1: The student uses mathematical processes to acquire and demonstrate mathematical understanding.

1.A: apply mathematics to problems arising in everyday life, society, and the workplace;

Determining a Spring Constant
Estimating Population Size

1.B: use a problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problem-solving process and the reasonableness of the solution;

Estimating Population Size

1.D: communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate;

Biconditional Statements
Using Algebraic Expressions

1.E: create and use representations to organize, record, and communicate mathematical ideas;

Describing Data Using Statistics
Stem-and-Leaf Plots
Using Algebraic Expressions

1.G: display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral communication.

Using Algebraic Expressions

2: The student uses process standards in mathematics to explore, describe, and analyze the attributes of functions. The student makes connections between multiple representations of functions and algebraically constructs new functions. The student analyzes and uses functions to model real-world problems.

2.C: represent a given function as a composite function of two or more functions;

Function Machines 1 (Functions and Tables)

2.F: graph exponential, logarithmic, rational, polynomial, power, trigonometric, inverse trigonometric, and piecewise defined functions, including step functions;

Absolute Value with Linear Functions
Compound Interest
Cosine Function
Exponential Functions
General Form of a Rational Function
Graphs of Polynomial Functions
Introduction to Exponential Functions
Logarithmic Functions
Logarithmic Functions: Translating and Scaling
Polynomials and Linear Factors
Quadratics in Factored Form
Quadratics in Vertex Form
Rational Functions
Sine Function
Tangent Function
Translating and Scaling Functions

2.G: graph functions, including exponential, logarithmic, sine, cosine, rational, polynomial, and power functions and their transformations, including af(x), f(x) + d, f(x - c), f(bx) for specific values of a, b, c, and d, in mathematical and real-world problems;

Absolute Value with Linear Functions
Compound Interest
Cosine Function
Exponential Functions
General Form of a Rational Function
Graphs of Polynomial Functions
Introduction to Exponential Functions
Logarithmic Functions
Logarithmic Functions: Translating and Scaling
Polynomials and Linear Factors
Quadratics in Factored Form
Quadratics in Vertex Form
Rational Functions
Sine Function
Tangent Function
Translating and Scaling Functions
Translating and Scaling Sine and Cosine Functions
Translations
Zap It! Game

2.I: determine and analyze the key features of exponential, logarithmic, rational, polynomial, power, trigonometric, inverse trigonometric, and piecewise defined functions, including step functions such as domain, range, symmetry, relative maximum, relative minimum, zeros, asymptotes, and intervals over which the function is increasing or decreasing;

Exponential Functions
General Form of a Rational Function
Graphs of Polynomial Functions
Introduction to Exponential Functions
Logarithmic Functions
Polynomials and Linear Factors
Radical Functions
Rational Functions

2.J: analyze and describe end behavior of functions, including exponential, logarithmic, rational, polynomial, and power functions, using infinity notation to communicate this characteristic in mathematical and real-world problems;

Exponential Functions
General Form of a Rational Function
Graphs of Polynomial Functions
Logarithmic Functions
Logarithmic Functions: Translating and Scaling
Rational Functions

2.K: analyze characteristics of rational functions and the behavior of the function around the asymptotes, including horizontal, vertical, and oblique asymptotes;

General Form of a Rational Function
Rational Functions

2.L: determine various types of discontinuities in the interval (-?, ?) as they relate to functions and explore the limitations of the graphing calculator as it relates to the behavior of the function around discontinuities;

General Form of a Rational Function

2.M: describe the left-sided behavior and the right-sided behavior of the graph of a function around discontinuities;

General Form of a Rational Function

2.N: analyze situations modeled by functions, including exponential, logarithmic, rational, polynomial, and power functions, to solve real-world problems;

Compound Interest
General Form of a Rational Function
Linear Functions
Rational Functions

2.O: develop and use a sinusoidal function that models a situation in mathematical and real-world problems; and

Translating and Scaling Sine and Cosine Functions

2.P: determine the values of the trigonometric functions at the special angles and relate them in mathematical and real-world problems.

Cosine Function
Sine Function
Tangent Function
Translating and Scaling Functions

3: The student uses the process standards in mathematics to model and make connections between algebraic and geometric relations.

3.F: determine the conic section formed when a plane intersects a double-napped cone;

Ellipses
Hyperbolas

3.H: use the characteristics of an ellipse to write the equation of an ellipse with center (h, k); and

Ellipses

3.I: use the characteristics of a hyperbola to write the equation of a hyperbola with center (h, k).

Hyperbolas

4: The student uses process standards in mathematics to apply appropriate techniques, tools, and formulas to calculate measures in mathematical and real-world problems.

4.A: determine the relationship between the unit circle and the definition of a periodic function to evaluate trigonometric functions in mathematical and real-world problems;

Cosine Function
Sine Function
Tangent Function

4.B: describe the relationship between degree and radian measure on the unit circle;

Cosine Function
Sine Function
Tangent Function

4.C: represent angles in radians or degrees based on the concept of rotation and find the measure of reference angles and angles in standard position;

Cosine Function
Rotations, Reflections, and Translations
Sine Function
Tangent Function

4.D: represent angles in radians or degrees based on the concept of rotation in mathematical and real-world problems, including linear and angular velocity;

Rotations, Reflections, and Translations

4.E: determine the value of trigonometric ratios of angles and solve problems involving trigonometric ratios in mathematical and real-world problems;

Cosine Function
Sine Function
Sine, Cosine, and Tangent Ratios
Tangent Function

4.F: use trigonometry in mathematical and real-world problems, including directional bearing;

Sine, Cosine, and Tangent Ratios

4.I: use vectors to model situations involving magnitude and direction;

Adding Vectors
Vectors

4.K: apply vector addition and multiplication of a vector by a scalar in mathematical and real-world problems.

Adding Vectors

5: The student uses process standards in mathematics to evaluate expressions, describe patterns, formulate models, and solve equations and inequalities using properties, procedures, or algorithms.

5.B: represent arithmetic sequences and geometric sequences using recursive formulas;

Arithmetic Sequences
Geometric Sequences

5.C: calculate the nth term and the nth partial sum of an arithmetic series in mathematical and real-world problems;

Arithmetic Sequences

5.E: calculate the nth term of a geometric series, the nth partial sum of a geometric series, and sum of an infinite geometric series when it exists;

Geometric Sequences

5.G: use the properties of logarithms to evaluate or transform logarithmic expressions;

Logarithmic Functions: Translating and Scaling

5.I: generate and solve exponential equations in mathematical and real-world problems;

Exponential Functions

5.M: use trigonometric identities such as reciprocal, quotient, Pythagorean, cofunctions, even/odd, and sum and difference identities for cosine and sine to simplify trigonometric expressions; and

Simplifying Trigonometric Expressions
Sum and Difference Identities for Sine and Cosine

5.N: generate and solve trigonometric equations in mathematical and real-world problems.

Sine, Cosine, and Tangent Ratios
Translating and Scaling Sine and Cosine Functions