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Grade Level Title Description Format
Secondary Applications of Rational Functions

Algebra 2 lesson: By developing a function to describe the annual cost of a refrigerator and given a function describing concentration of drug in the body, students relate the behavior of the graph of a rational function with the phenomenon it describes. Asymptotes and particular points become important information about the application. 

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Secondary, Post Secondary Area between two curves

Part of the NCSSM Online AP Calculus Collection: This video deals with determining the area between two curves. http://www.dlt.ncssm.edu 

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Secondary, Post Secondary Areas in Polar Coordinates

Part of the NCSSM Online AP Calculus Collection: This video deals with Areas in Polar Coordinates. http://www.dlt.ncssm.edu 

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Secondary, Post Secondary Attributes of Graphs

Part of the NCSSM Online AP Calculus Collection: This video deals with attributes of graphs. http://www.dlt.ncssm.edu

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Secondary Bivariate Curve-Fitting: Exponential Functions cost of Subway token

Modeling the Cost of a Subway Token in New York  

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Secondary Collecting and Fitting Quadratic Data with the CBL

Algebra 2 lesson: Using the CBL and the graphing calculator, students work in groups to collect data describing the freefall of an object over time. The data collected includes data not relevant and that must be eliminated, and data is shifted near the y-axis to make the intercept meaningful. The students describe the meaning of the coefficients. The experiment is run again with an object that has drag (like a hat) and a model is found. The follow-up problem works with the football data from the lesson: Football and Braking Distance: Model Data with Quadratic Functions. 

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Secondary Complex Numbers

Algebra 2 lesson: Using the definition of complex numbers and operations with complex numbers, students add, multiply, and graph with complex numbers using some sample items from the NC Algebra II Indicators. Once familiar with the operations and graphing, students iterate complex numbers in functions to determine whether the iteration stabilizes. With some experimentation, rules are developed that show patterns in stabilization that carry into graphs by special coloring schemes. The result is a fractal. Examples from the Julia Set and the Mandelbrot Set are shown. 

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Secondary Composition and Inverses of Functions

Algebra 2 lesson: Concepts of composition are used to develop functions that describe volumes of pyramids with specific bases and combinations of special discounts when purchasing a car. The connection between study time and number of courses leads to a function using inverse function that can help students determine the number of courses to take for available weekly study time. 

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Secondary, Post Secondary Continuous and Differentiable Functions

Part of the NCSSM Online AP Calculus Collection: This video deals with Continuous and Differentiable Functions. http://www.dlt.ncssm.edu

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Secondary Data Gathering: function model

The function model for each of four data gathering activities is a power function

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Secondary Data Gathering: function model

The function model for each of four data gathering activities is a power function

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Secondary, Post Secondary Definite Integral

Part of the NCSSM Online AP Calculus Collection: This video deals with the Integral formula. http://www.dlt.ncssm.edu

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Secondary, Post Secondary Definite Integral Interpretations

Part of the NCSSM Online AP Calculus Collection: This video deals with Definite Integral Interpretations. http://www.dlt.ncssm.edu

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Secondary, Post Secondary Derivative Formulas at a Point

Part of the NCSSM Online AP Calculus Collection: This video deals with Derivative Formulas at a Point. http://www.dlt.ncssm.edu

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Secondary, Post Secondary Derivatives of Implicit Relations

Part of the NCSSM Online AP Calculus Collection: This video deals with Derivatives of Implicit Relations. http://www.dlt.ncssm.edu

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Secondary Distance Formula

Algebra 2 lesson: Using rulers, students measure distances on a diagram to find a shortest path. They create ordered pairs and a scatterplot. With the motivation that the scatterplot has a clear message, the students develop a function that measures the distances using the distance formula. Based on the function, the shortest distance can be estimated and then considered on the diagram. A follow-up problem involving determining the best place to put a new Post Office is included. 

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Secondary End of Course Test: Developing Strategies

Algebra 2 lesson: Using nine sample items from the NC Algebra 2 End of Course test, students develop strategies for taking the end of course test. 

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Secondary Equations with Radical Expressions

Algebra 2 lesson: Data representing the period of a swinging pendulum versus the length of the pendulum can be best modeled by a square root function. Data and an appropriate model are both given to the students. Questions from the NC Algebra II Indicators require students to solve equations involving radical expressions. Solutions are also investigated from both a graphical and an analytical point of view. 

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Secondary, Post Secondary Errors in Taylor Polynomials

Part of the NCSSM Online AP Calculus Collection: This video deals with the Taylor/Maclauren series, geometric and binomial this is part 2 of 2. 

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Secondary Football and Braking Distance: Model Data with Quadratic Functions

Algebra 2 lesson: Students are given data to describe the trajectory of a football tossed from the tallest bleachers of a stadium. The data is fit with a quadratic function using least squares criteria. Given data extracted from page 288 of Glencoe’s Algebra II book, students investigate braking distance versus speed of a car. Using quadratic least squares, the student finds a best-fit function for the data. Data is given on reaction distance versus speed of the car. When reaction distance is added to braking distance to find total stopping distance, students fit another quadratic function. A Follow Up Problem relates number of sides of a polygon with the number of vertices to create a quadratic function. 

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