AP Calculus AB/BC
Topic(s)
Limits, Limits with Substitution, Solving Limits by
Algebraic Manipulation, One-Sided Limits, Limits
from a Graph, Limits of Piece-Wise Functions
Unit 2
Topics and Homework
Homework
p.66 (7-13odd)(15-18 Explain why the limit cannot be
taken at the given value using graphing
terminology.)(19-27odd)
Limits at Infinity (Asymptotes and Holes), L’Hôpital’s p.66 (39-44)(51-54)(57-58)
p.76 (13,15)
Rule, Continuity, and Limit Definition of Continuity
p.84 (11-16)(19-20)
Quiz: Cumulative from Unit 1 & Limits (topics from
9/13
both boxes above this one)
Limit Definition of the Derivative
p.93 (29-30 using limit definition of the derivative)
p.105 (5,7,8)
p.114 (12,14,15)
Intermediate Value Theorem, Mean Value Theorem,
Unit 2 Supplemental Worksheet: Part I
Rolles Theorem, and Extreme Value Theorem
Chapter Review and AP Practice
Unit 2 Supplemental Worksheet: Part II
Test: Unit 2
9/17
Cumulative Review
Cumulative Review Worksheet #2
AP Calculus AB/BC
Supplemental Worksheet
Unit 1
I.Combining Rules (excluding trigonometric functions)
Find the derivative.
1 5
4.𝑔(𝑥) = (𝑥 2 + 𝑥)
1. 𝑓(𝑥) = √1 − 𝑥 3
5
3
5. ℎ(𝑥) = (𝑥 2 − 1)2 (𝑥 3 + 5)
2. 𝑓(𝑥) = √𝑥 2 − 1
𝑥−3 2
6. ℎ(𝑥) = √𝑥(2𝑥 3 + 5 − 6𝑥 2 )
3. 𝑔(𝑥) = (𝑥 2 +1)
II. Inverse Functions and Their Derivatives (excluding trigonometric functions)
Find (𝑓 −1 )′ (𝑎).
1. 𝑓(𝑥) = 𝑥 3 + 2𝑥 − 1,
𝑎 = −1
2. 𝑓(𝑥) = √5𝑥 6 − 2𝑥 3 + 3𝑥,
𝑎=2
3. 𝑓(𝑥) = √𝑥 3 − 4𝑥 2 + 7,
4. 𝑓(𝑥) = √𝑥 + 3,
𝑎=2
𝑎=2
III.Combining Rules (including trigonometric functions)
1.
f (t ) for f (t ) 
t2
t 1
2.
f ( x ) for f ( x) 
x2  1
x3
3.
dz
3
4
for z  ( x  1) (5  x)
dx
4.
f ( ) for f ( ) 
5.
f (  ) for f (  ) 
6.
h( y ) for h( y ) 
7.
g ( ) for g ( )  3  tan 2 (4 )
15. g ( ) for g ( )  3 tan(5 )
8.
dy
3
for y  (csc1  sec u)
du
16. f ( x ) for f ( x)  x cos
1
tan(2 )
 y  y6
1 
cos y
1  sin y
9. g ( z ) for g ( z ) 
az 2
a2  z 2
10. f ( x ) for f ( x) 
x2
2  x
t
11. f (t ) for f (t ) 
12. f ( x ) for f ( x) 
13.
3
t3 1
x 2  bx  c
a
dz
3
4
for z  ( x  1) (5  x)
dx
14. f ( m ) for f (m) 
1
sec(2m)

3

x 1
Some problems borrowed from: Calculus 7th Edition: Larson, Hostetler and Edwards, Visual CalculusLawrence S. Husch and University of Tennessee, Knoxville, Mathematics Department, http://math.arizona.edu, AP College Board Released Questions
AP Calculus AB/BC
Cumulative Review #1
Complete the problems below on unlined paper. Label each problem and show all applicable work. Be sure to
highlight the answer and include the correct multiple choice letter. Draw a line to separate each problem.
Points will be deducted for not following the proper format.
Practice AB #6
__________________________________________________________________________________________
2008 AB #24
__________________________________________________________________________________________
1998 AB/BC #87
__________________________________________________________________________________________
1998 BC #92
_________________________________________________________________________________
1998 AB #8
1988 BC #11
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1998 AB #10
__________________________________________________________________________________________
1997 AB #12
__________________________________________________________________________________________
2008 BC #90
__________________________________________________________________________________________
1973 BC #39
__________________________________________________________________________________________
1998 AB #18
1988 BC #40
Some problems borrowed from: AP College Board Released Questions
AP Calculus AB/BC
Cumulative Review #1
Complete the problems below on unlined paper. Label each problem and show all applicable work. Be sure to
highlight the answer and include the correct multiple choice letter. Draw a line to separate each problem.
Points will be deducted for not following the proper format.
1.
__________________________________________________________________________________________
2.
__________________________________________________________________________________________
3.
__________________________________________________________________________________________
4.
_________________________________________________________________________________
5.
_________________________________________________________________________________
6.
______________________________________________________________________________________
7.
__________________________________________________________________________________________
8.
__________________________________________________________________________________________
9.
__________________________________________________________________________________________
10.
__________________________________________________________________________________________
11.
__________________________________________________________________________________________
12.
Some problems borrowed from: AP College Board Released Questions
AP Calculus AB/BC
Cumulative Review #1
Complete the problems below on unlined paper. Label each problem and show all applicable work. Be sure to
highlight the answer and include the correct multiple choice letter. Draw a line to separate each problem.
Points will be deducted for not following the proper format.
1.
__________________________________________________________________________________________
2.
__________________________________________________________________________________________
3.
__________________________________________________________________________________________
4.
_________________________________________________________________________________
5.
_________________________________________________________________________________
6.
______________________________________________________________________________________
7.
__________________________________________________________________________________________
8.
__________________________________________________________________________________________
9.
__________________________________________________________________________________________
10.
__________________________________________________________________________________________
11.
__________________________________________________________________________________________
12.
Some problems borrowed from: AP College Board Released Questions