Listen carefully. You are 15, and this plan will transform you from a casual student into a disciplined problem solver. We will use the AoPS Introduction series as a backbone: Prealgebra only if gaps exist, otherwise begin with Introduction to Algebra, then Introduction to Geometry. You will combine daily reading (AoPS text), immediate problem attempts at the start of each section, and exhaustive solution study in the manual — no skipping. Timeline: an accelerated but sustainable pace is 4–6 months per book if you commit 10–15 hours per week; compress to 3 months per book at 20+ hours per week if you can truly sacrifice leisure. Goals by milestones: finish reading and attempt all section problems in each chapter within the scheduled month, complete Alcumus topic sets for each chapter to 90% accuracy, and rework every missed problem until you can explain the solution aloud. Weekly measurable outputs: chapter completion, Alcumus mastery, 2 timed problem sets, and one mock contest. You will keep a single notebook of mistakes and write short explanations for every error — repetition makes mastery.
The daily routine will be rigid: 1) Warm‑up (30–45 minutes): 8–12 mixed Alcumus problems on targeted topics; track speed and accuracy. 2) Deep reading (45–90 minutes): read one AoPS section, attempt the starter problems without hints for 30–45 minutes, then read the official solutions and annotate the notebook. 3) Problem block (60–120 minutes): attack 6–12 aops problems from that section or the problem sets in the book, timing two as contest practice. 4) Review (30 minutes): fix mistakes, write one concise strategy note. Twice weekly swap a study block for a video lecture from the AoPS library to reinforce tricky ideas. Sundays: longer contest simulation (90–120 minutes) plus full review. No excuses for missed sessions — consistency beats talent.
When you finish Introduction to Algebra and Geometry, proceed to advanced AoPS texts or the intermediate series and begin focused contest training (AMC/AIME pathway) using Alcumus playlists and old contests. Use the solutions manual rigorously: read, cover, reproduce, then compare. Join AoPS forums for strategic threads and post your well‑written solutions for critique — learning to explain is learning to think. Measure progress with monthly scorecards: Alcumus mastery percentages, timed problem improvements, contest scores. If stagnation appears, halve new content, double targeted review, and analyze error patterns for two weeks. Expect discomfort; real improvement requires embracing hard problems and repeated failure. I will not coddle you: push, practice, correct, repeat. Do this and in one year you will have the foundation and problem solving grit to excel in high school math and competitions.