This review of the basics of probability shows how permutations can be used to solve probability problems in which order plays a role. New technology in DNA fingerprinting is one of the applications featured.
Languages: English
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General Quadratic Relation: Circles and Ellipses
Physical characteristics of the circle and ellipse are identified and related to the parameters of the general quadratic relation. The connection between A and C and the effects of changing D, E and F are determined.
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Probability: Combinatorics
The probability of card games demonstrates the application of combinatorics to probability problems. Explores questions involving complementary probabilities and the phrases “at least” and “at most.”
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General Quadratic Relations: Parabola and Hyperbolas
Provides an understanding of the general quadratic relation, Ax2 + Bxy + Cy2 + Dx + Ey + F = 0, where B = 0 with respect to parabolas and hyperbolas.
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Binomial Theorme (Pascal’s Triangle)
The connection between Pascal’s Triangle and binomial distribution is made using a model. Pascal’s Triangle is used to carry out binomial expansion and solve problems.
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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.