MAT1053

From Department of Mathematics at UTSA
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Course Catalog

MAT 1053 Mathematics for Business. (3-0) 3 Credit Hours. (TCCN = MATH 1324)

Prerequisite: Satisfactory performance on a placement examination. This course is designed to prepare the student for MAT1133 Calculus for Business. Topics include the application of common algebraic functions, including polynomial, exponential, logarithmic, and rational, to problems in business, economics, statistics, finance, and accounting. The applications include mathematics of finance, including simple and compound interest and annuities; systems of linear equations; matrices; linear programming; and probability, including expected value. May apply toward the Core Curriculum requirement in Mathematics. (Credit can be earned for only one of the following: MAT1053, MAT1063, or MAT1073.) Generally offered: Fall, Spring, Summer. Course Fees: LRC1 $12; LRS1 $45; STSI $21.

Topics List

Date Sections Topics Prerequisite Skills Student Learning Outcomes
Week 1

Module 1

  • Basic mathematical symbols and terminology
  • Basic arithmetic skills
  • Basic understanding of order of operations

Review of:

  • PEMDAS
Week 1

Module 1

  • Basic mathematical symbols and terminology
  • Basic understanding of Order of Operations
  • Basic understanding of exponents and radicals
  • Basic understanding of factoring polynomials and definition of a factor
  • Understanding operations with fractions

Review the following radical expression concepts:

  • evaluate square roots
  • use the product rule to simplify square roots
  • use the quotient rule to simplify square roots
  • add and subtract square roots
Week 1

Module 1

  • Basic mathematical symbols and terminology
  • Basic arithmetic skills
  • Basic understanding of Order of Operations
  • Basic understanding of exponents

Review the following rules of exponents:

  • product rule
  • quotient rule
  • power rule
  • zero exponent rule
  • negative rule

Review how to find the power of a product and a quotient Review how to simplify exponential expressions

Week 1

Module 1

  • Basic mathematical symbols and terminology
  • Basic arithmetic skills
  • Basic understanding of Order of Operations
  • Basic prime factorization
  • Basic understanding of factoring

Review factoring techniques for the following type of polynomials:

  • factor the greatest common factor of a polynomial
  • factor a trinomial
  • factor by grouping
  • factor a perfect square trinomial
  • factor a difference of squares
Week 1

Module 1

  • Basic mathematical symbols and terminology
  • Basic arithmetic skills
  • Basic understanding of Order of Operations
  • Basic understanding of factoring

Review the following linear equation topics:

  • Basic mathematical symbols and terminology
  • solving linear equations in one variable
  • finding a linear equation
  • write and interpret a linear equation
Week 1

Module 1

  • Basic mathematical symbols and terminology
  • Basic arithmetic skills
  • Basic understanding of Order of Operations
  • Basic understanding of factoring

Review the following linear inequality topics:

  • use interval notation
  • use properties of inequalities
  • solve inequalities in one variable algebraically
Week 1

Module 1

  • Basic mathematical symbols and terminology
  • Basic arithmetic skills
  • Basic understanding of Order of Operations
  • Basic understanding of factoring
  • Basic understanding of Solving Equations
Week 1

Module 1

  • Basic mathematical symbols and terminology
  • Basic arithmetic skills
  • Basic understanding of order of operations
  • Basic understanding of factoring
  • Basic understanding of solving Linear Equations
  • Understanding of the Cartesian coordinate system
Week 2

Module 2

  • Determine whether a relation represents a function.
  • Find the value of a Functions
  • Graph the functions listed in the library of functions.
  • Determine whether a function is one-to-one.
  • Use the vertical line test to identify functions.
Week 2

Module 1.2

  • Find the domain of a function defined by an equation.
  • Graph piecewise-defined functions.
Week 2

Module 1.2

  • Find the domain of a function defined by an equation.
  • Graph piecewise-defined functions.
Week 2

Module 1.2

Week 3

Module 2.1

  • Basic understanding of power expressions.
  • The student recalls the Graphs and equations of Toolkit Functions, and their associated Domain and Range (Module 1).
  • The student understands where the x-intercept and y-intercept are located given a graph.
  • The student understands interval notation for Domain and Range (Module 1).
  • The student can substitute values for variables in an Equations and solve for an unknown (Module R)
  • Identify power functions.
  • Identify end behavior of power functions.
Week 3

Module 2.1

  • Basic understanding of a polynomial expression.
  • The student recalls the Graphs and equations of Toolkit Functions, and their associated domains and ranges (Module 1).
  • The student understands where the x-intercept and y-intercept are located given a graph.
  • The student understands interval notation for Domain and Range (Module 1).
  • The student can substitute values for variables in an Equations and solve for an unknown (Module R).
  • Identify polynomial functions.
  • Identify the degree and leading coefficients of polynomial functions.
Week 3

Module 2.2

  • Fundamentals of Polynomials
  • The student understands the difference between a maximum and minimum.
  • Recognize characteristics of parabolas
  • Understand how the graph of a parabola is related to its quadratic function
  • Determine a quadratic function's minimum or maximum value
  • Solve problems involving a quadratic function's minimum or maximum value
Week 4

Module 3

  • Basic understanding of multiplying and dividing fractions.
  • Basic understanding of simplifying fractions by common factors.
  • Basic understanding of the rules of exponents. (Module R Simplifying Exponents)
  • Basic understanding of Factoring Polynomials
  • Simplify rational expressions.
  • Multiply rational expressions.
  • Divide rational expressions.
  • Add and subtract rational expressions.
  • Simplify complex rational expressions.
Week 5

Module 4.1

  • The student understands that zero in the denominator of a fraction is undefined.
  • The student recalls the graphs and equations of Toolkit Functions, and their associated Domain and Range (Module 1).
Week 5

Module 4.2

Week 6

Module 5.1

  • Understanding the Toolkit Functions for exponential functions (Module 1)
  • Understanding the Domain and Range for exponential functions (Module 1)
  • Evaluate exponential functions.
  • Find the equation of an exponential function.
  • Use compound interest formulas.
  • Evaluate exponential functions with base e.
Week 6

Module 5.2

  • Rewriting from exponential form to logarithmic form and vice versa
-y=b^x\equiv\log_b(y)=x
  • Evaluate logarithms.
  • Use common logarithms.
  • Use natural logarithms.
Week 7

Module 6.1

  • Use the product rule for logarithms.
  • Use the quotient rule for logarithms.
  • Use the power rule for logarithms.
  • Expand logarithmic expressions.
  • Condense logarithmic expressions.
  • Use the change-of-base formula for logarithms.
Week 7

Module 6.2

  • Use like bases to solve exponential equations.
  • Use logarithms to solve exponential equations.
Week 7

Module 6.2

  • Use the definition of a logarithm to solve logarithmic equations.
  • Use the one-to-one property of logarithms to solve logarithmic equations.
  • Solve applied problems involving exponential and logarithmic equations.
Week 8

Module 7.1

  • Compound interest
Week 8

Module 7.1

  • Compound interest
Week 8

Module 7.2

  • Ordinary Annuity Future Values
  • Annuity Due Future Values
Week 8

Module 7.2

  • Ordinary Annuity Future Values
  • Annuity Due Future Values
Week 9

Module 8.1

  • Find the amount of a loan given the payments.
  • Find the payments required given the loan amount.
Week 9

Module 8.2

  • Define a promissory note.
  • Calculate unknown values for interest bearing promissory notes.
  • Calculate unknown values for non interest bearing promissory notes.
Week 10

Module 9.1

  • Solve systems of equations by graphing.
  • Solve systems of equations by substitution.
  • Solve systems of equations by elimination
  • Identify inconsistent systems of equations containing two variables.
  • Express the solution of a system of dependent equations containing two variables.
Week 10

Module 9.1

  • Identify the solution region of a system of two inequalities.
Week 10

Module 9.2

  • Define an objective function.
  • Define constraint equations.
  • Define feasible regions and determine corner points.
  • Solve linear programming problems using a graph.
Week 11

Module 10.1

  • Basic operations with real numbers.
  • Find the sum and difference of two matrices.
  • Find the scalar multiples of a matrix.
  • Find the product of two matrices.
Week 11

Module 10.1

  • Basic operations with real numbers.
  • Find the sum and difference of two matrices.
  • Find the scalar multiples of a matrix.
  • Find the product of two matrices.
Week 11

Module 10.2

  • Find the inverse of a matrix.
  • Solve a system of linear equations using inverse matrix.
Week 12

Module 11.1

  • None
  • Sets, elements of sets, and subsets.
  • Union, intersection, and complement of sets
  • Universal set and empty set
Week 12

Module 11.2

  • Sets and Subsets (Module 11.1)
  • Unions and intersections of sets. (Module 11.1)
  • Provide a visual representation of sets
  • Provide a visual representation of the union and intersections of sets
Week 12

Module 11.2

  • Cardinality of a set and the properties
  • Finding cardinality using a Venn diagram
Week 13

Module 12.1

  • Basic operations with real numbers and fractions.
  • Conversion between fractions, decimals, and percents.
  • Basic probability
  • Complementary events
  • Odds
  • Probability for independent events
Week 13

Module 12.2

  • Basic operations with real numbers and fractions.
  • Conversion between fractions, decimals, and percents.
  • Expected value
  • Fair game
Week 14

Module 13.1

  • Conditional probability
  • Probability of “and” for conditional events
Week 14

Module 13.2

  • Basic counting techniques and rules
  • Factorial, Permutations, and Combinations
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