Diﬃculty:HardNCTM Standard:Geometry Standard for Grades 9–12:use Cartesian coordinates and othercoordinate systems, such as navigational, polar, or spherical systems, to analyze geometric situations.
A train, traveling at constant speed, passes throughtwo tunnels. In the graph below,tis elapsed time inseconds, andLis the length in meters of the portionof the train that is inside a tunnel. What is the sum,in meters, of the lengths of the two tunnels?Lt24016080122436486002010 AMC 10 A, Problem #24—2010 AMC 12 A, Problem #17—“The train is at least 240 meters long and the firsttunnel is 80 meters long.”Diﬃculty:HardNCTM Standard:Algebra Standard for Grades 9–12: identify essential quantitative relationshipsin a situation and determine the class or classes of functions that might model the relationships.
Tom drives in a city where there are 11 two-way streetsrunning north-south and 11 two-way streets running east-west.Unfortunately, the steering wheel in his car is damaged, soat intersections he can only make a left turn or keep goingstraight.Tom begins a drive by traveling one block eastfrom the center of the city. Assume he does not pass by thesame spot twice. How many different ways can he reach thenortheast corner of the city?2010 AMC 10 A, Problem #25—2010 AMC 12 A, Problem #22—“Model the intersections of the streets by the points(x, y)withinteger coordinates,−5≤x≤5and−5≤y≤5.”