Details
Course Overview
This course is the equivalent of an introductory collegelevel calculus course. In this course, students study functions, limits, derivatives, integrals, and infinite series. Calculus helps scientists, engineers, and financial analysts understand the complex relationships behind realworld phenomena. Students learn to evaluate the soundness of proposed solutions and apply mathematical reasoning to realworld models. Students also learn to understand change geometrically and visually (by studying graphs of curves), analytically (by studying and working with mathematical formulas), numerically (by seeing patterns in sets of numbers), and verbally. Students prepare for the AP Exam and further studies in science, engineering, and mathematics.
Course Outline
SEMESTER ONE
Unit 1: The Basics
Students prepare to study calculus by reviewing some basic precalculus concepts from algebra and trigonometry. They learn what calculus is, why it was invented, and what it is used for.
 PreCalculus Review
 Introduction to Calculus
 Using a Graphing Calculator
 Combining Functions
 Composite and Inverse Functions
 Graphical Symmetry
 Patterns in Graphs
Unit 2: Limits and Continuity
This unit addresses Topic I: Functions, Graphs, and Limits of the College Board's Calculus BC topic outline. Students learn two important concepts that underlie all of calculus: limits and continuity. Limits help students understand differentiation (the slope of a curve) and integration (the area inside a curved shape). Continuity is an important property of functions.
 Finding Limits Analytically
 Asymptotes as Limits
 Relative Magnitudes for Limits
 When Limits Do and Don't Exist
 Continuity
 Intermediate and Extreme Value Theorems
Unit 3: The Derivative
This unit addresses Topic II: Derivatives of the College Board's Calculus BC topic outline. Students learn how to calculate a derivative, the slope of a curve at a specific point. They learn techniques for finding derivatives of algebraic functions (such as y = x2) and trigonometric functions (such as y = sin x). Students also interpret the derivative as a rate of change and move fluidly between multiple representations including graphs, tables, and equations.
 Slope and Change
 Derivative at a Point
 The Derivative
 The Power Rule
 Sums, Differences, Products, and Quotients
 Graphs of Functions and Derivatives
 Continuity and Differentiability
 Rolles and Mean Value Theorems
 HigherOrder Derivatives
 Concavity
 Chain Rule
 Implicit Differentiation
Unit 4: Rates of Change
This unit focuses on Second Derivatives and Applications of Derivatives within Topic II: Derivatives of the College Board's Calculus BC topic outline. Students learn how to use calculus to model and analyze changing aspects of our world. In addition to the AB topics in this unit, BC students analyze polar and vectorvalued functions.
 Extrema
 Optimization
 Tangent and Normal Lines
 Tangents to Polar Curves
 Tangent Line Approximation
 Rates and Derivatives
 Related Rates
 Rectilinear Motion
 Motion with Vector Functions
Unit 5: The Integral, Part 1
This unit focuses on Topic III: Integrals in the College Board's Calculus BC topic outline. Students learn numerical approximations to definite integrals, interpretations and properties of definite integrals, the Fundamental Theorem of Calculus, and techniques of antidifferentiation. They learn how to find areas of curved shapes.
 Riemann Sums
 Area Approximations
 The Definite Integral
 Properties of Integrals
 Graphing Calculator Integration
 Applications of Accumulated Change
 Antiderivatives
 Composite Functions
SEMESTER TWO
Unit 1: The Integral, Part 2
This unit focuses on Topic III: Integrals in the College Board's Calculus BC topic outline. Students learn the Fundamental Theorem of Calculus, and techniques of antidifferentiation. They learn how to find areas of curved shapes.
 The Fundamental Theorems of Calculus
 Definite Integrals of Composite Functions
 Analyzing Functions and Integrals
Unit 2: Applications of the Integral
This unit focuses on Topic III: Integrals in the College Board's Calculus BC topic outline. Students learn to use integrals and antiderivatives to solve problems. In addition to the AB topics, BC students learn to calculate arc length for a smooth curve.
 Area Between Curves
 More Areas and Averages
 Volumes of Revolution
 Cross Sections
 Arc Length
 More Rectilinear Motion
 Other Applications of the Definite Integral
Unit 3: Inverse and Transcendental Functions
This unit focuses on Topic II: Derivatives and Topic III: Integrals in the College Board's Calculus BC topic outline. Students learn to calculate and use derivatives, antiderivatives, and integrals of exponential functions (such as y = 3x where the input variable is an exponent), logarithmic functions (the inverses of exponential functions), and trigonometric functions (such as y = secant x). In addition to the AB topics, BC students learn how to use L'Hopital's Rule and the methods of partial fractions and integration by parts. Also, students learn how to find improper integrals, and derivatives and integrals of parametric functions.
 Derivatives of Inverses
 Inverse Trigonometric Functions
 Logarithmic and Exponential Review
 Transcendentals and 1/x
 Derivatives of Logarithms and Exponentials
 L'Hopital's Rule
 Analysis of Transcendental Curves
 Integrating Transcendental Functions
 Partial Fractions
 Integration by Parts
 Improper Integrals
 Applications of Transcendental Integrals
 Derivatives of Parametric Functions
 Integrating Parametric and Polar Functions
Unit 4: Separable Differential Equations and Slope Fields
This unit focuses on Topic II: Derivatives of the College Board's Calculus BC topic outline, specifically, on Equations Involving Derivatives. Students investigate differential equations and solve the equations using a technique called "separating the variables." In addition to the topics covered in AB, BC students also learn to use Eulers method to estimate the solution of differential equations and use logistic equations to model growth.
 Slope Fields
 Differential Equations as Models
 Euler's Method
 Exponential Growth and Decay
 Logistic Growth
 More Applications of Differential Equations
Unit 5: Sequences and Series
This unit focuses on Topic IV: Polynomial Approximations and Series of the College Board's Calculus BC topic outline, specifically, on Series of Constants and Taylor Series.
 Sequences
 Series
 Convergence Tests
 Radius of Convergence
 Functions Defined by Power Series
 Taylor and Maclaurin Series
 Taylor's Theorem and Lagrange Error
Unit 6: AP Exam Review and Final Exam
Students review what they have learned and become more familiar with APtype questions in preparation for the AP Exam. Students are also provided with access to previously released AP Exams for practice.
 Exam Strategies
 Review of Topics
 Practice Exams
Unit 7: Calculus Project
Teachers may choose to assign a final project.
To use this course, you'll need a computer with an Internet connection. Some courses require additional free software programs, which you can download from the Internet.
Hardware and Browsers (Minimum Recommendations)
Windows OS

CPU: 1.8 GHz or faster processor (or equivalent)

RAM: 1GB of RAM

Browser: Microsoft Internet Explorer 9.0 or higher, Mozilla Firefox 10.0 versions or higher, Chrome 17.0 or higher
 At this time our users are encouraged not to upgrade to Windows 10 or Edge (the new browser)
Mac OS

CPU: PowerPC G4 1 GHz or faster processor; Intel Core Duo 1.83 GHz or faster processor

RAM: 1GB of RAM

Browser: Firefox 10.0 versions or higher, Chrome 17.0 or higher (Safari is not supported!)
Internet Connections
It is highly recommended that a broadband connection be used instead of dial up.