Imagine math as a rich, slow-simmered stew: each idea adds flavour, and we taste as we go. For a 15‑year‑old on an accelerated path, we first finish AoPS Prealgebra — a generous course of fractions, exponents, primes and divisors, ratios, percents, square roots, basic geometry, counting, probability, and more — relishing problem sets that build technique and curiosity.
Once Prealgebra is comfortably tasted, we begin Introduction to Algebra: linear equations, inequalities, quadratics, polynomials, functions, and early number theory — layered and deepened. All the while, Introduction to Geometry simmers alongside: similar and congruent triangles, circles, power of a point, funky areas, transformations, and an introduction to trigonometry, so spatial thinking grows in tandem with algebraic fluency.
The plan uses Richard Rusczyk’s problem-first texts, the adaptive Alcumus practice system, and AoPS’s free aligned videos. Rhythm: attempt section problems unaided, read guided solutions to learn techniques, drill related Alcumus exercises, and watch targeted videos. Assess progress by mastery of problem types, Alcumus scores and speed, and confident geometric reasoning. Serve with a generous spoonful of persistence and delight.