Year Course Prospectus for a 15-year-old: ACARA v9-aligned Algebra & Geometry with Alcumus, Business & Finance — Legal Brief Cadence

A 1-year ACARA v9-aligned course prospectus for a 15-year-old combining AoPS Alcumus, Rusczyk texts, algebra and geometry mastery, contest readiness, and applied business/finance mini-projects — presented as a legal brief with Ally McBeal cadence.

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IN THE MATTER OF The Education of Student, Age 15 (ACARA v9-aligned) — delivered with a cadence that hums, a lawyer in heels tapping a gavel between asides.

STATEMENT OF PURPOSE

This one-year prospectus prescribes daily Alcumus practice and Rusczyk reading to secure algebraic fluency, Euclidean proof skill, and practical financial modeling for real-world decision making.

PART I: INTRODUCTION TO ALGEBRA + ALCUMUS

  • Goals: linear equations and inequalities, systems, functions, polynomial basics, factoring, algebraic problem solving.
  • Reading: aim to complete one half to two thirds of Introduction to Algebra.
  • Practice: transition to Alcumus algebra tracks; weekly problem sets with rising challenge.
  • Business tie-in mini-project: model cost, revenue, profit for a small product; compute break-even, per-unit profit, and price-sensitivity.

PART II: INTRODUCTION TO GEOMETRY + SYNTHESIS

  • Goals: Euclidean basics, proof techniques, congruence, similarity, area/volume, circles, coordinate geometry.
  • Reading: cover major proof techniques and key chapters of Introduction to Geometry; integrate algebraic prerequisites.
  • Practice: Alcumus geometry modules plus mixed weeks to synthesize algebra and geometry.
  • Finance capstone: simulated business or savings portfolio using algebraic and geometric visual models.

ENRICHMENT AND APPLIED PROJECTS

  • Concrete ideas: break-even analysis, sensitivity charts, compound interest simulation, loan amortization tables, small-business pitch with spreadsheets and graphs.

TOOLS AND RESOURCES

  • Alcumus AoPS: https://artofproblemsolving.com/alcumus
  • Rusczyk textbooks: Prealgebra, Introduction to Algebra, Introduction to Geometry
  • Desmos and GeoGebra for visualization
  • Spreadsheets: Google Sheets or Excel for budgets and projections

ULTIMATE GOALS IN 2 YEARS

  1. Master Prealgebra and Intro to Algebra; complete Intro to Geometry with proof fluency.
  2. Contest readiness: AMC 10 year one; AMC 12 or AIME as progress allows.
  3. Daily disciplined study habits, Alcumus consistency, timed practice, written proofs.
  4. Concrete financial literacy: budgeting, investing basics, spreadsheets, business simulation.

BIG PICTURE SEQUENCING

  1. Foundations: Prealgebra + Alcumus.
  2. Algebra I mastery: Introduction to Algebra + Alcumus.
  3. Geometry and contest focus: Introduction to Geometry + past contest problems.
  4. Continuous financial modules and applied projects.

ORDER

Follow steady daily practice, weekly problem sets, monthly projects, and a final capstone presentation. Consider official contest coaching if progress stalls.

Cadence aside: keep curiosity like a soundtrack, ask why, and litigate every step until clarity prevails.

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