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Problems for CAS Solution

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samson
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Problems for CAS Solution. Lin McMullin MATH & SCIENCE TECHNOLOGY CONFERENCE January 18, 2008 Norman, Oklahoma. Cubic Symmetry. Show that any cubic polynomial has a point of rotational symmetry. . Cubic Symmetry. A Cubic’s Roots.

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Problems for CAS Solution
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  1. Problems for CAS Solution Lin McMullin MATH & SCIENCE TECHNOLOGY CONFERENCE January 18, 2008 Norman, Oklahoma

  2. Cubic Symmetry Show that any cubic polynomial has a point of rotational symmetry.

  3. Cubic Symmetry

  4. A Cubic’s Roots Show that the tangent line to a cubic at the point where x = the average of two of its roots, intersects the cubic at its third root.

  5. Ratios, We got Ratios

  6. Ratios, We got Ratios

  7. Analytic Geometry

  8. Find the length of Write the equation of the perpendicular bisector of Write the equation of the set of points such that the sum of the distances from A and B is 9. Graph the locus found above. Analytic Geometry Perpendicular bisector theorem: Investigate the set of all points (x, y) in a plane equidistant from P(–3,2) and Q(5,4). Find the

  9. Analytic Geometry Given the quadrilateral with vertices a. Show that ABCD is a parallelogram. b. Are the diagonals perpendicular? Show how you know. c. Show that the diagonals bisect each other.

  10. Trigonometry SSS triangle.

  11. Trigonometry SSA triangle. This approach can be used for SAS as well.

  12. Trigonometry ASA triangle.

  13. Quartic Points of Inflection Where else does the line through the points of inflection of a fourth degree polynomial intersect the polynomial?

  14. How is DOING Math Different with a CAS? • The CAS does the algemetic so we can concentrate on the mathematics. • You can improve the CAS by adding your own operations and routines. • New approaches are possible once you stop worrying about the algemetic. • “Go for the equation.” • Complicating can make the work go faster. • One still needs to know mathematics.

  15. Implications for teaching Good CAS use is a new skill, a new tool that students must be taught and encouraged to learn. To do this we need • A willingness to accept new ways of doing problems • A new style of showing work • A change in how we think about “simplifying” • A good source of better problems for students to attempt

  16. Problems for CAS Solution Lin McMullin MATH & SCIENCE TECHNOLOGY CONFERENCE January 18, 2008 Norman, Oklahoma

  17. DOING Math with a CAS The text of this presentation along with the slides, examples and solutions are available at www.LinMcMullin.net Click on “Resources” then on “CAS”

  18. The Trapezoid Problem • A trapezoid with base 1 = a, and base 2 = b. Draw a segment that is parallel to the bases and divides the trapezoid's area A into A1 and A2. Represent the length of the segment in terms of a and b if A1 = A2.

  19. The Trapezoid Problem

  20. Altitudes in a Right Triangle Given a right triangle with legs of a and b, express the lengths of the segments , in terms of a and b Geometry Expressions Altitudes

  21. Altitudes