Imagine a courtroom where the witness is x and the judge keeps asking “Why?” — that’s our cadence for a year-long Math & Finance prospectus for a 15‑year‑old. Act I (Weeks 1–20): AoPS Introduction to Algebra + Alcumus — linear equations, inequalities, systems, functions, factoring; daily Alcumus, weekly timed sets, mini business model (cost, revenue, break‑even). Intermission: assessment & reflections. Act II (Weeks 21–40): AoPS Introduction to Geometry — proofs, congruence, similarity, area/volume, coordinate synthesis; mixed-problem weeks and geometry proof portfolio. Finance capstone: spreadsheeted savings/investment and compound growth visuals with Desmos. Weekly rhythm: 30–45 min Alcumus, two lessons, one applied lab. ACARA v9-aligned to Number & Algebra, Measurement & Geometry, and Mathematical Reasoning — outcome: contest readiness, proof fluency, and practical financial numeracy. Stay curious; present boldly, explain why.