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Math 2 (682) Course Outline

1. Marvelous Matrices (Matrix Operations)
Organize and interpret data using matrices, use matrices in business applications, add and subtract two matrices, multiply a matrix by a scalar, multiply two matrices, and interpret the meaning of the elements within a product matrix.

2. A New Angle on an Old Pyramid (Pythagorean Theorem and right triangle trigonometry)

Use similarity to determine unknown measures in triangles, use the Pythagorean Theorem and its converse to solve right-triangle problems, use technology to develop a table of trigonometric values, develop and apply the sine, cosine, and tangent ratios, and develop and apply the inverses of sine, cosine, and tangent.

3. When to Deviate from a Mean Task (Measures of Central Tendency)
Create a frequency table from raw data, interpret data displayed in histograms, interpret data displayed in pie charts, interpret data displayed in stem-and-leaf plots, interpret data displayed in box-and-whiskers plots, find measures of central tendency, determine mean absolute deviation, and determine standard deviation.

4. What are My Child’s Chances (Probability)
Collect data and calculate experimental probabilities, use Punnet squares and tree diagrams to determine sample spaces, determine the theoretical probabilities of events, compare experimental probabilities and theoretical probabilities, investigate formulas for determining the probability of two or more events, identify complementary, independent, dependent and mutually exclusive events, and simulate a situation involving independent events.

5. There’s No Place Like Home (Volume and Surface Area)
Determine the areas of regular polygons and circles, determine the surface areas and volumes of prisms, pyramids, cylinders and cones, calculate the surface areas and volumes of spheres, and identify a circle as the limiting shape for its inscribed regular polygons, a cylinder as the limiting shape for its inscribed regular prisms and a cone as the limiting shape for its inscribed regular pyramids.

6. Making Concessions (Linear Programming and Solving Systems of Equations)
Determine constraints for linear programming problems, write objective functions, interpret the meaning of points in a feasible region, find the corner points of a feasible region, develop the corner principle for optimization, find solutions to systems of inequalities in two variables, solve systems of equations in two and three variables graphically, algebraically (by substitution) and by using matrices, and use linear programming to make decisions involving the buying and selling of goods.

7. Crazy Cartoons (Transformational Geometry)
Use the properties of similar figures, calculate distances between points in the Cartesian Plane, explore the geometric relationships in perspective drawings, dilations centered at the origin, translations, rotations about the origin, reflections and composite transformations, write matrices for dilations centered at the origin, translations, rotations about the origin and reflections, and use matrix equations to transform geometric figures on the Cartesian Plane.

8. Hurry! Hurry! Step Right Up! (Geometric Probability)
Use geometric models for determining probability, use expected value to determine fair games, explore probabilities of multistage experiments, examine the difference between independent and dependent events, and explore conditional probability.

9. Atomic Clocks are Ticking (Negative and Fractional Exponents)
Develop models of exponential decay, examine the relationship between negative and positive exponents, use equations containing negative exponents as mathematical models, examine the relationship between rational exponents and roots, and develop properties of exponents.

10. Traditional Design (Geometric Properties)
Use paper-folding constructions to examine angle bisectors, perpendicular lines, parallel lines, and midpoints, explore properties of angles formed by parallel lines and a transversal, explore geometric rep tiles, identify relationships between tangents and secants, examine properties of parallelograms (specifically rhombi), and examine similar triangles created by dilations.

11. If the Shoe Fits… (Linear Models)
Use the sum of the absolute values of the residuals to compare how well linear models fit a set of data, model data using the median-median line, use the least-squares method to find a linear regression equation, graph and analyze residual plots.

12. Take It to the Limit (Sequences and Series)
Identify sequences that are arithmetic, geometric or neither, develop formulas for finite arithmetic and geometric series, develop a formula for certain infinite geometric series, and explore limits graphically and geometrically.

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