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Math 100------------Math 100------------Math 100---------Math 100, Exams of Advanced Education

Abilene Christian University (ACU)Advanced Education

Math 100------------Math 100------------Math 100---------Math 100

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2025/2026

Available from 02/13/2026

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Math 100
Natural Number - correct answer - One of the numbers we use to count discrete
objects.
- 1 is this type of number. If ๐‘› is this type of number, then so is ๐‘› + 1.
Unit - correct answer - A natural number that divides all other natural numbers.
- Among the natural numbers, only 1 is one of these. Among the integers, โˆ’1 is too.
Prime Number - correct answer - A natural number that is neither a unit nor
composite.
- A non-unit natural number with only the "obvious" factors.
- Euclid proved about 2300 years ago that there are infinitely many of these.
Golden Ratio - correct answer - (1+โˆš5)/2
- The positive solution to ๐‘ฅ 2 โˆ’ ๐‘ฅ โˆ’ 1 = 0.
- Divide each Fibonacci number by the one that came before. The ratios approach
this number.
- If we keep replacing ๐‘ฅ with 1 ๐‘ฅ + 1, the value of ๐‘ฅ will approach this number.
Composite Number - correct answer - A natural number that can be broken down
into factors in a non-trivial way
- A product of two or more prime numbers (including, possibly, repeats of the same
prime number).
Fibonacci Number - correct answer - The first of these is 1, and so is the second.
Then, each number plus the one that came before will give you the next one.
- 1,1,2,3, 5,8, etc.
Lucas Number - correct answer - The first of these is 2 and the second is 1. After
this, the way we find each new number is the same as for the Fibonacci numbers.
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Download Math 100------------Math 100------------Math 100---------Math 100 and more Exams Advanced Education in PDF only on Docsity!

Math 100

Natural Number - correct answer - One of the numbers we use to count discrete objects.

  • 1 is this type of number. If ๐‘› is this type of number, then so is ๐‘› + 1. Unit - correct answer - A natural number that divides all other natural numbers.
  • Among the natural numbers, only 1 is one of these. Among the integers, โˆ’1 is too. Prime Number - correct answer - A natural number that is neither a unit nor composite.
  • A non-unit natural number with only the "obvious" factors.
  • Euclid proved about 2300 years ago that there are infinitely many of these. Golden Ratio - correct answer - (1+โˆš5)/
  • The positive solution to ๐‘ฅ 2 โˆ’ ๐‘ฅ โˆ’ 1 = 0.
  • Divide each Fibonacci number by the one that came before. The ratios approach this number.
  • If we keep replacing ๐‘ฅ with 1 ๐‘ฅ + 1, the value of ๐‘ฅ will approach this number. Composite Number - correct answer - A natural number that can be broken down into factors in a non-trivial way
  • A product of two or more prime numbers (including, possibly, repeats of the same prime number). Fibonacci Number - correct answer - The first of these is 1, and so is the second. Then, each number plus the one that came before will give you the next one.
  • 1,1,2,3, 5,8, etc. Lucas Number - correct answer - The first of these is 2 and the second is 1. After this, the way we find each new number is the same as for the Fibonacci numbers.

Condorcet Winner - correct answer - A candidate preferred by the majority to any single opponent. Condorcet's Paradox - correct answer - Sometimes there is no Condorcet winner.

  • Majority preference is not always transitive. Borda Count - correct answer - The voter puts numbers next to each candidate that rank them in order of preference. Then we add these ranks up and see whose score is most ideal (lowest if "1" means the top choice, or highest if "1" means the least preferred choice). Instant Runoff - correct answer - This is the type of "ranked choice voting" recently adopted by Maine.
  • If one candidate got a majority of "top choice" votes, that candidate wins. Otherwise we eliminate the candidate with the fewest "top choice" votes, transfer that candidate's votes to the next choice on each ballot, and repeat until there is a majority winner. Gerrymandering - correct answer - Drawing district lines in a way meant to produce unfair results.
  • If the voting districts have shapes with very low compactness, that's one indicator that this may have happened. But there are other indicators, such as the efficiency gap.
  • 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. Compactness - correct answer - How well a shape resembles a circle in not having too much perimeter per area - The coastline effect is one reason we should define this in a nuanced way for redistricting.
  • When drawing districts in densely populated areas, this should be treated less as a purely geometric concept, and also consider demographics. Wasted Vote - correct answer - A vote that could (in theory) have been allocated to another district to make its election more competitive with a different district map.

Cycle - correct answer - If there is more than one path from vertex A to vertex B, then your graph has one of these.

  • In the graph of a polyhedron, each face is bounded by one of these. - A sequence of edges that begins and ends at the same vertex, but doesn't repeat any vertex along the way. Tree - correct answer - It has just enough edges to be connected.
  • A connected graph with no cycles. Spanning Tree - correct answer - We can get one by picking just enough of a graph's original edges so the results is connected.
  • A connected, spanning subgraph w/ no cycles. Euler Characteristic Equation - correct answer - In the plane or on the surface of a sphere, it's ๐‘‰ + ๐น โˆ’ ๐ธ = 2. (Or you can say, ๐‘‰ โˆ’ ๐ธ + ๐น = 2).
  • This applies to connected graphs that you can draw without edges crossing. Platonic (a.k.a. Regular) Solid - correct answer - There are only five types of Minimum-Cost Spanning Tree - correct answer - A spanning tree where the total cost of the edges is as low as possible.
  • We can use Kruskal's algorithm to find one. Subdivision - correct answer - A of a graph is what we get when we replace at least one edge of that graph with a longer path. Bipartite Graph - correct answer - Even with just two colors, you can color the vertexes without giving adjacent vertexes the same color.
  • We can organize the vertexes into two "families" so that no two vertexes from the same "family" share an edge. K5 - correct answer - A complete graph on five vertexes.
  • A simple graph with five vertexes and edge for every pair of vertexes.

K3,3 - correct answer - A complete bipartite graph on three and three vertexes.

  • A simple graph that is not planar and has V= 6, E= 9 Fractal - correct answer - You can keep zooming in on any part of it and there is no limit to the detail you would keep discovering.
  • Its dimension might not be an integer. Coastline Paradox - correct answer - "How long is the coast?" doesn't have a good answer. Continuous Function - correct answer - As the inputs get closer the outputs tend to get closer; and there is no restriction on how close the outputs can tend to get if your inputs get close enough.
  • If the input ๐‘Ž gives a negative output and the input ๐‘ gives a positive output, somewhere between ๐‘Ž and ๐‘ must be an input that gives zero as the output. Arrow's Impossibility Theorem - correct answer - Every ordinal voting system must be unfair in at least one scenario. Kuratowski's Theorem - correct answer - The non-planar graphs are exactly those which contain a subdivision of either K5 or K3,3. Hot Loop Theorem - correct answer - On any circle where the temperature varies continuously, there must be some pair of opposite point with the same temperature. Four-Color Theorem - correct answer - For any planar, simple, connected graph, four colors are enough to color all of its vertexes so that no edge has the same color on both ends.
  • This arose from a question about maps which became a question about graph theory.
  • The only known proof are so complicated that they have to be partially done by computer.