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Virginia Mathematics Capstone Course
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(Random) 1. Solve practical problems involving rational numbers (including numbers in scientific notation), percents, ratios, and proportions.

(Random) 2. Collect and analyze data, determine the equation of the curve of best fit, make predictions, and solve real-world problems using mathematical models. (Random) 3. Use pictorial representations, including computer software, constructions, and coordinate methods, to solve problems involving symmetry and transformation. (Random) 4. Verify characteristics of quadrilaterals and use properties of quadrilaterals to solve real-world problems. (Random) 5. Solve real-world problems involving right triangles by using the Pythagorean Theorem and its converse, properties of special right triangles, and right triangle trigonometry. (Random) 6. Use formulas for surface area and volume of three-dimensional objects to solve real-world problems. (Random) 7. Use similar geometric objects in two- or three-dimensions (Random) 8. Compare distributions of two or more univariate data sets, analyzing center and spread (within group and between group variations), clusters and gaps, shapes, outliers, or other unusual features. (Random) 9. Design and conduct an experiment/survey. (Random) 10. Investigate and apply the properties of arithmetic and geometric sequences and series to solve real-world problems, (Random) 11. Use angles, arcs, chords, tangents, and secants (Random) 12. Transfer between and analyze multiple representations of functions (Random) 13. Investigate and describe the relationships among solutions of an equation, zeros of a function, x-intercepts of a graph, and factors of a polynomial expression. (Random) 14. Recognize the general shape of function (absolute value, square root, cube root, rational, polynomial, exponential, and logarithmic) families and convert between graphic and symbolic forms of functions (Random) 15. Use knowledge of transformations to write an equation, given the graph of a function (linear, quadratic, exponential, and logarithmic). (Random) 16. Investigate and analyze functions (linear, quadratic, exponential, and logarithmic families) algebraically and graphically. (Random) 17. Determine optimal values in problem situations by identifying constraints and using linear programming techniques.

(Random) 18. Use rational, radical, or polynomial expressions (Random) 19. Graph linear equations and linear inequalities in two variables. (Random) 20. Given a point other than the origin on the terminal side of an angle, use the definitions of the six trigonometric functions to find the sine, cosine, tangent, cotangent, secant, and cosecant of the angle in standard position. (Random) 21. Given the coordinates of the center of a circle and a point on the circle, write the equation of the circle. (Random) 22. Analyze graphical displays of univariate data (Random) 23. Analyze the normal distribution. (Random) 24. Describe orally and in writing the relationships between the subsets of the real number system. (Random) 25. Perform operations on complex numbers (Random) 26. Solve equations algebraically and graphically, (Random) 27. Investigate trigonometric functions. (Random) 28. Find the values of the trigonometric functions of the special angles and their related angles as found in the unit circle. (Random) 29. Investigate and identify the characteristics of conic section equations (Random) 30. Using two-way tables, analyze categorical data to describe patterns and departure from patterns and to find marginal frequency and relative frequencies, including conditional frequencies. (Random) 31, Calculate probabilities. (Random) 32. Use the relationships between angles formed by two lines cut by a transversal (Random) 33. Prove two triangles are congruent, using algebraic and coordinate methods as well as deductive proofs. (Random) 34. Prove two triangles are similar, using algebraic and coordinate methods as well as deductive proofs. (Random) 35. Construct and justify constructions (Random) 36. Verify basic trigonometric identities and make substitutions, using the basic identities.

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