ADVANCED PLACEMENT CALCULUS

This syllabus is intended as an outline of the activities to be undertaken in this class. The details, including assignments, will be filled in as the course progresses.

This course is the first course in the basic calculus sequence intended for all mathematics, engineering, science and statistics students. You will also find that most majors at any college require Calculus 1 as a math requirement. This course covers calculus of a single variable.

The primary goals of this course are:

  1. To provide a solid basis for students going on to higher education in math,

science or engineering.

  1. To provide, in an interesting and understandable manner, the fundamentals

of calculus to all students regardless of their chosen major in college.

  1. To provide an opportunity, through discovery and investigative

approaches, to see how and why calculus was developed.

You have two options available to you to acquire 4 college credits:

  1. You can take the AP Calculus Exam at the end of the year.

This test costs approximately $85. It occurs usually the 2nd week in May.

Most colleges or universities require a score of 4 or 5 to receive credit.

  1. You can enroll in the University of Pittsburgh’s College in High School

Program. The cost in $200 and the credits will transfer to almost any college

or University if you choose not to go to Pitt. The requirements are that you

take 5 exams and a 2 hour final exam. The final grade is based on 3 things:

45% -the 5 exams

30%-final exam

25%-final high school AP Calculus grade

Major units covered are:

Functions, limits, continuity, and derivatives

Derivative formulas

  • Polynomials, products, quotients, Chain Rule, trigonometric functions, hyperbolic functions, inverse functions, exponentials, logs, and inverse
  • Implicit differentiation
  • Logarithmic differentiation

Tangent lines to curves, including those defined implicitly or parametrically

Motion

  • Motion along a line: position, velocity, acceleration
  • Parametric equations

Application of Derivatives

  • Differentials and linear approximation
  • Newton's Method
  • Graphing using the first and second derivative
  • Horizontal and vertical asymptotes
  • Optimization: The First and Second Derivative Tests; Applied optimization problems
  • Related rates
  • L'Hopital's Rule

Integration

  • Riemann sums and the definite integral
  • Area under a curve
  • Formal properties: Additivity, linearity, triangle inequality
  • The Fundamental Theorem of Calculus (both versions)
  • Indefinite integrals: Recover a position from velocity, velocity from acceleration: Recover a function from its growth rate (derivative)
  • Integration by substitution
  • Intregration of powers of sines and cosines
  • Integration by parts
  • Integration of rational functions with linear or quadratic denominator
  • Trigonometric substitutions

Calculators:The calculus textbook that we will be using relies heavily on the use of a

graphing calculator. If you do not own a graphing calculator, one will be

issued to you along with your text. In this case, your parents will need to

sign a permission slip.

Grading Procedure:Grades are based upon total points in a 9-week period. Points will be assigned for tests, quizzes, homework and written lab exercises.

Testing procedure:Tests and quizzes will always be announced. They will consist

completely of problems, explanations and essays. You must show

all your work to receive partial or full credit.

Homework:Homework will assigned usually on weekly basis. The assignment will be

posted on the board and/or an assignment sheet will be given. You are

responsible for having the work ready for the start of class on the

scheduled homework day. Solutions will be reviewed in class together.

These homework assignments provide you with the opportunity to gauge

your understanding of the course material and to monitor your progress.

You should make a DILIGENT EFFORT to complete these assignments.

Lab Reports:Graphing calculators will be used for lab work and investigations. It is

recommended that you work together on them. Many labs will have an

assignment for you to complete on your own. These assignments will be

turned in for credit along with your answers and conclusions.

Final Exam:Every student will take a 2 hour cumulative final exam. It will be the Pitt

final examination. Every student will be required to take this examination.

Helpful Hints:1.Regular attendance is a must.

2.Keep notes organized and up to date.

3.Keep up with the work on the assignment sheets.

4.Study as you go; not the night before the test.

5.Bring materials to class.

6.Respect other’s rights, property, privacy and opinions.

7.After an absence, get notes from a classmate, then see me.

8.If necessary, ASK FOR HELP!!

9.OFFER HELP!!

10.Neatness counts.