arithmetic-expression-decomposition
"AMC가 매년 가장 많이 내는 패턴"
A multi-step numerical computation (sum of fractions, rate × time, area × thickness) is attacked by splitting it into a small number of independent subproblems whose answers are then combined. The key move is identifying the clean split, not the underlying topic.
복잡한 식을 작은 조각으로 — 27년간 AMC 8 문제의 35%가 이 패턴.
How to solve
- Keep the structure (rate × time) but swap context from CO2 to bacteria population or tuition inflation
- Make one of the sub-fractions reducible by 11 or 101 to mirror Problem 2's clean cancellation
- Adjust numeric_scale so the convenient round-number shortcut (e.g. 1.5 × 50) still applies
Sub-archetype mix (6)
Click a row to see member problems.
- fraction-sum-evaluation 37% (107)
Evaluate an explicit numeric or algebraic expression by computing each independent term (fraction, power, or polynomial piece) separately, then combining through addition or subtraction; the challenge is clean simplification and common-denominator work, not a real-world rate.
no figureamc10-2019A-1no figureamc10-2019A-19no figureamc10-2019A-2no figureamc10-2019A-5no figureamc10-2019B-1no figureamc10-2019B-24no figureamc10-2020A-1no figureamc10-2020A-3no figureamc10-2020B-1no figureamc10-2020B-22no figureamc10-2021A-1no figureamc10-2021A-5no figureamc10-2021A-9no figureamc10-2021B-2no figureamc10-2022A-1no figureamc10-2022B-1no figureamc10-2023B-1no figureamc10-2024A-1no figureamc10-2024B-1no figureamc8-1999-13
amc8-2000-13no figureamc8-2000-16no figureamc8-2001-12no figureamc8-2001-21no figureamc8-2001-3
amc8-2001-8no figureamc8-2002-13no figureamc8-2002-18no figureamc8-2002-3
amc8-2002-9
amc8-2003-10no figureamc8-2003-20no figureamc8-2003-3
amc8-2003-9no figureamc8-2004-1no figureamc8-2004-19no figureamc8-2004-5no figureamc8-2004-7no figureamc8-2005-10no figureamc8-2005-12no figureamc8-2005-18no figureamc8-2005-2no figureamc8-2006-1no figureamc8-2006-12no figureamc8-2006-15no figureamc8-2006-21no figureamc8-2006-3no figureamc8-2007-17
amc8-2007-2no figureamc8-2007-5no figureamc8-2007-7no figureamc8-2008-1
amc8-2008-8no figureamc8-2009-1no figureamc8-2009-5no figureamc8-2009-8no figureamc8-2010-1no figureamc8-2010-12no figureamc8-2010-15no figureamc8-2010-22no figureamc8-2010-4no figureamc8-2011-1
amc8-2011-11no figureamc8-2011-5no figureamc8-2012-1no figureamc8-2012-21no figureamc8-2012-3no figureamc8-2012-9no figureamc8-2013-11no figureamc8-2013-17no figureamc8-2013-2no figureamc8-2013-5no figureamc8-2013-7no figureamc8-2014-1no figureamc8-2014-10no figureamc8-2014-16no figureamc8-2014-6no figureamc8-2015-1no figureamc8-2015-9no figureamc8-2016-1no figureamc8-2016-10no figureamc8-2016-15no figureamc8-2016-4no figureamc8-2016-9no figureamc8-2017-19no figureamc8-2017-3no figureamc8-2017-7no figureamc8-2018-1no figureamc8-2018-18no figureamc8-2018-5
amc8-2018-8no figureamc8-2019-1
amc8-2019-10no figureamc8-2019-8no figureamc8-2020-1
amc8-2020-11no figureamc8-2020-15no figureamc8-2020-5no figureamc8-2022-2no figureamc8-2022-7no figureamc8-2022-9no figureamc8-2023-1no figureamc8-2023-3no figureamc8-2024-2amc8-2025-2
amc8-2025-9no figuresm-1 - linear-rate-accumulation 19% (55)
Multiply a constant rate by a count or duration to find a total accumulation, then add or subtract an initial baseline value; the decomposition is always rate-part versus base-part combined in a single linear expression.
no figureamc10-2019A-23no figureamc10-2020A-2no figureamc10-2020A-7no figureamc10-2020B-5no figureamc10-2021A-4no figureamc10-2022A-2no figureamc10-2022B-5no figureamc10-2024A-2no figureamc10-2024B-7no figureamc8-1999-10no figureamc8-1999-18
amc8-1999-2
amc8-2000-15no figureamc8-2001-1no figureamc8-2001-13no figureamc8-2001-5no figureamc8-2002-12
amc8-2002-7no figureamc8-2003-11no figureamc8-2003-5no figureamc8-2004-3no figureamc8-2004-9no figureamc8-2005-14no figureamc8-2005-4no figureamc8-2006-2no figureamc8-2006-7no figureamc8-2007-10no figureamc8-2007-3no figureamc8-2007-6no figureamc8-2008-5
amc8-2009-3
amc8-2009-9no figureamc8-2010-14no figureamc8-2010-2no figureamc8-2011-10no figureamc8-2011-2no figureamc8-2012-15no figureamc8-2012-2no figureamc8-2013-10no figureamc8-2013-4no figureamc8-2014-5no figureamc8-2015-17no figureamc8-2016-3no figureamc8-2017-4no figureamc8-2018-12no figureamc8-2018-2no figureamc8-2019-17no figureamc8-2019-3no figureamc8-2020-2
amc8-2022-10no figureamc8-2022-8no figureamc8-2023-10no figureamc8-2024-10no figureamc8-2025-4no figuresm-2 - weighted-group-aggregation 26% (75)
Decompose a total into contributions from two or more distinct groups or sources, compute each group's share independently as group-size times per-unit rate or fraction, then sum across all groups; the structural challenge is correctly identifying and weighting each group.
no figureamc10-2019A-11no figureamc10-2019A-17no figureamc10-2019B-6no figureamc10-2020A-8no figureamc10-2020B-2no figureamc10-2021A-10no figureamc10-2021A-3no figureamc10-2021B-10no figureamc10-2022B-4no figureamc10-2024B-2no figureamc8-1999-16no figureamc8-1999-17no figureamc8-1999-7no figureamc8-2000-10no figureamc8-2000-17no figureamc8-2001-10no figureamc8-2001-14no figureamc8-2001-6no figureamc8-2002-1
amc8-2002-10
amc8-2002-8no figureamc8-2003-1no figureamc8-2003-19
amc8-2003-6no figureamc8-2003-7no figureamc8-2004-10no figureamc8-2004-16no figureamc8-2004-6no figureamc8-2005-11
amc8-2005-9no figureamc8-2006-14no figureamc8-2006-16
amc8-2006-4no figureamc8-2006-9no figureamc8-2007-1no figureamc8-2007-14no figureamc8-2007-4no figureamc8-2008-10no figureamc8-2008-7no figureamc8-2009-6no figureamc8-2010-16
amc8-2010-3no figureamc8-2010-5no figureamc8-2010-9no figureamc8-2011-4
amc8-2011-9no figureamc8-2012-19no figureamc8-2012-4no figureamc8-2012-8no figureamc8-2013-12no figureamc8-2013-3
amc8-2013-6
amc8-2014-14no figureamc8-2014-24no figureamc8-2014-3
amc8-2014-9
amc8-2015-18no figureamc8-2015-3no figureamc8-2016-19no figureamc8-2016-8no figureamc8-2017-14no figureamc8-2017-5no figureamc8-2018-10no figureamc8-2018-6no figureamc8-2019-7no figureamc8-2019-9no figureamc8-2020-12
amc8-2020-14no figureamc8-2020-3no figureamc8-2022-11no figureamc8-2022-5no figureamc8-2023-11
amc8-2025-17no figureamc8-2025-3amc8-2025-8 - successive-multiplicative-steps 11% (33)
A value undergoes a chain of sequential multiplicative or fractional transformations where each step's output feeds the next; the key move is either applying factors in order or reversing the chain to recover an earlier value.
no figureamc10-2019A-15no figureamc10-2019A-24no figureamc10-2019B-15no figureamc10-2020A-14no figureamc10-2020B-12no figureamc10-2021B-12no figureamc10-2021B-19no figureamc10-2022B-9
amc10-2024A-12no figureamc10-2024B-22no figureamc10-2024B-9no figureamc8-1999-19no figureamc8-2000-1
amc8-2000-24no figureamc8-2001-19no figureamc8-2002-14no figureamc8-2004-12no figureamc8-2005-1
amc8-2006-19no figureamc8-2008-9no figureamc8-2009-17no figureamc8-2010-21no figureamc8-2011-15no figureamc8-2012-20no figureamc8-2013-15no figureamc8-2014-22no figureamc8-2016-14no figureamc8-2017-13no figureamc8-2018-16no figureamc8-2019-16no figureamc8-2019-22no figureamc8-2020-8no figureamc8-2022-16 - multi-segment-path-sum 7% (19)
A total length, count, or measure is found by splitting into independent geometric segments or independent parallel sub-computations, computing each piece with its own formula, then summing all pieces; covers arc-length sums, multi-leg distance problems, and independent income-minus-expense structures.
no figureamc10-2019A-13no figureamc10-2019A-21no figureamc10-2019B-18no figureamc10-2020A-21no figureamc10-2020A-4no figureamc10-2021B-15no figureamc10-2022B-15no figureamc10-2024B-23
amc8-1999-4no figureamc8-2009-14no figureamc8-2010-24
amc8-2013-23
amc8-2013-25
amc8-2014-15
amc8-2014-25no figureamc8-2016-18no figureamc8-2019-25
amc8-2020-24
amc8-2024-22 - unit-conversion-chain 1% (2)
Convert a measurement from one unit system to another by applying a chain of conversion factors (dimensional analysis); each factor is an independent multiplication or division, and the challenge is tracking which factors to multiply and which to invert.
More data (year-over-year, tool fingerprint, grade distribution, all members)
Tool fingerprint (1–17)
Grade distribution
- Gr 2 5
- Gr 3 9
- Gr 4 48
- Gr 5 40
- Gr 6 127
- Gr 7 23
- Gr 8 37