PETERS TOWNSHIP HIGH SCHOOL
COURSE SYLLABUS: CAL CULUS I HONORS
Course Overview and Essential Skills
This course is designed for the student who desires to study calculus in college. It will cover all of the
components and skills that are included in a typical first semester college calculus course. Some of the
topics taught are properties of functions, limits, and the derivative, techniques of integration, the definite
integral, and applications of the integral. Computers will be used where appropriate.
Course Textbook and Required Materials
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Title: Ron Larson Paul Battaglia, Calculus with Calc Chat and Calc View, Cengage Learning, 2017 ISBN#: 978-1-30594801-3
Website www.LarsonCalculusforAP.com contains videos explaining concepts and proofs from the book,
three-dimensional graphs, and sample scoring for AP Calculus free-response questions.
Website www.CalcView.com contains video solutions of selected exercises.
Website www.CalcChat.com provides free step-by-step solutions to all odd-numbered exercises (also you
can chat with a tutor, at no charge, during the hours posted at the site)
TI-83 or TI-84 Graphing Calculator
Course Outline of Material Covered:
Unit or Topic
Prerequisites
Concepts/Skills/Resources
Determine slope algebraically and
graphically
Write equations of lines
Apply linear functions
Function basics
Inverse functions
Trigonometric functions
Simplification and evaluation of
exponential and logarithmic functions
Chapter P in text
Timeframe
Limits and their properties
Finding limits Graphically and
Numerically
Evaluating limits analytically
Continuity and one-sided limits
Limits at infinity
Chapter 1 in text
6 Weeks
Differentiation
The derivative and the tangent line
problem
Basic differentiation rules and rates of
change
Product and Quotient rules and
higher-order derivatives
The chain rule
9 Weeks
2 weeks
Implicit Differentiation
Derivatives of Inverse Functions
Related Rates
Newton’s method
Chapter 2 in text
Applications of Differentiation
Integration
Differential Equations
Applications of Integration
Integration Techniques
Extrema on an interval
Rolle’s Theorem and Mean Value
Theorem
Increasing and decreasing Functions
and the first derivative test
Concavity and the second derivative
test
Curve Sketching
Optimization problems
Differentials
Chapter 3 in text
Indefinite Integration
Area
Riemann Sums and Definite Integrals
The Fundamental Theorem of Calculus
Integration by Substitution
Chapter 4 in text
Slope fields
Growth and Decay
Separation of Variables
Chapter 5 in text
Area of a region
Volume: Disk and Washer Methods
Arc Length
Chapter 6 in text
Integration by parts
Partial fractions
Chapter 7 in text
7 Weeks
9 Weeks
4 Weeks
5 Weeks
2 Weeks
*Depending on the needs of the class or changes in the school year, the course outline is subject to change.