2004 AMC 10 B, Problem #17—2004 AMC 12 B, Problem #15—“Set up an equation with two variables to represent thesituation.”Difficulty:MediumNCTM Standard:Number and Operations Standard for Grades 9–12: Understand numbers, waysof representing numbers, relationships among numbers, and number systems.Mathworld.com Classification:Number Theory>Arithmetic>General Arithmetic
CDEF9412155is the ratio of the area of4BDFto that of4ACE?(A)14(B)925(C)38(D)1125(E)7162004 AMC 10 B, Problem #18—“DrawFQ⊥CE.”SolutionDifficulty:HardNCTM Standard:Geometry Standard for Grades 9–12: Analyze characteristics and properties oftwo- and three-dimensional geometric shapes and develop mathematical arguments about geometricrelationships.Mathworld.com Classification:Geometry>Plane Geometry>Triangles>Special Triangles>Other Triangles>Right Triangle
In the sequence 2001, 2002, 2003,. . ., each term afterthe third is found by subtracting the previous termfrom the sum of the two terms that precede that term.For example, the fourth term is2001+2002-2003 =2000. What is the2004thterm in this sequence?(A)-2004(B)-2(C)0(D)4003(E)60072004 AMC 10 B, Problem #19—2004 AMC 12 B, Problem #12—“Look at the odd terms.”Difficulty:HardNCTM Standard:Algebra Standard for Grades 9–12: Use symbolic expressions, including iterativeand recursive forms, to represent relationships arising from various contexts.