Academic Standards

PC.1.1: Use paper and pencil methods and technology to graph polynomial, absolute value, rational, algebraic, exponential, logarithmic, trigonometric, inverse trigonometric and piecewise-defined functions. Use these graphs to solve problems, and translate among verbal, tabular, graphical and symbolic representations of functions by using technology as appropriate.

Exponential Functions - Activity A

Function Machines 2 (Functions, Tables, and Graphs)

General Form of a Rational Function

Logarithmic Functions - Activity A

Logarithmic Functions: Translating and Scaling

Rational Functions

Sine Function

Tangent Function

Using Algebraic Equations

Using Algebraic Expressions

PC.1.2: Identify domain, range, intercepts, zeros, asymptotes and points of discontinuity of functions represented symbolically or graphically, using technology as appropriate.

Function Machines 1 (Functions and Tables)

Function Machines 2 (Functions, Tables, and Graphs)

Function Machines 3 (Functions and Problem Solving)

Functions Involving Square Roots

PC.1.3: Solve word problems that can be modeled using functions and equations.

Function Machines 1 (Functions and Tables)

Function Machines 2 (Functions, Tables, and Graphs)

Function Machines 3 (Functions and Problem Solving)

Modeling Linear Systems - Activity A

PC.1.4: Recognize and describe continuity, end behavior, asymptotes, symmetry and limits and connect these concepts to graphs of functions.

Cosine Function

Exponential Functions - Activity A

Fourth-Degree Polynomials - Activity A

Function Machines 1 (Functions and Tables)

Function Machines 2 (Functions, Tables, and Graphs)

Function Machines 3 (Functions and Problem Solving)

Hyperbola - Activity A

Introduction to Functions

Quadratics in Factored Form

Quadratics in Polynomial Form - Activity A

Sine Function

Tangent Function

Translating and Scaling Functions

Unit Circle

Using Tables, Rules and Graphs

PC.1.5: Find, interpret and graph the sum, difference, product and quotient (when it exists) of two functions and indicate the relevant domain and range of the resulting function.

Addition and Subtraction of Polynomials

Cosine Function

Function Machines 1 (Functions and Tables)

Function Machines 2 (Functions, Tables, and Graphs)

Function Machines 3 (Functions and Problem Solving)

Functions Involving Square Roots

Introduction to Functions

Rational Functions

Sine Function

Tangent Function

PC.1.6: Find the composition of two functions and determine the domain and the range of the composite function. Conversely, when given a function, find two other functions for which the composition is the given one.

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)

PC.1.7: Define and find inverse functions, their domains and their ranges. Verify symbolically and graphically whether two given functions are inverses of each other.

Cosine Function

Function Machines 2 (Functions, Tables, and Graphs)

Function Machines 3 (Functions and Problem Solving)

Logarithmic Functions - Activity A

Logarithmic Functions: Translating and Scaling

PC.1.8: Apply transformations to functions and interpret the results of these transformations verbally, graphically and numerically.

Function Machines 1 (Functions and Tables)

Function Machines 2 (Functions, Tables, and Graphs)

Function Machines 3 (Functions and Problem Solving)

Introduction to Functions

Logarithmic Functions: Translating and Scaling

Translating and Scaling Functions

Using Algebraic Equations

Using Algebraic Expressions

Using Tables, Rules and Graphs

PC.2.1: Derive equations for conic sections and use the equations that have been found.

Circles

Ellipse - Activity A

Hyperbola - Activity A

Parabolas - Activity A

PC.2.2: Graph conic sections with axes of symmetry parallel to the coordinate axes by hand, by completing the square, and find the foci, center, asymptotes, eccentricity, axes and vertices (as appropriate).

Hyperbola - Activity A

Parabolas - Activity A

PC.3.1: Compare and contrast symbolically and graphically y = e to the x power with other exponential functions.

Exponential Functions - Activity A

Exponential Growth and Decay - Activity B

Function Machines 2 (Functions, Tables, and Graphs)

PC.3.2: Define the logarithmic function g(x) = log base a of x as the inverse of the exponential function f(x) = a to the x power. Apply the inverse relationship between exponential and logarithmic functions and the laws of logarithms to solve problems.

Exponential Functions - Activity A

Exponential Growth and Decay - Activity B

Function Machines 3 (Functions and Problem Solving)

Logarithmic Functions - Activity A

Logarithmic Functions: Translating and Scaling

PC.3.3: Analyze, describe and sketch graphs of logarithmic and exponential functions by examining intercepts, zeros, domain and range, and asymptotic and end behavior.

Exponential Functions - Activity A

Function Machines 2 (Functions, Tables, and Graphs)

Logarithmic Functions - Activity A

Logarithmic Functions: Translating and Scaling

PC.3.4: Solve problems that can be modeled using logarithmic and exponential functions. Interpret the solutions and determine whether the solutions are reasonable.

Exponential Functions - Activity A

Logarithmic Functions - Activity A

Logarithmic Functions: Translating and Scaling

Modeling Linear Systems - Activity A

Road Trip (Problem Solving)

PC.4.1: Define and use the trigonometric ratios cotangent, secant and cosecant in terms of angles of right triangles.

Sine and Cosine Ratios - Activity A

Sine, Cosine and Tangent

Tangent Ratio

PC.4.2: Model and solve problems involving triangles using trigonometric ratios.

Sine and Cosine Ratios - Activity A

Sine, Cosine and Tangent

Tangent Ratio

PC.4.4: Define sine and cosine using the unit circle.

Cosine Function

Sine Function

Sine and Cosine Ratios - Activity A

Sine, Cosine and Tangent

Tangent Function

Unit Circle

PC.4.6: Deduce geometrically and use the value of the sine, cosine and tangent functions at 0, pi/6, pi/4, pi/3 and pi/2 radians and their multiples.

Sine, Cosine and Tangent

Tangent Ratio

Unit Circle

PC.4.7: Make connections among right triangle ratios, trigonometric functions and the coordinate function on the unit circle.

Cosine Function

Sine Function

Sine and Cosine Ratios - Activity A

Sine, Cosine and Tangent

Tangent Function

Unit Circle

PC.4.8: Analyze and graph trigonometric functions, including the translation of these trigonometric functions. Describe their characteristics (i.e., spread, amplitude, zeros, symmetry, phase, shift, vertical shift, frequency).

Cosine Function

Function Machines 2 (Functions, Tables, and Graphs)

Holiday Snowflake Designer

Sine Function

Tangent Function

Translating and Scaling Functions

PC.4.9: Define, analyze and graph inverse trigonometric functions and find the values of inverse trigonometric functions.

Cosine Function

Function Machines 2 (Functions, Tables, and Graphs)

Sine Function

Tangent Function

Unit Circle

PC.4.10: Solve problems that can be modeled using trigonometric functions, interpret the solutions and determine whether the solutions are reasonable.

Cosine Function

Sine Function

Tangent Function

Unit Circle

PC.4.11: Derive the fundamental Pythagorean trigonometric identities; sum and difference identities; half-angle and double-angle identities; and the secant, cosecant and cotangent functions. Use these identities to verify other identities and simplify trigonometric expressions.

Simplifying Trigonometric Expressions

Sum and Difference Identities for Sine and Cosine

PC.4.12: Solve trigonometric equations and interpret solutions graphically.

Modeling and Solving Two-Step Equations

Solving Two-Step Equations

PC.5.1: Define and use polar coordinates and relate polar coordinates to Cartesian coordinates.

PC.5.2: Represent equations given in Cartesian coordinates in terms of polar coordinates.

PC.5.3: Graph equations in the polar coordinate plane.

PC.5.4: Define complex numbers, convert complex numbers to polar form and multiply complex numbers in polar form.

PC.5.5: Prove and use De Moivre's Theorem.

Points in the Complex Plane - Activity A

PC.6.1: Define arithmetic and geometric sequences and series.

Arithmetic Sequences

Arithmetic and Geometric Sequences

Geometric Sequences

PC.6.2: Derive and use formulas for finding the general term for arithmetic and geometric sequences.

Arithmetic Sequences

Arithmetic and Geometric Sequences

Geometric Sequences

PC.6.3: Develop, prove and use sum formulas for arithmetic series and for finite and infinite geometric series.

Arithmetic Sequences

Arithmetic and Geometric Sequences

Geometric Sequences

PC.6.4: Generate a sequence using recursion.

Arithmetic Sequences

Arithmetic and Geometric Sequences

PC.6.5: Describe the concept of the limit of a sequence and a limit of a function. Decide whether simple sequences converge or diverge. Recognize an infinite series as the limit of a sequence of partial sums.

Arithmetic and Geometric Sequences

PC.6.6: Model and solve word problems involving applications of sequences and series, interpret the solutions and determine whether the solutions are reasonable.

Arithmetic Sequences

Arithmetic and Geometric Sequences

Geometric Sequences

PC.6.7: Derive the binomial theorem by combinatorics.

Arithmetic Sequences

Arithmetic and Geometric Sequences

Geometric Sequences

PC.7.1: Define vectors as objects having magnitude and direction. Represent vectors geometrically.

PC.7.5: Model and solve problems using parametric equations.

Modeling and Solving Two-Step Equations

Road Trip (Problem Solving)

Solving Two-Step Equations

PC.8.1: Find linear models by using median fit and least squares regression methods. Decide which among several linear models gives a better fit. Interpret the slope in terms of the original context.

Box-and-Whisker Plots

Line Plots

Mean, Median and Mode

Slope - Activity B

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

Correlation last revised: 1/20/2017

This correlation lists the recommended Gizmos for this state's curriculum standards. Click any Gizmo title below for more information.