Mrs. La Massa - Math Classes

AP CALCULUS

CHAPTER 1 TOPICS

TOPIC 1: What is a function?

Sec. 1.1 #1-5, 6-14(calc), 15, 16, 17a, 18, 19, 20, 25-28

TOPIC 2: Basic Functions and Transformations

Sec. 1.2 #1-6, 7-12, 13-17, 19, 20-25

http://people.hofstra.edu/Stefan_Waner/calctopic1/scaledgraph.html

TOPIC 3: Linear functions and equations of lines

Sec. 1.3 #1-4

TOPIC 4: Exponential functions and rules for exponents

Sec. 1.4 # 1-5

TOPIC 5: Inverse functions

Sec. 1.6 # 1-4, 5-8, 9, 12-15, 16-23

http://www.ltcconline.net/greenl/java/IntermedCollegeAlgebra/Inverse/inverse1.html

TOPIC 6: Logs and the properties of logs

Sec. 1.7 #2-4

TOPIC 7: Combining functions

Sec. 1.8 # 1

http://www.ltcconline.net/greenl/java/IntermedCollegeAlgebra/FunctionOps/FunctionOps.html

TOPIC 8: Polynomial functions and their graphs

Sec. 1.8 # 5, 6, 10, 14

TOPIC 9: Rational functions

Sec. 1.8 # 2, 8, 11, 12, 13

http://www.explorelearning.com/index.cfm?method=cResource.dspView&ResourceID=152

TOPIC 10: Symmetry

Sec. 1.8 # 3, 21-24

TOPIC 11: Composite functions

Sec. 1.9 #1-8

http://www.ltcconline.net/greenl/java/IntermedCollegeAlgebra/PairOfTable/PairOfTable.html

TOPIC 12: Trig functions

Sec. 19 #1, 2

http://www.themathpage.com/atrig/graphs-trig.htm

AP CALCULUS - LIMITS AND CONTINUITY

TOPIC 1: WHAT IS A LIMIT? WHEN DOES A LIMIT EXIST?

WWW.CALCULUS-HELP.COM – LIMIT LESSONS

TOPIC 2; THEOREMS ON LIMITS

TEXT P. 129 – COPY INTO NOTEBOOK

WORKSHEET SEC. 2.1 FINNEY #1-18

TOPIC 3: FIND LIMIT FROM GRAPH

WORKSHEET 2.1 #19-26, 63-66

TOPIC 4: FIND LIMIT FROM A CHART OF VALUES

WORKSHEET 2.1 #27-32

TOPIC 5: LEFT-HAND AND RIGHT-HAND LIMITS

WORKSHEET 2.. PART II #39-56

WORKSHEET N

BEST TEXT P. 138 #12-21, 30 C-F

TOPIC 6: WHEN IS A FUNCTION CONTINUOUS?

WORKSHEET P #1-6, 15-30

` WORKSHEET Q

TOPIC 7: REMOVABLE DISCONTINUITIES

WORKSHEET P #31-38

TOPIC 8: DRAWING FUNCTIONS WITH DISCONTINUITIES

WORKSHEET S

TOPIC 9: MAX/MIN THEOREM

INTERMEDIATE VALUE THEOREM

TOPIC 10: TRIG LIMITS

WORKSHEET R TOP #1-16

TOPIC 11: LIMITS AT INFINITY

WORKSHEET R BOTTOM #1-20, 31-40

TOPIC 12: LIMITS WITH RADICALS IN NUMERATOR OR DENOMINATOR

TOPIC 13: END BEHAVIOR ASYMPTOTES

WORKSHEET R BOTTOM #21-28

REVIEW OF LIMITS AND CONTINUITY: WORKSHEET U

AP CALCULUS CHAPTER 2 – DERIVATIVES

TOPIC 1: AVERAGE RATE OF CHANGE

ESTIMATING INSTANTANEOUS RATE OF CHANGE

CALCULATOR WORKSHEET #10, WORKSHEET V

H/H TEXT P. 94 #4, 5, 6, 7

http://www.ies.co.jp/math/java/calc/heihen/heihen.html

http://www.ies.co.jp/math/java/calc/limsec/limsec.html

TOPIC 2: ESTIMATING SLOPES

WORKSHEET W

H/H TEXT P. 102 # 2, 3, 4, 8, 9, 12

TOPIC 3: USE THE DEFINITION OF THE DERIVATIVE

TO FIND THE DERIVATIVE AND THE

EQUATION OF THE TANGENT LINE

H/H TEXT P. 103 #13, 14, 20, 15, 19, 17, 22

TOPIC 4: SKETCH THE GRAPH OF THE DERIVATIVE

CALCULATOR WORKSHEET #11, WORKSHEET X

H/H TEXT P. 110 #1-10, 17, 18, 23-29

WORKSHEET Y – MATCHING COLUMN

Graph of the derivative:

http://mathdemos.gcsu.edu/mathdemos/derivative_sketch/sketch_the_derivative.html

http://people.hofstra.edu/Stefan_Waner/calctopic1/derivgraph.html

http://www.ltcconline.net/greenl/java/Other/DerivativeGraph/classes/DerivativeGraph.html

http://www.univie.ac.at/future.media/moe/tests/diff1/ablerkennen.html

http://www.ies.co.jp/math/java/calc/doukan/doukan.html

http://mathplotter.lawrenceville.org/mathplotter/mathPage/derivative.htm

TOPIC 5: EXISTENCE OF DERIVATIVES

WORKSHEET Z

TOPIC 6: DERIVATIVE RULES

POWER RULE (INC. FRACTIONAL AND NEGATIVE POWERS)

WORKSHEET 2A #1-16

TOPIC 7: SIMPLIFY FIRST TO FIND DERIVATIVES

WORKSHEET 2A #23, 24, 27, 28

WORKSHEET 2B #1, 2, 3, 7, 25-30

H/H TEXT P. 195 #4-23

http://www.ltcconline.net/greenl/DerivativeRules/WebForm1.aspx

TOPIC 8: DERIVATIVES OF e^x, ln(x), sin(x), cos(x), a^x

H/H TEXT P. 201 #1-10

TOPIC 9: PRODUCT RULE FOR DERIVATIVES

WORKSHEET 2A #17-22

WORKSHEET 2B # 31, 40, 43, 50-52, 54, 55

H/H TEXT P. 206 #3-10

TOPIC 10: QUOTIENT RULE FOR DERIVATIVES AND

DERIVATIVE OF tan(x) and sec(x)

WORKSHEET 2A # 25, 26, 33, 34

WORKSHEET 2B #8-11, 32, 33, 38, 18, 19

H/H TEXT P. 206 # 11-23, 34, 35

TOPIC 11: CHAIN RULE WITH POLYNOMIALS, a^u, e^u

H/H TEXT P. 211 #1-24, 34, 35

WORKSHET 2C, 2D

TOPIC 12: CHAIN RULE WITH TRIG FUNCTIONS

H/H TEXT P. 217 #1-26

WORKSHEET 2E

TOPIC 13: CHAIN RULE WITH ln(u)

H/H TEXT P. 222 #1-12

TOPIC 14: IMPLICIT DIFFERENTIATION

H/H TEXT P. 226 #1-6, 8, 13

TOPIC 15: DERIVATIVES OF ARCSIN(u) AND ARCTAN(u)

H/H TEXT P. 222 #15-18

REVIEW QUESTIONS: H/H TEXT P. 237 #1-99

BEST TEXT P.

Applications of Derivatives

1. Equation of the tangent line

Best p. 200 #18, p. 206 #17,18, p216 # 31,36 p. 206 #17,18 p. 225 #38-41

2. Find where the tangent is horizontal.

Best p. 200 #19

3. Find where the tangent is equal to a given (non-zero) value.

Best p. 201 #24, 25

4. Velocity and acceleration

Best p. 200 #20, 21,30, 31, 32 p. 206# 20, 21, 22 p. 269 # 22-27

5. Where a function is increasing, decreasing, concave up, down.

Best p. 201 #23, 28, 29

6. Find maximum, minimum, points of inflection

Best p. 260 # 1 – 12 p. 268 #1, 4 – 21 p. 269 # 28 - 31

7. Implicit differentiation

Best p. 229 # 1 - 26

8. Related rates

Best p. 235 # 1 -15, 18 – 24

9. Linear approximations and differentials

Best p. 243 # 1 - 9

10. Graph of derivative

Best p. 201 #26 p. 117 # 13-16, 18 – 21 p. 126 #5 p. 268 #3

11. Graph of second derivative

Best p. 201 #27 p. 126 #5

12. Absolute (global) maximum and minimum

Best p. 261 #20 – 31

13. Applied Maximum and Minimum

Best p. 281 # 1 – 18

14. Mean Value theorem

Best p. 285 # 1 -12