Syllabus
AP Calculus Syllabus Caroline Cochrane-Braswell
Contact Info:
E-mail: caroline@newschoolva.com
Class Overview:
This class is geared toward the AP Calculus AB test taking place in May. This means that we will cover Functions, Limits, Derivatives, and Integrals. Periodically we will review actual AP tests from past years in order to prepare for the AP test should you decide to take it. The final objective of this course is to have you ready to take the AP test, as a result we will be moving at a steady pace. If you feel yourself falling behind please see me for extra help.
Focus Skill:
The focus skill for this class is problem solving.
Textbook:
This class will be using the textbook Calculus: Graphical, Numerical, Algebraic, AP edition. You will be assigned a textbook, please write your name in the book in addition to telling me your textbook number. The class will follow the textbook, although lessons will not be taken directly from the text itself. Homework assignments will come from the text.
Grading Policy:
You will receive grades on homework, quizzes and tests throughout the year. In addition, class participation will be taken into account. If you are very close to the next highest grade I will bump you up if you have been present, prepared, and active member of the class.
Tests: 100 points each
Quizzes: 10 points each
Homework: 5 points each
Homework:
Homework will be due every Monday and Thursday (starting Sept. 10), unless otherwise specified. Assignments will be given out on the preceding Monday or Thursday (Monday for Thursday assignments, Thursday for Monday assignments). If I feel that a particular section in the homework was troublesome, I may assign additional practice problems.
Homework will be collected at the beginning of class on the due date and graded based on whether it has been completed and every problem requiring work has work shown. It will be graded out of five points for each assignment. You may turn in an assignment up to two days late, but it will lose a point each day it is late.
Quizzes:
Quizzes will be short and taken directly from homework assignments. They are meant to ascertain whether you understand the homework. Quizzes will be given every other week on Thursday.
Tests:
Tests will have questions similar to those given for homework and quizzes. Partial credit will be given if work is shown that demonstrates some understanding of the problem.
If you are absent the day before a test (review day) you do not have to take the test on the assigned test day, provided it is an excused absence. If you are absent the day of the test, you must talk to me, so that we can make arrangements for you to make it up.
Midterm and Final:
There will be a midterm and final for this class. The Midterm will cover all material from first semester; the final will cover all material from second semester only.
Portfolio Assignment:
In the fourth quarter, after the AP test, you will be assigned a project that you can add to your portfolio. You will also be reviewing as a class for the Midterm in second quarter. Each student will be responsible for presenting a section to the class. Your lesson plan can also be added to the portfolio.
Course Outline:
Unit 1: Prerequisites for Calculus (1 week)
A. Slopes and Equations of Lines
B. Functions and Graphs
a. Graphing Function
b. Domains and Ranges
c. Symmetry, even and odd functions
d. Piecewise functions
C. Exponential Functions
a. Exponential growth and decay
b. The number e
D. Functions and Logarithms
a. Inverses and finding inverses
b. Logarithmic functions
c. Properties of logarithms
E. Trigonometric Functions
a. Graphs of basic trigonometric functions
b. Trigonometric values
c. Inverse trigonometric functions
Unit 2: Limits and Continuity (2 weeks)
A. Rates of Change and Limits
a. Average and instantaneous speed
b. Definition of a limit
c. Properties of limits
d. One and two-sided limits
e. Sandwich theorem
B. Limits Involving Infinity
a. Asymptotes
b. Finite limits as x approaches infinity
c. Infinite limits as x approaches a constant
d. End behavior model
C. Continuity
a. Continuous functions
b. Points of discontinuity
i. Removable discontinuity
ii. Jump Discontinuity
iii. Infinite Discontinuity
iv. Oscillating Discontinuity
c. Intermediate value theorem
D. Rates of Change and Tangent Lines
a. Average Rates of Change
b. Tangent and Normal lines to a curve
c. Finding slope of both tangent and normal lines
Unit 3: Derivatives (5 weeks)
A. Derivatives of a Function
a. Definition and notation
b. Derivatives as instantaneous rates of change
c. Derivatives at a point
d. Relationship between the graphs of f and f’
B. Differentiability
a. Derivatives on a calculator
b. Differentiability implies continuity
C. Rules for Differentiation
a. Power rule, Sum and difference rule
b. Product and Quotient rules
c. Negatives integer powers
D. Velocity and Acceleration as Rates of Change
E. Derivatives of Trigonometric Functions
F. Chain Rule
G. Implicit Differentiation
H. Derivatives of Inverse Trigonometric Functions
I. Derivatives of Exponential and Logarithmic Functions
Unit 4: Applications of Derivatives (4 weeks)
A. Extreme Values of Functions
a. Absolute (Global) extreme values
b. Local (relative) extreme values
B. Mean Value Theorem
C. Connecting f’ and f’’ with the graph of f
a. First derivative test for local extrema
b. Concavity, inflection points and the second derivative
c. Second derivative test for local extrema
d. Identifying corresponding characteristics of f, f’, and f’’
D. Modeling and Optimization
E. Linearization
F. Related Rates
MIDTERM
Unit 5: The Definite Integral (3 weeks)
A. Estimating with Finite Sums; specifically Riemann Sums
B. Trapezoid Rule
C. Definite Integral
a. Notation
b. Integral as Area
c. Integral of a constant
D. Definite Integral and Antiderivatives
a. Properties of Definite integrals
b. Antiderivatives using rules of differentiation
c. Average value of a function
E. Fundamental Theorem of Calculus
a. Fundamental Theorem part 1 and part 2
b. Graphing the function of the integral
c. Analyzing antiderivatives graphically
d. Numerical approximations of definite integrals using tables
e. Solving definite integrals algebraically
Unit 6: Differential Equations and Mathematical Modeling (2 weeks)
A. Slope fields
a. Differential equations
b. Creating slope fields
B. Integration by Substitution
C. Exponential Growth and Decay
D. Separable differential equations
Unit 7: Applications of Definite Integrals (3 weeks)
A. Integrals as Net Change and motion along a line
B. Areas in the Plane
a. Areas between curves
b. Areas enclosed by intersecting curves
C. Volumes, specifically solids of revolution
a. Square cross sections
b. Circular cross sections
c. Cylindrical shells
d. Solids of revolution
FINAL
Absences and Late Policy:
o If you are absent from class, you will be given hand-outs you missed, however, you will be missing valuable lesson time in class that cannot be made up.
o In accordance with the New School’s absence policy, if you miss 8 days of class you will be withdrawn.
o When you arrive late to class you are creating a distraction to others in the class in addition to missing valuable information that will be on the test. Please get to class on time; your lateness times are being added up.
Spirit of the Classroom:
Please remember that the spirit of the classroom applies to our daily interactions and routine in class. The spirit of the classroom is given below.
We should:
1. Guarantee the physical and psychological safety of each person.
2. Focus each person’s attention on the subject at hand.
3. Create a sense of fairness and fair play within the classroom.
4. Invite everyone’s participation.
5. Challenge ourselves and each other to think in new and different ways.
6. Recognize that the foundation of knowledge begins with what each person already knows and believes.
7. Relate clearly and meaningfully to the objectives, goals, and standards of the class.
8. Encourage the best in each person.
9. Respect the class’s sense of organization and coherence.
10. Speak up when we perceive behaviors that undermine a positive, active educational space.
Other Important Info:
• If you need help on an assignment please let me know as soon as possible I am happy to help you as long as you take the initiative to ask.
• You may get help from other students in class if you are having difficulty, however, homework should be your own work. If your homework is a duplicate of someone else’s you will receive disciplinary measures.
• Please use pencil on all homework assignments, quizzes, and tests.
