| 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 |