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