# Mathematics (Grades 5–12) Subtest 1

## Subarea II. Functions, Algebra, and Calculus

0004
Understand the properties and representations of functions.

- applying the concept of patterns (e.g., series and sequences, iteration and recursion, induction, finite differences) to model situations, make predictions, and solve problems
- analyzing the characteristics of functions
- recognizing different representations of relations and functions (e.g., verbal descriptions, ordered pairs, graphs)
- applying the concepts of inverse and composite functions to solve problems

0005
Apply algebraic techniques.

- applying properties of group and field structures to algebraic expressions
- solving problems that involve variable quantities (e.g., simplifying algebraic expressions, factoring)
- applying the laws of exponents and logarithms
- demonstrating knowledge of linear algebra, including vectors and matrix operations on vectors

0006
Analyze linear and nonlinear functions and their applications.

- analyzing linear and nonlinear functions (e.g., slope, intercept, roots, asymptotes)
- identifying the effects of algebraic transformations on the graph of a function
- demonstrating knowledge of the use of technology (e.g., graphing utilities, spreadsheets) to analyze relationships between different representations (e.g., equations, graphs) of functions and inequalities
- applying linear and nonlinear functions to model real-world situations and solve problems using a variety of graphic and algebraic methods

0007
Apply knowledge of trigonometry and calculus.

- demonstrating knowledge of the concepts of limits and continuity
- applying unit circle trigonometry, identities, and equations to solve problems and model real-world situations
- demonstrating knowledge of the definition of the derivative and its relationship to rate of change
- demonstrating knowledge of the definite integral, area under the curve, and techniques of numerical integration
- applying the fundamental theorem of calculus to solve mathematical and real-world problems