Convex Region - Elementary Maths - Exam, Exams of Elementary Mathematics

Main points of this past exam are: Convex Region, Concepts, Simple Closed Curve, Scalene, Tetrahedron, Net, Mnemonic

Typology: Exams

2012/2013

Uploaded on 03/31/2013

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Prof. S. Brick Math 202
Spring’06 Elem Ed Math II Exam 1 section 101
Print your name:
Show all of your work, and explain your reasoning. Do not use any crude ap-
proximations for π. No calculators allowed and no calculator-type of calculations
are necessary.
1. In words, define the following concepts: convex region, simple closed curve, and scalene
triangle. (You need not define what a region is, what a curve is, or what a triangle is.)
2. Explain what a net is. Then draw a net for the tetrahedron.
3. Give a mnemonic for π(for more than 5 digits) and explain how it works.
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Prof. S. Brick Math 202

Spring’06 Elem Ed Math II Exam 1 section 101

Print your name:

Show all of your work, and explain your reasoning. Do not use any crude ap- proximations for π. No calculators allowed and no calculator-type of calculations are necessary.

  1. In words, define the following concepts: convex region, simple closed curve, and scalene triangle. (You need not define what a region is, what a curve is, or what a triangle is.)
  2. Explain what a net is. Then draw a net for the tetrahedron.
  3. Give a mnemonic for π (for more than 5 digits) and explain how it works.
  1. Give the names of all possible regular polyhedra. Which ones did we construct in class and what did we use to construct them? Is the sphere a poyhedron, regular or not regular ? Explain.
  2. Draw a sphere and a right cylinder. Then find the volumes and surface areas if the sphere has radius 4 inches and the right cylinder has radius 3 inches and height 7 inches. Be sure to include the units.
  1. Draw the image of the triangle E (and its label, the letter E) under the dilation with pictured center and scaling factor 12. Explain each steps of your construction. Without doing any measurements, describe how the dilation has changed the area of the triangle.
  2. Draw a cube. Is it possible or impossible to draw it without retracing and/or lifting your pen? (Here drawing a dashed line does not count as lifting your pen.) Explain.
  1. At noon a car leaves town heading due west at 40mph. At 1pm a second car leaves town heading due north at 70mph. How far apart (as the proverbial crow flies) are the two cars at 2pm? Draw a picture and show and explain your work. Give the name of the theorem you are using.
  2. Using the fact that there are 5280 feet in one mile, set up an equation that would convert speed of 70 mph (miles per hour) into the corresponding speed in feet per second. Write your equation so it is clear when and why you sometimes multiply and sometimes divide.