AP Calculus AB
Syllabus 3
Course Design and Philosophy
Students do best when they have an understanding of the conceptual underpinnings
of calculus. Rather than making the course a long laundry list of skills that students
have to memorize, we stress the
AP Calculus AB
Syllabus 2
Course Outline
By successfully completing this course, you will be able to:
Work with functions represented in a variety of ways and understand the
connections among these representations.
Understand the meaning of the deriva
AP Calculus AB
Syllabus 1
Course Overview
My main objective in teaching AP Calculus is to enable students to appreciate the
beauty of calculus and receive a strong foundation that will give them the tools to
succeed in future mathematics courses. Students
AP Calculus BC
2011 Free-Response Questions
Form B
About the College Board
The College Board is a mission-driven not-for-profit organization that connects students to college success and opportunity.
Founded in 1900, the College Board was created to expan
AP Calculus BC
2011 Scoring Guidelines
The College Board
The College Board is a not-for-profit membership association whose mission is to connect students to college success and
opportunity. Founded in 1900, the College Board is composed of more than 5,70
AP CALCULUS BC
2011 SCORING GUIDELINES
Question 6
()
Let f ( x ) = sin x 2 + cos x. The graph of y = f ( 5) ( x ) is
shown above.
(a) Write the first four nonzero terms of the Taylor series for
sin x about x = 0, and write the first four nonzero terms
()
AP CALCULUS BC
2011 SCORING GUIDELINES
Question 5
At the beginning of 2010, a landfill contained 1400 tons of solid waste. The increasing function W models
the total amount of solid waste stored at the landfill. Planners estimate that W will satisfy the d
AP CALCULUS BC
2011 SCORING GUIDELINES
Question 4
The continuous function f is defined on the interval 4 x 3.
The graph of f consists of two quarter circles and one line
segment, as shown in the figure above.
Let g ( x ) = 2 x +
x
0 f ( t ) dt.
(a) Find g
AP CALCULUS BC
2011 SCORING GUIDELINES
Question 3
Let f ( x ) = e2 x . Let R be the region in the first quadrant bounded by the
graph of f, the coordinate axes, and the vertical line x = k , where
k > 0. The region R is shown in the figure above.
(a) Writ
AP CALCULUS BC
2011 SCORING GUIDELINES
Question 2
t
(minutes)
0
2
5
9
10
H (t )
(degrees Celsius)
66
60
52
44
43
As a pot of tea cools, the temperature of the tea is modeled by a differentiable function H for 0 t 10, where
time t is measured in minutes an
AP CALCULUS BC
2011 SCORING GUIDELINES
Question 1
At time t, a particle moving in the xy-plane is at position ( x( t ) , y ( t ) ) , where x( t ) and y ( t ) are not explicitly
dy
dx
= 4t + 1 and
= sin t 2 . At time t = 0, x( 0 ) = 0 and y ( 0 ) = 4.
give
AP Calculus BC
2011 Scoring Guidelines
Form B
The College Board
The College Board is a not-for-profit membership association whose mission is to connect students to college success and
opportunity. Founded in 1900, the College Board is composed of more th
AP CALCULUS BC
2011 SCORING GUIDELINES (Form B)
Question 6
(
)
Let f ( x ) = ln 1 + x3 .
x 2 x3 x 4
xn
+
+ + ( 1)n +1
+
n
2
3
4
the first four nonzero terms and the general term of the Maclaurin series for f.
(a) The Maclaurin series for ln (1 + x ) is x
AP CALCULUS BC
2011 SCORING GUIDELINES (Form B)
Question 5
t
(seconds)
0
v( t )
(meters per second)
40
60
100 136
B( t )
(meters)
10
9
49
2.0
2.3
2.5 4.6
Ben rides a unicycle back and forth along a straight east-west track. The twice-differentiable functi
AP CALCULUS BC
2011 SCORING GUIDELINES (Form B)
Question 3
The functions f and g are given by f ( x ) = x and g ( x ) = 6 x.
Let R be the region bounded by the x-axis and the graphs of f and
g, as shown in the figure above.
(a) Find the area of R.
(b) The
AP CALCULUS BC
2011 SCORING GUIDELINES (Form B)
Question 2
The polar curve r is given by r ( ) = 3 + sin , where 0 2 .
(a) Find the area in the second quadrant enclosed by the coordinate axes and the graph of r.
(b) For
, there is one point P on the pola
AP Calculus BC
2010 Free-Response Questions
The College Board
The College Board is a not-for-profit membership association whose mission is to connect students to college success and
opportunity. Founded in 1900, the College Board is composed of more than
AP Calculus BC
2010 Scoring Guidelines
The College Board
The College Board is a not-for-profit membership association whose mission is to connect students to college success and
opportunity. Founded in 1900, the College Board is composed of more than 5,70
AP CALCULUS BC
2010 SCORING GUIDELINES
Question 5
dy
= 1 y. Let y = f ( x ) be the particular solution to this differential
dx
equation with the initial condition f (1) = 0. For this particular solution, f ( x ) < 1 for all values of x.
Consider the diffe
AP CALCULUS BC
2010 SCORING GUIDELINES
Question 3
A particle is moving along a curve so that its position at time t is ( x( t ) , y ( t ) ) , where x( t ) = t 2 4t + 8 and
y ( t ) is not explicitly given. Both x and y are measured in meters, and t is meas
AP CALCULUS BC
2010 SCORING GUIDELINES (Form B)
Question 6
The Maclaurin series for the function f is given by f ( x ) =
( 1)n ( 2 x )n
n 1
n=2
on its interval of convergence.
(a) Find the interval of convergence for the Maclaurin series of f. Justify you
AP CALCULUS BC
2010 SCORING GUIDELINES (Form B)
Question 5
1
4x
, for all x > 0.
and g ( x ) =
x
1 + 4 x2
(a) Find the absolute maximum value of g on the open interval ( 0, ) if the maximum exists. Find the
absolute minimum value of g on the open interval
AP CALCULUS BC
2010 SCORING GUIDELINES (Form B)
Question 3
t
0
2
4
6
8
10 12
P(t)
0
46 53 57 60 62 63
The figure above shows an aboveground swimming pool in the shape of a cylinder with a radius of 12 feet and a
height of 4 feet. The pool contains 1000 cu
AP CALCULUS BC
2010 SCORING GUIDELINES (Form B)
Question 2
The velocity vector of a particle moving in the plane has components given by
() ()
dx
= 14cos t 2 sin et
dt
and
()
dy
= 1 + 2sin t 2 , for 0 t 1.5.
dt
At time t = 0, the position of the particle
AP CALCULUS BC
2010 SCORING GUIDELINES (Form B)
Question 1
In the figure above, R is the shaded region in the first quadrant bounded by the
graph of y = 4ln ( 3 x ) , the horizontal line y = 6, and the vertical line x = 2.
(a) Find the area of R.
(b) Find