Download Exam 1 Study Guide - Math

Name:
Exam 1 Study Guide
Math 257: Geometry & Probability for Teachers, with Joe Champion, Fall 2013
Instructions
1. Exam 1 is one of two unit exams that combine for 50% of the overall course
grade. The exam covers content from Chapters 16-18 & 22 in the textbook,
including in-class activities, homework, handouts, and quizzes.
2. You may use a personal reference sheet on the exam. The reference sheet must be
on 1 side of an
page and be written entirely in your own hand-writing.
3. You may bring a writing utensil, calculator, protractor, ruler, and compass to the
exam. You may also use patty paper and a Mira during the exam.
4. Any resources not listed above are not allowed during the exam. At the
instructor’s discretion, use of additional resources may result in a 0 on the exam.
5. To earn full credit on problems, justify your solutions, make your reasoning clear, and
indicate your methods. These explanations may earn you partial credit, no matter what the
question format.
6. There are 15 tasks for 100 points on the exam. The tasks must be completed during the
scheduled time 75 minute time.
Suggested Practice Tasks for Exam 1
1. I am a polyhedron with a total of 9 faces. My lateral faces are isosceles triangles.
What is my full name?
2. Complete the following:
A) A prism with 16 vertices is (what kind of?) ______________ prism.
B) A hexagonal prism has ____ edges, ____ vertices, and ____ faces.
C) A pyramid with 60 edges has ____ vertices and ____ faces.
D) A pentagonal prism has ____ edges, ____ vertices, and ____ faces.
3. Complete the following:
A) A hexagonal prism has ____ lateral edges, ____ edges in all, and ____ vertices.
B) A rectangular pyramid has ____ edges, ____ vertices, and ____ faces.
C) A prism with 9 faces has ____ vertices and ____ edges.
D) A pyramid with 32 edges has ____ faces and ____ vertices.
E) A polyhedron with 6 vertices and 8 faces has ____ edges.
1
4. Which of the following is the most descriptive and correct name for the shape below?
A)
B)
C)
D)
E)
Polyhedron
Octagon
Hexagonal prism
Octahedron
L-pyramid
5. A polyhedron with 14 vertices and 6 faces will have how many edges?
A) 5
B) 6
C) 8
D) 18
E) Not enough information
6. Which of these is safe to say about every square pyramid?
X. Every lateral edge has the same length.
Y. all of the angles on each face are equal.
Z. Every base edge has the same length.
A) X only
B) Y only
C) Z only
D) X and Z only
E) Some choice among X, Y, and Z not given here
7. Name the 5 types of platonic solids, name the regular polygon each is made up of, and then list
the numbers of vertices, edges, and faces for each.
Name of solid
Polygon used for faces
#Vertices
#Edges
#Faces
2
Name:
8. Give the best name for the 3-D shapes represented by the following pictures. Angles that look
like right angles are right angles in the 3-D shape.
9. Draw, as carefully as possible, the following figures:
A) A right pentagonal prism
B) A triangular pyramid
10. Draw a net for a cube in two different ways.
11. What is the best name for every four-sided polygon with equal sides?
A) Square
B) Parallelogram
C) Rectangle
D) Rhombus
E) Kite
3
12. Sketch an example, if it is possible, of each shape described. If any are not possible to
sketch, explain why.
A) An isosceles triangle that is not an acute triangle
B) A quadrilateral with two 90-degree angles that is not a rectangle. Be sure to mark the 90degree angles.
C) A kite that is also a rectangle
D) A triangular right prism (show every hidden edge as a dashed segment)
13. Indicate whether each of the following is always true, sometimes true, or never true.
A) A parallelogram is an isosceles trapezoid.
B) A square is a rhombus.
C) A scalene triangle is an acute triangle.
14. Complete the following:
A) The measure of EACH interior angle of a regular decagon is ____.
B) If an interior angle of a regular polygon is 175 degrees, then the polygon has ____ sides.
C) The number of congruent sides on a scalene triangle is ____.
D) The number of diagonals in 16-gon is ____.
15. A) Add to the following design so that it has a reflection symmetry. Draw in the line of
symmetry.
B) Now, add to the original design so that it ahs a rotational symmetry. Show the center of
rotation.
16. Consider the following right regular hexagonal prism:
How many reflection symmetries does the figure have?
How many rotational symmetries does the figure have?
4
Name:
17. Add to following figure so that it has rotational symmetry. Show a center of rotation after the
addition.
18. Determine the smallest positive amount of the turn (in degrees) for the rotational symmetries in
each of the figures below:
19. A) How many rotational symmetries does a regular 12-gon have?
B) What is the minimum (positive) number of degrees of rotation for a symmetry of a regular
12-gon?
20. See below. The unlabeled figure at top left is the original figure. Each of the others, labeled a–
h, is the result of a rigid transformation of the original. Determine if each is the result of a
translation, rotation, reflection, or glide reflection.
a
original
b
c
f
g
d
e
h
5
21. Name the type of rigid motion involved in each of the listed motions. Take into account the
different types of "eyes."
A
D
C
B
A
B
A
C
A
D
22. “Figure X is congruent to Figure Y.” What does that statement mean?
23. A) Give an argument which shows this statement is true (write full sentences): Every rigid
motion can be expressed with at most three reflections.
B) Illustrate the statement given in part A, by showing the line(s) of reflection that, with
composition if necessary, give the image below.
original
image
6
Name:
24. Name the type of rigid motion involved in each of the listed motions. Take into account the
different types of “eyes.”
A --> B ___________________
A --> F ___________________
B --> C ___________________
B --> D ___________________
A --> E ___________________
25. Draw accurately each of the following.
A. the vector for this
translation
B. the line of
reflection involved
here
image
original
P
Q
R'
S
Q'
R
S'
P'
7