AP® CALCULUS AB 2010 SCORING GUIDELINES Question 1 © 2010 The College Board. Visit the College Board on the Web: www.collegeboard.com. There is no snow on Janet’s driveway when snow begins to fall at midnight. From midnight to 9 A.M., snow accumulates on the driveway at a rate modeled by ()cos7tftte= cubic feet per hour, where t is measured in hours since midnight. Janet starts removing snow at 6 A.M. ()t=6. The rate g(t), in cubic feet per hour, at which Janet removes snow from the driveway at time t hours after midnight is modeled by ()0for0 6125 for 67108 for 79 .tgttt≤<°=≤<®°≤≤ ̄(a)How many cubic feet of snow have accumulated on the driveway by 6 A.M.? (b) Find the rate of change of the volume of snow on the driveway at 8 A.M. (c) Leth(t) represent the total amount of snow, in cubic feet, that Janet has removed from the driveway at time t hours after midnight. Express h as a piecewise-defined function with domain09.t≤≤(d) How many cubic feet of snow are on the driveway at 9 A.M.? (a) ³()60ftdt=142.274 or 142.275 cubic feet 2 :{1 : integral1 : answer(b) Rate of change is ()()8859.582fg−=− or 59.583−cubic feet per hour. 1 : answer (c) ()00h=For 06,t<≤()()()0000tththgsdsds=+=+=³³00.For 67,t<≤()()()()66601251256.tththgsdsdst=+=+=−³³For 79,t<≤()()()()7712510781251087 .ttgsdsdshht=+=+=+−³³tThus, ()()(012561251087httt°=−®°+− ̄)for0t≤≤6for67t<≤for79t<≤3 : °®° ̄1 : ht() for 06t≤≤1 : h(t) for 67t<≤1 : ht() for 79t<≤(d) Amount of snow is ()()909ftdth−³=26.334 or 26.335 cubic feet. 3 : °®° ̄1 : integral1 : h()91 : answer
© 2010 The College Board. Visit the College Board on the Web: www.collegeboard.com.
© 2010 The College Board. Visit the College Board on the Web: www.collegeboard.com.
© 2010 The College Board. Visit the College Board on the Web: www.collegeboard.com.
© 2010 The College Board. Visit the College Board on the Web: www.collegeboard.com.
© 2010 The College Board. Visit the College Board on the Web: www.collegeboard.com.
