Missouri State University

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Mathematics 

MathMania 2001 Problems

  1. In the diagram shown, all angle measures are in degrees. Given that y = 80 degrees and z = 120 degrees , find x.
    Triangle ABC is shown with a point D on segment AB and a point E on the interior of triangle ABC. The measure of angle BAE is x, the measure of angle AEC is y, and the measure of angle BDC is z.

     

     

     

    Triangle ABC is shown with a point D on segment AB and a point E on the interior of triangle ABC. The measure of angle BAE is x, the measure of angle AEC is y, and the measure of angle BDC is z.

    Find the next term in the sequence: 4, 5, 8, 17, 44, 125, ...
  2. If 2x3 - 9x2 + 15x + k is evenly divisible by x - 2, what is the value of k?
  3. Find the equation of the circle passing through the points (0,0), (1,7), and (2,4).
  4. Solve the equation |x + 2| = 2|x - 3|.
  5. How many six-digit numbers contain at least one 7 in their decimal expansion?

Here are the answers.