MathMania 2012

  1. A car goes up a hill at a constant speed of 20 mph and then back down the same hill at a constant speed. The average speed for the round trip is 32 mph. What was the downhill speed?

  2. The graph of f (x) is shown. Sketch the graph of f (|x|).

  3. What is the next most likely term in the sequence 1, 1, 3, 5, 11, 21, 43, 85, …?

  4. If the polynomial x3 + 3x2 + kx + 6 has x − 2 as a factor, what must k be?

  5. What is the radius of the circle inscribed in a triangle with sides of length 5, 5, and 6?

  6. For how many values of n does an interior angle of a regular n-gon have a measure that is an integer number of degrees?

Here are the answers.