AP微积分AB（2022年）简答题及评分答案.pdfVIP

2022 ® AP Calculus AB Free-Response Questions © 2022 College Board. College Board, Advanced Placement, AP, AP Central, and the acorn logo are registered trademarks of College Board. Visit College Board on the web: collegeboard.org. AP Central is the official online home for the AP Program: apcentral.collegeboard.org. AP® Calculus AB 2022 Free-Response Questions CALCULUS AB SECTION II, Part A Time—30 minutes 2 Questions A GRAPHING CALCULATOR IS REQUIRED FOR THESE QUESTIONS. © 2022 College Board. Visit College Board on the web: collegeboard.org. GO ON TO THE NEXT PAGE. 2 AP® Calculus AB 2022 Free-Response Questions 1. From 5 A.M. to 10 A.M., the rate at which vehicles arrive at a certain toll plaza is given by A (t ) = 450 sin (0.62t) , where t is the number of hours after 5 A.M. and A (t ) is measured in vehicles per hour. Traffic is flowing smoothly at 5 A.M. with no vehicles waiting in line. (a) Write, but do not evaluate, an integral expression that gives the total number of vehicles that arrive at the toll plaza from A.M. ( ) to A.M. ( ). 6 t = 1 10 t = 5 (b) Find the average value of the rate, in vehicles per hour, at which vehicles arrive at the toll plaza from A.M. ( ) to A.M. ( ). 6 t = 1 10 t = 5 (c) Is the rate at which vehicles arrive at the toll plaza at A.M. ( ) increasing or decreasing? Give a reason 6 t