### Descriptive Statements:

- Apply trigonometric functions to solve problems involving distance and angles.
- Apply trigonometric functions to solve problems involving the unit circle.
- Manipulate trigonometric expressions and equations using techniques such as trigonometric identities.
- Analyze the relationship between a trigonometric function and its graph.
- Use trigonometric functions to model periodic relationships.

### Sample Item:

### Descriptive Statements:

- Evaluate limits.
- Demonstrate knowledge of continuity.
- Analyze the derivative as the slope of a tangent line and as the limit of the difference quotient.
- Calculate the derivatives of functions (e.g., polynomial, exponential, logarithmic).
- Apply differentiation to analyze the graphs of functions.
- Apply differentiation to solve real-world problems involving rates of change and optimization.

### Sample Item:

If *f*(*x*) = 3*x*^{4} – 8*x*^{2} + 6, what is the value of ?

- –4
- –1
- 1
- 4

Correct Response and Explanation (ShowHide)

**A. ** This question requires the examinee to analyze the derivative as the slope of a tangent line and as the limit of the difference quotient. The limit expression is equivalent to the derivative *f*'(1). Since it is much easier to evaluate the derivative of a polynomial, this is preferred over evaluating the limit expression. *f*'(*x*)= 12*x*^{3} – 16*x*, so *f*'(1) = 12 – 16 = –4.

### Descriptive Statements:

- Analyze the integral as the area under a curve and as the limit of the Riemann sum.
- Calculate the integrals of functions (e.g., polynomial, exponential, logarithmic).
- Apply integration to analyze the graphs of functions.
- Apply integration to solve real-world problems.

### Sample Item: