STANDARD COMPETENCIES:

 

 1.   Solve problems involving principles of set theory and logic.

 2.   Solve problems involving mathematical modeling.

 3.   Solve problems involving probability.

 4.   Solve problems involving statistics.

 5.   Solve problems involving consumer mathematics.

 6.   Read, analyze, and apply to new situations, written material related to the study of mathematics.

 7.   Write and speak clearly and logically in presentations and essays about topics related to mathematics.

 8.   Demonstrate the ability to select and apply contemporary forms of technology to solve problems or compile information in the study of mathematics.

 9.   Demonstrate the ability to solve one of the following competencies: solve problems involving Euclidean geometry, solve problems involving varying numeration systems, solve problems involving mathematics of social choice, or solve problems involving management science.

 TOPICAL OUTLINE:

 

 I.      Set Theory and Logic

         A.      Notation and Terminology

         B.      Subset

         C.      Venn Diagram

         D.      Union, Intersection & Complement

         E.      Applications

         F.      Inductive & Deductive

         G.      Conjunction, Disjunction, & Negation

         H.      Set Operations

         I.      Logic: Conditional & Biconditional

         J.      Logic: Converse, Inverse, & Contrapositive

         K.      Truth Tables

 II.     Mathematical Modeling

         A.      Function, Domain & Range

         B.      Relationship

         C.      Linear Graphs

         D.      Linear Programming

         E.      Linear Inequalities

         F.      Quadratics

         G.      Quadratic Applications

         H.      Exponentials

         I.      Exponential Applications

         J.      (Optional)  Logarithms

         K.      (Optional)  Logarithmic Applications

 III.    Probability

         A.      Sample Space

         B.      Probability

         C.      Theoretical & Experimental

         D.      Outcome

         E.      Permutation & Combination

         F.      Counting Rules

         G.      Union & Intersection

         H.      Odds & Expected Value

 IV.     Statistics

         A.      Descriptive & Inferential

         B.      Graphical Presentations

         C.      Population & Sample

         D.      Mean, Median & Mode

         E.      Range, Variance & Standard Deviation

         F.      Normal Distribution

         G.      Probability & Percent

 V.      Consumer Mathematics

         A.      Simple Interest

         B.      (Optional)  Credit Card Finance Charge

         C.      Compound Interest

         D.      Effective Rate

         E.      Inflation

         F.      Doubling

         G.      Annuities

         H.      Future & Present Value

         I.      Payment Size

         J.      Amortization Schedule

 VI.     ONE OF THE FOLLOWING TOPICS IS ALSO REQUIRED.

 VII.    Euclidean Geometry.

         A.      Point, line, & plane

         B.      Angles

         C.      Polygon

         D.      Fibonacci Sequence

         E.      Applications

         F.      Golden Ratio

         G.      Choose one of the following topics.

                 1.      Fractal Geometry

                         a.      Fractal

                         b.      Applications

                         c.      Fractal Construction

                 2.      Tessallations.

                         a.      Tessallation

                         b.      Regular Polygons that Tessallate a Plane

                         c.      Tessallate a small area.

                         d.      Applications

 VIII.   Numeration Systems

         A.      Counting Numbers - Different Cultures

         B.      Conversions

         C.      Add & Subtract - Different Cultures

         D.      Origin of Our System

         E.      Different Bases

         F.      Calculating Devices

         G.      Binary System

 IX.     Mathematics of Social Choice

         A.      Voting Systems

         B.      Voting Methods - Election Results

         C.      Logistics of Voting Systems

         D.      Weighted Voting Systems

         E.      Banzhaf Power Index

         F.      Apportionment Methods

         G.      Flaws & Paradoxes - Apportionment Methods

 X       Management Science

         A.      Euler circuit

         B.      Algorithm

         C.      Hamiltonian Cycle

         D.      Heuristic Algorithm - Traveling Salesman Problem (TSP)

         E.      Networking Applications

         F.      Minimum Spanning Tree

         G.      Network Linking

         H.      Flowchart

         I.      Scheduling Conditions