AP Calculus AP Review
Top 10 Errors on the AP
Calculus Exam

http://www.pleacher.com/mp/mlessons/c
alc2004/examprep.html
Calculus AP Review

3
f  2   3, f   2   , and g  x   f 1  x  ,
4
If
what is the equation of the tangent line to g(x)
at x = -3?
4
y  2   x  3
3
Calculus AP Review
The velocity of a particle moving along a line
is v  t    cos  t  meters per second.
 Find the distance traveled in meters during
the time interval 1  x  3
 Calculator ok

4
Calculus AP Review

Find any local extrema for the function. Use
1st or 2nd derivative test.
f  x  x
2
3
min imum of 0 at x=0
Calculus AP Review

Find max or min values of the function. Use
1st or 2nd derivative test.
f  x   2 x  3x  12 x  14
3
2
max of 34 at x = -2,
min of 7 at x=1
Calculus AP Review
x  14
lim
x  3  2 x
2

Evaluate
1

2
Calculus AP Review

Find the following limits:
sin x
lim
x 0
x
1
1  cos x
lim
x 0
x
0
Calculus AP Review

Find the following limit:
sin 4 x
lim
x 0
x
4
Calculus AP Review
2
d
y
x

y

25
 If
what is the value of
2
2
2
dx
at the point (4,3)?
25

27
Calculus AP Review

Calculate:
sin
x
cos
x
dx

2
3
sin
C
3
Calculus AP Review

No Calculator Question
What is the average value of
cos x
f  x    sin x  4
for the closed

interval 0  x 

2
?
6
 ln 4
Calculus AP Review
2

Find
 3x f  x  dx
2
0
3
8
if
 f t  dt  k
0
Hint: Let u=x3
k
Calculus AP Review
If F  x  
x2

t  3 dt , what is F   x  ?
0
2 x x2  3
No calculator problem

Region R is bounded by
f  y   y  3 and g  y   3 y  1
2

A) Set up but do not evaluate an integral that
gives the area of R.
  3 y  1   y  3 dy
4
2
1

B) Set up but do not evaluate an integral
that gives the volume when region R is rotated
about the line x  3
   3 y  4    y  dy
4
2
1
2 2
Math pick up line of the day By Leah
“I don’t like my current significant other.
Mind if I do a you-substitution?”
Find the volume of the solid that results
when the region bounded by the
2
y

16

x
curve
and the curve y  16  4 x
is revolved about the line x=8. Set up
but do not evaluate the integral.
16
   4 x  8    x  8  dx
2
0
2
2
Calculus AP Review

Find the horizontal asymptotes of the
x
5 2
graph of
in the xy-plane.
y
1  2x
y  1,
y 5
Evaluate each


1.
2.
d
sin 1 x 2
dx

dx
4  x2
2x
1  x4
x
arcsin  C
2
Evaluate each

3.
x
e dx
 1  e2 x
dx
 4.
 x2  4 x  5
arctan ex  C
arctan  x  2   C
or
1 x4
 ln
C
3 x 1
Math pick up line of the day by Leah

How is it that I can know so many digits
of pi and not know the 7 digits of your
phone number?
Calculus AP Review

The base of a solid is bounded by
2
2
y  tan x and y  4  x in the x-y plane.
Each cross section perpendicular to the
x-axis is a rectangle with one side in the
x-y plane, and whose height is 2. What
is the volume of the solid?
12.486
Math pick-up line of the day. By Leah
I
don’t know if you’re in my
range, but I’d sure like to take
you home to my domain.
Math pick-up line of the day by Leah

My love for you is like the first derivative
of a concave up function, because it
always increasing!
Calculus AP Review
A curve has a slope 2x+3 at each point
(x,y) on the curve. Find the equation of the
curve if it passes through the point (1,2)

y  x  3x  2
2
Calculus AP Review

A pizza, heated to a temperature of 350
degrees Fahrenheit, is taken out of an
oven and placed in a 75 degree room at
t=0. The temperature of the pizza is
changing at a rate of 110e0.4t degrees
Fahrenheit per minute. To the nearest
degree, what is the temperature of the
pizza at time t=5 minutes?
112 F
Calculus AP Review

Find the limit:
lim
x 
3x  2
2x 1
2
3
2
Leah’s Math Limerick
Because Leah loves math!
A dozen, a gross, and a score
Plus three times the square root of four
Divided by seven
Plus fives times eleven
Is nine squared, and not a bit more!
Top 10 Errors on the AP
Calculus Exam

http://www.pleacher.com/mp/mlessons/c
alc2004/examprep.html