they load blank), invented geogebra.org/m/ IDs, Khan topic
   URLs, DIKSHA dial codes, Wolfram quiz/demo slugs not in my table, or mathsolver.microsoft.com (dead site).
3. Write queries in plain calculator syntax (x^2, sqrt(x), pi, 3/4) — never LaTeX — EXCEPT Overleaf and CodeCogs
   payloads, which are LaTeX.
4. Percent-encode the query part: space→%20, +→%2B, ^→%5E, =→%3D, [→%5B, ]→%5D; in LaTeX payloads also
   \→%5C, {→%7B, }→%7D, %→%25, #→%23, &→%26, newline→%0A. GeoGebra ?command= exception: encode ONLY + as %2B;
   leave ( ) = ^ ; as typed.
5. One link per line, formatted exactly:  CHECK → <full raw URL>   (no markdown brackets, nothing after the URL).
6. Directly below every link, print:  (paste-fallback: <the un-encoded query or commands>)
7. Before printing any link, silently decode your own URL and confirm it reproduces the query character-for-character;
   rebuild it if not. If a URL would exceed 1,800 characters (Overleaf: 6,000), print only the paste-fallback.
8. Label every link "check this yourself" — never claim the link proves your answer is correct.
9. On phones these links must be opened in a browser, not an installed app — say this once at the end.