CALCULATOR SECTION. For y y 8 find d point (, ) on the curve. A. D. dy at the 7 E. 6. Suppose silver is being etracted from a.t mine at a rate given by A'( t) e, A(t) is measured in tons of silver and t in years from the opening of the mine. Which is an epression for the amount of silver etracted from the mine in the first years of its opening? A. A '() A() t dt A'( t) dt D. A () E. A'() A'(). Joe Student's calculus test grades (G) are changing at the rate of points per month. Which is the epression that says this? dg pts A. G dt month dt pts dg month dg pts dt D. G ( G t) pts dg pts E. dt month. If f is a continuous and differentiable function, then approimate the value of f '().. A.. D. / E. / f ' ( ) sin ( ) sin ( ). Over the open interval (,.7], at what value of is the tangent line to f horizontal? A..9..68 D..67 D..9 6. At which -value over the interval (, ] does the graph of f have a relative minimum? (refer to f' in #) A..98.6.68 D..7 E..67 7. At which -coordinate below does the graph of f (for f' defined in #) change concavity over the interval (, ]? A..98.6.667 D..7 E..67 8. At which interval is the graph of f (for f' defined in #) concave up over the interval (,.8]? A. (,.8) (.68,.78) (,.68) D. (.68,.8) 9. Given f() 6 6 6. g( ) e cos over (,.] give the -coordinate where the graph of g changes concavity. revised Aug AP Calculus BC semester one review Page of
. Given g( ) e cos over (, ]. give the -coordinate(s) where the line(s) tangent to g are horizontal.. tan d v 6 7 8 A.... D.. E... The graph of a twice-differentiable function is shown below. y=f(). Consider the graph shown to be the velocity of a turtle moving left and right in relation to my mailbo, with velocity in feet/minute for t minutes. The turtle, at t= is standing foot to the right of my mailbo. O A. Where is the turtle in relation to my mailbo at t= minutes? Which of the following is true? A. f () f '() f "() f () f "() f '() f "() f () f '() D. f '() f () f "() E. f "() f '() f () Where is the turtle in relation to my mailbo at t= minutes? 6. from AP AB A container has the shape of an open right circular cone, as shown. The height of the container is cm and the diameter of the opening is cm. Water in the container is evaporating so that its depth h is changing at a constant rate of cm/hr.. Find k k d in terms of the constant k. k ( V r h ). For k in the interval [ -, ], if f ( ) d and k f ( ) d then give the value of f ( ) d for k continuous function f. A. Find the volume V of water in the container when h= cm. Indicate units of measure. Find the rate of change of the volume of water in the container, with respect to time, when h= cm. Indicate units. revised Aug AP Calculus BC semester one review Page of
7. The function f is continuous and differentiable over the interval [-, ]. If f ( ) and f (6) then tell (true or false) which statements must be true. A B D A. Over [-, 6], the function f has a maimum value. Over [-, ] there eists a value. c so that f( c) Over [-, ] there eists a value. c so that f( c) D. Over [-, ] there eists a value c so that f '( c). E. Over [-, ] there eists a value c so that f '( c). F. Over [-, ], f is increasing. E. Over [-, ] f '( c ) eists for every c in [-, ]. 9. Consider the average rate of change of the graph of f above, between the points. C shown. Between which two points is the average rate of change the least? A. Points A and B Points A and D Points B and D D. Points B and C E. Points A and C The graph of y is shown above, on the interval [ -, ]. Which is true? 8. A rectangle with one side on the -ais has its upper vertices on the graph of y cos as shown in the figure above. what is the maimum area of the rectangle? A..86.98. D..6 E. 6. 77 A. The graph is continuous and differentiable. The graph is continuous but not differentiable. The graph is not continuous but is differentiable. D. The graph is not continuous nor differentiable. revised Aug AP Calculus BC semester one review Page of
g' - - - - -. Graph 6 7 8 g '( ) in the plane above, over the window [-, 8] X [-, ].. Give the -interval(s) where the graph of g is increasing. GIVE A REASON for your answer.. Give the -interval(s) where the graph of g is concave up. GIVE A REASON for your answer.. Give the -coordinates of any critical points for the graph of g. For each tell if it is a relative maimum, a relative minimum or neither. EXPLAIN. - - - - - g 7. If 6 7 8 v( t) t t t is the velocity function for a particle moving along the -ais, for time t seconds, tell A. when the particle changes direction. for t. for what intervals of time ( t ) the particle is moving to the left. for what intervals of time ( t ) the particle has increasing speed. D. for what intervals of time ( t ) the acceleration of the particle is positive?. Give the -coordinate of any points of inflection of the graph of g. 6. If g() = then sketch g on the grid following. 8. Given V r ; S r for a sphere, and the fact that the radius of the sphere is decreasing at / inches per minute, find the rate at which the volume is changing, in cubic inches per minute for a sphere at the time when the radius is 6 inches. revised Aug AP Calculus BC semester one review Page of
9. What is the slope of the line tangent to y cos ( ) at the point on the curve when =.86? -------------------------------------------------- NO CALCULATOR SECTION.. A ft ladder is sliding down a wall so that the base is moving along the ground at ft/hour. When the ladder is feet high (on the wall), how fast in ft/hour is the top of the ladder moving along the wall? A. - ft/hour -6.87 ft/hr -.869 ft/hr D..869 ft/hr E. 6.87 ft/hr. Use the equation p( t) 6t v t p to answer the following questions. Time t is measured in seconds, and position p is measured in feet above ground. Renaldo threw a ball from a height of 6 feet above ground, with an initial velocity of feet/second. A. How far above ground was the ball when the ball was at its maimum? What is the velocity of the ball when it is at its maimum height? When the ball hits ground is its velocity according to the model given? Eplain.. If the area of a circle is increased from sq. cm to. sq. cm, what is the corresponding change in radius?. f ( ) sin ( ) sin ( ). Find the interval of -coordinates for which the graph of f is concave up on the interval [,.78]. TRUE or FALSE, given the graph of f above. A.. Let lim f( ) lim f( ) eists. eists. f is continuous over the interval [-, ]. D. f is differentiable over the interval [-, ]. E. f is differentiable over the interval [-, -], g( ), Which of the following statements are TRUE? I) lim g( ) eists II) g() eists III) g is continuous at = A) Only I B) Only II C) I and II only D) None of them E) All of them revised Aug AP Calculus BC semester one review Page of
6. lim. lim A) Undefined B) 7 D) E) C). lim h ( h) h 7. n lim n n n A) Noneistent B) C) D) E) dy. Give an epression for at the point d (, y) for each function below. A. y y e 8. If g is a continuous function on the closed interval [-, ] and g(-) = and g() = 7, which of the following statements is necessarily TRUE? A) The absolute maimum value for g on [-,] is 7 B) If - < <, g() = for at least one value of C) g() = for at least one value of on the closed interval [-, ] D) g is increasing for all on [-, ] E) The absolute minimum value of g on [-, ] is y ln( 6) D. E. y y e F. y cos( ) G. H. y sin y 9... lim lim lim h 9 = 9 ( h) h. f ( ) 8, f '(), f "() for a twice- differentiable function f. Write an equation of the line tangent to f at =. A. y y y ` D. y 7 E. y revised Aug AP Calculus BC semester one review Page 6 of
6. Which is a line which can be used to approimate values of y near 8? A. y y y D. y 8 E. y 6 Use this graph of y f ( ) questions #7-9. to answer. Find the value of below, at the value A. d y d c given. y at for each function r. 8 s. t. -8 u. v. 8 y cos( ) at y e at =. If y cos ( ) dy then d = Consider the graph of f shown. Increments on both aes are one. 7. Over the interval [-, ], how many values on f appear to satisfy the conclusion of the Mean Value Theorem? A. D. E. 8. What is the average rate of change of f over the interval [-, ]? A. D. E. 9. Consider the interval [-, k]. For what value of k is the average rate of change of f equal to? A. D. E. cos ( ) sin ( ). The graph of cos ( ) cos ()sin( ) cos ()sin( ) y has A. two horizontal asymptotes two horizontal and one vertical asymptotes two vertical but no horizontal asymptotes D. one horizontal and one vertical asymptote E. one horizontal and two vertical asymptotes revised Aug AP Calculus BC semester one review Page 7 of
. A local minimum value of the function e y is at = A. /e - D. e E. 7. y z. A function f( ) equals for all ecept =. For the function to be continuous at =, the value of f() must be A. D. E. none of these. If f ( ) then f '() The sides of the rectangle above increase in such a way that the instant when dz dt d and dy dt dt = and y= what is the value of d dt A. D. E.?. At A. D. E. 6. Give the inflection POINT(S) of the graph of A. y 6 y 8 8. Given that y f ( ) is a continuous function, give lim f( ) A... D..99 E. no limit. 9. Which is an equation of the tangent line at y 6? a. y9 b. y c. y d. y 7 e. y 8 =, for the graph of revised Aug AP Calculus BC semester one review Page 8 of
6. Oil is leaking out of a tank into a reservoir. The rate of flow is measured every two hours for a -hour period. The data is in the table below. A. Use a left-hand Riemann sum to approimate the area under the rate of flow graph f where f is the function whose values are given in the table. equal subdivisions. Use a right-hand Riemann sum to approimate the area under the rate of flow graph f where f is the function whose values are given in the table. equal subdivisions. 6. Use a right hand Riemann sum with equal subdivisions to approimate the area bounded by the curve over the interval [.,.]. 6. Given time (hr) then find 8 6 6 8 6 8 8 Amt (gal/hr) y and the -ais f ( ), And f () ( f ())'. A. 9 /9 D. / E. / 6. Shown: the graph of f over[-, ]X[-,]. A. E. G. I. lim f( ) lim f( ) lim f( ) lim f( ) lim f( ) = f(-)= = D. f()= = F. = H. lim f( ) lim f( ) J. f() K. Estimate the -coordinates where f()=. L. lim f( ) 6. A position function p( t) t t t gives the position of a particle moving left and right along the -ais, for t seconds. A. What is the initial position of the particle? In what direction is the particle moving at t seconds? For what interval(s) for t is the particle moving to the left? y D. What is the acceleration of the particle at t= seconds? revised Aug AP Calculus BC semester one review Page 9 of
6. It's fundamental. A. For value of t dt what is the f ( ) f '()? b ( b ) d. Find the value of b. g '( ) d =? for the values below. g g' - 66. A. d sin d cos d (continued on net page) revised Aug AP Calculus BC semester one review Page of
Acceleration of Fred, in ft/sec/sec AP Calculus BC semester one review 67. A horse is moving with velocity given by the graph of v(t) above. He moves in feet per sec. left and right, along a corral railing. At t=, the horse, Fred, is foot to the left of a tree which is at the railing. a. What is Fred's velocity at t= sec.? b. Over time [, 9] seconds, when is Fred's speed constant? c. When is Fred slowing down? - - - - - v(t) 6 7 8 d. When is the acceleration of Fred negative? Fred e. What is Fred's acceleration at t= seconds? f. When does Fred change direction? g. At what time is Fred again foot to the left of the tree, after t=? foot to left of tree at t= h. What is Fred's speed at t= seconds? i. Sketch a graph that gives Fred's acceleration over time [, 8]. j. How many times do you think Fred passes the tree? Eplain your reasoning. revised Aug AP Calculus BC semester one review Page of