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 o
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
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 t
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.
AP Calculus BC
2011 Free-Response Questions Scoring Statistics
Question
Mean
Standard
Deviation
Number of
Points Possible
1
5.24
2.64
9
2
5.48
2.84
9
1 to 2
10.72
4.91
18
3
1.67
1.27
3
4
3.84
1.91
6
3
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 i
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
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 th
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 figur
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 >
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 functi
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
= si
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. Fo
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 seri
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 st
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 sho
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
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. Foun
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 i
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 soluti
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 gi
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
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. Fi
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
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