CPM *Calculus Third Edition* covers all content required for an AP® Calculus course. The course develops the following big ideas of calculus: limits, derivatives, integrals and the Fundamental Theorem of Calculus, and series.

Each chapter reviews the concepts developed previously and builds on them. The curriculum contains several key labs and hands-on activities to introduce concepts. Activities such as the “Slope Walk,” where students recognize that the rate of a walker relates to the slope of a graph and “Ramp Lab,” where students develop conceptual understanding of instantaneous velocity. The curriculum explores derivatives and integrals simultaneously during the first four chapters and both are presented geometrically and in context.

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The first four chapters cover:

- Precalculus topics, such as trigonometric functions, domain and range, end behavior, and composite functions The graphical relationship between slope and area, in the context of motion
- Ways to describe graphs and how a function is changing
- Average and instantaneous rates of change
- The relationship among position, velocity, and acceleration
- Applications of rates of change, such as velocity and acceleration
- Limits and continuity
- The Fundamental Theorem of Calculus
- The Intermediate Value Theorem
- Slope functions (i.e., derivatives)
- Differentiability
- Estimating the area under a curve with a Riemann Sum
- The definition of a derivative and the Power Rule
- Area functions (i.e. integrals)

Chapters 5 through 8 cover:

- The relationship among distance, velocity and acceleration functions
- The First and Second Derivative Tests
- The Product, Quotient, and Chain Rules
- Optimization
- Limits of indeterminate forms
- l’Hôpital's Rule
- Derivative and integrals of exponential and logarithmic function
- Implicit differentiation
- The Mean Value Theorem
- The Extreme Value Theorem
- Related Rates
- Integration using substitution
- Differential Equations and Slope Fields
- Volumes of solids with known cross-sections

Some material required for the BC Calculus Exam is introduced throughout the course in optional extensions of Chapters 5 through 8. These topics include:

- Improper integrals
- Euler’s Method
- Newton’s Method
- Integration with partial fractions
- Integration by parts
- Arc length

Chapters 9 through 12 cover additional BC Calculus content, including:

- Areas bounded by polar curves
- Convergence and divergence of infinite series
- Calculate derivatives and integrals of of polar functions, parametric functions, and vector-valued functions
- Logistic growth
- Approximating functions with polynomials
- Taylor and Maclaurin Polynomials, including error

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