Problems for CAS Solution

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Problems for CAS Solution

• Lin McMullin
• MATH SCIENCE
• TECHNOLOGY CONFERENCE
• January 18, 2008
• Norman, Oklahoma

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Cubic Symmetry

• Show that any cubic polynomial has a point of
  rotational symmetry.

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Cubic Symmetry
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A Cubics 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.
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Ratios, We got Ratios
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Ratios, We got Ratios
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Analytic Geometry

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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

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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.
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Trigonometry

• SSS triangle.

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Trigonometry

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

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Trigonometry

• ASA triangle.

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

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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

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Problems for CAS Solution

• Lin McMullin
• MATH SCIENCE
• TECHNOLOGY CONFERENCE
• January 18, 2008
• Norman, Oklahoma

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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

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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.

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The Trapezoid Problem
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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

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Altitudes