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1、AP Calculus Practice ExamBC Version - Section I - Part ACalculators ARE NOT Permitted On This Portion Of The Exam28 Questions 一 55 Minutes1) Given3戏一42%) -xy = 4Find dy/dx- 4J-6尹一xa)8 e(2j)b)8e(2x)6 y +c)& J-2Cd)& J-2C6尹一xe)7T (e2 +e )2) Give the volume of the solid generated by revolving the region
2、 bounded by the graph of y = In3, the xaxis, the lines x = 1 and x = e、about the 厂axisa)b)c)d)r 3+1)e)3) The graph of the derivative of f is shown below.Find the area bounded between the graph of f and the -raxis over the interval -2, 1, given that /(0) = 11329亘Tc)31 12d)4) Determine dy/dt, given th
3、aty = p + 4xand11x = cos (3 t)6 cos (3 f) sm(3 i)a)b -3 (2cos)+4)血(3f)6 cos (3 t) + 12c)-18sin(3i)d)3(2 cos(3 z) + 4) cos(3f)e)5) The functionfW =用 + 3力)is invertible Give the slope of the normal line to the graph ofatx 31、30 4- 6 e6a)-2b)丄yc)30 + 6d)-6e)6) Determine(sin(6 x) )2 (cos(6 x) )2 dx7- x-
4、y sin(24 x) + C8192a)+寺皿12却+ Cc)d)7) Give the polar representation for the circle of radius 2 centered at (0,2).r = 2 sin(&) + 2 cos(9)a)r = 4 cos (9)b)r = 4 sin(0)c)rsm(0) =2r = 4 sin(9) cos (0)e)8) DetermineInnf 3b)2a)1b)16c)1d) T32e)9) Determinea)b)c)d)10)Give the radius of convergence for the se
5、ries-3(I2)xi=The series diverts for all x.a) 1b)0c)13e)11) Determinelim貝(2)a)2c)0d)GOe)12) The position of a particle moving along the -raxis at time t is given by=(血(47Tf)2At which of the following values of t will the particle change direction?I) t = 1/8II) t = 1/6III) t = 1IV) t 二 2I, II and IIII
6、 and III, III and IVII, III and IV III and IV13) DetermineJOx cos(x) dxa)JUb)-2c)d)e)14)Determine the 厂intercept of the tangent line to the curve45Ta)6619b)_33c) 49135d)3315) The function f is graphed below.the MeanGive the number of values of c that satisfy the conclusion ofValue Theorem for deriva
7、tives on the interval 2, 5 3a)2b)c)d)3.2e)16) Give the average value of the functionon the interval 1,3a)_Ae(-3)+ e(-i)、33b)c) 3_2)+ e(Jd)-2e(-3) + 2 J T)e)17) A rectangle has both a changing height and a changing width, but the height and width change so that the area of the rectangle is always 20
8、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-21c)1而d)205e)18) The 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
9、 f has inflection.1a)2b)0c)3d)There is not enough information.e) 19) A rectangle has its base on the -raxis and its vertices on the positive portion of the parabola严 2 3/What is the maximum possible area of this rectangle?a)b)e)20) Compute()(tan(ea)sin (5)b)cos(5)c)e5d)sm(5)e)24) Determinelirn1 cos(
10、x)0a)1b)2c)undefinedd)3e) T25) Give the derivative of2(一 ) 2x(-2 叫(Ca)一”一1)+/-“)h(x)b)xx(2, l) 2 A 6 h(x)c)1)_ 2兀(-力)血(汇)d)小(I)e)26) Give the first 3 nonzero terms in the Taylor series expansion about-y = 0 for the function/(x) =cos(2 x)1 - 2 ? + 4 /a)1 - 2 x2 + x4b)c)1 + 2 x + 2 异d)1 2异e)27) Determ
11、inedx*ln(d 2) S + 4) + Ca)1 2斗 ln(|x2|) + 于 ln(|x + 4|) + Cb)2 1_|_ln(|x_2|)_*ln(|x + 4|) + Cc)2 1彳扭(口 + 4|) *ln(|x 2|) + Cd)*ln(|(x2) G + 4)|) + Ce)28) Which of the following series converge(s)?ndy aBc B c d d d n n n a a aBAAJ/ 7 J/ J/ 7 a b c d e.M/ lz XI/ VHZ VHZ )z JQ c c debb eac cb ) 7 .7 V)/ 7 n 12345678911113) c)14) e)15) a)16) d)17) a)18) b)19) a)20) d)21) b)b)23) a)24) c)25) d)26) b)27) b)28) 0
