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NC FINAL EXAM DISCRETE MATHEMATICS 2015 – 2016 BREAKDOWN OF TOPICS GOAL 1: The learner will use matrices and graphs to model relationships and solve problems. 1.01 Use matrices to model and solve problems. a) Display and interpret data. b) Write and evaluate matrix expressions to solve problems. 1.02 Use graph theory to model relationships and solve problems. GOAL 2: The learner will analyze data and apply probability concepts to solve problems. 2.01 Describe data to solve problems. a) Apply and compare methods of data collection. b) Apply statistical principles and methods in sample surveys. c) Determine measures of central tendency and spread. d) Recognize, define, and use the normal distribution curve. e) Interpret graphical displays of data. f) Compare distributions of data. 2.02 Use theoretical and experimental probability to model and solve problems. a) Use addition and multiplication principles. b) Calculate and apply permutations and combinations. c) Create and use simulations for probability models. d) Find expected values and determine fairness. e) Identify and use discrete random variables to solve problems. f) Apply the Binomial Theorem. 2.03 Model and solve problems involving fair outcomes: a) Apportionment. b) Election Theory. c) Voting Power. d) Fair Division. GOAL 3: The learner will describe and use recursively-defined relationships to solve problems. 3.01 Use recursion to model and solve problems. a) Find the sum of a finite sequence. b) Find the sum of an infinite sequence. c) Determine whether a given series converges or diverges. d) Write explicit definitions using iterative processes, including finite differences and arithmetic and geometric formulas. e) Verify an explicit definition with inductive proof. TEST SPECIFICATION WEIGHTS Goal NC Standard Course of Study Percent of Total Score Points Chapters of Curriculum 1.01 Matrices 1.02 Graphs 2.01 Stats 2.02 Probability and Counting 2.03 Modeling 3.01 Recursion 16% to 24% 8% to 16% 14% to 22% DMTA Lessons Chapters 5, 6, 7, 8 Chapters 13, 14, 16 19% to 27% Chapter 15 16% to 24% 9% to 16% Chapters 1, 2, 3, 4 Chapters 9, 10 , 12 Mathematics NC Final Exam 2015 - 16 Number of Items by Standard The following table shows the number of operational items for each standard. Note that future coverage of standards could vary within the constraints of the test specification weights in Table 1. Discrete Math Standard Number of Items Curriculum 1.01a 1.01b 1.02 2.01b 2.01c 2.01d 2.02a 2.02c 2.02f 2.03a 2.03b 2.03c 2.03d 3.01a 3.01b 3.01d 2 4 4 2 2 3 2 3 1 2 3 2 2 1 1 1 Matrices Matrices Chapters 5, 6, 7, 8 Chapter 13 Chapter 14 Chapter 16 Chapter 15 Chapter 15 Chapter 15 Chapter 4 Chapter 1 Chapter 2 Chapter 3 Chapter 9, 10, 12 (Finite Sum) Chapter 9, 10, 12 (Infinite Sum) Chapter 9, 10 (Sequences)