Accelerated AoPS Course for a 15-year-old

Think of this course as a rich, savoury tasting menu for the mathematical appetite. We whisk together Richard Rusczyk's Prealgebra, Introduction to Algebra, and Introduction to Geometry into an accelerated 24–28 week programme, with Alcumus practice and a generous drizzle of free instructional videos.

Course Overview

• Foundations (Weeks 1–6) — Prealgebra essentials: arithmetic properties, fractions, decimals, percents, exponents, ratios, unit conversions, basic equations and inequalities, simple geometry and counting. Problems first, solutions second; we let curiosity simmer.
• Algebra Core (Weeks 7–14) — Linear equations, inequalities, systems, quadratic equations, factoring, functions, polynomials, sequences, intro to complex numbers and graphing. Tasteful practice with Alcumus sets each topic al dente.
• Geometry Feast (Weeks 15–22) — Similarity, congruence, polygons, circles, power of a point, areas, 3D glimpses, transformations, introductory trig. Elegant proofs presented like recipes to be followed and then improvised.
• Discrete & Prep (Weeks 23–24+) — Counting, probability, number theory basics, contest strategy, review and synthesis. Timed rounds to sharpen instincts.

Resources & Rhythm

Daily: 30–60 minutes Alcumus practice tailored to weak spots. Weekly: 3–5 problem set problems drawn from the textbooks, with guided solution walkthroughs. Monthly: video lessons aligned to each chapter for flavour and reinforcement. Every section begins with problems to try unaided, then full solutions in the manual to study.

Assessment & Delight

Assess by Alcumus mastery, weekly scored problem sets, and short performance tasks. Expect conceptual depth, plentiful challenging problems, and a learning experience that rewards patience, play, and the slow joy of understanding.