Difficulty Medium hard NCTM Standard Geometry Standard explore relationships

Difficulty medium hard nctm standard geometry

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Difficulty:Medium-hardNCTM Standard:Geometry Standard: explore relationships (including congruence and similarity)among classes of two- and three-dimensional geometric objects, make and test conjectures aboutthem, and solve problems involving them.Mathworld.com Classification:Geometry>Plane Geometry>Triangles>Special Triangles>Other Triangles>Triangle
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Suppose thatP= 2mandQ= 3n.Which of thefollowing is equal to12mnfor every pair of integers(m, n)?2009 AMC 10 A, Problem #132009 AMC 12 A, Problem #0612 = 22·3.”Mathworld.com Classification:Calculus and Analysis>Special Functions>Powers>Power
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Four congruent rectangles are placed as shown. Thearea of the outer square is 4 times that of the innersquare. What is the ratio of the length of the longerside of each rectangle to the length of its shorter side?2009 AMC 10 A, Problem #142009 AMC 12 A, Problem #08“The ratio of the lengths of the outer and inner squareis4 = 2.”Difficulty:MediumNCTM Standard:Geometry Standard: explore relationships (including congruence and similarity)among classes of two- and three-dimensional geometric objects, make and test conjectures aboutthem, and solve problems involving them.Mathworld.com Classification:Geometry>Plane Geometry>Miscellaneous Plane Geometry>Area
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The figuresF1,F2,F3andF4shown are the first ina sequence of figures. Forn3,Fnis constructedfromFn-1by surrounding it with a square and placingone more diamond on each side of the new squarethanFn-1had on each side of its outside square.For example, figureF3has 13 diamonds. How manydiamonds are there in figureF20?3 F 4 2009 AMC 10 A, Problem #152009 AMC 12 A, Problem #11“The outside square forFnhas 4 more diamonds on itsboundary than the outside square forFn-1.”Difficulty:MediumNCTM Standard:Algebra Standard: generalize patterns using explicitly defined and recursivelydefined functions.Mathworld.com Classification:Number Theory>Sequences>Sequence
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Leta,b,c, anddbe real numbers with|a-b|= 2,|b-c|= 3, and|c-d|= 4
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