Quantitative Analysis
Algebra with a Business Perspective
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About the book
Reviews
Daniel ★★★★★
I have been looking for a book like this  to tutor my wife as well as to renew lost maths skills
Description
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 ebook 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 fulltime at Point Pleasant Borough High School. Due to a conflict with my fulltime 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 – PreAlgebra 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 ebook for querovidaesaude.org during the latter part of 2012…the result being this tutorial ebook entitled Quantitative Analysis – Algebra with a Business Perspective.
Donna M. Wacha
dwacha@monmouth.edu
Preface
 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 (querovidaesaude.org 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.
Content
 Equations, Inequalities & Linear Programming
 Tutorial 1.1: Solve onestep linear equations in one variable
 Tutorial 1.2: Solve twostep linear equations in one variable
 Tutorial 1.3: Solve multistep linear equations involving liketerms
 Tutorial 1.4: Solve multistep linear equations involving parentheses
 Tutorial 1.5: Solve multistep linear equations in one variable where the variable appears on each side of the equation
 Tutorial 1.6: Solve multistep linear inequalities in one variable
 Tutorial 1.7: Graph the solution of multistep 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 yintercepts
 Tutorial 1.10: Graph an equation (in slopeintercept form) using its slope and yintercept
 Tutorial 1.11: Graph a linear equation (in standard form) using its slope and yintercept
 Tutorial 1.12: Determine the slope of a line passing through 2 given points
 Tutorial 1.13: Use the slopeintercept formula to write the equation of a line with a given slope and point
 Tutorial 1.14: Use the pointslope formula to write the slopeintercept 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 breakeven 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 slopeintercept 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 onestep 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 realworld 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 nonunique 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 realworld 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 breakeven point(s)
 Tutorial 3.16: Maximize quadratic revenue and/or profit functions. Minimize quadratic cost functions
 Tutorial 3.17: Use quadratic functions to solve realworld 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 periodicallycompounded 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