Combination locks and the Braille alphabet are some applications used to review the permutations and combinations module. Topics include the Fundamental Counting Principle, permutations, combinations, combinatorics and the Binomial Theorem.
Producers: Alberta Advanced Education
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Describing Real World Phenomena Using Logarithms
Decibels, the Richter Scale, pH levels and the slide rule are applications of logarithms examined via experiments, interviews and solving problems.
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Alternate Locus Definitions: Ellipse and Circle
String and tacks are used to redefine the circle and ellipse using the concept of locus. Also shown: how to find the equation of a conic, use double-concentric graph paper, and solve problems that require an understanding of the concept of locus.
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Preparing for Examinations
A variety of strategies to make preparaton for writing a major mathematics exam more efficient and benefical are discussed. The information provided would transfer to many subject areas.
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Exponential and Logarithmic Functions: Review and Problem Solving
Reviews expressions, equations and graphs related to exponential and logarithmic functions. Graphs are presented as inverses, both in base 10 and base e. Demonstrates exponential growth and exponential decay.
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Locus and Eccentricity of the Hyperbolas
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.
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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.