CALCULUS AB
SECTION II, Part B
Time—60 minutes
Number of problems—4
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Calculus AB Practice Exam
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of three line segments and a quarter of a circle centered at the point (0, 2) . Let f be the function given by
f (=
x)
x
∫− 8 g (t ) dt.
(a) Find all values of x in the interval − 8 < x < 6 at which f has a critical point. Classify each critical point
as the location of a local minimum, a local maximum, or neither. Justify your answers.
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Calculus AB Practice Exam
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3. A continuous function g is defined on the closed interval − 8 £ x £ 6 . The graph of g, shown above, consists
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(c) Find lim
x → −4
f (x )
x 2 + 4x
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(b) Find f (0).
.
g (x )
(d) Let h be the function defined by h(x ) = 2
. Find h¢(1) .
x +1
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Calculus AB Practice Exam
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4. Consider the differential equation
dy
= ( y − 2)(x 2 + 1).
dx
(a) Find y = g (x ) , the particular solution to the given differential equation with initial condition g (0) =5.
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(b) For the particular solution y = g (x ) found in part (a), find lim g (x ).
x → −∞
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Calculus AB Practice Exam
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(c) Let y = f (x ) be the particular solution to the given differential equation with initial condition f (1) =3.
Find the value of
d 2y
dx 2
at the point (1, 3) . Is the graph of y = f (x ) concave up or concave down at the
point (1, 3) ? Give a reason for your answer.
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Calculus AB Practice Exam
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5. The function f is defined by
⎧⎪ 3 x 2 + 2 x for x £ 0
f (x ) =⎪⎨
⎪⎪ e2x + 2 for x > 0.
⎩
(b) Find f ¢(− 2) and f ¢(3).
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Calculus AB Practice Exam
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(a) Is f continuous at x = 0 ? Justify your answer.
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x)
(d) Let g be the function given by g (=
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(c) Explain why f ¢(0) does not exist.
x
∫− 1 f (t ) dt. Find g (1).
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6. A hive contains 35 hundred bees at time t = 0. During the time interval 0 £ t £ 4 hours, bees enter the hive at
a rate modeled by E (t ) =16 t − 3 t 2, where E (t ) is measured in hundreds of bees per hour. During the same
(t ) − 2 t + 15, where L(t ) is measured in hundreds of
time interval, bees leave the hive at a rate modeled by L=
bees per hour.
(b) Write an expression involving one or more integrals for the total number of bees, in hundreds, in the hive
at time t for 0 £ t £ 4 . Find the total number of bees in the hive at t = 4.
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Calculus AB Practice Exam
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(a) How many bees leave the hive during the time interval 0 £ t £ 2 ?
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(c) Find the minimum number of bees in the hive for 0 £ t £ 4 . Justify your answer.
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Calculus AB Practice Exam
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STOP
END OF EXAM
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Calculus AB Practice Exam