PS / Synthesis
Summit Challenge
Choose representations and arguments that turn difficult-looking problems into tractable ones.
Preparation: Algebra, geometry, counting and the logarithm definition. Later stages combine subjects.
Current coverage: 12 strategy stages: reversal, invariants, extremal reasoning, telescoping, induction and connections.
LEVEL 1 · DIFFICULTY 1/5 within this course
Reverse processes, track invariants and force repetition.
Choose an island to read its lesson.
3 stages · 24 library problems · 108 checked variations · 2 × 6 assessment questions
Read the lessons →LEVEL 2 · DIFFICULTY 2/5 within this course
Balance extremes, cancel terms and justify patterns.
Choose an island to read its lesson.
3 stages · 24 library problems · 108 checked variations · 2 × 6 assessment questions
Read the lessons →LEVEL 3 · DIFFICULTY 3/5 within this course
Use residues, bijections and shared-altitude geometry.
Choose an island to read its lesson.
3 stages · 24 library problems · 108 checked variations · 2 × 6 assessment questions
Read the lessons →LEVEL 4 · DIFFICULTY 4/5 within this course
Recover totals, telescope logarithms and transform recurrences.
Choose an island to read its lesson.
3 stages · 24 library problems · 108 checked variations · 2 × 6 assessment questions
Read the lessons →Clear a stage by independently solving two different routine problems and one application in a new context. Hints help you learn; hinted answers and repeated solves do not count toward that target. Clear every stage to clear a level.
Every stage includes an explanation, two worked examples and eight library practice problems, plus checked variations with changing numbers and applications. Each level also has a separate unit test and a later review form. Parents see actual attempts, hint use and results.
These are independently authored core-skills courses, with the current scope listed for each course. They do not reproduce complete textbook contents. Difficulty describes the teaching sequence within each course; course preparation matters when comparing subjects. This site is not affiliated with or endorsed by AoPS. Results reflect these exercises and are not standardized scores. Content release math-courses-2026.09.08-v4.
