Course Name:
Advanced Placement Calculus BC
Description:
An interactive text, graphing software and math symbol software combine
with the exciting on-line course delivery to make Calculus an adventure.
This course is designed to prepare the student for the AP Calculus BC
exam given each year in May. With continuous enrollment, students can
start the course and begin working on Calculus as early as spring of the
previous year!
An Advanced Placement (AP) course in calculus consists of a full high
school year of work that is comparable to calculus courses in colleges and
universities. It is expected that students who take an AP course in calculus
will seek college credit, college placement, or both, from institutions of
higher learning.
Most colleges and universities offer a sequence of several courses in
calculus, and entering students are placed within this sequence according
to the extent of their preparation, as measured by the results of an AP
examination or other criteria. Students with AP Calculus BC examination
credit are generally awarded 2 semesters of College Calculus credit.
Prerequisites:
Estimated
Completion
Time:
Algebra I, Geometry, Algebra II, Pre-Calculus or Trigonometry/Analytical
Geometry.
2 segments/32-36 weeks
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Major Topics
and Concepts:
Segment 1:
• Finding Limits Graphically and Numerically
• Evaluating Limits Analytically
• Continuity and One-Sided Limits
• Infinite Limits
• Differentiation
• The Derivative and Tangent Line Problem
• Basic Differentiation Rules and Rates of Change
• The Product and Quotient Rules and Higher Order Derivatives
• The Chain Rule
• Implicit Differentiation
• Logarithmic Differentiation
• Related Rates
• Applications of Differentiation
• Extrema on an Interval
• Rolle's Theorem and the Mean Value Theorem
• Increasing and Decreasing Functions and the First Derivative Test
• Concavity and the Second Derivative Test
• Limits at Infinity
• Summary of Curve Sketching
• Optimization Problems
• Differentials and Linear Approximation
• Integration
• Antiderivatives and Indefinite Integration
• Area
• Riemann Sums and Definite Integrals
• The Fundamental Theorem of Calculus
• Average Value of a function and the Mean Value Theorem for Integrals
• Integration by Substitution
• Numerical Integration
• The Integral as a Function
• Logarithmic, Exponential, and Other Transcendental Functions.
• The Natural Logarithmic Function and Differentiation
• The Natural Logarithmic Function and Integration
• Inverse Functions
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• Exponential Functions: Differentiation and Integration
• Bases other than e and Applications
• Inverse Trigonometric Functions and Differentiation
• Differential Equations: Slope Fields
• Differential Equations: Euler’s Method
• Differential Equations: Growth and Decay
• Differential Equations: Logistic Equations
• Differential Equations: Separation of Variables
Segment 2:
• Applications of Integration
• Area of Region between Two Curves
• Volume: Disk Method
• Volume: Shell Method
• Arc length
• Work
• Basic Integration Rules
• Integration by Parts
• Integration using Partial Fractions
• Indeterminate Forms and L'Hopital's Rule
• Improper Integrals
• Sequences
• Series and Convergence
• Integral Test and p-series
• Comparison of Series
• Alternating Series
• Ratio and Root Test
• Taylor Polynomials and Approximations
• LaGrange Error
• Power Series
• Representation of Functions by Power Series
• Taylor and Maclaurin Series
• Plane Curves and Parametric Equations
• Differentiation and Integration of Parametric Equations
• Arclength of a curve described by parametric equations
• Polar Coordinates and Polar Graphs
• Area and Arc length in Polar Coordinates
• Vector-valued Functions
• Differentiation and Integration of Vector-valued functions
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• Velocity and Acceleration: motion
• Tangent and Normal Vectors
• Arclength of a vector valued function
• AP Exam Review and Test Taking Tips and Practice
Course Assessment
and Participation Requirements:
Besides engaging students in challenging curriculum, FLVS guides students to reflect on their
learning and evaluate their progress through a variety of assessments. Assessments can be in
the form of self-checks, practice lessons, multiple choice questions, free-response questions,
matching questions discussion based oral assessments, and written discussions. Included
throughout the course are AP style questions so that students gain practice with the AP Exam
format. Instructors evaluate progress and provide interventions through the variety of
assessments built into a course, as well as through contact with the student in other venues.
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