Detailed Table of Contents for Finite Mathematics

Chapter 1 – Linear Functions in Business and Economics

Section 1 – Linear Functions

Question 1 – What are independent and dependent variables?

Question 2 – What is a linear function?

Question 3 – What is function notation?

Section 2 – Applications of Linear Functions

Question 1 – What are the pieces of a linear function?

Question 2 – How do you graph a linear function?

Question 3 – How do you find a linear function through two points?

Question 4 – How do you find cost and revenue functions?

Question 5 – What are demand and supply?

Section 3 – Approximate Linear Models

Question 1 – Which linear model is best?

Question 2 – How do you use linear regression functions?

Question 3 – How good is the linear model?

Section 4 – Linear Functions of Several Variables

Question 1 – What is a linear function of several independent variables?

Question 2 – What do the coefficients of the variables tell us?

Question 3 – How do you find cost, revenue and profit functions with several variables?

Chapter 2 – Solving Systems of Linear Equations

Section 1 – Systems of Linear Equations

Question 1 – What is a system of linear equations?

Question 2 – Where do systems of equations come from?

Section 2 – Solving a System of Two Linear Equations Algebraically

Question 1 – How do you solve a system of linear equations?

Section 3 – Systems with Many Solutions or No Solutions

Question 1 – Does every system have a unique solution?

Question 2 – How do you solve a system of three equations in two variables?

Question 3 – How do you set up and solve an application involving a system of equations in two variables?

Section 4 – Solving a System of Linear Equations with Matrices

Question 1 – What is a matrix?

Question 2 – How do you form an augmented matrix from a system of linear equations?

Question 3 – How do you use row operations to determine the reduced row echelon form of a matrix?

Question 4 – Do all systems of linear equations have unique solutions?

Question 5 – How do you mix different grades of ethanol to create a new grade of ethanol?

Chapter 3 – Matrices

Section 1 – Matrix Addition and Subtraction

Question 1 – How is information organized in a matrix?

Question 2 – How do you multiply a matrix by a scalar?

Question 3 – How do you add matrices?

Question 4 – How do you subtract matrices?

Section 2 – Matrix Multiplication

Question 1 – How do you multiply two matrices?

Question 2 – How do you interpret the entries in a product of two matrices?

Section 3 – Matrix Inverses

Question 1 – What is a matrix inverse?

Question 2 – How do you find a matrix inverse?

Section 4 – Solving Matrix Equations with Inverses

Question 1 – How do you write a system of equations as a matrix equation?

Question 2 – How do you solve a matrix equation using the matrix inverse?

Chapter 4 – Linear Programming

Section 1 – Solving Systems of Linear Inequalities

Question 1 – How do you graph a linear inequality?

Question 2 – How do you graph a system of linear inequalities?

Section 2 – Graphical Linear Programming

Question 1 – What is a linear programming problem?

Question 2 – How do you solve a linear programming problem with a graph?

Question 3 – How do you solve a linear programming application with a graph?

Section 3 – The Simplex Method and the Standard Maximization Problem

Question 1 – What is a standard maximization problem?

Question 2 – What are slack variables?

Question 3 – How do you find a basic feasible solution?

Question 4 – How do you get the optimal solution to a standard maximization problem with the Simplex Method?

Question 5 – How do you find the optimal solution for an application?

Section 4 – The Simplex Method and the Standard Minimization Problem

Question 1 – What is a standard minimization problem?

Question 2 – How is the standard minimization problem related to the dual standard maximization problem?

Question 3 – How do you apply the Simplex Method to a standard minimization problem?

Question 4 – How do you apply the Simplex Method to a minimization application?

Section 5 – Sensitivity Analysis

Question 1 – How will changes in a constraint’s constant change the optimal solution?

Question 2 – How will changes in the objective function’s coefficients change the optimal solution?

Chapter 5 – The Mathematics of Finance

Section 1 – Simple and Compound Interest

Question 1 – What is simple interest?

Question 2 – What is compound interest?

Question 3 – What is an effective interest rate?

Question 4 – What is continuous compound interest?

Section 2 – Exponential and Logarithm Functions in Finance

Question 1 – How do you convert between the exponential and logarithmic forms of an equation?

Question 2 – How do you evaluate a logarithm?

Question 3 – How do you solve problems involving using logarithms?

Section 3 – Annuities

Question 1 – What is an ordinary annuity?

Question 2 – What is an annuity due?

Question 3 – What is a sinking fund?

Section 4 – Amortization

Question 1 – How do you find the present value of an annuity?

Question 2 – How is a loan amortized?

Question 3 – How do you make an amortization table?

Chapter 6 – Introduction to Statistics

Section 1 – Representing Data

Question 1 – What is a frequency distribution?

Question 2 – How do you make a histogram?

Question 3 – What is a bar chart?

Section 2 – Measuring Central Tendency

Question 1 – What is the difference between a sample and a population?

Question 2 – What is the mean of a dataset?

Question 3 – What is the median of a dataset?

Question 4 – What is the mode of a dataset?

Section 3 – Measuring Variation

Question 1 – What is the range of the dataset?

Question 2 – What is the variance and standard deviation of a dataset?

Chapter 7 – Introduction to Probability

Section 1 – Basic Concepts of Probability

Question 1 – What is an event?

Question 2 – What is a probability?

Question 3 – How is probability assigned?

Section 2 – Probability Rules

Question 1 – How do you find the probability of an event?

Question 2 – What is the complement of an event?

Question 3 – How do you find the probability of a compound event?

Question 4 – What is the difference between marginal and joint probability?

Section 3 – Conditional Probability

Question 1 – What is conditional probability?

Question 2 – How is conditional probability computed?

Question 3 – What are independent events?

Question 4 – What is the product rule for probability?

Question 5 – How is Bayes’ Rule used to compute conditional probability?

Chapter 8 – Counting Principles

Section 1 – Permutations

Question 1 – How do you count choices using the Multiplication Principle?

Question 2 – What is factorial notation?

Question 3 – What is a permutation?

Section 2 – Combinations

Question 1 – What is a combination?

Question 2 – What is the difference between a permutation and combination?

Section 3 – Probability with Permutations and Combinations

Question 1 – How do you find the likelihood of a certain type of license plate?

Question 2 – How do you find the likelihood of a particular committee?

Question 3 – How do you find the probability of winning a lottery?

Question 4 – How do you find the likelihood of detecting a defective product?

Chapter 9 – Introduction to Probability Distributions

Section 1 – Discrete Probability Distributions

Question 1 – What is a random variable?

Question 2 – How is the expected value of a probability distribution calculated?

Question 3 – How is the standard deviation of a probability distribution calculated?

Section 2 – Binomial Probability Distribution

Question 1 – What is binomial probability?

Question 2 – What are the characteristics of a binomial probability distribution?

Section 3 – Poisson Probability Distribution

Question 1 – What is Poisson probability?

Question 2 – What are the characteristics of a Poisson distribution?

Section 4 – Continuous Probability Distributions

Question 1 – What is a normal probability distribution?

Question 2 – What is a standard normal probability distribution?

Section 5 – Uniform and Exponential Probability Distributions

Question 1 – What is a uniform probability distribution?

Question 2 – What is an exponential probability distribution?

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