Accelerated AoPS Plan for a 15‑Year‑Old: Finish Prealgebra, Begin Intro Algebra, Geometry Concurrently — 9‑Month Intensive

A comforting, practical overview — think of this as a rich spoonful of math, savoured and energising

This accelerated plan is written for a 15‑year‑old who will finish AoPS Prealgebra, begin Introduction to Algebra, and study Introduction to Geometry concurrently. Total length: about 9 months (36 weeks). Weekly time: 8–12 hours. The cadence is intentional: a steady, delicious rhythm of reading, watching, practising, and refining.

Why this recipe works

• AoPS books are problem‑driven: each section starts with problems, then solutions that teach techniques — perfect for active learners.
• Alcumus provides adaptive practice tuned to where the student is struggling; use it every session.
• Videos complement reading: watch to prime the mind, read to concentrate, practise to internalise.

Big picture schedule (36 weeks)

1. Weeks 1–12: Finish Prealgebra (intensive). Focus: arithmetic foundations, fractions, exponents, basic number theory, ratios, percents, introductory geometry pieces, counting & probability basics.
2. Weeks 13–36: Introduction to Algebra (main study, 24 weeks). Focus: linear equations, polynomials, quadratics, functions, inequalities, sequences, complex numbers, exponents and logs.
3. Weeks 1–36: Introduction to Geometry runs concurrently. Take it steady: ~1–2 sections per week so geometry matures alongside algebraic skills — similar triangles, congruence, polygons, circles, power of a point, basic trig, and 3D geometry.

Weekly time and micro‑schedule

Aim for 8–12 hours per week, broken into 5 weekday sessions of 1.5–2 hours and a light review on the weekend. The split keeps momentum and avoids burnout.

• Day 1 (60–90 min): Watch AoPS video for the week’s chapter, read that chapter’s problems and examples in the book.
• Day 2 (60–90 min): Attempt book’s opening problems (trust your instincts), then try 10–15 Alcumus problems on the same topic.
• Day 3 (60–90 min): Work through more challenging book problems; reserve 2–3 problems for deep thought (don’t peek yet!).
• Day 4 (60–90 min): Study solutions in the book / solutions manual; annotate, summarise, and extract techniques into a one‑page cheat sheet.
• Day 5 (60 min): Mixed practice — Alcumus review plus 1 timed mini‑test (20–30 minutes) using previous problems or AMC practice if ready.
• Weekend (30–60 min): Light review, reflection journal entry: what surprised you, what felt like a new flavour.

How to balance Algebra and Geometry concurrently

Think of algebra like the spices and geometry like the textures. They complement one another. When you learn linear equations in algebra, tackle similar triangles in geometry in the same week to see ratios in action. When you study quadratics, pair with geometry problems on areas and coordinate geometry.

• Split weekly sessions roughly: 60% algebra, 40% geometry. Adjust if a topic demands more time.
• Use Geogebra for geometric constructions and to visualise algebraic relationships.
• Alternate problem sets: one algebra heavy week includes two geometry sections and vice versa, keeping both muscles exercised.

Milestones and assessments

• End of Week 12: Prealgebra final assessment — complete a cumulative 90‑minute mock covering all Prealgebra chapters and Alcumus performance at 80%+ in topics targeted.
• Every 6 weeks: Cumulative check for Algebra + Geometry. Use book chapter tests and mixed Alcumus sets. Goal: mastery score rising toward 85–90%.
• Throughout: Track Alcumus mastery trees; when you reach consistent green in a topic, reduce drilling and move on.
• If aiming for contests: trial AMC 8/10 style problems after Week 12 to gauge problem‑solving speed; incorporate contest problems weekly.

Use of resources

• AoPS Prealgebra, Intro to Algebra, Intro to Geometry: read the opening problems, attempt them, then study the full solutions manual only after forming your own approach.
• Alcumus: daily practice. Use the adaptive recommendations and set a weekly problem target (30–50 problems depending on difficulty).
• AoPS video collection: watch the short targeted videos before attempting new sections — treat them like a gentle, precise demonstration.
• AoPS Community: post 1–2 tough problems you’re stuck on. Explaining your attempt helps build clarity and posture.

Study habits, the little rituals

• Attempt before reading answers. The friction of struggle is where understanding forms.
• Keep a problem journal: one page per week summarising new techniques, mistakes, and favourite problems.
• Use spaced repetition for facts: primes, exponent rules, special factorisations — flashcards for quick recall.
• Sleep on it: if a problem resists, sleep and return with fresh eyes — insights often come in the morning.

Adjustments and troubleshooting

• If Alcumus shows consistent struggle in a cluster (e.g., fractions or inequality logic), pause new chapters and do a 1–2 week targeted repair block.
• If boredom creeps in, inject contest problems or tiny research projects: explore number theory proofs or an original geometry construction.
• If pace feels too fast, stretch the plan to 12 months — depth over haste wins in math.

Final flourish — how you’ll know you’ve succeeded

By the end of this plan you will have finished AoPS Prealgebra, completed most of Introduction to Algebra, and studied Introduction to Geometry in tandem. You’ll feel confident with problem‑driven learning: you won’t just know formulas, you’ll have strategies, a problem journal, Alcumus mastery traces, and the habit of solving before reading. That blend — practice, reflection, and community — is the recipe for a mathematician’s appetite to grow.

Enjoy the process. Treat each problem like a small, perfect bite: examine it, savour the structure, and let the solution unfold slowly and wholly.