IN THE MATTER OF: A Year of Mathematics — ACARA v9 v. Candidate (Age 15)
Your Honour (and dear student), the case is simple, delivered with a lawyer's structure and Ally McBeal's aside: we will learn, we will practice, we will model real money — and occasionally sing to a graph.
STATEMENT OF ISSUES (Learning Goals)
- Algebra: linear equations & inequalities, systems, functions, basic polynomials, factoring, algebraic problem solving.
- Geometry: Euclidean proofs, congruence, similarity, area/volume, circles, coordinate geometry and synthesis with algebra.
- Financial application: cost, revenue, profit, break-even, compound interest; spreadsheet modelling and sensitivity analysis.
EVIDENCE & METHOD
Reading: Rusczyk's Introduction to Algebra (complete 1/2–2/3) then Introduction to Geometry (major proof techniques). Practice: AoPS Alcumus — daily adaptive sets; weekly increasing-challenge problem sets; mixed-topic synthesis weeks to meet ACARA v9 content descriptions for Number & Algebra, Measurement & Geometry, and Mathematical Reasoning.
APPLICATIONS & PROJECTS
- Mini-business model: linear revenue/cost model, break-even point, per-unit profit, price-sensitivity analysis (spreadsheet required).
- Finance capstone: simulated savings/investment portfolio; compound growth curves and geometric interpretation; graphical presentation.
TOOLS
Alcumus (AoPS), Rusczyk texts, Desmos & GeoGebra for visual proofs and graphs, Google Sheets/Excel for budgets and sensitivity tests.
CONCLUSION (Rhythm & Success)
Daily Alcumus, weekly problem sets, monthly projects and a final public capstone showcase. In two years: mastery of Prealgebra & Introduction to Algebra, strong geometry proof skills, financial fluency, and readiness for AMC 10/12 or further contest work. Relief sought: curiosity preserved, competence awarded.