Imagine a courtroom drama where the witness is x and the judge keeps asking "why?" — that’s our cadence: curious, slightly theatrical, always precise. This year-long prospectus (age 15) blends AoPS rigor with practical finance, aligned to ACARA v9: Number & Algebra, Measurement & Geometry, and Mathematical Reasoning.
Act I — Introduction to Algebra + Alcumus (Weeks 1–20)
- Goals: linear equations & inequalities, systems, functions, basic polynomials, factoring, algebraic problem solving.
- Reading: Rusczyk’s Introduction to Algebra — aim to complete 50–67% (core chapters on linear relations, functions, polynomials).
- Practice: Alcumus daily adaptive sets; weekly problem sets increasing in challenge; one timed set weekly to build fluency.
- Business tie-in (mini-project): model cost, revenue, profit for a small product. Calculate break-even, per-unit profit, and sensitivity to price changes using linear equations and simple sensitivity analysis.
Intermission: Assessment & Reflection — Alcumus mastery report, written solutions for 3 graded problems, and short reflective journal on methods and errors.
Act II — Introduction to Geometry + Synthesis (Weeks 21–40)
- Goals: Euclidean geometry basics — proof techniques, congruence, similarity, area/volume, circle theorems, coordinate geometry synthesis with algebra.
- Reading: Rusczyk’s Introduction to Geometry — focus on major proof techniques and connecting geometry problems to algebraic methods.
- Practice: Alcumus geometry modules plus mixed-problem weeks to synthesize algebra & geometry.
- Finance tie-in (capstone): simulated savings/investment or small business. Present profit graphs, compound growth curves, and break-even visuals created with spreadsheets and Desmos.
Enrichment & Applied Projects
- Concrete ideas: product pricing model, loan amortization table, compound interest simulation, supply-demand mini study, margin optimization using inequalities.
- Final capstones: a geometry proof portfolio and a financial-business model presentation (spreadsheet + Desmos graphs).
Tools & Resources: AoPS Alcumus, Rusczyk texts (Prealgebra, Intro to Algebra, Intro to Geometry), Desmos, GeoGebra, Google Sheets/Excel.
Weekly Rhythm (example): 5–6 days Alcumus (30–45 min), 2 focused lessons (book + proofs), 1 applied lab (finance/project), weekly timed problem set, weekly written proof.
ACARA v9 alignment: emphasizes Number & Algebra (linear relations, polynomials, functions), Measurement & Geometry (Euclidean reasoning, coordinate geometry), and Mathematical Reasoning (problem solving, proof, modelling). Projects map to practical numeracy and financial mathematics elements of the curriculum.
Outcomes in 2 years: mastery of Prealgebra & Intro to Algebra, strong proof skills from Intro to Geometry, contest readiness (AMC 10/12/AIME targets), disciplined daily practice, and real-world financial literacy (budgets, investing basics, business modelling).
Final note (spoken like Ally McBeal, slightly sotto voce): keep curiosity as your spice. Daily Alcumus sharpens the wit, Rusczyk builds the backbone, and your projects make the math live. Present boldly — with graphs, spreadsheets, and clear proofs — and watch abstract x become a story that pays.