Be Prepared
for the
AP
Calculus
Exam
Mark Howell
Gonzaga High School, Washington, D.C.
Martha Montgomery
Fremont City Schools, Fremont, Ohio
Practice exam contributors:
Benita Albert
Oak Ridge High School, Oak Ridge, Tennessee
Thomas Dick
Oregon State Uni
Solutions to the 1999 AP Calculus BC Exam Free Response Questions
Louis A. Talman Department of Mathematical & Computer Sciences Metropolitan State College of Denver
Problem 1.
a.
t2 ParametricPlotA9 - Log@1 + tD, 3 Sin@tD=, 2 8t, 0, p<, AspectRatio Auto
Solutions to the 2000 AP Calculus BC Exam Free Response Questions
Louis A. Talman Department of Mathematical & Computer Sciences Metropolitan State College of Denver
Problem 1.
a.
We must first find the point in the first quadrant where -x = 1 - cos x. W
APCalcBC2001.nb
1
Solutions to the 2001 AP Calculus BC Exam
Louis A. Talman Metropolitan State College of Denver
1.
a.
Because the object is at H4, 5L when t = 2, we can obtain the slope of the line tangent to the curve when t = 2 by finding the y y x va
BC2002b.nb
1
Solutions to the 2002 AP Calculus BC Exam (Form B)
Louis A. Talman Metropolitan State College of Denver
1.
a.
The graph should look like this:
In[1]:=
x@t_D = Sin@3 tD; y@t_D = 2 t; ParametricPlot@8x@tD, y@tD<, 8t, -p, p<, PlotRange 88-2.5,
BC2002.nb
1
Solutions to the 2002 AP Calculus BC Exam
Louis A. Talman Metropolitan State College of Denver
1.
a.
Here is the region between the graphs on the specified interval:
1 p1 = PlotA8x , Log@xD<, 9x, , 1=, PlotRange 88-1, 3<, 8-1, 3<, 2 AspectRat
BC2003b.nb
1
Solutions to the 2003 AP Calculus BC Exam (Form B)
Louis A. Talman Department of Mathematical & Computer Sciences Metropolitan State College of Denver
Problem 1.
a.
If f @xD = 4 x2 - x3 , and g@xD = 18 - 3 x, then the curves have an intersec
BC2003.nb
1
Solutions to the 2003 AP Calculus BC Exam
Louis A. Talman Department of Mathematical & Computer Sciences Metropolitan State College of Denver
Problem 1.
a.
The curves intersect where
a = x . FindRootA 0.2387341
! x = e-3 x :
1 ! x -3 x , 9x,
Solutions to the 2004 AP Calculus BC Exam (Form B) Free Response Questions
Louis A. Talman Department of Mathematical & Computer Sciences Metropolitan State College of Denver
Problem 1. (Thanks to Bill Kehlenbeck for pointing out a careless error that ren
Solutions to the 2004 AP Calculus BC Exam Free Response Questions
Louis A. Talman Department of Mathematical & Computer Sciences Metropolitan State College of Denver
Problem 1.
We are given the traffic flow, i.e., the rate at which cars pass through an in
Solutions to the 2005 AP Calculus AB (Form B) Exam Free Response Questions
Louis A. Talman Department of Mathematical & Computer Sciences Metropolitan State College of Denver
Problem 1.
a)
The general acceleration vector is: D@812 t - 3 t2 , Log@1 + Ht -
Solutions to the 2005 AP Calculus BC Exam Free Response Questions
Louis A. Talman Department of Mathematical & Computer Sciences Metropolitan State College of Denver
Problem 1.
a)
1 FindRootA + Sin@p xD 4-x , 8x, 0<E 4 8x 0.17821805< a = x . % So the req
BC 2006B.nb
1
Solutions to the 2006 AP Calculus BC Exam (Form B) Free Response Questions
Louis A. Talman Department of Mathematical & Computer Sciences Metropolitan State College of Denver
Part A
Problem 1:
a)
We must first find the intersection of the c
BC2006.nb
1
Solutions to the 2006 AP Calculus BC Exam Free Response Questions
Louis A. Talman Department of Mathematical & Computer Sciences Metropolitan State College of Denver
Part A
Problem 1.
a)
The curves intersect where ln x = x - 2.
In[1]:= Out[1]
Solutions to the 2007 AP Calculus BC (Form B) Exam Free Response Questions
Louis A. Talman Department of Mathematical & Computer Sciences Metropolitan State College of Denver
Part A
Problem 1
a)
The curve y = e2 x - x intersects the line y = 2 where 2 x
Solutions to the 2007 AP Calculus BC Exam Free Response Questions
Louis A. Talman Department of Mathematical & Computer Sciences Metropolitan State College of Denver
Part A
Problem 1.
a)
The limits of the integral that gives the area are the solutions of
Solutions to the 1999 AP Calculus BC Exam Free Response Questions
Louis A. Talman Department of Mathematical & Computer Sciences Metropolitan State College of Denver
Problem 1.
a.
t2 ParametricPlotA9 - Log@1 + tD, 3 Sin@tD=, 2 8t, 0, p<, AspectRatio Auto
APCalcAB2001.nb
1
Solutions to the 2001 AP Calculus AB Exam
Louis A. Talman Metropolitan State College of Denver
1.
a.
Let's solve the equation 2 - x3 = Tan@xD numerically and call the solution b:
FindRoot@2 - x3 Tan@xD, 8x, 1.0<D 8x 0.90215508< b = x .
Solutions to the 2008 AP Calculus BC Exam Free Response Questions
Louis A. Talman Department of Mathematical & Computer Sciences Metropolitan State College of Denver
Part A
Problem 1.
a)
The area of the given region R is 0 Asin Hp xL - Ix3 - 4 xME x.
2
3
Be Prepared
for the
AP
Calculus
Exam
Mark Howell
Gonzaga High School, Washington, D.C.
Martha Montgomery
Fremont City Schools, Fremont, Ohio
Practice exam contributors:
Benita Albert
Oak Ridge High School, Oak Ridge, Tennessee
Thomas Dick
Oregon State Uni
Be Prepared
for the
Calculus
Exam
Mark Howell
Gonzaga High School, Washington, D.C.
Martha Montgomery
Fremont City Schools, Fremont, Ohio
Practice exam contributors:
Benita Albert
Oak Ridge High School, Oak Ridge, Tennessee
Thomas Dick
Oregon State Univer
Be Prepared
for the
Calculus
Exam
Mark Howell
Gonzaga High School, Washington, D.C.
Martha Montgomery
Fremont City Schools, Fremont, Ohio
Practice exam contributors:
Benita Albert
Oak Ridge High School, Oak Ridge, Tennessee
Thomas Dick
Oregon State Univer
Be Prepared
for the
Calculus
Exam
Mark Howell
Gonzaga High School, Washington, D.C.
Martha Montgomery
Fremont City Schools, Fremont, Ohio
Practice exam contributors:
Benita Albert
Oak Ridge High School, Oak Ridge, Tennessee
Thomas Dick
Oregon State Univer
Be Prepared
for the
Calculus
Exam
Mark Howell
Gonzaga High School, Washington, D.C.
Martha Montgomery
Fremont City Schools, Fremont, Ohio
Practice exam contributors:
Benita Albert
Oak Ridge High School, Oak Ridge, Tennessee
Thomas Dick
Oregon State Univer
Be Prepared
for the
Calculus
Exam
Mark Howell
Gonzaga High School, Washington, D.C.
Martha Montgomery
Fremont City Schools, Fremont, Ohio
Practice exam contributors:
Benita Albert
Oak Ridge High School, Oak Ridge, Tennessee
Thomas Dick
Oregon State Univer
Solutions to the
1998 AP Calculus AB Exam
Free Response Questions
Louis A. Talman
Department of Mathematical & Computer Sciences
Metropolitan State College of Denver
Problem 1.
a.
The area of the region R is
4
0
!
x x
16
3
b.
SolveA
h
0
8
!
x x , hE
3
8
Solutions to the
1999 AP Calculus AB Exam
Free Response Questions
Louis A. Talman
Department of Mathematical & Computer Sciences
Metropolitan State College of Denver
Problem 1.
a.
If v@tD = t sin t2 for t 0, then when t = 1.5, we have
v@t_D = t Sin@t2 D
Solutions to the 2000 AP Calculus AB Exam Free Response Questions
Louis A. Talman Department of Mathematical & Computer Sciences Metropolitan State College of Denver
Problem 1.
a.
We must first find the point in the first quadrant where -x = 1 - cos x. W
AP Calculus Solutions
2009 Calculus AB Free Response
Alexander MacLane
APCalculusTips.com
2
http:/APCalculusTips.com
2009 AP Calculus AB Free
Response Solutions
Problem 1
0.3
0.2
y 0.1
0
0
0.1
0.2
5
10
x
Caren rides her bicycle along a straight road from
Solutions to the
1998 AP Calculus BC Exam
Free Response Questions
Louis A. Talman
Department of Mathematical & Computer Sciences
Metropolitan State College of Denver
Problem 1.
a.
The area of the region R is
32
I8 - x M x
4
0
96
5
b.
The volume of the