AP微積分BC選擇題樣卷一

1、AP Calculus Practice ExamBC Version 一 Section I 一 Part ACalculators ARE NOT Permitted On This Portion Of The Exam28 Questions 一 55 Minutes1) Given莎一4e(-一心=4Find dy/dxa)8e(2x)3+ Xb)8e(-c)8e(2x)d)8訂一3) 尹a)13Tb)2912d)311211T4) Determine dy/dt,given thatandr (/ + 1)3) The graph of the derivative of f is

2、 shown below.Find the area bounded between the graph of f and the -raxis over the interval 一2, 1, given that /(0) = 1b)sin(12x) + Cc)the graph of 廠 atx = cos(3 f)6 cos (3 f) sin(3 f)a)S 3 (2co$(3Z) +4) sin(3Z)6 cos(3 /) + 12c)-18sin(3/)d)3 (2 cos(3 t) 4) cos (3 f)e)5) The function/()=5? + 3e(2x)is i

3、nvertible Give the slope of the normal linex 31、30+6a)-2b)10 y30+ 6 e6d)-6e)6) Determine(sin(6 x) )2 (cos(6 x) )2 dxa)4c)r = 4 sin(O)d)r sin(0) =2e)8)r = 4 sm(9) cos(0)Determinelimf T的f4?X.f . f 2sma)b)c)16d)e)9)32Determinea)x+_l_sin(24x) + Cd)y - -sin(12 J) + Ce)7) Give the polar representation for

4、 the circle of radius 2 centered at (o , 2 ).r = 2 sin(9)亠 2 cos (0)b)a)b)c)d)e)10)Give the radius of convergence for the seriesThe series diverges for all 天.a)1b)0c)1d)ye)311) Determine*lna)2b)limc)e)14)0d)Ke)12)The position of a particle moving along the 曠axis at time t is given byxO) = (sin(4 K 0

5、 )2At which of the following values of twill the particle change direction?I)t = 1/8II)t = 1/6III)t = 1IV)t = 2I, II and IIII and III, III and IVII,III and IV III and IV13)Determinex COS(J) dxa)b)c)d)Determine the 廠intercept of the tangent line to the curve2the Meanat x = 4.45a)7_330) 49135d) 4933T1

6、5)The function f is graphed below.Give the number of values of c that satisfy the conclusion ofValue Theorem for derivatives on the interval 2, 5 3a)b)b)6649xc)d)3.2e)16)Give the average value of the functionon the interval 1,3JT)+宀a)Ae(-n33b)c)3_尸 + (一1)d)-2eC_3) + 2e(_1)e)17)A rectangle has both a

7、 changing height and a changing width, but the height and width change so tha t the area of the rec tangle is always 20 square feet Give the rate of change of the width (in ft/sec) when the height is 5 feet, if the height is decreasing at that moment at the rate of 1/2 ft/sec.2a)y-2b)o金丄d)205e)18)Th

8、e graph of the derivative of f is shown below.Give the number of values of x in the interval -3, 3一 where the graph of f has inflection.1a)2b)0c)3d)There is not enough informatione)19) A rectangle has its base on the -raxis and its vertices on the positive portion of the parabolaWhat is the maximum

9、possible area of this rectangle?b)c)e)20)Compute2)伽(亡)%a) 2fsec (2)c、占如cWs + c4tan（e（2”）（$ec （）2 &（2彳）十d)y tan(e()_ J_ e(2x)十亡e)21)y tan(e(2j) + -1 e(2x) +。Determinea)b)c)1127T(Od)6 7Te)22)Determine117b)tcc)zed)e)1123) Give the exact value ofg)a)sin(5)b)cos(5)c)e5d)-sin(5)e)24)Determine3 TLlim (傘+尸)

10、x-* G)Inn廠“+對一2、a)b)2c)undefinedd)3e)T25) Give the derivative of一一力)一 2八一力)ln(x)a)-2XJ(_2X_1) +xC_2x)h()b)開 J2上_1) _ 2乳(4) ln(x)c)-2xxC-2x-n -2x(2j)ln(r)d)e)26) Give the first 3 nonzero terms in the Taylor series expansion about-Y = 0 for the function子(x) = cos(2 x)1 一 2 F + 4 Ja)1 2 +竿b)c)151 + 2 z

11、 + 2 z1 2 d)1 -2z2e)27)DetermineK= 1J/ JZ 7 J/ J/ a b c d ec B c d d d n n n aaa / / lzlz HZHZ HZHZ / / XI/XI/ V)/V)/ XI/XI/ JuJu c c d d ebbeaebbea ccb)ccb) .7.7 77 .7.7 .7.7 XI/XI/ 77 n n 12341234 5 5 678911678911*ln(x 2) (x + 4) + Ca)1 2才 ln(-2|) + 令 ln(|x + 4|) + Cb)2 1一芻血(口_2|) _ 才 ln(K + 4|) + Cc)2 1一芻 ln(|4|) _ 才 ln(|x_2|) + Cd)*ln( 2) (4)|) + Ce)28)Which of the following series converge(s)?ndy a12) c)13) c)14) e)15) a)16) d)17) a)18) b)19) a)20) d)21) b)22) b)23) a)24) c)25) d)26) b)27) b)28) c)（注：文檔可能無法思考全面，請瀏覽后下載，供參考?？蓮?fù)制、編制，期待 你的好評與關(guān)注）_ xe)2) Give t