Choices pervade our lives. From concrete examples to questions with restrictions, students count choices and solve problems involving combinations. Practical and technological examples are included.
Producers: Alberta Advanced Education
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General Quadratic Relation: An Introduction
Discusses the difference between a relation and a function, and focuses on developing the general quadratic relation and the conic sections that it defines.
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Probability
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.
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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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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.