MATH 305 Topics for the Final Exam
Spring 2014

Recall that this is an individual exam, worth 150 points. It is a comprehensive exam, covering the entire semester but with extra emphasis on the material since Test 2. You should also consult the Topics lists from the previous exams, available on the website.

The exam will consist of problems similar to the exercises at the end of the chapters. However an exam problem may combine two or more concepts, perhaps from different chapters. You may use your book, notes, homework, and old tests as references during the exam. You will be expected to use Sketchpad.




Chapter 10

  1. The concept of a symmetry
  2. Composing symmetries; computing by cycle notation
  3. Symmetry group for a figure in the plane
  4. Cyclic and dihedral groups; Leonardo’s Theorem
  5. Identifying symmetry groups for plane figures
  6. Identifying symmetries for friezes


  1. A1, A2
  2. A5, E2, E3
  3. A3, A5, E5, E14, E16
  4. E6, E9, E10
  5. A4, E1, E11
  6. A6, E7, E8

Chapter 11

  1. The Poincaré disk model: reinterpreting lines, angles, distance.
  2. Parallel lines and the hyperbolic parallel postulate
  3. Asymptotic triangles
  4. Limiting parallels and the angle of parallelism
  5. Saccheri quadrilaterals
  6. Angle sum in a triangle or a quadrilateral


  1. A1, A2, A3, E3, E4, E6
  2. A8
  3. A5, E8, E9
  4. A9, E15, E16, E17
  5. A10, A12, E19, E20
  6. A4, A11, E24, E25, E26