Download AP Calculus BC Syllabus - Fort Thomas Independent Schools

Highlands High School
270514– AP Calculus BC
2016 – 2017 Course Syllabus
Instructor: Kevin Kampschmidt
Phone: 859 – 815 – 2618
E-mail Address: [email protected]
Grade: 12
Credit: 1
Prerequisite: AP Calculus AB and Teacher Recommendation
Description
AP Calculus BC is an enriched mathematics course and curriculum that is designed to help
students in their understanding of the calculus curriculum and to provide and prepare them for
the mathematics needed to be successful in post-secondary education. Students are introduced to
this curriculum through a comprehensive study of all of the objectives outlined in the AP
Calculus Course Description.
Course Standards:
 Students should be able to work with functions numerically, graphically, analytically, and
verbally
 The derivative should be understood as the instantaneous rate of change of a function and as
the local linear approximation of the function
 The definite integral should be understood as the limit of a Riemann sum and as the net
accumulation of the rate of change
 The relationship between derivatives and the definite integral should be understood in terms
of both parts of the Fundamental Theorem of Calculus
 Students should learn to communicate about mathematics verbally and in writing
 Students should be able to model a written description of a physical situation with a function,
a differential equation, or an integral
 Students should learn to use technology to analyze problems, experiment, and verify and
interpret results
 Students are expected to learn to judge the reasonableness of their solutions
 Develop an appreciation of calculus as a coherent body of knowledge and as a human
accomplishment
Textbook: Larson, Ron, and Bruce Edwards. Calculus of a Single Variable AP Edition Tenth
Edition. Boston: Brooks/Cole, Cengage Learning, 2014
Required Materials: Three ring binder or notebook, Loose leaf paper, graph paper, TI 84 plus
graphing calculator, Pencils, Eraser, Red pen.
Technology: A graphing handheld calculator is mandatory and a TI84 plus is recommended.
With a Graphing Calculator students must be able to:
Graph a Function in a Specific Window
Find the zeros of a given function
Find the value of a derivative at a specific point
Evaluate a Definite Integral
Method of Grade Calculation: Homework, Tests, quizzes, projects and in-class assignments.
All assignments will be added together and averages will be determined by points earned divided
by total points possible.
Participation and Attendance
Students will be expected to be on time and prepared for class with all necessary materials and
assignments. Attendance is of vital to the class. Work must be made up after school and must
be arranged with the teacher. If student is unable to attend class please email my school account
to attain the material missed while student was absent.
Classroom Expectations
I expect all my students to…
Come to class everyday ready to learn.
Show respect to yourself and everyone around you at all times.
Do not use any offensive or vulgar language.
Stay in your seat unless given permission to do otherwise.
Follow all listed rules in the Highlands High School Student Handbook.
Academic Integrity
All academic integrity issues will be reported to Mr. Schneider or another administrator.
Additionally, zeroes will be issued in place of the grade. Examples include copying homework,
claiming another person’s work as your own, and distributing and/or receiving answers to an
assessment.
Class Disruptions: The third misbehavior or disruption in a class will result in a detention to be
served with me after school. These misbehaviors would include talking in class, goofing off in
class, throwing things in class, basically anything that disrupts me or another students learning.
After serving 2 detentions with me any further disruptions will be dealt with through Mr.
Schneider. Any major misbehavior will result in a dismissal from class down to Disciplinary
Office.
Course Content/Calendar
Review of Summer Assignment (4 days)
Limits and Continuity (8 days)
1.1: A Preview of Calculus
1.2: Finding Limits Graphically and Numerically
1.3: Evaluating Limits Analytically
1.4: Continuity and One-Sided Limits
1.5: Infinite Limits
8.7 Indeterminate Forms and L’Hopital’s Rule
Activities: Students will draw functions from different descriptions.
Differentiation (15 days)
2.1: The Derivative and the Tangent Line Problem
2.2: Basic Differentiation Rules and Rates of Change
2.3: Product and Quotient Rules and Higher-Order Derivatives
2.4: The Chain Rule
5.1; The Natural Log Differentiation
5.3: Inverse Functions and Derivatives
5.4: Exponential Functions: Differentiation
5.5: Bases Other Than e and Applications
5.6: Inverse Trigonometric Functions: Differentiation
Activities: Students will prove the 6 trigonometric derivatives
Applications of Differentiation (18 days)
2.5: Implicit Differentiation
2.6: Related Rates
3.1: Extrema on an Interval
3.2: Rolle’s Theorem and the Mean Value Theorem
3.3: Increasing and Decreasing Functions and the First Derivative Test
3.4: Concavity and the Second Derivative Test
3.5: Limits at Infinity
3.6: A Summary of Curve Sketching
3.7: Optimization Problems
3.9: Differentials/Linear Approximations
Activities: Students will review derivative applications with an activity called Take Your
Seats
Optimization will be taught by students designing a Game Tank with the most volume
Parametric Equations and Applications (8 days)
10.2: Plane Curves and Parametric Equations
10.3: Parametric Curves and Calculus
Polar Coordinates and Derivatives (6 days)
10.4: Polar Coordinates, Polar Graphs, and Derivatives
Vectors and Derivatives (4 days)
12.1: Vector Valued Functions
12.2: Differentiation of Vector Valued Functions
12.3: Velocity and Acceleration
Integration and Integration Techniques (20 days)
4.1: Antiderivatives and Indefinite Integration
4.2: Area
4.3: Riemann Sums and Definite Integrals
4.4: The Fundamental Theorem of Calculus
4.5: Integration by Substitution
4.6: Numerical Integration
8.2: Integration by Parts
8.3: Trigonometric Integrals
8.5: Partial Fractions
8.8: Improper Integrals
Activities: Students will work with position, velocity, and acceleration problems
Application of Integration (18 days)
6.1: Slope Fields and Euler’s Method
6.2: Differential Equations: Growth and Decay
6.3: Separation of Variables
7.1: Area of a Region Between Two Curves
7.2: Volume: The Disk Method
7.3: Volume: The Shell Method
7.4: Arc Length and Surface of Revolution
Activities: Students will plot a differential equation to connect it to a Slope Field
Arc Length of Parametric Equations (2 days)
10.3: Parametric Equations and Calculus
Polar Coordinates and Integration (5 days)
10.5: Area and Arc Length in Polar Coordinates
Sequence and Series (30 days)
9.1: Sequences
9.2: Series and Convergence
9.3: The Integral Test and p-series
9.4: Comparisons of Series
9.5: Alternating Series
9.6: The Ratio and Root Tests
9.7: Taylor Polynomials and Approximations
9.8: Power Series
9.9: Representation of Functions by Power Series
9.10 Taylor and Maclaurin Series
Activities: Use the Exercises from AP Module on Series
AP Review (20 days)
Students will complete practice Multiple Choice and Free Response Problems.
NOTE: The times above are subject to change.