A. Patterns

1. Use models and algebraic formulas to represent and analyze sequences and series.
   • Explicit formulas for nth terms
   • Sums of finite arithmetic series
   • Sums of finite and infinite geometric series
2. Develop an informal notion of limit.
3. Use inductive reasoning to form generalizations.

B. Functions and Relationships

1. Understand relations and functions and select, convert flexibly among, and use various representations for them, including equations or inequalities, tables, and graphs.
2. Analyze and explain the general properties and behavior of functions of one variable, using appropriate graphing technologies.
   • Slope of a line or curve
   • Domain and range
   • Intercepts
   • Continuity
   • Maximum/minimum
   • Estimating roots of equations
   • Intersecting points as solutions of systems of equations
   • Rates of change
3. Understand and perform transformations on commonly-used functions.
   • Translations, reflections, dilations
   • Effects on linear and quadratic graphs of parameter changes in equations
   • Using graphing calculators or computers for more complex functions
4. Understand and compare the properties of classes of functions, including exponential, polynomial, rational, and trigonometric functions.
   • Linear vs. non-linear
   • Symmetry
   • Increasing/decreasing on an interval

C. Modeling

1. Use functions to model real-world phenomena and solve problems that involve varying quantities.
   • Linear, quadratic, exponential, periodic (sine and cosine), and step functions (e.g., price of mailing a first-class letter over the past 200 years)
   • Direct and inverse variation
   • Absolute value
   • Expressions, equations and inequalities
   • Same function can model variety of phenomena
   • Growth/decay and change in the natural world
   • Applications in mathematics, biology, and economics (including compound interest)
2. Analyze and describe how a change in an independent variable leads to change in a dependent one.
3. Convert recursive formulas to linear or exponential functions (e.g., Tower of Hanoi and doubling).

D. Procedures

1. Evaluate and simplify expressions.
   • Add and subtract polynomials
   • Multiply a polynomial by a monomial or binomial
   • Divide a polynomial by a monomial
2. Select and use appropriate methods to solve equations and inequalities.
   • Linear equations - algebraically
   • Quadratic equations - factoring (when the coefficient of x² is 1) and using the quadratic formula
   • All types of equations using graphing, computer, and graphing calculator techniques
3. Judge the meaning, utility, and reasonableness of the results of symbol manipulations, including those carried out by technology.