AP Exam Practice Questions for Chapter 4

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Roland Craig
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1 AP Exam Practice Questions for Chapter AP Exam Practice Questions for Chapter f x = x +. f x = f x dx = x + dx. The equation of the line is ( ) ( ) ( ) ( ) Use f ( ) = to find C. ( ) ( ) C f( x) = x + x + f ( ) ( ) ( ) x x C = + +. = + + C = = + + =. ( ) = ( ) + ( ) f x dx f x dx f x dx = + + = 8 ( ) ( ). Let u = 6 x du = 6 x dx. 6 ( 6 x ) ( ) x 6 x dx = 6 x 6x dx a = x dx o = x = = 8 = 8 = = + C 6 = ( 6 x ) + C 9 a. Average value = ( ) f x dx. vt () = t t, t v() t = ( t t) = t t = ( 6 8 ) = units sec So, the answer is A. 6. g( ) = f( t) = f() t = () () () = ( ) ( )( ) ( ) 7. = [ x] f t f t f t sin xdx =. cos =. cos + cos =. + cos =. cos =.6. = + a =, = 8. f ( x) x 6 a = ( ) ( ) ( ) f = f a + f x dx () () f f x dx +.67 = ( sin ) x + x dx = x cos x 9 = ( ) Cengage Learning. All Rights Reserved. May not e scanned, copied or duplicated, or posted to a pulicly accessile wesite, in whole or in part.

Note: Could simply explain as change in temperature from time pts: completes difference quotient with units (c) () () Ct = C t = cos. t = cos(.t)(.). ( t) = sin. + K = sin.

2 AP Exam Practice Questions for Chapter. (a) C () t = C( ) C( ) = 6 = C The total temperature lost from t = to t = is C. () C ( ) ( ) C( ) C 7 = =. So, when t =, the temperature of the coffee is changing aout. C per minute. Note: Could simply explain as change in temperature from time pts: completes difference quotient with units (c) () () Ct = C t = cos. t = cos(.t)(.). ( t) = sin. + K = sin.t + K Because Ct () is continuous at, to find K. sin. ( ) + K = K 8.88 So, C ( ) = sin(. ) C. C = use ( ) C = Note: Use more than three decimal places when representing the constant of integration (avoid premature rounding in this intermediate step) so that the final answer can e rounded to three decimal places. Perhaps store the value of the constant in your calculator for use in the susequent computation. Note: Round each answer to at least three decimal places to receive credit on the exam. 8 Cengage Learning. All Rights Reserved. May not e scanned, copied or duplicated, or posted to a pulicly accessile wesite, in whole or in part.

AP Exam Practice Questions for Chapter 6 6 =.

during the 6 hour period. () It () St () Mt () = + t = t t + + 6 t =.6t.t +.87 sin 6.

h (d) Because I(t) is decreasing over [, 6 ], the maximum is at t =. I ( ) =.

Note: Round each answer to at least three decimal places to receive credit on

3 AP Exam Practice Questions for Chapter 6 6 =. (a) M () t t sin 6 6 t = sin 6 t = cos = ( ) = So, inches of snow will melt during the 6 hour period. () It () St () Mt () = + t = t t t =.6t.t +.87 sin sin t (c) I () t =.t. cos 6 I () =.(). cos 7.8 in. h (d) Because I(t) is decreasing over [, 6 ], the maximum is at t =. I ( ) =.87, so the maximum amount of snow is.87 inches. Note: Round each answer to at least three decimal places to receive credit on the exam. 8 Cengage Learning. All Rights Reserved. May not e scanned, copied or duplicated, or posted to a pulicly accessile wesite, in whole or in part.

() 9 sin t pt: definite integral t (c) v () t = cos a() = v () = cos is in Quadrant II, ( ) Because cos is negative. So, a () <.

4 AP Exam Practice Questions for Chapter vt =. (a) () sin t The particle is moving to the right on the t-intervals, and 8, 9 ecause vt > on these intervals. ( ) ( ) ( ) pts: answers with justification Note: Be sure to explicitly identify each function y name. Referring to as it, the function, or the graph may not receive credit on the exam. () 9 sin t pt: definite integral t (c) v () t = cos a() = v () = cos is in Quadrant II, ( ) Because cos is negative. So, a () <. Because v () >, the acceleration and velocity are in opposite directions. This means that the particle is slowing down. Note: does not need to e evaluated or simplified. Leaving the answer as is sufficient. or (d) st () = () = vt t sin t = sin t = cos + C Use s ( ) = to find C. Note: The answer does not need to e evaluated or simplified. = cos + C + = C t So, st () = cos +. Therefore, s() = cos +. 8 Cengage Learning. All Rights Reserved. May not e scanned, copied or duplicated, or posted to a pulicly accessile wesite, in whole or in part.

AP Exam Practice Questions for Chapter. F( x) ( ) = x f t (a) F( ) = ( ) = f t () f t ( ) ( )( ) = + +.

() The graph of Fx ( ) does not have a minimum value ecause F ( x) f( x) = does not change from negative to

pt: answer with justification does not change from negative to positive on this (c) Because F ( x) f( x) =

pts: answer with reason = = the slope of the tangent (d) Because F ( ) f( ), line is.

5 AP Exam Practice Questions for Chapter. F( x) ( ) = x f t (a) F( ) = ( ) = f t () f t ( ) ( )( ) = ( ) f( ) F = = F ( ) = ( ) f t ( )( ) = =. () The graph of Fx ( ) does not have a minimum value ecause F ( x) f( x) = does not change from negative to positive at any point. pt: answer with justification does not change from negative to positive on this (c) Because F ( x) f( x) = changes from increasing to decreasing at x =, an inflection point of the graph of Fx ( ) is x =. pts: answer with reason = = the slope of the tangent (d) Because F ( ) f( ), line is. Use F( ) ( ) f t and m = = = to write the equation of the tangent line. ( x ) y + = y = x So, the equation of the line tangent to the graph of F at x = is y = x. 8 Cengage Learning. All Rights Reserved. May not e scanned, copied or duplicated, or posted to a pulicly accessile wesite, in whole or in part.

6 AP Exam Practice Questions for Chapter. (a) f( x) dx F() F( ) F( ) F( ) =. =. 9 =. f( x) dx () F() F() F() =.

. () Because F( ) F( ) and F( x) on [, ], there is at least one x-value in this interval where Fx ( ) = y the Intermediate Value

So, F( x) must equal at least times on [, ].

6 6 AP Exam Practice Questions for Chapter. (a) f( x) dx F() F( ) F( ) F( ) =. =. 9 =. f( x) dx () F() F() F() =. = 6 F = 6 9 = 6 f( x) dx ( ) F( ) F( ) F( ) = =. F =. =. = 8. So, F( ) F( ) =. and = 8.. () Because F( ) F( ) and F( x) on [, ], there is at least one x-value in this interval where Fx ( ) = y the Intermediate Value Theorem. Because F() < < F() and F( x) is continuous on [, ], there is at least one x-value in this interval where F( x ) =. So, F( x) must equal at least times on [, ]. > > is continuous pts: answer with reason (c) Because F ( x) = f( x) > on the interval ( ) F is increasing on the interval (, ).,, pts: answer with justification 8 Cengage Learning. All Rights Reserved. May not e scanned, copied or duplicated, or posted to a pulicly accessile wesite, in whole or in part.

AP Exam Practice Questions for Chapter 3

AP Exam Practice Questions for Chapter 3 AP Eam Practice Questions for Chapter AP Eam Practice Questions for Chapter f + 6 7 9 f + 7 0 + 6 0 ( + )( ) 0,. The critical numbers of f are and. So, the answer is B.. Evaluate each statement. I: Because