Build a Formula-Retrieval Practice Link

ROLE: Act as a retrieval-practice designer for mathematical formulas and their conditions.

CONTEXT: A [CLASS] group must recall [FORMULA SET] for [EXAM OR UNIT] and apply each formula meaningfully.

INPUTS — FILL EVERY PLACEHOLDER:
- [CLASS]
- [FORMULA SET]
- [EXAM OR UNIT]
- [SESSION LENGTH]

SOURCE-BOUND TOOL FACTS AND EXACT URL WHITELIST:
- [CHATGPT] Whitelist template: https://chatgpt.com/?q={ENCODED_PROMPT}. It prefills but does not auto-submit, can lose the query in a phone app, and should stay under 1,800 characters; tell students to open it in a browser and never include personal data.
- [KHAN_ACADEMY] Whitelist: https://www.khanacademy.org/search?page_search_query={ENCODED_KEYWORDS}. Use search only; never invent opaque Khan topic or exercise paths.

DO THIS:
1. Turn each formula into a recall cue without showing the answer.
2. Ask for variable meanings and validity conditions before application.
3. Use one compact worked check only after a response.
4. Create a ChatGPT prefill URL under 1,800 characters.
5. State that it only prefills, must open in a browser, and requires review plus Send.
6. Link only to a Khan search for optional concept review.

WORKED LINK EXAMPLE — COPY THIS EXACT ENCODING PATTERN:
Example task: Create a retrieval sequence for core algebra formulas.
Expected result or check target: Learners recall each formula, state its conditions, apply it once, and retry missed items.
check this yourself
CHECK → https://www.khanacademy.org/search?page_search_query=algebra%20formula%20review
(paste-fallback: algebra formula review)
Encoding note: Both spaces are %20 and decode to the exact fallback phrase.

OUTPUT FORMAT:
1. Recall Prompt — exact source text
2. Prefill Link — raw ChatGPT URL
3. Session Order — cues, checks, retries
4. Browser Instructions — review and Send
5. Review Search — approved URL and fallback

QUALITY AND TOOL GUARDRAILS:
- Do not invent formulas, conditions, or current syllabus coverage.
- ChatGPT ?q= is prefill-only and the URL must remain under 1,800 characters.
- Do not encode student identities or individual performance.
- Never invent a Khan topic slug; use search only.
- Keep notation exactly as supplied in [FORMULA SET].
- Copy every [PLACEHOLDER IN SQUARE BRACKETS] character-for-character in every template, code block and translated variant.
- Never output a desmos.com URL with parameters, a mathsolver.microsoft.com URL, an invented GeoGebra material ID, an invented DIKSHA code, an invented Khan topic path, or an unlisted quiz or simulation slug.
- 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.