Accelerated AoPS course outline for a focused 15-year-old student, two semesters.
This rigorous program compresses Prealgebra, Introduction to Algebra, Introduction to Geometry, and essential discrete topics into one accelerated year. Materials: Richard Rusczyk’s Prealgebra, Introduction to Algebra, Introduction to Geometry; Alcumus adaptive practice; and the free AoPS video library. Expect daily discipline, precise written solutions, and regular timed assessments.
Term One — Foundation and Algebra (18 weeks). Weeks 1–6: Prealgebra consolidation — arithmetic structure, fractions, decimals, ratios, percents, exponents, square roots, basic equations and inequalities. Daily Alcumus drills and book problem sets; weekly written solution submission. Weeks 7–12: Algebra fundamentals — linear equations, systems, polynomial basics, factoring, exponents, functions, graphing. Emphasize proof-writing and solution clarity. Weeks 13–18: Number Theory and Counting — divisibility, primes, modular reasoning, prime factorization, permutations, combinations, basic probability. Weekly contest-style problem sets and targeted Alcumus badges.
Term Two — Geometry and Integration (18 weeks). Weeks 1–6: Geometry essentials — congruence, similarity, triangles, quadrilaterals, area and perimeter, coordinate approaches; daily diagram practice and short proofs. Weeks 7–12: Advanced geometry — circles, power of a point, polygons, three-dimensional geometry, transformations, elementary trigonometry. Weekly proof examinations. Weeks 13–18: Integration, review and competition preparation — mixed problem sets, cumulative mock exams, Alcumus mastery goals, and video remedial lessons.
Assessment and expectations: nightly problem write-ups, weekly timed tests, monthly comprehensive assessments, and mastery required before progression. Practice is compulsory; excellence is the only acceptable outcome.
Daily schedule: two hours on weekdays devoted to lesson reading, Alcumus targeted practice, and one contest problem; three to four hours on weekend days for problem sets, mock tests, and video review. Parents or mentors will check nightly write-ups and correct solutions. Monthly parent-student review meetings enforce accountability. By year end the student will have mastered core problem solving techniques, earned Alcumus badges across topics, and completed over one thousand graded problems with distinction.