Settle in like a warm bowl of custard: this 32‑week accelerated plan for a curious 15‑year‑old stitches together AoPS Prealgebra 1 & 2 and Introduction to Geometry with Alcumus practice and short video lessons, serving rigor with a spoonful of delight.
Semester 1 — Weeks 1–16 (Foundations & Prealgebra mastery)
- Wk 1: Arithmetic rules; quick diagnostic & Alcumus baseline
- Wk 2: Squares, exponent laws, zero/negative exponents
- Wk 3: Multiples, divisibility tests, primes & factorization
- Wk 4: LCM, GCD; fractions (part 1)
- Wk 5: Fractions (part 2); mixed numbers
- Wk 6: Linear equations intro; basic word problems
- Wk 7: Advanced linear equations & inequalities
- Wk 8: Decimals; ratios & proportions
- Wk 9: Unit conversions, rates, speed
- Wk 10: Percents; increase/decrease problems
- Wk 11: Squares & square roots; arithmetic with roots
- Wk 12: Angles, parallel lines, polygon basics
- Wk 13: Perimeter, area; triangles & circles intro
- Wk 14: Pythagorean theorem & special right triangles
- Wk 15: Quadrilaterals; applied problems
- Wk 16: Cumulative review, Alcumus mastery set, reflection
Semester 2 — Weeks 17–32 (Geometry deep dive + discrete math)
- Wk 17–18: Similarity, congruence, triangle centers
- Wk 19–20: Special parts of triangles; advanced proofs
- Wk 21–22: Quadrilaterals & polygon geometry
- Wk 23: Geometric inequalities; problem strategies
- Wk 24–25: Circles, tangents, power of a point
- Wk 26–27: 3D geometry, volumes, intro analytic geometry
- Wk 28: Transformations & basic trigonometry
- Wk 29–30: Counting & probability; combinatorics techniques
- Wk 31: Basic statistics, graphs, data interpretation
- Wk 32: Final project, contest-style review, next-step plan
Daily rhythm: 20–40 minutes: 3 Alcumus problems (targeted), 1 short video lesson, 1 written problem with solution writeup. Weekly: one timed challenge, one reflection. This is cosy, rigorous, and deliciously challenging—exactly the way real learning should feel.