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 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 BC
2009 SCORING GUIDELINES
Question 1
Caren rides her bicycle along a straight road from home to school, starting at home at time t = 0 minutes
and arriving at school at time t = 12 minute
AP CALCULUS BC
2009 SCORING GUIDELINES
Question 2
The rate at which people enter an auditorium for a rock concert is modeled by the function R given by
R( t ) = 1380t 2 675t 3 for 0 t 2 hours; R( t )
AP CALCULUS BC
2009 SCORING GUIDELINES
Question 3
A diver leaps from the edge of a diving platform into a pool below. The
figure above shows the initial position of the diver and her position at a lat
AP CALCULUS BC
2009 SCORING GUIDELINES
Question 4
dy
= 6 x 2 x 2 y. Let y = f ( x ) be a particular solution to this
dx
differential equation with the initial condition f ( 1) = 2.
Consider the differ
AP CALCULUS BC
2009 SCORING GUIDELINES
Question 5
x
2
3
5
8
13
f ( x)
1
4
2
3
6
Let f be a function that is twice differentiable for all real numbers. The table above gives values of f for
selected po
AP CALCULUS BC
2009 SCORING GUIDELINES
Question 6
The Maclaurin series for e x is e x = 1 + x +
x 2 x3
+
+
2
6
+
xn
+
n!
. The continuous function f is defined
2
e( x 1) 1
for x 1 and f (1) = 1. The f
AP Calculus BC
2009 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 (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 th
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
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 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 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 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
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
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 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
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
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 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 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
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
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
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