Imagine mathematics like a slow, sumptuous simmer: warm, deliberate, and teasingly rich. This accelerated 1‑year plan (ideal for a 15‑year‑old ready to gorge on challenge) stitches Prealgebra and Introduction to Geometry into a feast, paired with Alcumus practice and a free aligned video pantry.
Semester 1 — Foundations & Algebra: exponents and laws, primes, divisibility, LCM/GCD, fractions, decimals, linear equations, inequalities, ratios, rates and conversions; practice servings on Alcumus to build fluency. (Mapped to ACARA v9: Number & Algebra — ACMNA; relevant content focuses on factors, fractions, indices, linear relationships.)
Semester 2 — Expansion & Discrete Flavours: percents, square roots, geometry basics (angles, polygons, areas), Pythagoras, special triangles, quadrilaterals; intro to counting, probability and statistics. (Mapped to ACARA v9: Measurement & Geometry — ACMMG; Statistics & Probability — ACMSP.)
Geometry Module (concurrent): similar and congruent triangles, circles, power of a point, transformations, 3D solids and basic trigonometry — a concentrated, problem‑first sequence inspired by Rusczyk’s rigor.
Pedagogy: each lesson opens with problems, then guided solutions, followed by deeper explorations and curated Alcumus sets; assessment is mastery-based, with a solutions compendium for independent refinement. The rhythm is indulgent yet exacting: savor the problems, return for seconds, and emerge mathematically replete.