Quantitative Analysis is written by an experienced mathematics teacher, this e-book is presented in tutorial fashion as if a tutor was sitting next to you . . . talking you through the examples.

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Have you ever thought that you would be able to learn algebra if only you had a tutor on whom you could call whenever you wanted? Well, Quantitative Analysis – Algebra with a Business Perspective is the next best thing. Written by an experienced mathematics teacher, this e-book is presented in tutorial fashion as if a tutor was sitting next to you . . . talking you through the examples. All you need to do is turn to whatever presentation you wish . . . without having to schedule mutual meeting times and without having to pay an hourly rate.

About the author

I received my BS degree from Trenton State College (now known as the College of New Jersey, Ewing Township, New Jersey 08618, USA) in 1973. From February 1977 to the end of June 2003, I worked as a full time mathematics teacher at Point Pleasant Borough High School (Point Pleasant, New Jersey 08742, USA). Throughout my years at this school, I taught several courses offered through the mathematics department: Algebra 1, Algebra 2, Algebra 2 Honors, Basic Skills Math, Computer Programming (BASIC), Computer Programming (QBASIC), Discrete Mathematics, Geometry, Geometry Honors, SAT Preparation.

I received my MA degree from Georgian Court College (now known as Georgian Court University, Lakewood, New Jersey 08701) in 1983 after following the Supervision & Curriculum Graduate Program.

I taught at Monmouth University (West Long Branch, New Jersey 07764, USA) as an adjunct professor (through the Mathematics Department) during three semesters (SP98, SP99, FA98) while still working full-time at Point Pleasant Borough High School. Due to a conflict with my full-time teaching position, I declined any adjunct teaching duties until several years later.

After teaching secondary mathematics for more than 25 years, I retired from the Point Pleasant Borough School district at the end of June 2003. After taking some time off, I discovered that I was still in love with teaching mathematics. So, I asked to return to the list of adjunct professors at Monmouth University.

I returned to Monmouth University in September 2004. During my time at Monmouth, I have taught several courses offered through the University’s Mathematics Department:

- MA050 – Pre-Algebra Math
- MA100 – Quantitative Reasoning & Problem Solving
- MA101 – College Algebra
- MA105 – Mathematical Modeling in the Social Sciences
- MA117 – Quantitative Analysis for Business I
- MA203 – Foundations of Elementary Mathematics I
- MA204 – Foundations of Elementary Mathematics II

Always looking to expand my academic achievements, I agreed to compose an e-book for Bookboon.com during the latter part of 2012…the result being this tutorial e-book entitled Quantitative Analysis – Algebra with a Business Perspective.

Donna M. Wacha

dwacha@monmouth.edu

- acknowledgements…

First of all, I would like to thank Lynn Dietrich (director of the Math Learning Center at Monmouth University, West Long Branch, New Jersey, USA) for her help in producing this tutorial text. Without her help, many typographical errors might not have been caught before submitting the final draft.

I would also like to extend my thanks to Sophie Tergeist (bookboon.com Ltd. – Davenport House, 16 Pepper Street, London E14 9RP, United Kingdom) for her constant patience in answering my numerous questions during the production of this text.

- explanation of how the textbook is organized…

This tutorial textbook has been organized into 4 chapters (units) with several individual tutorial lessons within each chapter. As presented in the table of contents, each of the tutorials has been listed separately with its objective and its starting page. For coding purposes: “Tutorial N.M” means that the tutorial is the Mth lesson in chapter N.

I attempted to present each of the tutorials as if a person (teacher, tutor) was sitting next to the reader talking each of the concepts through. My goal was to make sure that each of the lessons was fully explained but still fully understandable. Hopefully this goal was met.

- description of whom I believe might be interested in using these tutorials…

The purpose of this tutorial textbook is to present mathematical skills (algebraic concepts) and their various applications that may be important to students of management (business) science. The applications included should allow readers to view math in a practical setting relevant to their intended careers.

- Equations, Inequalities & Linear Programming
- Tutorial 1.1: Solve one-step linear equations in one variable
- Tutorial 1.2: Solve two-step linear equations in one variable
- Tutorial 1.3: Solve multi-step linear equations involving like-terms
- Tutorial 1.4: Solve multi-step linear equations involving parentheses
- Tutorial 1.5: Solve multi-step linear equations in one variable where the variable appears on each side of the equation
- Tutorial 1.6: Solve multi-step linear inequalities in one variable
- Tutorial 1.7: Graph the solution of multi-step linear equations or inequalities in one variable on a number line
- Tutorial 1.8: Graph a line that passes through two given points
- Tutorial 1.9: Graph a linear equation using its x- and y-intercepts
- Tutorial 1.10: Graph an equation (in slope-intercept form) using its slope and y-intercept
- Tutorial 1.11: Graph a linear equation (in standard form) using its slope and y-intercept
- Tutorial 1.12: Determine the slope of a line passing through 2 given points
- Tutorial 1.13: Use the slope-intercept formula to write the equation of a line with a given slope and point
- Tutorial 1.14: Use the point-slope formula to write the slope-intercept form of an equation of a line with a given slope and point
- Tutorial 1.15: Write the standard form of an equation of a line with a given slope and point
- Tutorial 1.16: Write an equation of a line that passes through two given points
- Tutorial 1.17: Determine whether the lines for a pair of equations are parallel, perpendicular or coincide with each other
- Tutorial 1.18: Write the equation of a line through a given point that is parallel to a given line
- Tutorial 1.19: Write the equation of a line through a given point that is perpendicular to a given line
- Tutorial 1.20: Solve a system of linear equations by graphing
- Tutorial 1.21: Solve a system of linear equations by substitution
- Tutorial 1.22: Solve a system of linear equations by elimination
- Tutorial 1.23: Solve a system of three equations in three variables
- Tutorial 1.24: Solve applications involving systems of equations
- Tutorial 1.25: Find the marginal cost, the marginal cost revenue and the marginal cost profit of given linear total cost functions, linear total revenue functions and linear profit functions
- Tutorial 1.26: Evaluate linear total cost functions, linear total revenue functions and linear profit functions
- Tutorial 1.27: Write the equations for linear total cost functions, linear total revenue functions and linear profit functions by using information given about the functions
- Tutorial 1.28: Find the break-even point for the given cost and revenue functions
- Tutorial 1.29: Evaluate and graph supply and demand functions
- Tutorial 1.30: Write the equation (in slope-intercept form) of a supply or a demand function
- Tutorial 1.31: Determine the market equilibrium for a given scenario
- Tutorial 1.32: Graph a linear inequality in two variables
- Tutorial 1.33: Solve a system of linear inequalities in two variables
- Tutorial 1.34: Name the vertices for the feasible solution region for the given system of linear inequalities
- Tutorial 1.35: Use the vertices for the feasible solution region for a given system of linear inequalities to determine the optimal (minimum or maximum) value of a given linear function that is subject to constraints as defined by the given system of inequalities
- Tutorial 1.36: Use graphing to determine the optimal maximum value of a linear function subject to constraints
- Tutorial 1.37: Use graphing to determine the optimal minimum value of a linear function subject to constraints
- Tutorial 1.38: Solve applications involving linear programming

- Tutorial 1.1: Solve one-step linear equations in one variable
- Matrices & Array Operations
- Tutorial 2.1: Determine the number of rows or columns in a matrix
- Tutorial 2.2: Determine the order (dimensions) of a matrix
- Tutorial 2.3: Identify square matrices
- Tutorial 2.4: Identify the element (entry) at a given location (MRC)
- Tutorial 2.5: Determine a zero matrix with a given order (dimensions)
- Tutorial 2.6: Find the transpose of a matrix
- Tutorial 2.7: Determine the negative of a matrix
- Tutorial 2.8: Use matrices to present and interpret given data
- Tutorial 2.9: Add matrices
- Tutorial 2.10: Subtract matrices
- Tutorial 2.11: Use matrix addition/subtraction to solve real-world business applications
- Tutorial 2.12: Multiply a matrix by a scalar (real number)
- Tutorial 2.13: Find the product of given matrices
- Tutorial 2.14: Complete matrix multiplication involving zero matrices
- Tutorial 2.15: Complete multiplication involving identity matrices
- Tutorial 2.16: Use matrix multiplication to solve business applications
- Tutorial 2.17: Write the augmented matrix for a system of equations
- Tutorial 2.18: Use a reduced matrix to determine the solutions for a given system
- Tutorial 2.19: Use matrices to solve systems with unique solutions
- Tutorial 2.20: Use matrices to solve systems with non-unique solutions
- Tutorial 2.21: Find the inverse of a 2 × 2 square matrix
- Tutorial 2.22: Use 2 × 2 inverse matrices to solve systems of equations
- Tutorial 2.23: Use row operations to find the inverse matrix of a square matrix
- Tutorial 2.24: Use N × N inverse matrices to solve systems of equations
- Tutorial 2.25: Use matrix inverses to solve real-world applications
- Tutorial 2.26: Use a computer spreadsheet to determine the number of rows and columns contained in a matrix and thereby determine the order of the matrix
- Tutorial 2.27: Use a computer spreadsheet to determine the transpose and/or the negative of a matrix
- Tutorial 2.28: Use a computer spreadsheet to add or subtract matrices
- Tutorial 2.29: Use a computer spreadsheet to complete a scalar multiplication
- Tutorial 2.30: Use a computer spreadsheet to complete a matrix multiplication
- Tutorial 2.31: Use a computer spreadsheet to solve systems of equations involving row operations
- Tutorial 2.32: Use a computer spreadsheet to determine the inverse and/or determinant of a matrix
- Tutorial 2.33: Use a computer spreadsheet to solve a system of equations involving inverse matrices

- Tutorial 2.1: Determine the number of rows or columns in a matrix
- Quadratic & other Special Functions
- Tutorial 3.1: Factor a polynomial expression by finding its greatest common monomial factor
- Tutorial 3.2: Factor a polynomial expression by grouping
- Tutorial 3.3: Factor a polynomial expression (x2 + bx + c) as a product of binomials
- Tutorial 3.4: Factor a polynomial expression (ax2 + bx + c) as a product of binomials
- Tutorial 3.5: Factor “special” polynomial expressions through patterning
- Tutorial 3.6: Use factoring to complete business applications
- Tutorial 3.7: Solve quadratic equations by factoring
- Tutorial 3.8: Solve quadratic equations by completing the square
- Tutorial 3.9: Derive the quadratic formula by completing the square
- Tutorial 3.10: Solve quadratic equations using the quadratic formula
- Tutorial 3.11: Determine the number and the nature of the solutions for a quadratic equation
- Tutorial 3.12: Solve business applications involving quadratic functions
- Tutorial 3.13: For any quadratic function
- Tutorial 3.14: Use quadratic functions to find market equilibrium
- Tutorial 3.15: Use quadratic functions to find break-even point(s)
- Tutorial 3.16: Maximize quadratic revenue and/or profit functions. Minimize quadratic cost functions
- Tutorial 3.17: Use quadratic functions to solve real-world applications
- Tutorial 3.18: Identify the graphs of basic functions

- Tutorial 3.1: Factor a polynomial expression by finding its greatest common monomial factor
- Mathematics of Finance
- Tutorial 4.1: Find the amount of interest for a simple interest loan or investment
- Tutorial 4.2: Find the future value for a simple interest investment
- Tutorial 4.3: Find the amount that was invested into an account where simple interest is used
- Tutorial 4.4: Find the simple interest rate earned on an investment
- Tutorial 4.5: Find the time needed for an account with a simple interest rate to reach a desired future value
- Tutorial 4.6: Find the future value for an account that is compounded periodically
- Tutorial 4.7: Find the amount of interest earned for an account that is compounded periodically
- Tutorial 4.8: Find the amount that was invested into an account that is compounded periodically
- Tutorial 4.9: Find the interest rate for a periodically-compounded account
- Tutorial 4.10: Solve an exponential equation using logarithms
- Tutorial 4.11: Find the time needed for an account that is compounded periodically to reach a certain future value
- Tutorial 4.12: Find the future value for an account when interest is compounded continuously
- Tutorial 4.13: Find the amount that was invested into an account that is compounded continuously
- Tutorial 4.14: Find the interest rate for an account that is compounded continuously
- Tutorial 4.15: Find the time needed for an account that is compounded continuously to reach a specified amount
- Tutorial 4.16: Find the annual percentage yield (APY) of money in an account where the interest is compounded periodically
- Tutorial 4.17: Find the annual percentage yield (APY) of money in an account where the interest is compounded continuously
- Tutorial 4.18: Compute the future value of an ordinary annuity
- Tutorial 4.19: Compute the payment amounts required in order for an ordinary annuity to have a specified future value
- Tutorial 4.20: Find out how long it will take for an ordinary annuity to reach a savings goal
- Tutorial 4.21: Compute the future values of an annuity due
- Tutorial 4.22: Compute the payment amounts required in order for an annuity due to have specified future values
- Tutorial 4.23: Find out how long it will take for an annuity due to reach a savings goal
- Tutorial 4.24: Compute the present value of an ordinary annuity
- Tutorial 4.25: Compute the payments for a specified present value for an ordinary annuity
- Tutorial 4.26: Compute the present value of an annuity due
- Tutorial 4.27: Compute the payments for a specified present value for an annuity due
- Tutorial 4.28: Compute the present value of a deferred annuity
- Tutorial 4.29: Compute the payments for a specified present value for a deferred annuity
- Tutorial 4.30: Find the regular payments to amortize a debt
- Tutorial 4.31: Find the amount that can be borrowed for a specified payment
- Tutorial 4.32: Find the unpaid balance of a loan

- Tutorial 4.1: Find the amount of interest for a simple interest loan or investment