Ap 2005 calculus bc cover - College Board

AP? Calculus BC

2005 Scoring Guidelines

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AP? CALCULUS BC

2005 SCORING GUIDELINES

Question 1

1

+ sin (¦Ð x ) and g ( x ) = 4? x. Let

4

R be the shaded region in the first quadrant enclosed by the y-axis and the graphs

of f and g, and let S be the shaded region in the first quadrant enclosed by the

graphs of f and g, as shown in the figure above.

Let f and g be the functions given by f ( x ) =

(a) Find the area of R.

(b) Find the area of S.

(c) Find the volume of the solid generated when S is revolved about the horizontal

line y = ?1.

1

+ sin (¦Ð x ) = 4? x .

4

f and g intersect when x = 0.178218 and when x = 1.

Let a = 0.178218.

f ( x ) = g ( x ) when

(a)

a

¡Ò0 ( g ( x ) ? f ( x ) ) dx = 0.064 or 0.065

? 1 : limits

?

3 : ? 1 : integrand

?? 1 : answer

1

(b)

¡Òa ( f ( x ) ? g ( x ) ) dx = 0.410

(c)

¦Ð ¡Ò ( f ( x ) + 1)2 ? ( g ( x ) + 1)2 dx = 4.558 or 4.559

1

a

(

? 1 : limits

?

3 : ? 1 : integrand

?? 1 : answer

)

3:

{

2 : integrand

1 : limits, constant, and answer

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2

AP? CALCULUS BC

2005 SCORING GUIDELINES

Question 2

The curve above is drawn in the xy-plane and is described by the equation in

polar coordinates r = ¦È + sin ( 2¦È ) for 0 ¡Ü ¦È ¡Ü ¦Ð , where r is measured in

meters and ¦È is measured in radians. The derivative of r with respect to ¦È is

dr

= 1 + 2cos ( 2¦È ) .

given by

d¦È

(a) Find the area bounded by the curve and the x-axis.

(b) Find the angle ¦È that corresponds to the point on the curve with

x-coordinate ?2.

(c) For

¦Ð

................
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