1. Determine the domain and range of elementary functions, including functions defined by graphs.
2. Use slope to find the equation of a line and express the rate of change of a linear function; introduce the average rate of change for a nonlinear function.
3. Recognize and calculate composite functions; find the difference quotient and inverse for a function.
4. Graph simple polynomial, rational, exponential and logarithmic functions.
5. Construct and solve simple mathematical models using elementary algebraic functions; introduce the concept of relative extrema.
6. Solve direct and inverse variation problems.
7. Convert between degree and radian measure.
8. Solve problems involving arc length, angular speed and linear speed.
9. Find the trigonometric functions for any angle, and know the values of these functions for the quadrantal and special angles, using the unit circle.
10. Define the amplitude, period and phase shift for trigonometric graphs.
11. Apply the basic trigonometric identities, along with the sum and difference formulas, double angle and half angle formulas to simplify expressions.
12. Define the domain and range of the inverse trigonometric functions and construct their graphs.
13. Solve trigonometric equations on either a restricted or a general interval.
14. Perform vector addition, subtraction and scalar multiplication.
15. Use vectors to solve displacement and force applications.
16. Consider various plane curves in parametric and polar form (optional).
17. Recognize general sequences of numbers, and express their sums using sigma notation.
18. Use the binomial theorem to expand an expression and determine a given term in an expansion.