North Carolina SCOS Discrete Math

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Select the number of each type of objective: (Selecting Random will randomly generate all subtypes) Click on any title to see the free sample worksheet. (only the first few samples are free) (Random) 1.01 Use matrices to model and solve problems. a. Performing Matrix Operations (Addition/Subtraction/Scalar Multiplication) b. Performing Matrix Multiplication c. Finding the determinants of Matrices d. Finding Matrix Inverses (3x3) e. Finding Matrix Inverses (4x4) f. Apply Adjacency Matrices g. Apply the Leslie matrix model to population models h. Apply the Markov chain to probability models i. Apply the Leontief model to economic situations j. Create a Game Matrix k. Determine the Expected Value of the Game Matrix l. Identifying and Using Game terms such as Zero-Sum and Minimax m. Nash equilibrium, the Prisoner's Dilemma, and the Game of Chicken n. Nash Equilibrium for 3x3 and 4x4 Games o. Rules of TOM (Theory of Moves) p. Creating a Tree Diagram in TOM (Theory of Moves) and Determining if it is Cyclic q. Finding all NME (Nonmyopic Equilibria) r. Larger TOM Games (Theory of Moves) (Random) 1.02 Use graph theory to model relationships and solve problems. a. Define a graph and its parts b. Finding Bridges, Loops, and Multiple Edges c. Identifying if Graph has an Open or Closed Unicursal Tracing d. Applying Euler's Graph Theory e. Creating Eulerizations and Semi-Eulerizations f. Solving Euler Path/Circuit Word Problems g. Finding Hamilton Circuits and Paths h. Using and Identifying Complete Graphs i. Solving the Traveling Salesman Problem (Brute Force) j. Solving the Traveling Salesman Problem (Nearest Neighbor) k. Solving the Traveling Salesman Problem (Repetitive Nearest Neighbor) l. Solving the Traveling Salesman Problem (Cheapest Link) m. Using and Identifying Trees n. Find the Number of Spanning Trees (simple cases) o. Find Minimum Spanning Trees Using Kruskal's Algorithm p. Find Minimum Spanning Trees Using Prim's Algorithm q. Find Minimum Spanning Trees Using Dijkstra's Algorithm r. The Shortest Network and Steiner Points s. Find the chromatic number of a graph t. Find the chromatic index of a graph u. Identifying Snarks v. Identifying Planar Graphs w. Coloring Graphs vs. Maps x. Use Graph Coloring for Scheduling Problems y. Directed Graph (Digraph) Terminology z. Applying Euler's Graph Theory for Directed Graphs aa. Finding Hamilton Circuits and Paths for Directed Graphs bb. Facts about Schedules cc. Applying the List Processing Algorithm dd. Applying the Decreasing Time Algorithm ee. Compute the earliest Completion Time using Critical Paths ff. Applying the Critical Path Algorithm gg. Identifying Bin Packing vs. Scheduling Problems hh. Bin Packing Problems (Random) 2.01 Describe data to solve problems. a. Center and Spread b. Clusters and Gaps c. Outliers and other Unusual Features d. Shape e. Situational Problems f. Measuring Center: Median, Mean g. Measuring Spread: Range, Interquartile Range, Standard Deviation h. Comparing Center and Spread i. Comparing Clusters and Gaps j. Comparing Outliers and other Unusual Features k. Comparing Shapes l. Census m. Sample Survey n. Experiment o. Observational Study p. Properties of Normal Distribution q. Using Tables of the Normal Distribution r. The Normal Distribution as a Model for Measures	(Random) 2.02 Use theoretical and experimental probability to model and solve problems. a. Empirical vs. Theoretical vs. Subjective Probability b. Law of Large Numbers c. Finding Sample Space d. Mutually Exclusive and Basic Probabilities e. Finding Probability of Independent Events f. Finding Probability of Dependent Events g. Identifying Permutations and Combinations h. Calculating Permutations (And other cases where order matters) i. Calculating Combinations j. Calculating Rearrangements of Words k. Using Formulas l. Discrete vs. Continuous Random Variables m. Probability Distributions n. Mean of a Discrete Random Variable o. Variance and Standard Deviation of a Discrete Random Variable p. Definition of a Binomial Probability Distribution q. Mean and Standard Deviation of Binomial Distributions r. Finding the Sample Space s. Multiplication Rule t. Addition Rule u. Combining Probabilities v. Probability Trees w. Probability using Combinatorics x. Probability with Replacement y. Probability without Replacement z. Binomial Probability aa. Expected Value bb. Pigeonhole Principle (Random) 2.03 Model and solve problems involving fair outcomes: a. Creating a Preference Schedule b. Using Plurality c. Using Borda d. Using Plurality with Elimination e. Using Condorcet (Pairwise Comparisons) f. Using Extended Rankings g. Using Plurality with Runoff h. Fairness Criterion and Arrow's Theorem i. Using Approval Voting j. Using Weighted Voting Systems k. Computing Power Index (Banzhaf) l. Computing Shapley-Shubik Power Index m. Fair Division: The value of things n. Allocating Items with Adjusted Winner Procedure o. Resolving A Dispute with Adjusted Winner Procedure p. Divider-Chooser Method q. Lone-Divider Method r. Lone-Chooser Method s. Last Diminisher Method t. Method of Sealed Bids (Knaster Inheritance) u. Method of Markers v. Trimming Procedure w. Equitable, Envy-Free, and Pareto-Optimal x. Standard Divisors and Quotas y. Hamilton's Method z. Jefferson's Method aa. Adam's Method bb. Webster's Method cc. Huntington-Hill Method (Random) 3.01 Use recursion to model and solve problems a. Identifying Arithmetic/Geometry Sequences b. Writing the first n terms of an Arithmetic Sequence c. Defining an Arithmetic Sequence with Recursion d. Finding the n^th term formula for an Arithmetic Sequence e. Finding Arithmetic Means f. Evaluating Summations of Arithmetic Series (Number Arches Video) g. Writing the first n terms of a Geometric Sequence h. Defining a Geometric Sequence with Recursion i. Finding the n^th term formula for a Geometric Sequence j. Finding Geometric Means k. Evaluating Finite Summations of Geometric Series l. Evaluating Infinite Summations of Geometric Series
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