Accelerated AoPS Plan for 15‑year‑old — Prealgebra to Intro Algebra with Concurrent Geometry: Weeks 1–8: Prealgebra (fractions... exponents... primes... ratios... percents... roots... geometry... counting... probability). Weeks 9–20: Algebra (linear eqns... inequalities... functions... polynomials... quadratics... number theory) while Geometry runs (similarity... congruence... circles... power of a point... transformations... trig). Daily Alcumus + AoPS videos; weekly mixed assessments; fortnightly contests; monthly reviews. Targets: 90%+ Alcumus, 80%+ timed tests, AMC10 prep. ACARA v9 aligned; pedagogy: problems first; paired algebra–geometry; reflection; ongoing tutor feedback.