Mathematics (Grades 5–12) Subtest 1

Subarea II. Functions, Algebra, and Calculus

0004

Understand the properties and representations of functions.

identifying, completing, and extending patterns (e.g., series, arithmetic and geometric sequences, iteration and recursion, induction, finite differences) presented in various forms to model situations, make predictions, and solve problems
analyzing the characteristics and properties of functions (e.g., domain, range, continuity) and performing arithmetic operations on functions
recognizing and translating between different representations of relations and functions (e.g., verbal descriptions, ordered pairs, graphs, function notation, piecewise-defined)
applying the concepts of inverse and composite functions to represent and solve problems

0005

Apply algebraic techniques.

applying properties of group and field structures to manipulate and simplify algebraic expressions (e.g., linear, absolute value, polynomial, rational, radical)
solving problems that involve variable quantities (e.g., linear, quadratic, polynomial, rational, radical, and absolute value equations and inequalities), including systems of equations and inequalities
applying the properties of exponents and logarithms to manipulate exponential and logarithmic expressions and solve exponential and logarithmic equations
representing and solving mathematical and real-world problems using linear algebra, including matrices and vectors

0006

Analyze linear and nonlinear functions and their applications.

analyzing linear, absolute value, quadratic, polynomial, radical, rational, exponential, logarithmic, and multivariate functions (e.g., slopes, intercepts, roots, asymptotes, critical points, symmetry)
identifying the effects of algebraic transformations (e.g., shifts, stretches, reflections) on the graph of a function
demonstrating knowledge of the use of technology (e.g., dynamic graphing utilities, spreadsheets) to analyze relationships between different representations (e.g., equations, graphs) of functions and inequalities
applying linear, absolute value, quadratic, polynomial, radical, rational, exponential, and logarithmic functions to model real-world situations and solve problems (e.g., joint variation, inverse variation, compound interest, exponential growth and decay) using a variety of graphic and algebraic methods

0007

Apply knowledge of trigonometry and calculus.

representing trigonometric functions in symbolic, numerical, graphic, and verbal forms
applying trigonometric identities and equations to solve problems and model real-world situations (e.g., periodic)
applying the concepts of limits and continuity to analyze properties of functions
demonstrating knowledge of the definition of the derivative, the relationship between the derivative and average and instantaneous rates of change, and techniques of differentiation
demonstrating knowledge of the definite integral, area under the curve, and techniques of numerical integration
applying concepts of derivatives and integrals to solve mathematical and real-world problems