ap微積分是大學(xué)微積分入門課程，主要讓學(xué)生通過參與圖形等方式表示的的顯示世界問題，探索變化、極限、函數(shù)分析等時(shí)使用定義、定理建立論點(diǎn)&證明結(jié)論。下面來看看2022年ab部分的考題和答案。

一、考試真題

1.From5 AM to10 AM. Therateatwhichvehiclesarriveatacertaintollplazaisgivenby A(1)= 450sin(0.62r),where t is the number of hours after 5 A.M.and A(1) 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 6AM(t=1to10AM(t=5).

(b)Find the average value of the rate in vehicles per hour. at which vehicles arrive at the toll plaza from 6 A.M.(t=1)to 10 A.M.(t=5).

cis the rate at which vehicles arrive at the toll plaza at 6 A.M.(t=1)increasing or decreasing? Give a reason for your answer.

(d) A line forms whenever A(t) ≥ 400.The number of vehicles in line at time t,for a ≤≤ 4. is given by N(1)=(A(x)-400)dx,where a is the time when a line first begins to form.To the nearest whole number,find the greatest number of vehicles in line at the toll plaza in the time interval a ≤≤4. Justify your answer

2. Let f and g be the functions defined by fx =lnx+ 3) and g(x) = (x2)2+ 2x3. The graphs of f and g shown in the figure above intersect at x=-2and x=Bwhere B>0.

(a)Find the area of the region enclosed by the graphs of f and g.

(b) For -2 ≤x ≤ B,let h(x) be the vertical distance between the graphs of f and g. Is h increasing or decreasing at x=-0.5?Give a reason for your answer.

(c)The region enclosed by the graphs off and g is the base of a solid.Cross sections of the solid taken perpendicular to the x-axis are squares.Find the volume of the solid.

(d) A vertical line in the xy-plane travels from left to right along the base of the solid described in part(c). The vertical line is moving at a constant rate of 7 units per second.Find the rate of change of the area of the cross section above the vertical line with respect to time when the vertical line is at position x=-0.5.

3.Letfbeadifferentiablefunctionwithf4)= 3. Ontheinterval0≤x≤ 7. the graph off,the derivative

of f.consists of a semicircle and two line segments as shown in the figure above.

(a)Find f(0) and f(5).

(b)Find the x-coordinates of all points of inflection of the graph off for 0

(c)Let g be the function defined by g(x)=f(x) - x. On what intervals,if any,is g decreasing for

O≤x≤7? Show the analysis that leads to your answer.

(d)For the function g defined in part(c),find the absolute minimum value on the interval 0 ≤x≤7.Justify Your answer

二、答案解析

三、ab微積分備考方法

1.復(fù)習(xí)所有核心的知識點(diǎn)和概念

2.做大量題目練習(xí)并反思總結(jié)

3.考前沖刺復(fù)習(xí)，參加模擬考試或做真題

4.調(diào)整好考試心態(tài)，積極應(yīng)對

以上是ap微積分ab課程的相關(guān)內(nèi)容，希望對大家有所幫助。學(xué)習(xí)上有任何問題，記得找我們留求藝的專業(yè)老師一對一指導(dǎo)喲!