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1. Critical Thinking & Problem Solving1h 59m

Inductive and Deductive Reasoning
46m

Estimation and Graphs
49m

Problem Solving
24m

2. Sets4h 25m

Basic Set Concepts and Notation
24m

The Empty Set
6m

Subsets
43m

Complement of a Set
23m

Intersections and Unions
1h 40m

Venn Diagrams and Operations with Three Sets
35m

Set Applications: Survey Problems
32m

3. Logic4h 33m

Statements and Negations
18m

Quantifiers
20m

Logical Connectives
1h 0m

If-Then Statements (Conditionals)
21m

Truth Tables for Negations, Conjunctions, and Disjunctions
42m

Truth Tables for If-Then Statements
29m

Equivalent Statements
30m

Logical Arguments
33m

Standard Forms of Arguments
15m

4. Numeration Systems3h 14m

Hindu-Arabic Numeration System
16m

Babylonian Numeration System
17m

Mayan Numeration System
17m

Converting Between Bases
54m

Performing Computations in Other Base
1h 28m

5. The Real Number System3h 5m

Integers & the Order of Operations
15m

Rational Numbers
39m

Irrational Numbers
16m

Dividing Square Roots
18m

Exponent Rules
1h 0m

Power Rules
34m

6. Algebra Review8h 53m

Evaluating Algebraic Expressions
15m

Simplifying Algebraic Expressions
1h 2m

Linear Equations
38m

Direct & Inverse Variation
27m

Linear Inequalities in One Variable
41m

Quadratic Equations
1h 24m

Rectangular Coordinate System
28m

Intro to Functions and Notation
29m

Domain and Range
10m

Using Intercepts to Graph Lines
4m

Slope and Slope-Intercept Form
1h 8m

Systems of Linear Equations
1h 25m

Systems of Linear Inequalities
37m

10. Geometry3h 37m

Intro to Geometry
14m

Introduction to Angles
27m

Intro to Polygons
3m

Basics of Triangles
8m

Similar Figures
28m

Right Triangles and Pythagorean Theorem
9m

Perimeter and Area of Polygons
30m

Circles
23m

Special Right Triangles
13m

Trigonometry
39m

Intro to Fractals
18m

11. Voting and Apportionment3h 3m

Preference Ballots and the Plurality Method
29m

Borda Count Method
18m

Plurality With Elimination Method
15m

Pairwise Comparison Method
16m

Fairness Criterion
33m

Intro to Apportionment
26m

Hamilton's Method
16m

Jefferson's Method
15m

Alabama Paradox
12m

12. Graph Theory3h 1m

Intro to Graph Theory
31m

Degrees of Vertices
22m

Paths and Circuits
14m

Euler Paths and Euler Circuits
11m

Euler's Theorems
31m

Hamilton Paths and Hamilton Circuits
1h 9m

12. Graph Theory

Degrees of Vertices

Liberal Arts Math

12. Graph Theory

Degrees of Vertices

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Multiple Choice

Determine which graph fits the criteria: exactly five vertices and four odd vertices.

A

Graph with five vertices labeled P, Q, R, S connected forming a square with one diagonal, showing vertex degrees.

B

Graph with five vertices labeled P, Q, R, S, T connected by edges forming a square with diagonals.

C

Graph with five vertices labeled P, Q, R, S, T connected by edges forming a square with diagonals intersecting at T.

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Master Degrees of Vertices Example 1 with a bite sized video explanation from Colleen Daly

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Related Practice

Multiple Choice

Label the degree and parity (even/odd) of each vertex on each graph.

Multiple Choice

Label the degree and parity (even/odd) of each vertex on each graph.

Multiple Choice

Label the degree and parity (even/odd) of each vertex on each graph.

Multiple Choice

Graph $G$ is composed of vertices $H, I, J, K, L$ , and edges $H I, H J, H K, I K, J K, J L, K L$ .

Which vertices are adjacent to vertex $J$ ?

Multiple Choice

Graph $G$ is composed of vertices $H, I, J, K, L$ , and edges $H I, H J, H K, I K, J K, J L, K L$ .

Find the degree of vertex $K$ .

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