Mathematics for Business and Social Sciences was published in August of 2020. The textook, written by Kathryn Bollinger and Venessa Coffelt is currently being used at Texas A&M University.

From the course and textbook description: “Topics covered include application of common algebraic functions, including polynomial, exponential, logarithmic and rational, to problems in business, economics and the social sciences; includes mathematics of finance, including simple and compound interest and annuities; systems of linear equations; matrices; linear programming; and probability, including expected value.”

Students should have completed high school algebra I and II along with geometry. Additionally, each chapter in the textbook begins with a list of topics students should have proficiency with. For example, chapter 1 suggests students be familiar with:

- Simplifying Fractions
- Decimals
- Properties of Real Numbers
- Using Variables and Algebraic Symbols Simplifying Expressions
- Translating an English Phrase to an Algebraic Expression or Equation Solving Linear Equations with One Variable
- Using Problem-Solving Strategies

The textbook includes an appendix that covers a number of these topics. We would also recommend that you check out our section of high school algebra textbooks and precalculus textbooks to find more in-depth coverage of these topics.

Mathematics for Business and Social Sciences contains the answers to ALL of the practice questions and exercises. It is a great resource for self-study or to supplement a different textbook.

## Table of Contents for *Mathematics for Business and Social Sciences*

#### 1 Matrices

1.1 Basic Matrix Operations

Adding and Subtracting Matrices

Multiplying a Matrix by a Scalar

Transposing a Matrix

Matrix Equality

ApplyingBasicMatrixOperations

#### 2 Linear Models and Systems of LinearEquations

2.1 Review of Lines

Plotting Ordered Pairs in the Cartesian Coordinate System

Graphing Linear Equations by Plotting Points

Graphing Linear Equations using Technology

Writing a Linear Equation

Finding x-intercepts and y-intercepts

Interpreting Slope

2.2 Modeling with Linear Functions

Defining a Linear Function

Modeling with Linear Functions

2.3 Systems of Two Equations in Two Unknowns

Identifying Solutions to Linear Equations

Solving Systems of Two Linear Equations in Two Unknowns

Relating Solutions of Systems to Business Applications

2.4 Setting Up and Solving Systems of Linear Equations

Setting up Systems of Linear Equations

Converting between Systems and Augmented Matrices

Solving Systems using Gauss-Jordan Elimination

Solving Systems using Gauss-Jordan Elimination with Technology.

Chapter Review

#### 3 LinearProgramming

3.1 Setting Up Linear Programming Problems

Linear Programming Problems

3.2 Graphing Systems of Linear Inequalities in Two Variables

Graphing Linear Inequalities

Graphing Systems of Linear Inequalities

Determining the Types of Solutions Sets and Corner Points

3.3 Graphical Solution of Linear Programming Problems

3.4 Simplex Method

Performing the Simplex Method on a Standard Maximization Problem

Comparing the Simplex Method and the Method of Corners

Applying the Simplex Method to Real-World Scenarios

Chapter Review

#### 4 BasicProbabilityandApplications

4.1 Mathematical Experiments

Defining a Sample Space and Events

Operating on Events

4.2 Basics of Probability

Defining Probability

Constructing Probability Distributions

4.3 Rules of Probability

Computing a Probability Using a Probability Distribution

Applying the Rules of Probability

4.4 Probability Distributions and Expected Value

Defining a Random Variable

Computing Expected Value
Chapter Review

#### 5 Functions

5.1 Relations and Functions

Writing Interval Notation

Differentiating Between a Relation and a Function

Using Function Notation

5.2 Polynomial Functions

DescribingPolynomialFunctions

DescribingQuadraticFunctions

5.3 Rational Functions

Describing Rational Functions

Combining and Simplifying Rational Expressions

Computing the Difference Quotient

5.4 Power and Radical Functions

Defining Power Functions

Describing Properties of Radical Functions

Computing Domains of Algebraic Functions

Rationalizing Numerators and Denominators

5.5 Piecewise-Defined Functions

Describing Piecewise-Defined Functions

Domain of a Piecewise-Defined Function

Graphs of Piecewise-Defined Functions

Real-World Applications

5.6 Exponential Functions

Reviewing Laws of Exponents

Describing Exponential Functions

Computing Domain

Solving Equations Involving Exponential Expressions

Applying Exponential Functions to Real-World Applications

5.7 Combining and Transforming Functions

Transforming Parent Functions

Performing Function Arithmetic

Finding the Composition of Functions

5.8 Inverse Functions and Logarithms

Defining an Inverse Function

Defining Logarithmic Functions

Properties of Logarithmic Functions

Computing the Domain of a Logarithmic Function

Using Algebraic Properties of Logarithms

Applying Exponential and Logarithmic Functions

Chapter Review

#### 6 Mathematical Finance

6.1 Interest and Effective Rates

Working with Simple Interest

Working with Compound Interest

Comparing Interest Rates

6.2 Annuities, Sinking Funds, and Amortization

Understanding Annuities Involving Deposits

Understanding Annuities Involving Withdrawals

Understanding Loans

Understanding Amortization

Summarizing Finance Problems

Chapter Review

#### A Appendix

A.1 Number Sense

Introduction to Whole Numbers

Integers

Fractions

Simplifying Fractions

Decimals Integer Exponents and Scientific Notation

The Real Numbers .

Properties of Real Numbers

Systems of Time Measurement

A.2 Introduction to Algebra

Using Variables and Algebraic Symbols

Simplifying Expressions

Evaluating an Expression

Translating an English Phrase to an Algebraic Expression or Equation

Solving Linear Equations with One Variable

Using Problem-Solving Strategies

Graphing Inequalities on the Number Line and Interval Notation

Solving Inequalities using the Addition and Subtraction Properties of Inequality

Solving Inequalities using the Multiplication and Division Properties of Inequality

A.3 Introduction to Algebraic Expressions

Describing Polynomials

Adding and Subtracting Polynomials

Evaluating a Polynomial for a Given Value

Simplifying Expressions with Exponents

Multiplying Polynomials

Observing Special Products

Simplifying Expressions Involving Quotients and Exponents

Dividing Monomials

Simplifying Rational Expressions

Evaluating Rational Expressions

Dividing a Polynomial by a Monomial

Simplifying Variable Expressions with Roots

Simplifying Expressions with Rational Exponents

Rationalizing a Two-Term Denominator

A.4 Factoring

Greatest Common Factor

Factor by Grouping

Factoring Quadratic Trinomials with Leading Coefficient 1

Factor Quadratic Trinomials with Leading Coefficient Other than 1

Factoring Differences of Squares

A.5 Solving Quadratic Equations

Solving Quadratic Equations Using the Zero Product Property

Solving Quadratic Equations by Factoring

Completing the Square of a Binomial Expression

Solving Quadratic Equations of the Form x2 +bx+c = 0 by Completing the Square

Solving Quadratic Equations of the form ax2 + bx + c = 0 by Completing the Square

Solving Quadratic Equations Using the Quadratic Formula

Identifying the Most Appropriate Method to Use to Solve a Quadratic Equation

Solving Equations in Quadratic Form

#### B Exercise Answers

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Mathematics for Business and Social Sciences