Descriptive Statements:
- Apply trigonometric functions to solve problems involving distance and angles.
- Apply trigonometric functions to solve problems involving the unit circle.
- Rewrite trigonometric expressions to solve equations or prove expressions equivalent by using trigonometric identities.
- Analyze the relationship between a trigonometric function and its graph.
- Model periodic relationships using trigonometric functions.
- Solve mathematical and real-world problems using the law of sines and the law of cosines.
Sample Item:
Descriptive Statements:
- Connect the concepts of limit, derivative, and integration.
- Analyze limits, rates of change, and continuity for algebraic functions and their graphs.
- Analyze the concept of the derivative (e.g., instantaneous rate of change, the slope of the line tangent to a curve) and apply this concept to polynomial functions.
- Analyze the concept of the integral (e.g., area under a curve, cumulative change) and apply this concept to polynomial functions.
Sample Item:
What is the instantaneous rate of change of f(x) = 4 + 2 x − 5x4 f of x equals 4 plus 2 x minus 5 x to the fourth power at x = – negative 1?
- – negative 18
- – negative 3
- 4
- 22
Correct Response and Explanation (Show Correct ResponseHide Correct Response)
D. The instantaneous rate of change for a function at a given x value can be found by differentiating the function and evaluating it at the given x value. The derivative of f(x) f of x is f'(x) = 2 − 20x3 f prime of x equals 2 minus 20 x cubed . Evaluating this at x equals – negative 1 yields f'(–1) = 2 − 20(–1)3 = 22 f prime of negative 1 equals 2 minus 20 times negative 1 cubed equals 22 , the rate of change of f(x) f of x at x = – negative 1.
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