Ch 4-Integrals Practice AP Calculus Exam Questions 1 sin = 2003 (no calc) A B C 1 D +1 E 1 2 A curve has slope 2x + 3 at each point (x, y) on the curve Which of the following is an equation for this curve if it passes through the point (1, 2)? 2003 (no calc) A y = 5x 3 B y = x 2 + 1 C y = x 2 + 3x D y = x 2 + 3x 2 E y = 2x 2 + 3x 3 3 The rate of change of the altitude of a hot-air balloon is given by r(t) = t 3 4t 2 + 6 for 0 t 8 Which of the following expressions gives the change in altitude of the balloon during the time the altitude is decreasing? 2003 (calc) A B C D E 4 A pizza, heated to a temperature of 350 degrees Fahrenheit ( F), is taken out of an oven and placed in a 75 F room at time t=0 minutes The temperature of the pizza is changing at a rate of 110! degrees Fahrenheit per minute To the nearest degree, what is the temperature of the pizza at time t=5 minutes? 2003 (calc) A 112 F B 119 F C 147 F D 238 F E 335 F 5 #= 2008 (no calc) A ln +% B ln +% C x 1 + C D x 1 + C E 2x 3 + C
6 A particle moves along the x-axis with velocity given by v(t) = 3t 2 + 6t for time t 0 If the particle is at position x = 2 at time t = 0, what is the position of the particle at time t = 1? 2008 (no calc) A 4 B 6 C 9 D 11 E 12 7 If &= 17 and &= 4, what is the value of &? 2008 (calc) A 21 B 13 C 0 D 13 E 21 8 If G(x) is an antiderivative for f(x) and G(2) = 7, then G(4) = 2008 (calc) A f (4) B 7 + f (4) C & D * 7+&+ E 7+ & 9 If f is continuous for a x b and differentiable for a < x < b, which of the following could be false? 1998 (no calc) A &,= - - for some c such that a < c < b B f (c) = 0 for some c such that a < c < b C f has a minimum value on a x b D f has a maximum value on a x b E & exists 10 If f is a linear function and 0 < a < b, then & = 1998 (no calc) A 0 B 1 C D b a E # # 11 If 0= +1, then F (2)= 1998 (no calc) A 3 B 2 C 2 D 3 E 18
12 1 cos2566 is 1 A 0 B 7 sin 1993 (calc) C cos25 D cos (2πx) E 2π cos (2πx) 7 13 sin = 1998 (no calc) A sin x B cos x C cos x D cos x 1 E 1 cos x 14 Let g be the function given by 8= sin intervals is g decreasing? A 1 x 0 B 0 x 1772 C 1253 x 2171 D 1772 x 2507 E 2802 x 3 for 1 x 3 On which of the following 2003 (calc) 15 = 2003 (no calc) A 9 : B 4e - 4 C e - 4 1 D 9: E 4 4e - 4 16 cos = 2003 (no calc) A sin +% B sin +% C ; sin +% D ; sin +% E ; sin< =+% 17 Using the substitution u = 2x + 1, 2+1 is equivalent to 2003 (no calc) A 6 6 B 6 6 C 6 6 D 6 6 E 6 6
# 18 1 < 1 sin == 2003 (no calc) A cos B sin C sin D 2sin E 2sin 19 A particle moves along the x-axis so that at any time t > 0, its acceleration is given by @= ln1+2! If the velocity of the particle is 2 at time t = 1, then the velocity of the particle at time t=2 is 2003 (calc) A 0462 B 1609 C 2555 D 2886 E 3346 20 On the closed interval [2, 4], which of the following could be the graph of a function f with the property that &=1? 2003 (calc) A B C D E 21 The graph of f, the derivative of f, is the line shown in the figure below If f(0)=5, then f(1)= 2003 (no calc) A 0 B 3 C 6 D 8 E 11
22 The regions A, B, and C in the figure below are bounded by the graph of the function f and the x- axis If the area of each region is 2, what is the value of &+1? 2003 (calc) A 2 B 1 C 4 D 7 E 12 23 If a trapezoidal sum over-approximates &, and a right Riemann sum underapproximates &, which of the following could be the graph of y=f(x)? 2003 (calc) A B C D E 24 The graph of the piecewise linear function f is shown in the figure below If 8= &, which of the following values is greatest? 2008 (no calc) A g( 3) B g( 2) C g(0) D g(1) E g(2) 25 The table below gives values of a function f and its derivative at selected values of x If f is continuous on the interval [ 4, 1], what is the value of &? 2008 (calc) A 45 B 225 C 0 D 225 E 45
26 The graph of the function f is shown below for 0 x 3 Of the following, which has the least value? 2008 (no calc) A & B Left Riemann sum approximation of & subintervals of equal length C Right Riemann sum approximation of & subintervals of equal length D Midpoint Riemann sum approximation of & E Trapezoidal sum approximation of & with 4 with 4 with 4 subintervals of equal length with 4 subintervals of equal length 27 A city located beside a river has a rectangular boundary as shown in the figure below The population density of the city at any point along a strip x miles from the river s edge if f(x) persons per square mile Which of the following expressions gives the population of the city? 2008 (calc) A & B 7 & C 28 & D & E 4 & 28 The function f is continuous on the closed interval [2, 8] and has values that are given in the table below Using the subintervals [2, 5], [5, 7], and [7, 8], what is the trapezoidal approximation of &? 1998 (calc) A 110 B 130 C 160 D 190 E 210
Questions 29 and 30 refer to the following situation A bug begins to crawl up a vertical wire at time t = 0 The velocity v of the bug at time t, 0 t 8, is given by the function whose graph is shown below 1997 (no calc) 29 At what value of t does the bug change direction? A 2 B 4 C 6 D 7 E 8 30 What is the total distance the bug traveled from t=0 to t=8? A 14 B 13 C 11 D 8 E 6 31 The flow of oil, in barrels per hour, through a pipeline on July 9 is given by the graph shown below Of the following, which best approximates the total number of barrels of oil that passes through the pipeline that day? 1998 (no calc) A 500 B 600 C 2,400 D 3,000 E 4,800 32 The graph of f is shown in the figure below If &=23 and F (x) = f(x), then F(3) F(0)= 1997 (calc) A 03 B 13 C 33 D 43 E 53
33 Let &= h, where h has the graph shown below Which of the following could be the graph of f? 1997 (calc) A B C D E 34 sin2+cos 2= 2008 (no calc) A cos2+ sin2+% B cos2+ sin2+% C 2cos(2x)+2sin(2x)+C D 2cos(2x) 2sin(2x)+C E 2cos(2x)+2sin(2x)+C = 2008 (no calc) 35 # A # #+% B # +% C ln 4 +% D 2ln 4 +% E arctan< =+% 36 An object traveling in a straight line has position x(t) at time t If the initial position is x(0)=2 and ; the velocity of the object is H= 1+, what is the position of the object at time t=3? 2008 (calc) A 0431 B 2154 C 4512 D 6512 E 17408 37 #= 1998 (no calc) A ½ B 724 C ½ D 1 E 2 ln2
38 4 6= 1997 (no calc) A 2 B 4 C 6 D 36 E 42 39 +1 = 1993 (calc) A *# J+ ; +% B *# J+ ; D *# J+ ; +% C < ; += +% +% E K +; ++% 40 Which of the following are antiderivatives of f(x)=sin x cos x? 1997 (calc) I 0= LMN# II 0= OPL# III 0= QRS A I only B II only C III only D I and III only E II and III only 41 If the second derivative of f is given by f (x)=2x cos x, which of the following could be f(x)? A ; 1993 (calc) ; +cos +1 B cos +1 C +cos +1 D sin+1 E +sin+1 42 T #= 1997 (no calc) A e t + C B e -t2 +C C e t2 +C D 2e t2 +C E e t + C 43 13 11 + 11 13 = A 0000 B 14946 C 34415 D 46000 E 136364 1993 (calc)
44 Let F(x) be an antiderivative of UV; If F(1)=0, then F(9) = 1998 (calc) A 0048 B 0144 C 5827 D 23308 E 1, 640250 45 If &=@+2W, then &+5= A a + 2b + 5 B 5b 5a C 7b 4a D 7b 5a E 7b 6a 1997 (no calc) Y 46 What are all values of k for which =0? 1998 (no calc) A 3 B 0 C 3 D 3 and 3 E 3, 0, and 3 47 If f is a continuous function and if F (x)=f(x) for all real numbers x, then &2= 1998 (calc) A 2F(3) 2F(1) B ½ F(3) ½ F(1) C 2F(6) 2F(2) D F(6) F(2) E ½ F(6) ½ F(2) 48 The acceleration of a particle moving along the x-axis a time t is given by a(t)=6t 2 If the velocity is 25 when t = 3 and the position is 10 when t=1, then the position x(t)= 1993 (calc) A 9t 2 +1 B 3t 2 2t + 4 C t 3 t 2 + 4t + 6 D t 3 t 2 + 9t 20 E 36t 3 4t 2 77t+55