### 1: Students develop number sense and use numbers and number relationships in problem-solving situations and communicate the reasoning used in solving these problems.

#### 1.1: Investigate limiting processes by examining infinite sequences and series.

Arithmetic and Geometric Sequences

Geometric Sequences

#### 1.2: Explain relationships among real numbers, complex numbers, and vectors using models.

Points in the Complex Plane - Activity A

Vectors

### 2: Students use algebraic methods to explore, model, and describe patterns and functions involving numbers, shapes, data, and graphs in problem-solving situations and communicate the reasoning used in solving these problems.

#### 2.1: Use rational, polynomial, trigonometric, and inverse functions to model real-world phenomena.

Cosine Function

Cubic Function Activity

Fourth-Degree Polynomials - Activity A

General Form of a Rational Function

Rational Functions

Sine Function

Tangent Function

#### 2.2: Represent and solve problems using linear programming and difference equations.

Linear Programming - Activity A

#### 2.5: Perform operations on and between functions.

Addition and Subtraction of Polynomials

#### 2.6: Make the connections between trigonometric functions and polar coordinates, complex numbers, and series.

Arithmetic and Geometric Sequences

Complex Numbers in Polar Form

Cosine Function

Geometric Sequences

Points in Polar Coordinates

Sine Function

Tangent Function

Unit Circle

### 3: Students use data collection and analysis, statistics, and probability in problem-solving situations and communicate the reasoning used in solving these problems.

#### 3.1: Create and interpret discrete and continuous probability distributions, and understanding their application to realworld situations (for example, insurance).

Binomial Probabilities

#### 3.4: Solve real-world problems with formal use of combinations and permutations.

Binomial Probabilities

Permutations

Permutations and Combinations

### 4: Students use geometric concepts, properties, and relationships in problem-solving situations and communicate the reasoning used in solving these problems.

#### 4.1: Deduce properties of figures using vectors.

Vectors

#### 4.2: Apply transformations, coordinates, and vectors in problem-solving situations.

Dilations

Reflections

Rotations, Reflections and Translations

Vectors

#### 4.3: Describe, analyze, and extend patterns produced by processes of geometric change (for example, limits and fractals).

Finding Patterns

Correlation last revised: 1/24/2009