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.
Grade levels: Senior High (10-12)
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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.
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Logarithmic and Exponential Equations
Describes how to solve and verify exponential equations and logarithmic equations, both base 10 and non base 10. Presents historical facts about calculating devices, such as the abacus and Napier’s Bones.
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Radian Measurement
The discovery approach is used to examine an angle of one radian. Introduces the concept of radian measure and shows how to convert from radians to degrees and vice versa. Applications of radian measure to arc length and angular velocity are explained.
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Development of Circular Functions
Reviews previously learned vocabulary and concepts of the primary trigonometric ratios, degree/radian relationship and the development and application of special, quadrantal, reference and coterminal angles.
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Applications of Circular Functions
Students learn how to solve trigonometric equations of primary or reciprocal functions either algebraically or graphically.
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Graphing Trigonometric Functions
Students explore the relationship between radians and degrees and learn how to graph primary and reciprocal functions. Emphasis is placed on the importance of understanding the function’s properties including domain, range, period, and y-intercepts.