Investigates several approaches used to study the hyperbola’s shape: locus involving two fixed points; double concentric circles; the focus-directrix (eccentricity) definition; and computer graphing programs.
Languages: English
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Introduction to Sequences
Identifies finite and infinite sequences, the terms of a sequence given a function that describes it, and functions that describe simple sequences. Provides an observation of the Fibonacci sequence in nature.
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Identification, Connections and Applications of Quadratic Relations
Shows how to identify the type of conic given a description based on any of the four forms, connect the various conics to their definitions and solve a variety of problems.
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Sequences: Recursive Forms
Addresses how to write the terms of a sequence, given its recursive definition, and the converse: how to define a sequence recursively, given its terms. Shows how a computer program performs the calculations indicated by a recursive definition.
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Quadratic Relations: Review
Each conic is studied individually in terms of its locus and eccentricity definition, identifying characteristics of the general form of the equation, and providing examples of questions that can be solved with this information.
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Arithmetic Sequences
Emphasis is placed on understanding the patterns in arithmetic sequences and the general term formula is manipulated to solve for a, n, tn, and d. A system of equations is used to solve an arithmetic means problem.
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Normal Distribution
This program shows some of the ways in which statistics play a role in today’s society. The measures of central tendency — mean, median and mode — are reviewed and standard deviation is introduced as a measure of dispersion.
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Geometric Sequences
Students learn to identify what makes a sequence geometric, and using the principles behind its definition, derive its general term. Examples of geometric sequences found in music are explored.
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Characteristics of Normal Distribution
Characteristics of normal distribution are applied to a variety of problems involving data that is normally distributed. Problems involve topics such as the mean length of Walleye fish and hockey games.
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Arithmetic Series
Develops both forms of the sum formula used for arithmetic series questions. Manipulation of the formula demonstrates how to solve for a variety of unknowns. Demonstrates several different problem solving approaches using an open-ended question.