MAT 119 FINITE MATHEMATICS, SECTION 7, Fall 2003

Final Study Guide

Date: The final exam will hold on December 11 in class from 7:30-9:30

Formulae-and-facts sheet: You are allowed into the exam, one page containing formulae and facts you need.

Questions: There will be approximately two questions from each chapter. The final examination will cover the following topics.

Chapter 1: Lines

Concepts: ¨Finding intercepts

¨Finding and interpreting slope

¨Finding point-slope equation of a line

¨Finding slope-intercept equation of a line

¨Point-slope equation of a line

¨When are two lines parallel, perpendicular or intersecting?

¨Point-slope equation of a line

¨Applications to finding break-even point and market price

Chapter 2: Solving Linear Systems

Concepts: ¨Solving simultaneous linear system using substitution or elimination

¨Finding augmented matrix form of linear system

¨Solving linear system by transforming the augmented matrix to

row-echelon form and using back-substitution

¨Solving linear system by transforming the augmented matrix to reduced

row-echelon

¨Know how to transform word real-world problems into linear systems.

Do not fear them, they are easier than you think!

Chapter 3: Solving Linear Programming Geometrically

Concepts: ¨Know how to graph system of linear inequalities

¨Know how to find corner points of the graph of linear inequalities

¨Solving linear programming problem by finding corner points

Chapter 5: Finance

Concepts: ¨Know how to use the simple interest formula to find future amount,

principal, rate of interest or time

¨Know how the discounted loan formula to find proceeds, interest rate or

amount

¨Know how to use the compound interest formula to find future amount,

principal, rate of interest or time

¨Know how to find the effective rate of interest given a compound interest

¨How to use the savings formula to calculate the future value of annuity

¨How to use the savings formula to determine periodic payments to a

sinking fund, etc.

¨Know how to use the amortization formula to calculate the present value

of an annuity

¨Know how to use the amortization formula to determine periodic payments

to pay off an amortized loan, etc

Chapter 6: Sets: Counting Techniques

Concepts: ¨Know the set operations: intersection, union, complement of a set.

When are two sets called disjoint?

¨Know how to find all subsets of a set.

¨Know the De Morgan’s properties of sets

¨Know how to use the counting formula

¨Know how to construct Venn diagram and to use it to count set elements

¨Know the multiplication principle and how it works

¨Know the permutation formula and how to use it

¨Know the combination formula and how to use it

¨Know where to use the permutation formula and where to use the

combination formula

¨Know the permutation formula with repetition and how to use it

Chapter 7: Sets: Probability

Concepts: ¨Know how to find the sample space of an experiment

¨Know how to construct the probability model of an experiment

¨Know how to construct events and how to compute their probabilities

¨When are two events called mutually exclusive?

¨Additive rule and how to use it to find probabilities

¨Additive rule when two events are mutually exclusive

¨Properties of the probability of an event

¨Probability of the complement of an event

¨Finding probability of an event when all outcomes are equally likely

¨Finding odds for and odds against an event given its probability

¨Finding probabilities using counting techniques

¨When are two events called independent?

¨Conditional probability formula and how to use it

¨Product rule and how to use it

¨Using a tree diagram and the product rule to find probabilities

¨When are two events independent?

¨How to test if two events are independent?

Chapter 8: Additional Probability Topics

Concepts: ¨Know the Bayes’ formula and how to use it to find probabilities

¨What is a binomial experiment (Bernoulli trials)?

¨Know the formula for finding probability of k successes in n trials in a

binomial experiment

¨What is the expected value of an experiment means?

¨Know how to compute expected values

¨Know how to compute expected number of successes in a binomial

experiment

Chapter 9: Statistics

Concepts:¨Know how construct and analyze bar graph and pie chart

¨Know how construct and analyze line chart, frequency polygon, histogram, cumulative

frequency distribution

¨How to calculate mean, median, mode(s)

¨How to calculate mean for grouped data

¨How to calculate standard deviation, variance

¨How to calculate standard deviation, variance for grouped data

¨Know how to use Chebyschev’s Theorem