PC.1: Students use polynomial, rational, and algebraic functions to write functions and draw graphs to solve word problems, to find composite and inverse functions, and to analyze functions and graphs. They analyze and graph circles, ellipses, parabolas, and hyperbolas.

PC.1.1: Recognize and graph various types of functions, including polynomial, rational, algebraic, and absolute value functions. Use paper and pencil methods and graphing calculators.

Translating and Scaling Functions

PC.1.2: Find domain, range, intercepts, zeros, asymptotes, and points of discontinuity of functions. Use paper and pencil methods and graphing calculators.

Radical Functions

PC.1.3: Model and solve word problems using functions and equations.

Solving Equations on the Number Line
Using Algebraic Equations

PC.1.4: Define, find, and check inverse functions.

Function Machines 3 (Functions and Problem Solving)
Logarithmic Functions

PC.1.7: Apply transformations to functions.

Absolute Value with Linear Functions
Exponential Functions
Introduction to Exponential Functions
Rational Functions
Translating and Scaling Functions
Translating and Scaling Sine and Cosine Functions
Translations
Zap It! Game

PC.1.10: Write the equations of conic sections in standard form (completing the square and using translations as necessary), in order to find the type of conic section and to find its geometric properties (foci, asymptotes, eccentricity, etc.).

Ellipses
Hyperbolas

PC.2: Students solve word problems involving logarithmic and exponential functions. They draw and analyze graphs and find inverse functions.

PC.2.2: Find the domain, range, intercepts, and asymptotes of logarithmic and exponential functions.

Exponential Functions
Logarithmic Functions

PC.2.3: Draw and analyze graphs of logarithmic and exponential functions.

Compound Interest
Exponential Functions
Introduction to Exponential Functions
Logarithmic Functions

PC.2.4: Define, find, and check inverse functions of logarithmic and exponential functions.

Logarithmic Functions

PC.4: Students define trigonometric functions using the unit circle and use degrees and radians. They draw and analyze graphs, find inverse functions, and solve word problems.

PC.4.1: Define sine and cosine using the unit circle.

Cosine Function
Sine Function
Translating and Scaling Sine and Cosine Functions

PC.4.2: Convert between degree and radian measures.

Cosine Function
Sine Function
Tangent Function

PC.4.4: Solve word problems involving applications of trigonometric functions.

Sine, Cosine, and Tangent Ratios

PC.4.5: Define and graph trigonometric functions (i.e., sine, cosine, tangent, cosecant, secant, cotangent).

Cosine Function
Simplifying Trigonometric Expressions
Sine Function
Sine, Cosine, and Tangent Ratios
Sum and Difference Identities for Sine and Cosine
Tangent Function
Translating and Scaling Sine and Cosine Functions

PC.4.6: Find domain, range, intercepts, periods, amplitudes, and asymptotes of trigonometric functions.

Cosine Function
Sine Function
Tangent Function

PC.4.8: Define and graph inverse trigonometric functions.

Tangent Function

PC.4.9: Find values of trigonometric and inverse trigonometric functions.

Translating and Scaling Functions

PC.4.11: Make connections between right triangle ratios, trigonometric functions, and circular functions.

Cosine Function
Sine Function
Tangent Function

PC.5: Students prove trigonometric identities, solve trigonometric equations, and solve word problems.

PC.5.2: Use basic trigonometric identities to verify other identities and simplify expressions.

Simplifying Trigonometric Expressions
Sum and Difference Identities for Sine and Cosine

PC.5.3: Understand and use the addition formulas for sines, cosines, and tangents.

Sum and Difference Identities for Sine and Cosine

PC.6: Students define polar coordinates and complex numbers and understand their connection with trigonometric functions.

PC.6.4: Define complex numbers, convert complex numbers to trigonometric form, and multiply complex numbers in trigonometric form.

Points in the Complex Plane
Roots of a Quadratic

PC.7: Students define and use arithmetic and geometric sequences and series, understand the concept of a limit, and solve word problems.

PC.7.4: Use recursion to describe a sequence.

Arithmetic Sequences
Geometric Sequences

PC.8: Students model data with linear and nonlinear functions.

PC.8.1: Find linear models using the median fit and least squares regression methods. Decide which model gives a better fit.

Correlation
Least-Squares Best Fit Lines
Solving Using Trend Lines
Trends in Scatter Plots

PC.8.2: Calculate and interpret the correlation coefficient. Use the correlation coefficient and residuals to evaluate a ?best-fit? line.

Correlation
Least-Squares Best Fit Lines
Solving Using Trend Lines

PC.8.3: Find a quadratic, exponential, logarithmic, power, or sinusoidal function to model a data set and explain the parameters of the model.

Zap It! Game

PC.9: Mathematical Reasoning and Problem Solving

PC.9.4: Use the properties of number systems and order of operations to justify the steps of simplifying functions and solving equations.

Solving Algebraic Equations II
Solving Equations on the Number Line

PC.9.5: Understand that the logic of equation solving begins with the assumption that the variable is a number that satisfies the equation, and that the steps taken when solving equations create new equations that have, in most cases, the same solution set as the original. Understand that similar logic applies to solving systems of equations simultaneously.

Solving Linear Systems (Standard Form)