Virginia 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) DM.LR.1 Logic Reasoning: Logic a. Check Digits b. Weighted Check Digits c. Using Codabar d. Postnet Bar Codes e. Information: ZIP, UPC, and Social Security Numbers f. Using the Soundex Code g. Binary Codes (Random) DM.LR.2 Logic Reasoning: Proofs a. Filling In Algebraic Proofs (Simplifying Expressions) b. Filling In Algebraic Proofs (Equations) c. Using Induction d. Truth Tables e. Truthtellers and Liars f. Logically Equivalent Statements g. Conditional Statements h. Valid/Invalid Arguments, Syllogism, Modus Pollens and Modus Tollens i. Digital Logic Circuits j. Boolean Algebra (Random) DM.LR.3 Logic Reasoning: Logical Gates and Circuits a. Partitions (Random) DM.LR.4 Logic Reasoning: Induction a. Writing Terms from Recursion form b. Finding Recursive Formulas c. Using Induction in Proofs d. Finding Polynomial Formulas for a Finite Sequence (Random) DM.SNT.4 Set and Number Theory: Sets a. Set Notation b. Unions, Intersections, Differences and Complements c. Venn Diagrams d. DeMorgan's Laws and Other Properties e. Subsets f. Power Sets g. Set Cardinality and Inclusion-Exclusion Principle (Random) DM.SNT.2 Set and Number Theory: Probability a. Combinations b. Permutations (And other cases where order matters) c. Simplifying Factorial Expressions d. Combinations with Replacement e. Binomial Theorem f. Multinomial Coefficients g. Counting Subsets h. Identifying Bin Packing vs. Scheduling Problems i. Bin Packing Problems (Random) DM.SNT.3 Set and Number Theory: Pascal's Triangle a. Extending Pascal's Triangle b. Finding Numerical Patterns in Pascal's Triangle c. Defining Binomial Coefficients d. Using Pascal's triangle to find the k^th term of (x + y)ⁿ (Binomial Theorem) e. Using Pascal's triangle to expand (x + y)ⁿ (Binomial Expansion) f. Using Pascal's triangle with Numbers g. Combinatoric Problems h. Coloring Multiples in Pascal's Triangle i. Petal Problems in Pascal's Triangle (Pascal's Flower) j. Finding the n^th Term of a Binomial Expansion (Pascal's Triangle) k. Finding the n^th Term of a Binomial Expansion (Combinatorics) l. Expanding Binomials (Random) DM.GT.1 Graph Theory: Using Graphs in Modeling a. Define a graph and its parts b. Finding Bridges, Loops, and Multiple Edges c. Using and Identifying Complete Graphs d. Using and Identifying Trees e. Directed Graph (Digraph) Terminology 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. Reading Venn Diagrams k. Identifying Union, Intersection, Complement, Etc. Venn Diagrams l. Highlighting Correct Parts of a Venn Diagram m. Drawing A Venn Diagram to Represent Logical Statements n. Count Vertices, Edges, and Faces for 3-D Figures	(Random) DM.GT.2 Graph Theory: Euler and Hamilton a. Identifying if Graph has an Open or Closed Unicursal Tracing b. Applying Euler's Graph Theory c. Creating Eulerizations and Semi-Eulerizations d. Solving Euler Path/Circuit Word Problems e. Finding Hamilton Circuits and Paths f. Solving the Traveling Salesman Problem (Brute Force) g. Solving the Traveling Salesman Problem (Nearest Neighbor) h. Solving the Traveling Salesman Problem (Repetitive Nearest Neighbor) i. Solving the Traveling Salesman Problem (Cheapest Link) (Random) DM.GT.3 Graph Theory: Coloring a. Find the chromatic number of a graph b. Find the chromatic index of a graph c. Identifying Snarks d. Identifying Planar Graphs e. Coloring Graphs vs. Maps f. Use Graph Coloring for Scheduling Problems g. Directed Graph (Digraph) Terminology (Random) DM.GT.4 Graph Theory: Trees a. Find the Number of Spanning Trees (simple cases) b. Find Minimum Spanning Trees Using Kruskal's Algorithm c. Find Minimum Spanning Trees Using Prim's Algorithm d. Find Minimum Spanning Trees Using Dijkstra's Algorithm e. The Shortest Network and Steiner Points (Random) DM.GT.5 Graph Theory: Scheduling a. Facts about Schedules b. Applying the Decreasing Time Algorithm c. Applying the Critical Path Algorithm (Random) DM.CM.1 Computational Methods: Coding a. Parity Check Sums b. Data Compression c. Cryptograms d. RSA Encryption (Random) DM.CM.2 Computational Methods: Recursion and Fractals a. Calculating Compound Interest Word Problems b. Applying Iteration c. Iterative Fractals d. Evaluating Polynomials with Complex Numbers e. The Game of Chaos f. Mandelbrot Set g. Julia Set h. Sierpinski's Triangle and Carpet i. Von Koch Snowflake and Anti-Snowflake j. Menger Sponge k. Cantor Set and Cantor Dust l. Tessellations (Tilings) m. Fibonacci Numbers n. The Golden Ratio o. Fibonacci Numbers and Quadratic Equations p. Gnomons and Similarity q. General Recursive Definitions r. Hand Shake Problem s. The Tower of Hanoi Puzzle t. Using Recursive Relations u. Linear Growth v. Exponential Growth w. Logistic Growth (Verhulst Law of Restrained Growth) x. Percentages of Percentages (Random) DM.CM.3 Computational Methods: Cryptographic Methods a. Applying a bubble sort b. Applying a merge sort c. Using a ROT code d. Distinguishing Ciphers and Codes e. Using the Fundamental Theorem of Arithmetic f. Divisibility vs Modulus g. Operations with Modular Arithmetic
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