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