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.
Countries: CA
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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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Locus and Eccentricity of the Parabola
Presents several approaches that can be used to investigate the shape of the parabola. Locus and eccentricity are explained and then used to solve problems that involve determining and analysing equations of various parabolas.
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Binomial Theorem
Expansions of powers of a binomial are examined from the point of view of patterns, including the link between the coefficients and Pascal’s Triangle. Binomial expressions are then expanded using the Binomial Theorem.
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Eccentricity of the Ellipse
Orbits and sewers are just two of the examples used in this study of the eccentricity definition of ellipses. Eccentricity is defined, the shape of an ellipse as e approaches 0 and 1 is observed, and problems are solved using the eccentricity.
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Permutations and Combinations: Review
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.
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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.