# Universal Formula Sheet Generator > A Claude skill from pinakdhabu/Exam-prompt. - **Type:** Skill - **Install:** `agentstack add skill-pinakdhabu-exam-prompt-formula-sheet-generator` - **Verified:** Yes — security-reviewed for prompt injection and unsafe behavior - **Seller:** [pinakdhabu](https://agentstack.voostack.com/s/pinakdhabu) - **Installs:** 0 - **Category:** [Agent Skills](https://agentstack.voostack.com/c/agent-skills) - **Latest version:** 0.1.0 - **License:** MIT - **Upstream author:** [pinakdhabu](https://github.com/pinakdhabu) - **Source:** https://github.com/pinakdhabu/Exam-prompt/tree/main/skills/formula-sheet-generator - **Website:** https://pinakdhabu.github.io/Exam-prompt/ ## Install ```sh agentstack add skill-pinakdhabu-exam-prompt-formula-sheet-generator ``` Requires the [AgentStack CLI](https://agentstack.voostack.com/docs/cli). Works with Claude Code, Cursor, and any MCP-compatible agent. ## About # Universal Formula Sheet Generator ## Overview Creates dense, well-organized formula sheets that serve as both study aids and exam-day quick references. Every formula is presented with its variables clearly defined, applicable conditions stated, and cross-referenced to related formulas. ## How This Skill Works 1. **User provides**: Subject, course code, university, specific units/topics, exam type (open/closed book) 2. **System collects**: All relevant formulas organized by unit and topic 3. **System formats**: In compact, scannable layout with consistent notation 4. **System annotates**: Variable definitions, units, applicability conditions, and common pitfalls ## 1. Formula Entry Format Each formula is presented as: ``` Formula Name f(x) = expression WHERE: x = description [unit], f(x) = description [unit] WHEN: Applicable conditions or assumptions WATCH: Common mistakes or special cases SEE ALSO: Related formula #12 ``` ## 2. Organization Structure ``` Subject Name Unit 1 — Topic Name F1: Formula name F2: Formula name ... Unit 2 — Topic Name ... Appendix Constants Conversion Factors Greek Letters Used Index (formula name -> F-number) ``` ## 3. Formula Categories | Category | Subjects | Presentation Style | | ------------------------- | ----------------------------- | --------------------------------------- | | **Algebraic** | Mathematics, Physics | Standard equation, variable definitions | | **Differential/Integral** | Calculus, Physics | Standard notation with limits | | **Statistical** | Statistics, ML, Data Science | Summation/probability notation | | **Chemical** | Chemistry, Biology | Molecular structure, reaction equations | | **Electrical** | E&TC, Electrical, Electronics | Circuit parameters, phasors | | **Mechanical** | Mechanical, Civil, Aerospace | Force/momentum/energy equations | | **Financial** | Finance, Economics, Business | Time value of money, ratio formulas | | **Algorithmic** | Computer Science | Pseudocode, complexity expressions | | **Logical** | Mathematics, CS | Set notation, logical operators | ## 4. Sample Formula Sheet **Subject**: Engineering Mathematics — Calculus (VTU, 1st Semester) ``` UNIT 1: Differential Calculus F1: Derivative definition f'(x) = lim(h->0) [f(x+h) - f(x)] / h WHERE: f = function, x = variable, h = infinitesimal increment WATCH: Limit must exist for derivative to exist F2: Product rule d/dx [u(x) * v(x)] = u'v + uv' WHERE: u, v = differentiable functions of x NOTE: "First derivative of second + second derivative of first" F3: Quotient rule d/dx [u(x) / v(x)] = (u'v - uv') / v^2 WHERE: v(x) != 0 WATCH: Order matters — numerator is (u'v - uv') not (uv' - u'v) F4: Chain rule dy/dx = dy/du * du/dx WHERE: y = f(u), u = g(x) NOTE: "Derivative of outer times derivative of inner" UNIT 2: Integral Calculus F5: Power rule (integration) int x^n dx = x^(n+1)/(n+1) + C, n != -1 WHERE: n = real number WATCH: n = -1 gives int x^(-1) dx = ln|x| + C (special case) F6: Integration by parts int u dv = uv - int v du WHERE: u = function to differentiate, dv = function to integrate NOTE: Choose u using LIATE (Log, Inverse trig, Algebraic, Trig, Exponential) ... (continues) ``` ### Finance Formulas #### Time Value of Money (TVM) ``` F1: Present Value PV = FV / (1 + r)^n WHERE: FV = future value, r = discount rate, n = periods NOTE: For annuity: PV = PMT × [1 - (1+r)^(-n)] / r F2: Future Value FV = PV × (1 + r)^n WHERE: PV = present value, r = rate, n = periods NOTE: For annuity: FV = PMT × [(1+r)^n - 1] / r F3: Net Present Value NPV = Σ(CF_t / (1+r)^t) - Initial Investment WHERE: CF_t = cash flow at time t, r = discount rate DECISION: NPV > 0 → Accept project F4: Discounted Cash Flow (DCF) DCF = Σ(CF_t / (1+r)^t) WHERE: CF_t = projected cash flow at time t, r = discount rate NOTE: DCF estimates investment value based on future cash flow projections DIFFERENCE: DCF is the sum of discounted cash flows; NPV subtracts initial investment from DCF F5: Internal Rate of Return 0 = Σ(CF_t / (1+IRR)^t) - Initial Investment NOTE: IRR is the discount rate that makes NPV = 0 WATCH: May give multiple IRRs for non-conventional cash flows F5: Capital Asset Pricing Model E(R_i) = R_f + β_i × (E(R_m) - R_f) WHERE: R_f = risk-free rate, β_i = stock beta, E(R_m) = expected market return NOTE: CAPM gives the expected return compensating for systematic risk F6: Weighted Average Cost of Capital WACC = (E/V) × R_e + (D/V) × R_d × (1 - T_c) WHERE: E = equity value, D = debt value, V = E+D, R_e = cost of equity, R_d = cost of debt, T_c = tax rate ``` #### Medical Formulas ``` F1: Body Mass Index BMI = weight(kg) / height(m)² CLASSIFICATION: 60 F4: Anion Gap AG = Na⁺ - (Cl⁻ + HCO₃⁻) NORMAL RANGE: 8-12 mEq/L NOTE: Elevated gap → metabolic acidosis (MUD PILES: Methanol, Uremia, DKA, etc.) F5: Mean Arterial Pressure MAP = DBP + 1/3 × (SBP - DBP) WHERE: SBP = systolic BP, DBP = diastolic BP TARGET: MAP ≥ 65 mmHg for organ perfusion ``` ## Session Config This skill integrates with the session config system (`deps/session-profile.json`). Before executing, check for an existing session profile: - If `deps/session-profile.json` exists, read `university`, `subject`, `pattern`, and `exam_type` fields to auto-configure the skill. - If the file does not exist, fall back to user-provided context or prompt the user to run `setup-exam-prompt` (or `npm run init`) first. - Session config eliminates redundant context detection — detection happens once and is reused across all skill calls. --- ## Error Handling | Situation | Action | | ----------------------------- | ------------------------------------------------------------------------------------------------------------------------------------------- | | Formula domain not recognized | Respond: "Unrecognized formula domain. Supported domains: engineering, mathematics, physics, chemistry, finance, statistics, data science." | | Variable definition missing | Flag undefined variables during generation and request clarification | | Unit inconsistency | Auto-convert to SI units; warn if conversion may introduce error | | Circular formula reference | Detect cycles in formula dependencies and break at the simplest formula | ## Quality Gate — Check Before Output - [ ] Every formula includes variable definitions with units - [ ] Applicability conditions stated (WHEN clause present) - [ ] Common mistakes noted (WATCH clause present) - [ ] Cross-references to related formulas included - [ ] Consistent notation maintained across all formulas - [ ] Sample calculation provided for non-trivial formulas - [ ] Maximum 3 formulas per page for readability in exam conditions ## 5. Integration with Other Skills | Skill | Integration | | ------------------------------------ | ------------------------------------------------------------- | | **universal-session-config** | Reads university/subject/pattern from session profile | | **universal-notes-generator** | Provides the full context from which formulas are extracted | | **universal-a-plus-answer-writer** | Uses formula sheets for numerical problem solutions | | **universal-last-minute-crammer** | Formula sheets are the primary cram resource | | **universal-mcq-practice-generator** | MCQs can be generated targeting specific formula applications | ## Source & license This open-source skill is cataloged on AgentStack and links to its original source — we do not rehost the code. - **Author:** [pinakdhabu](https://github.com/pinakdhabu) - **Source:** [pinakdhabu/Exam-prompt](https://github.com/pinakdhabu/Exam-prompt) - **License:** MIT - **Homepage:** https://pinakdhabu.github.io/Exam-prompt/ Install and usage instructions live in the source repository linked above. ## Pricing - **Free** — Free ## Security capabilities Automated source analysis of v0.1.0 — what this tool can access: - **Network access:** no - **Filesystem access:** no - **Shell / process execution:** no - **Environment & secrets:** no - **Dynamic code execution:** no *"Yes" means the capability is present in the source — more access means more to trust, not that it is unsafe.* ## Versions - **0.1.0** — security scan: passed — Imported from the upstream source. ## Links - Listing page: https://agentstack.voostack.com/l/skill-pinakdhabu-exam-prompt-formula-sheet-generator - Seller: https://agentstack.voostack.com/s/pinakdhabu - Browse the marketplace: https://agentstack.voostack.com/browse --- Listed on AgentStack — the marketplace for AI agent skills and MCP servers. Every listing is security-reviewed. Creators keep 70%.