A review of trigonometric and circular functions. Topics receiving special attention include radian measure, transformation of trigonometric functions, solving trigonometric equations, and proving identities.
Countries: CA
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Division of Polynomial Functions and Their Graphs
Historical anecdotes intersperse the teaching of long division with linear and nonlinear divisors. The concept of synthetic division is also presented, along with a strategy for finding missing coefficients.
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Sketching and Graphing Exponential Functions
Students learn to recognize the general characteristics of the graphs of exponential functions with various bases. Situations involving exponential growth and decay are explored. Students solve and verify exponential equations.
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The Remainder and Factor Theorems
The Remainder Theorem is illustrated, proven, and then used to prove the Factor Theorem.
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Exponential Growth and Decay
Through a variety of real world applications, this program explores the concepts of exponential growth and decay. Examples include carbon dating, bacterial growth, DNA splicing and the effect of the bubonic plague on current world populations.
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Factoring and Graphing Polynomial Functions
Prior knowledge of factoring, the Remainder and Factor Theorems, the division algorithm and the graphs of functions are all brought together in this program. The concept of multiplicity is modelled in a unique way and its effects are shown with graphics.
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Inverse of the Exponential Function: The Logarithmic Function
Examines inverses, logarithms and their graphs and introduces the formal definition of logarithms and the characteristics of their graphs. Presents rewriting logarithmic expressions in exponential form and vice versa and the properties of logarithms.
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Applications and Problem Solving
Discusses the problem solving process. Students are taught to derive equations of integral polynomial functions when given the zeros, a point and a zero, or the zeros and any other information that uniquely defines the functions.
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Laws of Logarithms: Evaluating Logarithmic Expressions
A review of the exponent laws is used to establish and prove the laws of logarithms. Students learn how to simplify and evaluate logarithmic expressions using the laws. Log and semi-log graph paper is demonstrated.
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Polynomial Functions Review
This program reviews concepts relating to polynomial functions. Topics include the Factor and Remainder Theorems, division of polynomials, graphing and writing the equation of a polynomial function.