Accelerated 12–24 Week Plan (for a focused 15-year-old)

You will finish AoPS Prealgebra quickly, begin Introduction to Algebra, and study Introduction to Geometry concurrently. This plan is rigorous: expect 10–15 hours per week (more if you want to dominate math). You will practice deliberately, test frequently, and show measurable mastery. No excuses.

Philosophy (straightforward, demanding)

• Try first, struggle deliberately. Attempt all problems before looking at solutions.
• Practice daily. Mistakes are data; fix them immediately.
• Quality over quantity: deeply understand the reasoning behind each solution.
• Use Alcumus and videos as tools — not crutches. Videos clarify after persistent struggle.

Overall Timeline (two-speed options)

• Fast track (12 weeks): Finish Prealgebra in 6 weeks; start and complete core of Intro Algebra in the remaining 6 weeks while doing 1–2 geometry chapters per week concurrently. (Requires 15+ hours/week.)
• Balanced accelerated (18–24 weeks): Finish Prealgebra in 8–10 weeks; complete Intro Algebra in 10–12 weeks while doing Intro Geometry chapters concurrently at 1 chapter every 1–2 weeks. (Recommended: 10–12 hours/week.)

Weekly Structure (sample, 12–15 hours/week)

1. Daily (5–6 days/week):
   • Warm-up 15–30 min: 10–12 Alcumus problems targeted to current topic.
   • Reading & guided problems 60–90 min: Read the section in AoPS text, attempt starter problems in the book without help for 30–45 min, then watch a targeted AoPS video only if stuck after 30–45 min.
   • Problem set 45–60 min: Complete assigned book problems (aim for 10–15 problems), record mistakes, write corrected solutions in a notebook.
2. Weekly wrap-up (1 session, 60–90 min):
   • Timed mixed set: 20–30 minutes of contest-style practice (AMC 10/12 level as appropriate) or Alcumus mixed-topic test.
   • Review: Go through mistakes, consult solutions manual only after multiple attempts, and re-attempt corrected problems.

How to Use the Books, Videos, and Alcumus

• Pre-Read Instructions: Skim the section, then attempt the starter problems. If you can solve them, great — move on to deeper problems. If not, fight for 30–45 minutes, then watch a short AoPS video or re-read the explanation.
• Problems First: Attempt the book problems with pen and paper before consulting hints or the solutions manual. Write full solutions; partial answers do not count.
• Alcumus: Use it to reinforce and diagnose. Set it to topic mode for current chapter; aim for >90% accuracy and track the weak topics list. Use Alcumus review sessions weekly to target weak areas.
• Videos: Use as clarification — short, focused clips. Do not binge videos instead of practice.
• Solutions Manual: Use after serious effort. Read the official solution once, then re-solve it without looking and write your version.

Specific Topic Cadence and Milestones

Below is a conservative plan for the balanced accelerated path (18 weeks). Scale up or down for faster/slower pace.

• Weeks 1–8: Finish Prealgebra
  • Weeks 1–3: Arithmetic properties, fractions, decimals, percents, exponents, prime factorizations, GCD/LCM.
  • Weeks 4–5: Linear equations, inequalities, ratios, proportions, rates, unit conversions, speed problems.
  • Weeks 6–7: Geometry basics — angles, perimeters, areas of polygons, triangles, quadrilaterals; square roots and radicals.
  • Week 8: Counting & probability basics, basic statistics; comprehensive Prealgebra test (timed, mixed problems). Mastery target: 90%+ on Alcumus topic sets and 80%+ on the timed test.
• Weeks 9–20: Introduction to Algebra (start at week 9) while continuing Introduction to Geometry concurrently
  • Algebra weeks 9–16: Linear equations and inequalities, functions, graphing, systems, ratios, quadratic equations, factoring, special factorizations, exponents and simple logs.
  • Algebra weeks 17–20: Quadratic functions, complex numbers intro, sequences and series, polynomials.
  • Geometry (concurrent weeks 9–20): Cover similar triangles, congruence, polygons, circles, area/volume, power of a point, transformations, intro trig. Aim for 1 section every 5–10 days depending on difficulty.
  • Mastery target by week 20: 90%+ Alcumus accuracy on covered topics, 80%+ on timed mixed-topic tests; ability to solve typical AMC 10 problems reliably.

Assessments & Metrics

• Initial diagnostic: 40–60 minute mixed problem set to identify weak areas.
• Biweekly timed practice: 30–40 min sets to simulate contest pressure and measure speed+accuracy.
• Mastery definition: Consistent >90% on Alcumus practice for a topic and >80% on timed mixed tests.
• Final checkpoint: Full-length AoPS-style cumulative test (or AMC 10 practice) and a geometry project: written proofs for 6 geometry problems.

Parent / Coach Role (accountability)

• Ensure the schedule is kept: daily practice, weekly wrap-up, biweekly tests.
• Check the student’s written solutions notebook — insist on neat, full solutions, corrected mistakes, and reflection notes for each error.
• Require Alcumus progress screenshots weekly and review weak-topic lists together.

Final Notes (tough but fair)

This plan is demanding because accelerated learning requires repetition, deliberate practice, and accountability. You will struggle. That’s the point. Struggle until concepts are automatic. Immediate action items: set up Alcumus, acquire the three AoPS texts (Prealgebra, Introduction to Algebra, Introduction to Geometry), schedule 10–15 hours/week on the calendar, and take the initial diagnostic this week. Then begin Week 1 of the plan.

Do not accept mediocrity. Practice, correct, improve — then repeat.