ap10_frq_calculus_ab_formb

8/7/2019 ap10_frq_calculus_ab_formb

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AP Calculus AB

2010 Free-Response Questions

Form B

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2010 AP CALCULUS AB FREE-RESPONSE QUESTIONS (Form B)

2010 The College Board.Visit the College Board on the Web: www.collegeboard.com.

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CALCULUS AB

SECTION II, Part A

Time45 minutes

Number of problems3

A graphing calculator is required for some problems or parts of problems.

1. In the figure above, R is the shaded region in the first quadrant bounded by the graph of ( )4ln 3 ,= -y x thehorizontal line 6,=y and the vertical line 2.=x

(a) Find the area ofR.

(b) Find the volume of the solid generated when R is revolved about the horizontal line 8.=y (c) The region R is the base of a solid. For this solid, each cross section perpendicular to the x-axis is a square.

Find the volume of the solid.

WRITE ALL WORK IN THE EXAM BOOKLET.


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2. The function g is defined for 0>x with ( )1 2,=g ( ) ( )1sin ,= +g x x x and ( ) ( )21 1

1 cos . = - + g x x xx

(a) Find all values ofx in the interval 0.12 1 x at which the graph of g has a horizontal tangent line.

(b) On what subintervals of ( )0.12, 1 , if any, is the graph ofg concave down? Justify your answer.

(c) Write an equation for the line tangent to the graph ofg at 0.3.=x (d) Does the line tangent to the graph of g at 0.3=x lie above or below the graph of g for 0.3 1 ?<


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CALCULUS AB

SECTION II, Part B

Time45 minutes

Number of problems3

No calculator is allowed for these problems.

4. A squirrel starts at building A at time 0=t and travels along a straight, horizontal wire connected tobuilding B. For 0 18, t the squirrels velocity is modeled by the piecewise-linear function definedby the graph above.

(a) At what times in the interval 0 18,<


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5. Consider the differential equation1

.+=

dy x

dx y

(a) On the axes provided, sketch a slope field for the given differential equation at the twelve points indicated,

and for 1 1,- <

ap10_frq_calculus_ab_formb

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