### 1: Determine the relationships of subsets of complex numbers.

Points in the Complex Plane - Activity A

### 2: Simplify expressions involving complex numbers, using order of operations and including conjugate and absolute value.

Absolute Value of a Complex Number

Points in the Complex Plane - Activity A

### 3: Analyze families of functions, including shifts, reflections, and dilations of y = k/x (inverse variation), y = kx (direct variation/linear), y = [x] (greatest integer), y = x² (quadratic), y = a to the x power (exponential), and y = log to the base a of x (logarithmic).

#### 3.1: Identifying the domain and range of a relation given its graph, a table of values, or its equation, including those with restricted domains

Cosine Function

Distance-Time Graphs

Functions Involving Square Roots

Introduction to Functions

Rational Functions

Sine Function

Tangent Function

Using Tables, Rules and Graphs

### 4: Determine approximate real zeros of functions graphically and numerically and exact real zeros of polynomial functions.

#### 4.1: Using the zero product property, completing the square, and the quadratic formula

Polynomials and Linear Factors

Roots of a Quadratic

#### 4.2: Deriving the quadratic formula

Roots of a Quadratic

### 5: Identify the characteristics of quadratic functions from their roots, graphs, or equations.

#### 5.1: Generating an equation when given its roots or graph

Hyperbola - Activity A

Polynomials and Linear Factors

Solving Equations By Graphing Each Side

#### 5.2: Graphing a function when given its equation

Function Machines 2 (Functions, Tables, and Graphs)

#### 5.3: Determining the maximum or minimum values of quadratic functions both graphically and algebraically

Parabolas - Activity A

Quadratic and Absolute Value Functions

Quadratics in Factored Form

Quadratics in Polynomial Form - Activity A

Roots of a Quadratic

#### 5.4: Applying functions to real-world problems

Function Machines 1 (Functions and Tables)

Function Machines 2 (Functions, Tables, and Graphs)

Function Machines 3 (Functions and Problem Solving)

### 6: Perform operations on functions, including addition, subtraction, multiplication, division, and composition.

#### 6.1: Determining the inverse of a function or a relation

Function Machines 3 (Functions and Problem Solving)

#### 6.2: Performing operations on polynomial and rational expressions containing variables

Addition of Polynomials - Activity A

Dividing Exponential Expressions

#### 6.3: Constructing graphs by analyzing their functions as sums, differences, or products

Addition and Subtraction of Polynomials

Function Machines 1 (Functions and Tables)

Function Machines 2 (Functions, Tables, and Graphs)

Function Machines 3 (Functions and Problem Solving)

Linear Functions

Using Tables, Rules and Graphs

### 7: Solve equations, inequalities, and applied problems involving absolute values, radicals, and quadratics over the complex numbers, as well as simple trigonometric, exponential, and logarithmic functions.

#### 7.1: Solving equations using laws of exponents, including rational and irrational exponents

Modeling and Solving Two-Step Equations

Solving Two-Step Equations

#### 7.2: Expressing the solution of an equation, inequality, or applied problem as a graph on a number line or by using set or interval notation

Compound Inequalities

Solving Linear Inequalities using Addition and Subtraction

Solving Linear Inequalities using Multiplication and Division

### 9: Graph trigonometric functions of the form y=a sin(bx), y=a cos(bx), and y=a tan(bx).

#### 9.1: Determining period and amplitude of sine, cosine, and tangent functions from graphs or basic equations

Cosine Function

Sine Function

Sine and Cosine Ratios - Activity A

Sine, Cosine and Tangent

Tangent Function

Tangent Ratio

Translating and Scaling Functions

Translating and Scaling Sine and Cosine Functions - Activity A

#### 9.2: Determining specific unit circle coordinates associated with special angles

Cosine Function

Sine Function

Tangent Function

Unit Circle

### 10: Solve general triangles, mathematical problems, and real-world applications using the Law of Sines and the Law of Cosines.

#### 10.2: Determining area of oblique triangles

Classifying Triangles

### 11: Define the six trigonometric functions using ratios of the sides of a right triangle, coordinates on the unit circle, and the reciprocal of other functions.

Cosine Function

Sine Function

Sine and Cosine Ratios - Activity A

Sine, Cosine and Tangent

Tangent Function

Tangent Ratio

### 12: Verify simple trigonometric identities using Pythagorean and/or reciprocal identities.

Simplifying Trigonometric Expressions

### 14: Determine an equation of linear regression from a set of data.

#### 14.1: Examining data to determine if a linear, quadratic, or exponential relationship exists and to predict outcomes

Exponential Functions - Activity A

Function Machines 2 (Functions, Tables, and Graphs)

Quadratics in Factored Form

Roots of a Quadratic

### 15: Calculate probabilities of events using the laws of probability.

#### 15.1: Using permutations and combinations to calculate probabilities

Binomial Probabilities

Permutations

Permutations and Combinations

#### 15.2: Calculating conditional probability

Binomial Probabilities

#### 15.3: Calculating probabilities of mutually exclusive events, independent events, and dependent events

Binomial Probabilities

Compound Independent Events

Compound Independent and Dependent Events

Correlation last revised: 3/17/2015