Unit 1: Review of Pre-Calculus PI 1.1 Complete operations on functions 1.1 Coordinate Increments and the Equation of a Line 1.2a Using the vertical line test and finding the domain and range of functions 1.2b Working with even and odd functions 1.2c Graphing piecewise-defined functions 1.2d Working with composite functions PI 1.2 Graph, simplify, and solve exponential equations 1.3a Graphing exponential functions and finding their domain and range 1.3b Rewriting exponential functions with different bases and finding zeroes 1.5a Find the inverse of a function 1.5b Solve exponential and logarithmic equations 1.5c Determine the domain and range of logarithmic functions PI 1.3 Use parameterized expressions to describe functions 1.4 Graphing parameterized functions and writing parameterizations for curves PI 1.4 Graph and solve trigonometric equations 1.6a Working with radian measure and trigonometric values of angles 1.6b Determine whether trigonometric functions are even or odd 1.6c Graphing and interpreting graphs of trigonometric functions 1.6d Evaluate expressions involving trigonometric functions and solve trigonometric equations Unit 2: Introduction to Limits PI 2.1 Interpret and evaluate simple limits 2.1a Finding average and instantaneous speeds 2.1b Apply the properties of limits 2.1c Determine limits by substitution, tables, or graphs 2.1d Finding one-sided limits PI 2.2 Deduce and interpret behavior of functions using limits 2.2a Finding limits involving infinity 2.2b Finding vertical and horizontal asymptotes of functions 2.2c Finding power function end behavior models for functions, and identify any horizontal asymptotes PI 2.3 Analyze and determine intervals of continuity and points of discontinuity 2.3 Determine where functions are continuous and find/classify points of discontinuity PI 2.4 Solve problems involving the slope of a tangent line 2.4a Find average rates of change of functions over intervals 2.4b Find equations of tangent and normal lines 2.4c Find instantaneous rates of change Unit 3: Differentiability PI 3.1 Identify the derivative of a function as the limit of a difference quotient and estimate derivatives 3.1a Find derivatives of functions at indicated points 3.1b Match graphs of functions with graphs of derivatives PI 3.2 Recognize the connection between differentiability and continuity 3.2a Determine where functions are continuous and/or differentiable 3.2b Determine whether functions have corners, cusps, vertical tangents, or discontinuities 3.2c Find numerical derivatives of functions at indicated points PI 3.3 Determine higher order derivatives 3.3a Find derivatives using the product and quotient rules 3.3b Find horizontal tangents of curves with product and quotient rules 3.3c Find the first four derivatives of functions 3.4 Find rates of change related to velocity, including estimating from a graph 3.5a Find derivatives of trigonometric functions 3.5b Find velocity, speed, acceleration, and jerk of a function Unit 4: Advanced Differentiation PI 4.1 Evaluate derivatives using the chain rule 4.1a Use given substitutions and the Chain Rule to find derivatives 4.1b Evaluate derivatives of composite functions at given values 4.1c Find equations of lines tangent to curves using the chain rule PI 4.2 Evaluate derivatives using implicit differentiation 4.2a Find derivatives using implicit differentiation 4.2b Find slopes of curves using implicit differentiation 4.2c Find equations of lines that are tangent or are normal to curves at given points using implicit differentiation PI 4.3 Evaluate derivatives of the inverse trigonometric functions 4.3a Find derivatives of inverse trigonometric functions 4.3b Find equations for tangent lines at indicated points of inverse trigonometric functions PI 4.4 Evaluate derivatives of exponential and logarithmic functions 4.4a Find the derivative of exponential and logarithmic functions 4.4b Find equations for tangent lines at indicated points for exponential and logarithmic functions Unit 5: Application of Derivatives PI 5.1 Use derivatives to analyze properties of a function 5.1 Find the extreme values of functions and where they occur using critical points 5.3a Determine local extrema, identify any absolute extrema, or find points of inflection of a function 5.3b Determine the interval on which the graph of a function is concave up or concave down 5.3c Use the graph of f' to estimate the intervals on which a function is increasing or decreasing PI 5.2 Apply the Mean Value Theorem to describe the behavior of a function over an interval 5.2a Find the values that satisfy the hypotheses of the Mean Value Theorem 5.2b Find all possible functions with a given derivative PI 5.3 Calculate linearizations to estimate functions 5.5a Find linearizations of functions at given values 5.5b Use linearizations to approximate expressions 5.5c Find differentials 5.5d Use Newton's Method to estimate solutions PI 5.4 Interpret the meaning of a derivative within a problem 5.6 Solve related rates application problems Unit 6: Integration PI 6.1 Calculate a definite integral using areas and properties of definite integrals 6.1a Find the exact area under a curve using finite sums 6.1b Use the rectangular approximation method to approximate areas under a curve 6.5 Use the Trapezoidal Rule to approximate values of integrals PI 6.2 Express the limit of a Riemann sum in integral notation 6.2a Express limits of desired quantitites as definite integrals 6.2b Evaluate the integral of constant functions 6.2c Use graphs of integrands and areas to evaluate integrals 6.2d Evaluate the integral of a function using technology PI 6.3 Apply definite integrals to problems involving the average value of a function 6.3a Evaluate integrals 6.3b Find average values of functions PI 6.4 Recognize antiderivatives of basic functions 6.4a Find derivatives of integrals 6.4b Construct functions that satisfy given conditions 6.4c Evaluate definite integrals using the Fundamental Theorem of Calculus Unit 7: Advanced Integration PI 7.1 Estimate and verify solutions to differential equations 7.1a Find general solutions to exact differential equations 7.1b Solve initial value problems explicitly 7.1c Match differential equations with the appropriate graphs 7.1d Use Euler's method to approximate the value of y PI 7.2 Calculate antiderivatives and evaluate definite integrals 7.2a Find indefinite integrals 7.2b Use substitution to evaluate definite and indefinite integrals 7.3a Use integration by parts to evaluate definite and indefinite integrals 7.3b Use tabular integration to evaluate indefinite integrals PI 7.3 Analyze, interpret, create, and solve differential equations from problems in context 7.4a Solve initial value problems related to exponential growth and decay 7.4b Solve problems where interest is compounded continuously 7.4c Find exponential functions whose graphs pass through two points Unit 8: Applications of Integration PI 8.1 Apply definite integrals to problems involving motion 8.1a Solve particle motion and projectile motion problems 8.1b Solve application problems related to the integral as net change PI 8.2 Apply definite integrals to problems involving area and volume 8.2 Find the areas of regions in the plane 8.3 Find the volumes of solids