Picture a courtroom where x is on the stand and the judge asks, “Why?” — that cadence guides a year-long course for a 15‑year‑old blending AoPS Intro Algebra & Geometry with Alcumus, aligned to ACARA v9 (Number & Algebra; Measurement & Geometry; Mathematical Reasoning).
Act I (Weeks 1–20): Focus on linear relations, functions, systems, polynomials, factoring and inequalities. Read Rusczyk’s Intro to Algebra (cover core chapters ~50–67%). Daily Alcumus (adaptive practice), weekly timed fluency set, and a mini business project modeling cost, revenue, break‑even and sensitivity.
Intermission: Alcumus mastery report, three written solutions, reflective journal.
Act II (Weeks 21–40): Euclidean geometry, proofs, congruence, similarity, area/volume, circle theorems, coordinate synthesis with algebra. Read Intro to Geometry; weekly proof-writing and mixed-problem synthesis.
Capstone: Financial-business presentation using spreadsheets and Desmos — compound growth, amortization, pricing optimization; plus a geometry proof portfolio.
Weekly rhythm: 5–6 Alcumus sessions (30–45 min), two book/proof lessons, one applied lab, one timed set. Outcomes: strong algebraic foundations, proof skills, contest readiness (AMC targets), and practical financial literacy.
Keep curiosity as your spice; present boldly — x tells a compelling story. Listen closely, practise daily, and let each solved problem be a small dramatic reveal — your math is both argument and applause.