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Free Textbook

Quantitative Analysis

Algebra with a Business Perspective

by Donna M. Wacha
(30 ratings)
1 review
347
Language:  English
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.

  1. Equations, Inequalities & Linear Programming 
    1. Tutorial 1.1: Solve one-step linear equations in one variable
    2. Tutorial 1.2: Solve two-step linear equations in one variable
    3. Tutorial 1.3: Solve multi-step linear equations involving like-terms
    4. Tutorial 1.4: Solve multi-step linear equations involving parentheses
    5. Tutorial 1.5: Solve multi-step linear equations in one variable where the variable appears on each side of the equation
    6. Tutorial 1.6: Solve multi-step linear inequalities in one variable
    7. Tutorial 1.7: Graph the solution of multi-step linear equations or inequalities in one variable on a number line
    8. Tutorial 1.8: Graph a line that passes through two given points
    9. Tutorial 1.9: Graph a linear equation using its x- and y-intercepts
    10. Tutorial 1.10: Graph an equation (in slope-intercept form) using its slope and y-intercept
    11. Tutorial 1.11: Graph a linear equation (in standard form) using its slope and y-intercept
    12. Tutorial 1.12: Determine the slope of a line passing through 2 given points
    13. Tutorial 1.13: Use the slope-intercept formula to write the equation of a line with a given slope and point
    14. 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
    15. Tutorial 1.15: Write the standard form of an equation of a line with a given slope and point
    16. Tutorial 1.16: Write an equation of a line that passes through two given points
    17. Tutorial 1.17: Determine whether the lines for a pair of equations are parallel, perpendicular or coincide with each other
    18. Tutorial 1.18: Write the equation of a line through a given point that is parallel to a given line
    19. Tutorial 1.19: Write the equation of a line through a given point that is perpendicular to a given line
    20. Tutorial 1.20: Solve a system of linear equations by graphing
    21. Tutorial 1.21: Solve a system of linear equations by substitution
    22. Tutorial 1.22: Solve a system of linear equations by elimination
    23. Tutorial 1.23: Solve a system of three equations in three variables
    24. Tutorial 1.24: Solve applications involving systems of equations
    25. 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
    26. Tutorial 1.26: Evaluate linear total cost functions, linear total revenue functions and linear profit functions
    27. 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
    28. Tutorial 1.28: Find the break-even point for the given cost and revenue functions
    29. Tutorial 1.29: Evaluate and graph supply and demand functions
    30. Tutorial 1.30: Write the equation (in slope-intercept form) of a supply or a demand function
    31. Tutorial 1.31: Determine the market equilibrium for a given scenario
    32. Tutorial 1.32: Graph a linear inequality in two variables
    33. Tutorial 1.33: Solve a system of linear inequalities in two variables
    34. Tutorial 1.34: Name the vertices for the feasible solution region for the given system of linear inequalities
    35. 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
    36. Tutorial 1.36: Use graphing to determine the optimal maximum value of a linear function subject to constraints
    37. Tutorial 1.37: Use graphing to determine the optimal minimum value of a linear function subject to constraints
    38. Tutorial 1.38: Solve applications involving linear programming
  2. Matrices & Array Operations 
    1. Tutorial 2.1: Determine the number of rows or columns in a matrix
    2. Tutorial 2.2: Determine the order (dimensions) of a matrix
    3. Tutorial 2.3: Identify square matrices
    4. Tutorial 2.4: Identify the element (entry) at a given location (MRC)
    5. Tutorial 2.5: Determine a zero matrix with a given order (dimensions)
    6. Tutorial 2.6: Find the transpose of a matrix
    7. Tutorial 2.7: Determine the negative of a matrix
    8. Tutorial 2.8: Use matrices to present and interpret given data
    9. Tutorial 2.9: Add matrices
    10. Tutorial 2.10: Subtract matrices
    11. Tutorial 2.11: Use matrix addition/subtraction to solve real-world business applications
    12. Tutorial 2.12: Multiply a matrix by a scalar (real number)
    13. Tutorial 2.13: Find the product of given matrices
    14. Tutorial 2.14: Complete matrix multiplication involving zero matrices
    15. Tutorial 2.15: Complete multiplication involving identity matrices
    16. Tutorial 2.16: Use matrix multiplication to solve business applications
    17. Tutorial 2.17: Write the augmented matrix for a system of equations
    18. Tutorial 2.18: Use a reduced matrix to determine the solutions for a given system
    19. Tutorial 2.19: Use matrices to solve systems with unique solutions
    20. Tutorial 2.20: Use matrices to solve systems with non-unique solutions
    21. Tutorial 2.21: Find the inverse of a 2 × 2 square matrix
    22. Tutorial 2.22: Use 2 × 2 inverse matrices to solve systems of equations
    23. Tutorial 2.23: Use row operations to find the inverse matrix of a square matrix
    24. Tutorial 2.24: Use N × N inverse matrices to solve systems of equations
    25. Tutorial 2.25: Use matrix inverses to solve real-world applications
    26. 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
    27. Tutorial 2.27: Use a computer spreadsheet to determine the transpose and/or the negative of a matrix
    28. Tutorial 2.28: Use a computer spreadsheet to add or subtract matrices
    29. Tutorial 2.29: Use a computer spreadsheet to complete a scalar multiplication
    30. Tutorial 2.30: Use a computer spreadsheet to complete a matrix multiplication
    31. Tutorial 2.31: Use a computer spreadsheet to solve systems of equations involving row operations
    32. Tutorial 2.32: Use a computer spreadsheet to determine the inverse and/or determinant of a matrix
    33. Tutorial 2.33: Use a computer spreadsheet to solve a system of equations involving inverse matrices
  3. Quadratic & other Special Functions 
    1. Tutorial 3.1: Factor a polynomial expression by finding its greatest common monomial factor
    2. Tutorial 3.2: Factor a polynomial expression by grouping
    3. Tutorial 3.3: Factor a polynomial expression (x2 + bx + c) as a product of binomials
    4. Tutorial 3.4: Factor a polynomial expression (ax2 + bx + c) as a product of binomials
    5. Tutorial 3.5: Factor “special” polynomial expressions through patterning
    6. Tutorial 3.6: Use factoring to complete business applications
    7. Tutorial 3.7: Solve quadratic equations by factoring
    8. Tutorial 3.8: Solve quadratic equations by completing the square
    9. Tutorial 3.9: Derive the quadratic formula by completing the square
    10. Tutorial 3.10: Solve quadratic equations using the quadratic formula
    11. Tutorial 3.11: Determine the number and the nature of the solutions for a quadratic equation
    12. Tutorial 3.12: Solve business applications involving quadratic functions
    13. Tutorial 3.13: For any quadratic function
    14. Tutorial 3.14: Use quadratic functions to find market equilibrium
    15. Tutorial 3.15: Use quadratic functions to find break-even point(s)
    16. Tutorial 3.16: Maximize quadratic revenue and/or profit functions. Minimize quadratic cost functions
    17. Tutorial 3.17: Use quadratic functions to solve real-world applications
    18. Tutorial 3.18: Identify the graphs of basic functions
  4. Mathematics of Finance 
    1. Tutorial 4.1: Find the amount of interest for a simple interest loan or investment
    2. Tutorial 4.2: Find the future value for a simple interest investment
    3. Tutorial 4.3: Find the amount that was invested into an account where simple interest is used
    4. Tutorial 4.4: Find the simple interest rate earned on an investment
    5. Tutorial 4.5: Find the time needed for an account with a simple interest rate to reach a desired future value
    6. Tutorial 4.6: Find the future value for an account that is compounded periodically
    7. Tutorial 4.7: Find the amount of interest earned for an account that is compounded periodically
    8. Tutorial 4.8: Find the amount that was invested into an account that is compounded periodically
    9. Tutorial 4.9: Find the interest rate for a periodically-compounded account
    10. Tutorial 4.10: Solve an exponential equation using logarithms
    11. Tutorial 4.11: Find the time needed for an account that is compounded periodically to reach a certain future value
    12. Tutorial 4.12: Find the future value for an account when interest is compounded continuously
    13. Tutorial 4.13: Find the amount that was invested into an account that is compounded continuously
    14. Tutorial 4.14: Find the interest rate for an account that is compounded continuously
    15. Tutorial 4.15: Find the time needed for an account that is compounded continuously to reach a specified amount
    16. Tutorial 4.16: Find the annual percentage yield (APY) of money in an account where the interest is compounded periodically
    17. Tutorial 4.17: Find the annual percentage yield (APY) of money in an account where the interest is compounded continuously
    18. Tutorial 4.18: Compute the future value of an ordinary annuity
    19. Tutorial 4.19: Compute the payment amounts required in order for an ordinary annuity to have a specified future value
    20. Tutorial 4.20: Find out how long it will take for an ordinary annuity to reach a savings goal
    21. Tutorial 4.21: Compute the future values of an annuity due
    22. Tutorial 4.22: Compute the payment amounts required in order for an annuity due to have specified future values
    23. Tutorial 4.23: Find out how long it will take for an annuity due to reach a savings goal
    24. Tutorial 4.24: Compute the present value of an ordinary annuity
    25. Tutorial 4.25: Compute the payments for a specified present value for an ordinary annuity
    26. Tutorial 4.26: Compute the present value of an annuity due
    27. Tutorial 4.27: Compute the payments for a specified present value for an annuity due
    28. Tutorial 4.28: Compute the present value of a deferred annuity
    29. Tutorial 4.29: Compute the payments for a specified present value for a deferred annuity
    30. Tutorial 4.30: Find the regular payments to amortize a debt
    31. Tutorial 4.31: Find the amount that can be borrowed for a specified payment
    32. Tutorial 4.32: Find the unpaid balance of a loan
Daniel
I have been looking for a book like this - to tutor my wife as well as to renew lost maths skills
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Donna M. Wacha

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