AP Calculus Standards

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
1.3a Graphing exponential functions and finding their domain and range
1.3b Rewriting exponential functions with different bases and finding zeroes
1.4 Graphing parameterized functions and writing parameterizations for curves
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
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
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
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
2.3 Determine where functions are continuous and find/classify points of discontinuity
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
3.1a Find derivatives of functions at indicated points
3.1b Match graphs of functions with graphs of derivatives
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
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
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
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
4.3a Find derivatives of inverse trigonometric functions
4.3b Find equations for tangent lines at indicated points of inverse trigonometric 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
5.1 Find the extreme values of functions and where they occur using critical points
5.2a Find the values that satisfy the hypotheses of the Mean Value Theorem
5.2b Find all possible functions with a given derivative
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
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
5.6 Solve related rates application problems
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
6.2a Express limits or 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
6.3a Evaluate integrals
6.3b Find average values of 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
6.5 Use the Trapezoidal Rule to approximate values of integrals
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
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
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
8.1a Solve particle motion and projectile motion problems
8.1b Solve application problems related to the integral as net change
8.2 Find the areas of regions in the plane
8.3 Find the volumes of solids

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