摘要：真題是離AP實戰考試最近的復習資料，好好把握往年的AP真題對準備AP考試的考生來說十分重要。為此，三立小編為大家整理了2010-2018年AP各科考試真題大全。本文，小編為大家帶來的是2016年AP微積分AB真題及下載-簡答題(FRQ)部分，希望對你有所幫助！ 1. Water is pumped into a tank at a rate modeled by W (t) 2000e-t2 20 liters per hour for 0 ? t ? 8, where t is measure
1. Water is pumped into a tank at a rate modeled by W (t) 2000e-t2 20 liters per hour for 0 ? t ? 8, where t is measured in hours. Water is removed from the tank at a rate modeled by R(t ) liters per hour, where R is differentiable and decreasing on 0 ? t ? 8. Selected values of R(t ) are shown in the table above. At time t 0, there are 50,000 liters of water in the tank.
(a) Estimate R?(2). Show the work that leads to your answer. Indicate units of measure.
(b) Use a left Riemann sum with the four subintervals indicated by the table to estimate the total amount of water removed from the tank during the 8 hours. Is this an overestimate or an underestimate of the total amount of water removed? Give a reason for your answer.
(c) Use your answer from part (b) to find an estimate of the total amount of water in the tank, to the nearest liter, at the end of 8 hours.
(d) For 0 ? t ? 8, is there a time t when the rate at which water is pumped into the tank is the same as the rate at which water is removed from the tank? Explain why or why not.
2. For t ? 0, a particle moves along the x-axis. The velocity of the particle at time t is given by È t 2 Ø v(t) 1 + 2 sin ÉÊ 2 ÙÚ . The particle is at position x 2 at time t 4.
(a) At time t 4, is the particle speeding up or slowing down?
(b) Find all times t in the interval 0 < t < 3 when the particle changes direction. Justify your answer.
(c) Find the position of the particle at time t 0.
(d) Find the total distance the particle travels from time t 0 to time t 3.