AP Calculus
Teacher: Mr. Bloom
E-mail:
blooma@northwest.k12.pa.us
Wikispace: http://mrbloomsmath.wikispaces.com
Class Rules- I have a few simple rules:
I expect you to be quiet and cooperative when I am speaking.
Be respectful of others.
Be responsible. (This includes seeing me for any missed work when you are absent.)
Always use a pencil for doing math problems.
I am here to help you, please let me know if you need help with any of the material we
cover.
Grading policy
Each marking period your grade will be based on quizzes, tests, homework (possibly),
and group work.
Homework- Doing your homework is also very important. You get good at something by
practicing and homework is the way you practice math. Some homework’s may be
collected and checked for correctness.
Tests
Tests will include the material that has been covered since the previous test. The first test
will be the material covered since the beginning of the year.
Quizzes
There will be quizzes during the marking period. Save your returned quizzes to study for
the final exam.
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Notebooks- Taking good notes is very important. Get a notebook that you can use for
this class. Get a notebook partner. If you are absent, you are still responsible for the
notes, get them from your notebook partner if you are absent.
Primary Text
Stewart, James. Calculus – Concepts and Contexts. 3rd ed. Thomson Brooks/Cole, 2006
Technology
Texas Instruments 89 Titanium graphing calculators will be used in class almost daily.
Students will also be issued a Texas Instruments 89 graphing calculator for use at home
to complete homework assignments.
Methodologies and Strategies
Mathematics is a subject that continues to build upon previously learned concepts and
material. A major focus of the course will be instruction that facilitates student
understanding of the connection between concepts. The students not only will need to see
the connection between concepts, but also see how the material that is covered can be
represented in multiple ways: verbally, numerically, graphically, and/or analytically.
Students will need to apply all previously gained mathematical knowledge to understand
and at times discover links between concepts or to learn new ones. The Texas
Instruments 89 graphing calculators will be used to assist in discovery exercises and to
expedite mathematical procedures to lead to higher-level concepts. Examples of
calculator usage to expedite mathematical procedures would be to factor a trinomial or to
solve a polynomial.
Students will be able to clearly write and/or verbally explain mathematical concepts and
answers to exercises. As important as it is for students to understand material and
concepts, it is just as important that they can convey concepts and solutions to others. The
ability to be able to communicate Calculus concepts is vital because Calculus is
something that can be found in many other disciplines such as Physics, Finance, and
Chemistry. The concept of communication, both written and oral, will be reinforced
throughout the course with the use of free-response questions.
Topic Outline
The topic outline was taken from the section break down used in the primary text
Calculus – Concepts and Contexts
I. Functions and Graphs
A. Functions and Models (Chapter 1) Approximately 2 weeks
1. Four Ways to Represent a Function
2. Essential Functions
3. Transformations and Combinations of Functions
4. Graphing Calculators and Computers
5. Exponential Functions
6. Inverse Functions and Logarithms
II. Limits and Derivatives
B. Limits and Derivatives (Chapter 2) Approximately 3 weeks
1. Tangents and Velocity
2. The Limit of a Function
3. Using Limit Laws
4. Continuity
5. Limits Involving Infinity
6. Tangents, Velocities, and Other Rates of Change
7. Derivatives
8. The Derivative as a Function
9.
What Derivatives Tell Us About the Original Function
C. Differentiation Rules (Chapter 3) Approximately 5 weeks
1. Derivatives of Polynomials and Exponential Functions
2. The Product and Quotient Rules
3. Rates of Change in the Natural and Social Sciences
4. Derivatives of Trigonometric Functions
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5. The Chain Rule
6. Implicit Differentiation
7. Derivatives of Logarithmic Functions
8. Linear Approximations and Differentials
D. Applications of Differentiation (Chapter 4) Approximately 5 weeks
1. Related Rates
2. Maximum and Minimum Values
3. Derivatives and the Shapes of Curves
4. Graphing with Calculus and Calculators
5. Indeterminate Forms and l’Hospital’s Rule
6. Optimization Problems
7. Application to Business and Economics
8. Newton’s Method
9. Antiderivatives
III. Integrals
A. Integrals (Chapter 5) Approximately 5 weeks
1. Areas and Distances
2. The definite Integral
3. Evaluating Definite Integrals
4. The Fundamental Theorem of Calculus
5. The Substitution Rule
6. Integration by Parts
7. Additional Techniques of Integration
8. Integration Using Tables
9. Approximate Integration
10. Improper Integrals
B. Applications of Integration (Chapter 6) Approximately 5 weeks
1. More about Area
2. Volumes
3. Arc Length
4. Average Value of a Function
5. Applications to Physics and Engineering
6. Applications to Economics and Biology
7. Probability
IV. Differential Equations
A. Differential Equations (Chapter 7) Approximately 1 week
1. Direction Fields and Euler’s Method
Review for AP Exam Approximately 4 weeks
V. Infinite Sequences and Series
A. Infinite Sequences and Series (Chapter 8) Approximately 4 weeks
1. Sequences
2. Series
3. Power Series
4. Taylor and Maclaurin Series
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The following is the proposed list of sections and assignments we will complete this
year. This list is subject to change.
QUARTER 1
Section 1.1 #’s 1-4, 8, 11, 15, 19, 27-31, 41, 43, 57, 61, 65-67
Section 1.2 #’s 1, 3, 4, 10, 11, 15(chirps are independent temperature is dependent), 19
Section 1.3 #’s 1, 3, 4, 5-7, 10, 13, 29, 32, 35, 36, 51
Quiz 1 Sec 1.1-1.3
Section 1.4 #’s 3, 5, 17, 18, 19, 27, 28
Section 1.5 #’s 1, 2, 3, 7, 13, 15, 17, 20, 25 skip part d
Section 1.6 #’s 1, 2, 8, 12, 15, 26, 29
Chapter 1 Test Sec. 1.1-1.6
Section 2.1 #’s 2, 5, 7a
Section 2.2 #’s 1, 2, 4, 9, 13, 18
Section 2.3 #’s 1, 2, 8, 13, 15, 16, 18, 25, 26, 29
Section 2.4 #’s 1, 2, 4, 8, 14, 23, 25, 39
Section 2.5 #’s 1, 4, 5, 6, 11, 13, 15-24, 27, 28, 44
Quiz 2
Section 2.6 #’s 2, 3, 4, 7, 8, 9, 15, 17, 24ab, 27
Section 2.7 #’s 4, 10, 13-16, 28, 31
Section 2.8 #’s 1, 2, 3, 14-16, 17abc, 19, 21, 30ab, 31-33, 50
Test 2 Sec. 2.1-2.8
Section 2.9 #’s 2, 3, 6, 8, 15-17
Section 3.1 #’s 4-15, 19, 26, 29, 30, 37-42
Section 3.2 #’s 1, 2, 4-8, 18, 24, 36a, 42
Section 3.3 #’s 1, 3, 7, 9a, 11ab, 13, 14ab, 16
Quiz 3
Section 3.4 #’s 1-5, 8, 9, 31, 33
Section 3.5 #’s 7-13, 16, 18, 21, 23, 35
Section 3.6 #’s 1, 3, 4, 7, 8, 15, 17, 27, 29-31
Section 3.7 #’s 2, 3, 4, 5, 7, 10, 11, 16
#’s 14, 19, 23, 24, 27, 29, 31
Section 3.8 #’s 1 only the first part, 5, 33 only part a
QUARTER 2
Test All chapter 3
Section 4.1 #’s 1-11, 13, 17, 18, 25, 31
Quiz 4.1
Section 4.2 #’s 1, 4, 7, 9, 23, 29, 32, 39
Section 4.3 #’s 7, 8, 10, 19, 24, 29, 30
Section 4.4 #’s 1 ignore directions, do with calculators then use calculus methods to confirm as
in examples 1-3
Quiz Sec 4.1-4.4
Section 4.5 #’s 5-16, 17-24, 29, 30, 31, 32
Quiz Sec. 4.5
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Section 4.6 #’s 4-7, 13
Section 4.7 #’s 1, 3, 5, 9, 10, 13-15
Section 4.8 #’s 1, 3, 4, 6, 11
Section 4.9 #’s 4, 6, 8, 10, 15, 18, 20, 24, 28, 41
Test Chapter 4
Section 5.1 #’s 2, 5, 13
Section 5.2 #’s 1, 5, 9, 18, 21(just do regular Def. integral), 32, 34, 41
Section 5.3 #’s 6-14, 19, 20, 22, 24-28
Section 5.4 #’s 2, 3, 5, 7, 8, 10-14
Test Sec. 5.1-5.4
QUARTER 3
Section 5.5 #’s 1-51 skip 35-38
Quiz Sec. 5.5 Integral Substitution
Section 5.6 #’s 2, 4, 9, 10, 14*, 15-17, 23*
Quiz Sec. 5.6
Test Sec. 5.5 and 5.6 Integration by Substitution and by Parts
Section 5.7 #’s 1-6, 15-19
Section 5.8 #’s 25-32 and a few from 1-10 (using calculators and wolfram alpha)
Section 5.9 #’s 7-11 only a and c
Section 5.10 #’s 1, 2, 3 only the first part, not for x greater than or equal to 1, 5, 6, 8, 9, 7,
12, 13, 14, 23, 24, 26, 28, 30
Chapter 5 Review Work on any problems you want. I will pick 12 problems from the
review for a quest (60 points)
Section 6.1 #’s 1-11, 12-14, 38
Quiz Sec. 6.1 Area between curves
Section 6.2 #’s 1-4, 5-9, 10-14, 15-18, supplemental worksheet
Helpful information:
Disk Method Rotate x axis, x bounds, y=equations dx “upper-lower”
Rotate y axis, y bounds, x=equations dy “outer-inner”
Cylindrical shell (2πr) Rotate about y axis, x bounds, y=equations dx “upper-lower”
Rotate about x axis, y bounds, x=equations dy “outer-inner”
Quiz Sec. 6.2 Volume using integration
QUARTER 4
Section 6.3 #’s 5-7
Section 6.4 #’s 1-4, 5 and 6 only parts a and b
Section 6.5 #’s 1, 5, 6, 9 only integral part not Riemann sums, 15, 35
Section 7.1 #’s 1, 3a, 4a, 6a, 9
Section 7.2 #’s 10, 19 part a only (i)h=.4
Section 7.3 #’s 1, 2, 9
AP EXAM REVIEW