Imagine the school year as a soundtrack: quick, witty, and somehow melodic — you, a cup of tea, Alcumus humming in the background. This prospectus is for a 15‑year‑old who wants rigorous algebra, Euclidean geometry, and money that actually means something.
Act I — Introduction to Algebra + Alcumus
Goals: linear equations & inequalities, systems, functions, basic polynomials, factoring, and algebraic problem solving. Read: Introduction to Algebra (aim to finish half–two thirds). Daily Alcumus: adaptive practice with weekly themed problem sets that increase in challenge. Mini‑project (business tie‑in): choose a simple product; build cost, revenue and profit models with linear equations; compute break‑even point, per‑unit profit, and sensitivity to price changes (use spreadsheets for sensitivity tables and charts).
Act II — Introduction to Geometry + Synthesis
Goals: Euclidean basics — proof techniques, congruence and similarity, circle theorems, area/volume, and coordinate geometry. Read: Introduction to Geometry — focus on major proof strategies and interleave algebraic problems. Alcumus: geometry tracks plus mixed weeks to synthesise algebra and geometry. Finance capstone: simulate savings growth and investing; present profit graphs, compound growth curves, and break‑even visuals that use algebraic and geometric representations.
Enrichment & Applied Projects
Concrete ideas: break‑even posters, spreadsheet amortisation schedules, mini market analysis, supply‑demand sketches, optimisation problems (minimising cost or maximising profit), and a final simulated small business or investment portfolio presentation.
Tools & Resources
AoPS Alcumus; Rusczyk texts (Prealgebra, Intro to Algebra, Intro to Geometry); Desmos & GeoGebra for interactive graphs and proofs; Google Sheets/Excel for budgets and charts.
ACARA v9 alignment & success markers
This course maps to ACARA v9 strands: Number & Algebra (linear models, functions), Measurement & Geometry (Euclidean reasoning, coordinate geometry), and Statistics & Probability for data displays in projects. In two years: mastery of Prealgebra and Introduction to Algebra; completion of Introduction to Geometry with strong proof skills; contest readiness (AMC paths) and concrete financial literacy (budgets, investing basics, spreadsheet fluency).
Rhythm: daily Alcumus (30–60 min), 3 focused lessons/week, 1 applied project session/week, monthly portfolio reviews. Keep curiosity as your spice — ask why, and let algebra turn numbers into the kinds of stories you actually want to tell.