Curriculum for the high school grades (9-12) for the state of North Carolina (US) : Curriculum for the high school grades (9-12) for the state of North Carolina (US)
Objectives : Objectives This module explains the curriculum for the high school grades (9-12) for the state of North Carolina (US) Country: United States
State: North Carolina
Time Zone: Eastern Standard Time (GMT-5) till 11th March 2007
Subject: Mathematics
Topic: Discrete Mathematics
Language: English
Grade: Grade 9-12
Introduction : Students will be expected to
Learn application of matrix arithmetic and probability
Applications and modeling are central to this course of study
Appropriate technology, from manipulatives to calculators and application
Software should be used regularly for instruction and assessment Introduction
Contents : Discrete Mathematics includes:
Introduction to the mathematics of networks, social choice, and decision making Contents
Pre-requisites : What your student must already know?
Describe phenomena as functions graphically, algebraically and verbally; identify independent and dependent quantities, domain, and range, input/output, mapping
Translate among graphic, algebraic, numeric, tabular, and verbal representations of relations
Define and use linear and exponential functions to model and solve problems
Operate with matrices to model and solve problems
Define complex numbers and perform basic operations with them Pre-requisites
Competency Goal 1 : Competency Goal 1 1.01 Use matrices to model and solve problems.
a) Display and interpret data.
b) Write and evaluate matrix expressions to solve problems. Sample Problem: Solution: Find the price of a pencil and an eraser when the difference in the costs of 5 pencils and 7 erasers is $2 and 7 pencils and 5 erasers is $3.
Competency Goal 1 : Competency Goal 1 Solution: (contd.)
Competency Goal 1 : 1.02 Use graph theory to model relationships and solve problems. Sample Problem: Competency Goal 1 Solution:
Competency Goal 2 : Competency Goal 2 Sample Problem: 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. Find the missing frequencies in the following frequency distribution if it is given that the mean of the distribution is 1.46. 200 5 10 25 ? ? 46 Frequency (y) Total 5 4 3 2 1 0 Number of accidents (x)
Competency Goal 2 : Competency Goal 2 Let the missing frequencies be f1 & f2. The following table shows the calculation of mean: 140 + f1 + 2f2 N = 86 + f1 + f2 Total 25 5 5 40 10 4 75 25 3 2f2 f2 2 f1 f1 1 0 46 0 fixi fi xi Solution:
Competency Goal 2 : Competency Goal 2 Sample Problem 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. How many four digit numbers divisible by 4 can be made with the digits 1, 2, 3, 4, 5 if the repetition of digits is not allowed?
Competency Goal 2 : Competency Goal 2 2 5 x x 2 3 X X 4 2 X X 2 1 X X U T H Th Solution: We know that the number is divisible by 4 if the last two digits of the number is divisible by 4.The digits at unit’s & ten’s place can be arranged as follows
Competency Goal 2 : Competency Goal 2 Sample Problem: 2.03 Model and solve problems involving fair outcomes:
a) Apportionment.
b) Election Theory.
c) Voting Power.
d) Fair Division. What is the probability that a number selected from the numbers 1, 2, 3, …….. 20 is a prime number, when each of the given numbers is equally likely to be selected. Solution:
Competency Goal 3 : 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. Sample Problem: Competency Goal 3 Find the sum of 20 terms of the series 1,4,7,10,…….. As the common difference between two consecutive terms of the given series are 3 therefore, the series is in A.P. The first term, a = 1
Competency Goal 3 : Competency Goal 3 Solution: