Brief Description of Course
AP Calculus consists of coursework that is comparable to calculus courses offered at colleges and universities. Students who take the course will be prepared to seek college credit through the College Board Advanced Placement Exam for Calculus AB, which gives a semester credit at most universities. The course contents include the study of functions, graphs and limits, derivatives, integrals and the applications of each. The course emphasizes a multi-representational approach to calculus, with concepts, results, and problems, expressed graphically, numerically, analytically, and verbally. There is an emphasis placed on the connections among these representations. The course contents are demanding and require work both in and outside class, as would any college course. AP Calculus AB gives students a chance to bring together concepts from previous math courses, used in new and challenging ways, and should provide students with a strong foundation for courses they will take in college.

COURSE PLANNER:
First Semester
Unit Name and Timeframe:
PRECALCULUS REVIEW (2 Weeks – One Test)
Content and/or skills taught:
• Parent functions and their attributes
• Trigonometric Functions and Values
• Function Properties
• Piece-wise Functions
• Graphical Models

Unit Name and Timeframe:
LIMITS AND THEIR PROPERTIES (3 Weeks – Two Tests)
Content and/or skills taught:
• Lab on limits
• Introduction to limits using an intuitive understanding of the limit process
• Finding limits graphically and numerically using tables
• Properties of limits
• Evaluating limits analytically and algebraically
• Comparing relative magnitudes of functions and their rates of change
• Continuity and one-sided limits, including an intuitive understanding of continuity
• Geometric understanding of the graphs of continuous functions
• Intermediate and Extreme Value Theorems
• Infinite limits
• Using limits to find asymptotes of a function and understanding asymptotic behavior of a graph

Unit Name and Timeframe:
DERIVATIVES (6 Weeks – Four Tests)
Content and/or skills taught:
• Zooming-In Activity using local linearity
• Understanding the derivative graphically, analytically, and numerically
• Finding rates of change from tables of data and graphs
• Understanding derivatives as average rates of change and instantaneous rates of change
• Understanding derivatives as the limit of the difference quotient
• Finding the slope of the curve at a point
• Understanding the meaning of the derivative by translating verbal descriptions into equations and equations into verbal descriptions
• The relationship between differentiability and continuity
• Functions with vertical tangents at a point
• Functions with points at which there are no tangents
• Differentiation rules for basic functions, including trig and power functions
• Differentiation rules for sums, differences, products, and quotients
• The chain rule
• Finding derivatives using the calculator
• Implicit differentiation
• Related rates

Unit Name and Timeframe:
APPLICATIONS OF DERIVATIVES (7 Weeks – Two Tests)
Content and/or skills taught:
• Extrema (relative and absolute) on an interval
• Rolle’s Theorem and the Mean Value Theorem and their geometric consequences
• First Derivative Test
• Increasing and decreasing functions and the First Derivative Test
• Concavity and Points of Inflections
• Concavity of a function and its relationship to first and second derivatives
• Second Derivative Test
• Limits at Infinity
• Curve Sketching using geometric and analytic information, as well as calculus to predict behavior of a function
• The relationship between f , f’ , and f’’ , including characteristics of the graphs of each
• Optimization including relative and absolute extrema
• Tangent line to a curve, and linear approximations
• Application problems including rectilinear motion, position, velocity, and acceleration

Second Semester
Unit Name and Timeframe:
INTEGRATION (6 Weeks – Three Tests)
Content and/or skills taught:
• Introduction to integration as an accumulator
• Antiderivatives and indefinite integration, including antiderivatives following directly from derivatives of basic functions
• Basic properties of definite integrals
• Area under the curve
• Meaning of definite integral and its properties
• Definite integral as a limit of a Riemann sum
• Riemann sums, including left, right, and midpoint sums
• Trapezoidal sums
• Use Riemann sums and trapezoidal sums to approximate definite integrals of functions represented by tables of data, graphically, and algebraically
• Use the First Fundamental Theorem of Calculus to evaluate definite integrals
• Use substitution of variables to find antiderivatives and to evaluate definite integrals, including change of limits of integration
• Use the Second Fundamental Theorem of Calculus in relation to functions defined by integrals
• Mean Value Theorem for Integrals and the Average Value of a Function

Unit Name and Timeframe:
LOGARITHMIC, EXPONENTIAL, AND OTHER TRANSCENDENTAL FUNCTIONS
(2 Weeks – Two Tests)
Content and/or skills taught:
• The natural logarithmic function and differentiation
• The natural logarithmic function and integration
• Inverse functions
• Exponential functions, including differentiation and integration
• Bases other than e and applications
• Inverse trig functions and differentiation
• Inverse trig functions and integration

Unit Name and Timeframe:
Differential Equations (1 Week – One Test)
Content and/or skills taught:
• Solving separable differential equations
• Applications of differential equations, including exponential growth
• Use of slope fields to interpret a differential equation geometrically
• Drawing slope fields and solution curves for differential equations

Unit Name and Timeframe:
APPLICATIONS OF INTEGRATION (3 Weeks – Two Tests)
Content and/or skills taught:
• Motion along a line, including total distance traveled by a particle
• The integral as an accumulator of rates of change
• Area of a region between two curves
• Volume of a solid with known cross sections
• Volume of solids of revolution

Unit Name and Timeframe:
REVIEW FOR AP EXAM (3 Weeks)
Content and/or skills taught:
• Review Packets on Derivatives and Integrals
• Practice AP Released Free Response Questions
• Practice Exam (Latest Released Multiple Choice and Free Response Questions)

NOTE: After the AP exam, students have a choice of various projects that reinforce calculus concepts from the AB course.