Math 100 Final exam Test Questions And
Answers Verified 100% Correct
Efficiency Gap - ANSWER -The disparity between two parties' numbers of
wasted votes across the state, divided by the total number of votes in the state.
Gerrymandering - ANSWER -If there are 35 voters and 7 districts, and only 12
voters support the Orange Party, it's possible to draw the district lines so that 4 out
of 7 districts go to the Orange Party.
Graph - ANSWER -In our class, it's an arrangement of vertexes and edges that
represents a network of connections
among objects or locations.
Vertex - ANSWER -In the "Bridges of Königsberg" problem, each landmass is
represented with one of these.
Vertex - ANSWER -Usually represented as a dot.
Edge - ANSWER -A direct connection between two vertexes (which may both be
the same vertex).
Edge - ANSWER -In the "Bridges of Königsberg" problem, each bridge is
represented with one of these.
Euler Circuit - ANSWER -An Euler trail that ends up at the same vertex where it
started.
Euler Circuit - ANSWER -This is only possible if no vertex has odd degree.
Euler Trail - ANSWER -This can still be possible if there are exactly two vertexes
with odd degree. One of these must be where we start and the other must be where
we end up.
, Euler Trail - ANSWER -A way of walking around the graph that crosses each
edge exactly once.
Connected Graph - ANSWER -A graph in which we can get from any vertex to
any other vertex by walking along edges.
Simple Graph - ANSWER -A graph with no loops or repeated edges.
Planar Graph - ANSWER -You can draw it in the plane without edges
crossing.
Cycle - ANSWER -If there is more than one path from vertex A to vertex B, then
your graph has one of these.
Cycle - ANSWER -In the graph of a polyhedron, each face is bounded by one of
these.
trees - ANSWER -It has just enough edges to be connected.
Tree - ANSWER -A connected graph with no cycles.
cycle - ANSWER -A sequence of edges that begins and ends at the same vertex,
but doesn't repeat any vertex along the way.
spanning tree - ANSWER -We can get one by picking just enough of a graph's
original edges so the result is connected.
spanning tree - ANSWER -A connected, spanning subgraph w/ no cycles.
Euler Characteristic Equation - ANSWER -In the plane or on the surface of a
sphere, it's
𝑉 + 𝐹 − 𝐸 = 2. (Or you can say, 𝑉 − 𝐸 + 𝐹 = 2)
Answers Verified 100% Correct
Efficiency Gap - ANSWER -The disparity between two parties' numbers of
wasted votes across the state, divided by the total number of votes in the state.
Gerrymandering - ANSWER -If there are 35 voters and 7 districts, and only 12
voters support the Orange Party, it's possible to draw the district lines so that 4 out
of 7 districts go to the Orange Party.
Graph - ANSWER -In our class, it's an arrangement of vertexes and edges that
represents a network of connections
among objects or locations.
Vertex - ANSWER -In the "Bridges of Königsberg" problem, each landmass is
represented with one of these.
Vertex - ANSWER -Usually represented as a dot.
Edge - ANSWER -A direct connection between two vertexes (which may both be
the same vertex).
Edge - ANSWER -In the "Bridges of Königsberg" problem, each bridge is
represented with one of these.
Euler Circuit - ANSWER -An Euler trail that ends up at the same vertex where it
started.
Euler Circuit - ANSWER -This is only possible if no vertex has odd degree.
Euler Trail - ANSWER -This can still be possible if there are exactly two vertexes
with odd degree. One of these must be where we start and the other must be where
we end up.
, Euler Trail - ANSWER -A way of walking around the graph that crosses each
edge exactly once.
Connected Graph - ANSWER -A graph in which we can get from any vertex to
any other vertex by walking along edges.
Simple Graph - ANSWER -A graph with no loops or repeated edges.
Planar Graph - ANSWER -You can draw it in the plane without edges
crossing.
Cycle - ANSWER -If there is more than one path from vertex A to vertex B, then
your graph has one of these.
Cycle - ANSWER -In the graph of a polyhedron, each face is bounded by one of
these.
trees - ANSWER -It has just enough edges to be connected.
Tree - ANSWER -A connected graph with no cycles.
cycle - ANSWER -A sequence of edges that begins and ends at the same vertex,
but doesn't repeat any vertex along the way.
spanning tree - ANSWER -We can get one by picking just enough of a graph's
original edges so the result is connected.
spanning tree - ANSWER -A connected, spanning subgraph w/ no cycles.
Euler Characteristic Equation - ANSWER -In the plane or on the surface of a
sphere, it's
𝑉 + 𝐹 − 𝐸 = 2. (Or you can say, 𝑉 − 𝐸 + 𝐹 = 2)
