AP Calculus AP Review

Top 10 Errors on the AP Calculus Exam

http://www.pleacher.com/mp/mlessons/calc2004/examprep.html

Calculus AP Review

If

what is the equation of the tangent line to g(x) at x = -3?

132 3, 2 , ,

4f f and g x f x

42 3

3y x

Calculus AP Review

The velocity of a particle moving along a line is meters per second.

Find the distance traveled in meters during the time interval

Calculator ok

cosv t t

1 3x

4

Calculus AP Review

Find any local extrema for the function. Use 1st or 2nd derivative test.

23f x x

min imum of 0 at x=0

Calculus AP Review

Find max or min values of the function. Use 1st or 2nd derivative test.

3 22 3 12 14f x x x x

max of 34 at x = -2,

min of 7 at x=1

Calculus AP Review

Evaluate 2 14

lim3 2x

x

x

1

2

Calculus AP Review

Find the following limits:

0

sinlimx

x

x 0

1 coslimx

x

x

1 0

Calculus AP Review

Find the following limit:

0

sin 4limx

x

x

4

Calculus AP Review

If what is the value of

at the point (4,3)?

2 2 25x y 2

2

d y

dx

25

27

Calculus AP Review

Calculate:

2sin cosx x dx

3sin

3C

Calculus AP Review

No Calculator Question

What is the average value of

for the closed

interval ?

cossin 4 xf x x

02

x

6

ln 4

Calculus AP Review

Find 2 8

2 3

0 0

3 if x f x dx f t dt k

k

3Hint: Let u=x

Calculus AP Review

2

0

If 3 , what is ?x

F x t dt F x

22 3x x

No calculator problem

Region R is bounded by

A) Set up but do not evaluate an integral that gives the area of R.

B) Set up but do not evaluate an integral that gives the volume when region R is rotated

about the line

2 3 and 3 1f y y g y y

3x

4

2

1

3 1 3y y dy

4

22 2

1

3 4y y dy

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

curve and the curve

is revolved about the line x=8. Set up but do not evaluate the integral.

216y x 16 4y x

16

22 2

0

4 8 8x x dx

Calculus AP Review

Find the horizontal asymptotes of the graph of in the xy-plane.5 2

1 2

x

xy

1, 5y y

Evaluate each

1.

2.

1 2sind

xdx

24

dx

x

4

2

1

x

x

arcsin2

xC

Evaluate each

3.

4.

21

x

x

e dx

e

2 4 5

dx

x x

arctan xe C

arctan 2

41ln

3 1

x C

or

xC

x

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

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?

2 2tan and 4y x y x

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)

2 3 2y x x

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 degrees Fahrenheit per minute. To the nearest degree, what is the temperature of the pizza at time t=5 minutes?

0.4110 te

112 F

Calculus AP Review

Find the limit:

2

3 2lim

2 1x

x

x

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/calc2004/examprep.html