Department of Mathematics at UTSA - User contributions [en]

Properties of Functions

2020-08-21T14:25:28Z

Johnraymond.yanez: Added Links to materials

* [https://mathresearch.utsa.edu/wikiFiles/MAT1053/Function_and_Function_Notation/MAT1053_M1.1Functions_and_Function_Notation.pdf Function and Function Notation],Book Chapter
* [https://mathresearch.utsa.edu/wikiFiles/MAT1053/Function_and_Function_Notation/MAT1053_M1.1_Functions_and_Function_NotationGN.pdf Function and Function Notation Guided Notes]

MAT1053

2020-08-21T14:23:48Z

Johnraymond.yanez: Condensed the Function and Function Notation Topics into Properties of Functions

==Course Catalog==

[https://catalog.utsa.edu/undergraduate/sciences/mathematics/#courseinventory 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==
{| class="wikitable sortable"
! Date !! Sections !! Topics !! Prerequisite Skills !! Student Learning Outcomes
|-
|Week 1
||
Module 1
||
* [[Order of Operations]]
||
* Basic mathematical symbols and terminology
* Basic arithmetic skills
* Basic understanding of order of operations
||
'''Review of:'''
* PEMDAS
|-
|Week 1
||
Module 1
||
* [[Simplifying Radicals]]
||
* 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
||
* [[Simplifying Exponents]]
||
* 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
||
* [[Factoring Polynomials]]
||
* 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
||
* [[Solving Equations]]
||
* 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
||
* [[Solving Inequalities]]
||
* 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
||
* [[Linear Equations]]
||
* Basic mathematical symbols and terminology
* Basic arithmetic skills
* Basic understanding of [[Order of Operations]]
* Basic understanding of factoring
* Basic understanding of [[Solving Equations]]
||
* Solving and constructing [[Linear Equations]]
|-
|Week 1
||
Module 1
||
* [[Graphs]]
||
* 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
||
* Being able to graph a [[Linear Equations]]
|-
|Week 2
||
Module 2
||
* [[Properties of Functions]]
||
* Basic understanding of [[Linear Equations]]
* Basic understanding of [[Solving Equations]]
* Basic understanding of [[Graphs]]
||
* 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
||
* [[Domain]]
||
* Basic understanding of interval notation (Module R [[Solving Inequalities]])
||
* Find the domain of a function defined by an equation.
* Graph piecewise-defined functions.
|-
|Week 2
||
Module 1.2
||
* [[Range]]
||
* Basic understanding of interval notation (Module R [[Solving Inequalities]])
||
* Find the domain of a function defined by an equation.
* Graph piecewise-defined functions.
|-
|Week 2
||
Module 1.2
||
* [[Toolkit Functions]]
||
* Basic understanding of Cartesian coordinate system (Module R [[Graphs]])
* Basic understanding of interval notation (Module R [[Solving Inequalities]])
||
* Identify the basic toolkit functions
* Determine [[Domain]] and [[Range]] for the basic toolkit functions (Module 1.2)
* [[Graphs]] the basic toolkit functions. (Module R)
|-
|Week 3
||
Module 2.1
||
* [[Intro to Power Functions]]
||
* 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 [[Solving Equations|Equations]] and solve for an unknown (Module R)
||
* Identify power functions.
* Identify end behavior of power functions.
* Identify polynomial functions.
* Identify the degree and leading coefficients of polynomial functions.
|-
|Week 3
||
Module 2.1
||
* [[Intro to Polynomial Functions]]
||
* 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 [[Solving Equations|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
||
* [[Quadratic Functions]]
||
* Fundamentals of [[Intro to Polynomial Functions|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
||
* [[Rational Expressions]]
||
* 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
||
* [[More on Polynomial Functions]]
||
* 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).
||
* [[Zeros of Polynomials]].
* [[Graphs of Polynomials]].
* Solving applied problems involving [[Intro to Polynomial Functions|Polynomial Functions]].
* Use arrow notation.
|-
|Week 5
||
Module 4.2
||
* [[Rational Functions]]
||
* [[Rational Expressions]].
* 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).
||
* [[Zeros of Polynomials]].
* [[Graphs of Polynomials]].
* Solving applied problems involving [[Intro to Polynomial Functions|Polynomial Functions]].
* Use arrow notation.
* Solve applied problems involving rational functions.
* Find the [[Domain]] of rational functions.
* Identify vertical asymptotes.
* Identify horizontal asymptotes.
|-
|Week 6
||
Module 5.1
||
* [[Exponential Functions]]
||
* 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
||
* [[Logarithmic Functions]]
||
* Understanding the [[Toolkit Functions]] for logarithmic functions
* Understanding the [[Domain]] and [[Range]] for logarithmic functions (Module 1)
* Difference between [[Linear Equations|Linear]] and [[Exponential Functions]]
||
* 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
||
* [[Logarithmic Properties]]
||
* Understanding how to convert between [[Logarithmic Functions|logarithm]] and [[Exponential Functions|exponential]] forms. (Module 5.1 & 5.2)
* Understanding [[Order of Operations]]. (Module R)
* Understanding of [[Simplifying Exponents|Exponential Rules]]. (Module R)
||
* 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
||
* [[Exponential Equations]]
||
* Understanding rules for solving [[Linear Equations]]
* Understanding rules for solving [[Quadratic Equations]]
* Understanding how to check a solution to an [[Solving Equations|equations]]
* Understanding of [[Logarithmic Properties]]
||
* Use like bases to solve exponential equations.
* Use logarithms to solve exponential equations.
|-
|Week 7
||
Module 6.2
||
* [[Logarithmic Equations]]
||
* Understanding rules for solving [[Linear Equations]]
* Understanding rules for solving [[Quadratic Equations]]
* Understanding how to check a solution to an [[Solving Equations|equations]]
* Understanding of [[Logarithmic Properties]]
||
* 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
||
* [[Simple Interest]]
||
* Understanding percents and percentages
* Understanding [[Order of Operations]]
* Understanding of [[Exponential Functions]]
* Solving [[Linear Equations]]
* Solving [[Exponential Equations]]
||
* Compound interest
|-
|Week 8
||
Module 7.1
||
* [[Compound Interest]]
||
* Understanding percents and percentages
* Understanding [[Order of Operations]]
* Understanding of [[Exponential Functions]]
* Solving [[Linear Equations]]
* Solving [[Exponential Equations]]
||
* Compound interest
|-
|Week 8
||
Module 7.2
||
* [[Annuities]]
||
* Understanding percents and percentages
* Understanding [[Order of Operations]]
* Solving [[Linear Equations]]
* Solving [[Exponential Equations]]
||
* Ordinary Annuity Future Values
* Annuity Due Future Values
|-
|Week 8
||
Module 7.2
||
* [[Payout Annuities]]
||
* Understanding percents and percentages
* Understanding [[Order of Operations]]
* Solving [[Linear Equations]]
* Solving [[Exponential Equations]]
||
* Ordinary Annuity Future Values
* Annuity Due Future Values
|-
|Week 9
||
Module 8.1
||
* [[Loans]]
||
* Understanding percents and percentages
* Understanding [[Simple Interest|Simple]] and [[Compound Interest|Compound]] Interest
* Understanding [[Order of Operations]]
* Solving [[Linear Equations]]
* Solving [[Exponential Equations]]
||
* Find the amount of a loan given the payments.
* Find the payments required given the loan amount.
|-
|Week 9
||
Module 8.2
||
* [[Promissory Notes]]
||
* Understanding percents and percentages
* Understanding percents and percentages
* Understanding [[Order of Operations]]
* Solving [[Linear Equations]]
* Solving [[Exponential Equations]]
||
* 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
||
* [[Systems of Linear Equations in Two Variables]]
||
* Solving [[Linear Equations|linear equations]] in 2 variables.
* Understanding [[Order of Operations]] (Module R)
* Basic understanding of [[Graphs|graphing]] lines (Module R / Module 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
||
* [[Systems of Inequalities in Two Variables]]
||
* Solving [[Linear Equations|linear equations]] in 2 variables.
* Basic understanding of linear [[Solving Inequalities|inequalities]] (Module R).
* Understanding [[Order of Operations]] (Module R).
* Basic understanding of [[Graphs|graphing]] lines (Module R / Module 1).
||
* Identify the solution region of a system of two inequalities.
|-
|Week 10
||
Module 9.2
||
* [[Linear Programming]]
||
* Understanding [[Order of Operations]] (Module R)
* Understanding how to solve [[Systems of Linear Equations in Two Variables]] (Module 9)
* Understanding how to interpret the solution of a system of equations in two variables. ([[Systems of Linear Equations]] Module 9)
* Understanding how to graph linear inequalities in two variables using Cartesian coordinate system ([[[Systems of Linear Equations in Two Variables]]] Module 9)
* Understanding how to shade linear inequalities in two variables using Cartesian coordinate system ([[Systems of Linear Equations in Two Variables]]] Module 9)
||
* 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
||
* [[Matrices]]
||
* 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
||
* [[Matrix Operations]]
||
* 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
||
* [[Solving Systems with Inverses]]
||
* Solving [[Systems of Linear Equations in Two Variables]] (Module 9)
* [[Matrices]]
* [[Matrix Operations]], emphasis on multiplication
||
* Find the inverse of a matrix.
* Solve a system of linear equations using inverse matrix.
|-
|Week 12
||
Module 11.1
||
* [[Sets]]
||
* None
||
* Sets, elements of sets, and subsets.
* Union, intersection, and complement of sets
* Universal set and empty set
|-
|Week 12
||
Module 11.1
||
* [[Subsets]]
||
* None
||
* Subsets, elements of sets
* Union, intersection, and complement of sets
* Universal set and empty set
|-
|Week 12
||
Module 11.2
||
* [[Venn Diagrams]]
||
* [[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]]
||
* [[Sets]] and [[Subsets]] (Module 11.1)
* Unions and intersections of sets. (Module 11.1)
* [[Venn Diagrams]]. (Module 11.2)
||
* Cardinality of a set and the properties
* Finding cardinality using a Venn diagram
|-
|Week 13
||
Module 12.1
||
* [[Introduction to Probability]]
||
* 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
||
* [[Expected Value]]
||
* Basic operations with real numbers and fractions.
* Conversion between fractions, decimals, and percents.
||
* Expected value
* Fair game
|-
|Week 14
||
Module 13.1
||
* [[Conditional Probability]]
||
* Review of [[Introduction to Probability]]. (Module 12.1)
||
* Conditional probability
* Probability of “and” for conditional events
|-
|Week 14
||
Module 13.2
||
* [[Counting Rules]]
||
* Basic operations with real numbers and fractions.
* Review of [[Introduction to Probability]]. (Module 12.1)
||
* Basic counting techniques and rules
* Factorial, Permutations, and Combinations
|}

MAT1073

2020-08-21T13:42:27Z

Johnraymond.yanez: Removed Redundancy topics

==Course Catalog==
[https://catalog.utsa.edu/search/?P=MAT%201073 MAT 1073. Algebra for Scientists and Engineers]. (1-4) 3 Credit Hours. (TCCN = MATH 1314).

Prerequisite: Satisfactory performance on a placement examination. This course is designed to prepare the student for [[MAT1093]] Precalculus and [[MAT1214]] Calculus I. Topics may include algebraic expressions; equations; inequalities over the real numbers; relations; functions; polynomial and rational functions; logarithmic and exponential functions; systems of linear equations and inequalities; matrices and determinants; complex numbers; sequences; series binomial expansion; mathematical induction; permutations, and combinations. (Formerly MTC 1073. Credit can be earned for only one of the following: MAT 1073, MTC 1073, [[MAT1063]], MTC 1023, or [[MAT1023]]. NOTE: For the purpose of the Three-Attempt Rule, these courses are considered to be equivalent and additional fees may be charged for the third or subsequent attempt to take any of these courses in any combination.) May apply toward the Core Curriculum requirement in Mathematics. Generally offered: Fall, Spring, Summer. Course Fees: LRC1 $12; LRS1 $45; STSI $21.

==Topics List==
{| class="wikitable sortable"
! Date !! Sections !! Topics !! Prerequisite Skills !! Student Learning Outcomes
|-
|Week 2
||
Module 0.1
||
* [[Order of Operations]]
||
* Basic mathematical symbols and terminology
* Basic arithmetic skills
* Basic understanding of order of operations
||
'''Review of:'''
* PEMDAS
|-
|Week 2
||
Module 0.1
||
* [[Simplifying Radicals]]
||
* Basic mathematical symbols and terminology
* Basic understanding of [[Order of Operations]] (Module 0.1)
* 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 3
||
Module 0.2
||
* [[Factoring Polynomials]]
||
* Basic mathematical symbols and terminology
* Basic arithmetic skills
* Basic understanding of [[Order of Operations]] (Module 0.1)
* 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 3
||
Module 0.3
||
* [[Solving Equations and Inequalities]]
||
* Basic mathematical symbols and terminology
* Basic arithmetic skills
* Basic understanding of [[Order of Operations]] (Module 0.1)
* 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 3
||
Module 0.4
||
* [[Linear Equations]]
||
* Basic mathematical symbols and terminology
* Basic arithmetic skills
* Basic understanding of factoring
* Basic understanding of [[Solving Equations and Inequalities]] (Module 0.3)
||
* Solving and constructing [[Linear Equations]]
|-
|Week 3
||
Module 0.4
||
* [[Graphs]]
||
* Basic mathematical symbols and terminology
* Basic arithmetic skills
* Basic understanding of order of operations
* Basic understanding of factoring
* Basic understanding of solving [[Linear Equations]] (Module 0.4)
* Understanding of the Cartesian coordinate system
||
* Being able to graph a [[Linear Equations]]
|-
|Week 4
||
Module 1.1
||
* [[Systems of Equations in Two Variables]]
||
* Solving and [[Graphs|Graphing]] [[Linear Equations|linear equations]] in 2 variables. (Module 0.4)
||
* 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 4
||
Module 1.2
||
* [[Systems of Equations in Three Variables]]
||
* Solving [[Systems of Equations in Two Variables]] (Module 1.1)
||
* Solve systems of equations in three variables
* Identify inconsistent systems of equations containing three variables
* Express solutions of a system of dependent equations containing three variables
|-
|Week 5
||
Module 2.1
||
* [[Functions]]
||
* Basic understanding of [[Linear Equations]] (Module 0.4)
||
* Determine whether a relation represents a function.
|-
|Week 5
||
Module 2.2
||
* [[Function Notation]]
||
* Basic understanding of [[Graphs]] (Module 0.4)
* Basic understanding of [[Functions]] (Module 2.1)
||
* 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 5
||
Module 2.2
||
* [[Domain of a Function]]
||
* An understanding of [[Solving Equations and Inequalities]]
||
* Find the domain of a function defined by an equation.
* Graph piecewise-defined functions.
|-
|Week 5
||
Module 2.2
||
* [[Range of a Function]]
||
* An understanding of [[Solving Equations and Inequalities]]
||
* Find the domain of a function defined by an equation.
* Graph piecewise-defined functions.
|-
|Week 5
||
Module 2.2
||
* [[Toolkit Functions]]
||
* Basic understanding of Cartesian coordinate system (Module 0.4: [[Graphs]])
||
* Identify the basic toolkit functions
* Determine [[Domain of a Function|Domain]] and [[Range of a Function| Range]] for the basic toolkit functions (Module 1.2)
* [[Graphs|Graph]] the basic toolkit functions. (Module 0.4)
|-
|Week 6
||
Module 3.1
||
* [[Intro to Power Functions]]
||
* Basic understanding of power expressions.
* The student recalls the graphs and equations of [[Toolkit Functions]], and their associated [[Domain of a Function|Domain]] and [[Range of a Function| Range]] (Module 2.2).
* The student understands where the x-intercept and y-intercept are located given a graph.
* The student understands interval notation for [[Domain of a Function|Domain]] and [[Range|Range]] (Module 2.2).
||
* Identify power functions.
* Identify end behavior of power functions.
* Identify polynomial functions.
* Identify the degree and leading coefficients of polynomial functions.
|-
|Week 6
||
Module 3.1
||
* [[Intro to Polynomial Functions]]
||
* Basic understanding of a polynomial expression.
* The student recalls the graphs and equations of [[Toolkit Functions]], and their associated [[Domain of a Function|Domain]] and [[Range of a Function| Range]] (Module 2.2).
* The student understands where the x-intercept and y-intercept are located given a graph.
* The student understands interval notation for [[Domain of a Function|Domain]] and [[Range of a Function| Range]] (Module 2.2).
||
* Identify polynomial functions.
* Identify the degree and leading coefficients of polynomial functions.
|-
|Week 6
||
Module 3.2
||
* [[Quadratic Functions]]
||
* Fundamentals of [[Intro to Polynomial Functions|Polynomials]] (Module 2.1)
* 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 7
||
Module 4.1
||
* [[Dividing Polynomials]]
||
* Basic understanding of multiplying and dividing fractions.
* Basic understanding of simplifying fractions by common factors.
* Basic understanding of [[Factoring Polynomials]] (Module 0.2)
||
* Use long division to divide polynomials
* Use synthetic division to divide polynomials
|-
|Week 7
||
Module 4.2
||
* [[Zeros of Polynomials]]
||
* Basic understanding of multiplying and dividing fractions.
* Basic understanding of simplifying fractions by common factors.
* Basic understanding of [[Solving Equations and Inequalities]] (Module 0.3)
* Basic understanding of [[Functions]] (Module 1.1)
* An understanding of [[Dividing Polynomials]] (Module 4.1)
||
* Evaluate a polynomial using the Remainder Theorem
* Use the Factor Theorem to solve a polynomial equation
* Use the Rational Zero Theorem to find rational zeros
* Find zeros of a polynomial function
* Solve real-world applications of polynomial equations
|-
|Week 8
||
Module 5.1
||
* [[More on Polynomial Functions]]
||
* The student understands that zero in the denominator of a fraction is undefined.
* Basic understanding of [[Intro to Polynomial Functions|Polynomial Functions]] (Module 3.1)
||
* Solving applied problems involving [[Intro to Polynomial Functions|Polynomial Functions]].
* Use arrow notation.
|-
|Week 8
||
Module 5.2
||
* [[Rational Functions]]
||
* 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 of a Function|Domain]] and [[Range of a Function| Range]] (Module 2.2).
||
* Solving applied problems involving [[Intro to Polynomial Functions|Polynomial Functions]]. (Module 2.1)
* Use arrow notation.
* Solve applied problems involving rational functions.
* Find the [[Domain|Domain]] of rational functions.
* Identify vertical asymptotes.
* Identify horizontal asymptotes.
|-
|Week 9
||
Module 6.1
||
* [[Graphs of Polynomials]]
||
* An understanding of [[More on Polynomial Functions]] (Module 5.1)
||
* Recognize characteristics of graphs of polynomial functions
* Use factoring to find zeros of polynomial functions
* Identify zeros and their multiplicities
* Determine end behavior
* Understand the relationship between degree and turning points
* Graph polynomial functions
|-
|Week 9
||
Module 6.2
||
* [[Graphs of Rational Functions]]
||
* Basic understanding of [[Rational Functions]] (Module 5.1)
||
* Identify and graph vertical asymptotes
* Identify and graph horizontal asymptotes
* Determine behavior of rational functions around vertical asymptotes
* Graph rational functions
|-
|Week 10
||
Module 7.1
||
* [[Single Transformations of Functions]]
||
* Understanding of [[Function Notation]] (Module 2.1)
||
* Graph functions using vertical and horizontal shifts
* Graph functions using reflections about the x-axis and the y-axis
* Determine whether a function is even, odd, or neither from it's graph
* Graph functions using compressions and stretches
* Combine transformations
|-
|Week 10
||
Module 7.2
||
* [[Multiple Transformations of Functions]]
||
* Understanding of [[Single Transformations of Functions]] (Module 7.1)
||
* Combine transformations
|-
|Week 11
||
Module 8.1
||
* [[Composition of Functions]]
||
* An understanding of [[Multiple Transformations of Functions]] (Module 7.2)
||
* Combine functions using algebraic operations
* Create a new function by composition of functions
* Evaluate composite functions
* Find the domain of a composite function
* Decompose a composite function into its component functions
|-
|Week 11
||
Module 8.2
||
* [[Inverse Functions]]
||
* An understanding of [[Composition of Functions]] (Module 7.1)
||
* Verify inverse functions
* Determine the domain and range of an inverse function, and restrict the domain of a function to make it one-to-one
* Find or evaluate the inverse of a function
* Use the graph of a one-to-one function to graph its inverse function on the same axes
|-
|Week 12
||
Module 9.1
||
* [[Exponential Properties]]
||
* Understanding [[Order of Operations]]. (Module 0.1)
* Use the product rule for exponents.
* Use the quotient rule for exponents.
* Use the power rule for logarithms.
|-
|Week 12
||
Module 9.2
||
* [[Exponential Functions]]
||
* Understanding the [[Domain of a Function|Domain]] and [[Range of a Function| Range]] of the [[Toolkit Functions]] for exponential functions (Module 2.2)
* An understanding of [[Exponential Properties]] (Module 9.1)
||
* Evaluate exponential functions.
* Find the equation of an exponential function.
* Use compound interest formulas.
* Evaluate exponential functions with base e.
|-
|Week 13
||
Module 10.1
||
* [[Logarithmic Functions]]
||
* Understanding the [[Domain of a Function|Domain]] and [[Range of a Function| Range]] of [[Toolkit Functions]] for logarithmic functions. (Module 2.2)
* Difference between [[Linear Equations|Linear]] and [[Exponential Functions]] (Module 0.4 & 9.2)
||
* 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 13
||
Module 10.2
||
* [[Logarithmic Properties]]
||
* Understanding how to convert between [[Logarithmic Functions|logarithm]] and [[Exponential Functions|exponential]] forms. (Module 9.2 & 10.1)
||
* 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 14
||
Module 11
||
* [[Modeling using Variation]]
||
* Understanding of [[Logarithmic Properties]] (Module 10.2)
||
* Solve direct variation problems
* Solve inverse variation problems
* Solve problems involving joint variation
|}

Solving Systems with Inverses

2020-08-17T15:08:55Z

Johnraymond.yanez: Added Links to materials

* [https://mathresearch.utsa.edu/wikiFiles/MAT1053/Solving_Systems_with_Inverses/MAT1053_M10.2Solving_Systems_with_Inverses.pdf Solving Systems with Inverses], Book Chapter
* [https://mathresearch.utsa.edu/wikiFiles/MAT1053/Solving_Systems_with_Inverses/MAT1053_M10.2Solving_Systems_with_InversesGN.pdf Guided Notes]

MAT1053

2020-08-17T15:07:14Z

Johnraymond.yanez:

==Course Catalog==

[https://catalog.utsa.edu/undergraduate/sciences/mathematics/#courseinventory 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==
{| class="wikitable sortable"
! Date !! Sections !! Topics !! Prerequisite Skills !! Student Learning Outcomes
|-
|Week 1
||
Module R
||
* [[Order of Operations]]
||
* Basic mathematical symbols and terminology
* Basic arithmetic skills
* Basic understanding of order of operations
||
'''Review of:'''
* PEMDAS
|-
|Week 1
||
Module R
||
* [[Simplifying Radicals]]
||
* 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 R
||
* [[Simplifying Exponents]]
||
* 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 R
||
* [[Factoring Polynomials]]
||
* 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 R
||
* [[Solving Equations]]
||
* 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 R
||
* [[Solving Inequalities]]
||
* 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 R
||
* [[Linear Equations]]
||
* Basic mathematical symbols and terminology
* Basic arithmetic skills
* Basic understanding of [[Order of Operations]]
* Basic understanding of factoring
* Basic understanding of [[Solving Equations]]
||
* Solving and constructing [[Linear Equations]]
|-
|Week 1
||
Module R
||
* [[Graphs]]
||
* 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
||
* Being able to graph a [[Linear Equations]]
|-
|Week 2
||
Module 1.1
||
* [[Functions]]
||
* Basic understanding of [[Linear Equations]]
* Basic understanding of [[Solving Equations]]
||
* Determine whether a relation represents a function.
|-
|Week 2
||
Module 1.1
||
* [[Function Notation]]
||
* Basic understanding of [[Linear Equations]]
* Basic understanding of [[Solving Equations]]
* Basic understanding of [[Graphs]]
||
* 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
||
* [[Domain]]
||
* Basic understanding of interval notation (Module R [[Solving Inequalities]])
||
* Find the domain of a function defined by an equation.
* Graph piecewise-defined functions.
|-
|Week 2
||
Module 1.2
||
* [[Range]]
||
* Basic understanding of interval notation (Module R [[Solving Inequalities]])
||
* Find the domain of a function defined by an equation.
* Graph piecewise-defined functions.
|-
|Week 2
||
Module 1.2
||
* [[Toolkit Functions]]
||
* Basic understanding of Cartesian coordinate system (Module R [[Graphs]])
* Basic understanding of interval notation (Module R [[Solving Inequalities]])
||
* Identify the basic toolkit functions
* Determine [[Domain]] and [[Range]] for the basic toolkit functions (Module 1.2)
* [[Graphs]] the basic toolkit functions. (Module R)
|-
|Week 3
||
Module 2.1
||
* [[Intro to Power Functions]]
||
* 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 [[Solving Equations|Equations]] and solve for an unknown (Module R)
||
* Identify power functions.
* Identify end behavior of power functions.
* Identify polynomial functions.
* Identify the degree and leading coefficients of polynomial functions.
|-
|Week 3
||
Module 2.1
||
* [[Intro to Polynomial Functions]]
||
* 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 [[Solving Equations|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
||
* [[Quadratic Functions]]
||
* Fundamentals of [[Intro to Polynomial Functions|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
||
* [[Rational Expressions]]
||
* 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
||
* [[More on Polynomial Functions]]
||
* 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).
||
* [[Zeros of Polynomials]].
* [[Graphs of Polynomials]].
* Solving applied problems involving [[Intro to Polynomial Functions|Polynomial Functions]].
* Use arrow notation.
|-
|Week 5
||
Module 4.2
||
* [[Rational Functions]]
||
* [[Rational Expressions]].
* 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).
||
* [[Zeros of Polynomials]].
* [[Graphs of Polynomials]].
* Solving applied problems involving [[Intro to Polynomial Functions|Polynomial Functions]].
* Use arrow notation.
* Solve applied problems involving rational functions.
* Find the [[Domain]] of rational functions.
* Identify vertical asymptotes.
* Identify horizontal asymptotes.
|-
|Week 6
||
Module 5.1
||
* [[Exponential Functions]]
||
* 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
||
* [[Logarithmic Functions]]
||
* Understanding the [[Toolkit Functions]] for logarithmic functions
* Understanding the [[Domain]] and [[Range]] for logarithmic functions (Module 1)
* Difference between [[Linear Equations|Linear]] and [[Exponential Functions]]
||
* 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
||
* [[Logarithmic Properties]]
||
* Understanding how to convert between [[Logarithmic Functions|logarithm]] and [[Exponential Functions|exponential]] forms. (Module 5.1 & 5.2)
* Understanding [[Order of Operations]]. (Module R)
* Understanding of [[Simplifying Exponents|Exponential Rules]]. (Module R)
||
* 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
||
* [[Exponential Equations]]
||
* Understanding rules for solving [[Linear Equations]]
* Understanding rules for solving [[Quadratic Equations]]
* Understanding how to check a solution to an [[Solving Equations|equations]]
* Understanding of [[Logarithmic Properties]]
||
* Use like bases to solve exponential equations.
* Use logarithms to solve exponential equations.
|-
|Week 7
||
Module 6.2
||
* [[Logarithmic Equations]]
||
* Understanding rules for solving [[Linear Equations]]
* Understanding rules for solving [[Quadratic Equations]]
* Understanding how to check a solution to an [[Solving Equations|equations]]
* Understanding of [[Logarithmic Properties]]
||
* 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
||
* [[Simple Interest]]
||
* Understanding percents and percentages
* Understanding [[Order of Operations]]
* Understanding of [[Exponential Functions]]
* Solving [[Linear Equations]]
* Solving [[Exponential Equations]]
||
* Compound interest
|-
|Week 8
||
Module 7.1
||
* [[Compound Interest]]
||
* Understanding percents and percentages
* Understanding [[Order of Operations]]
* Understanding of [[Exponential Functions]]
* Solving [[Linear Equations]]
* Solving [[Exponential Equations]]
||
* Compound interest
|-
|Week 8
||
Module 7.2
||
* [[Annuities]]
||
* Understanding percents and percentages
* Understanding [[Order of Operations]]
* Solving [[Linear Equations]]
* Solving [[Exponential Equations]]
||
* Ordinary Annuity Future Values
* Annuity Due Future Values
|-
|Week 8
||
Module 7.2
||
* [[Payout Annuities]]
||
* Understanding percents and percentages
* Understanding [[Order of Operations]]
* Solving [[Linear Equations]]
* Solving [[Exponential Equations]]
||
* Ordinary Annuity Future Values
* Annuity Due Future Values
|-
|Week 9
||
Module 8.1
||
* [[Loans]]
||
* Understanding percents and percentages
* Understanding [[Simple Interest|Simple]] and [[Compound Interest|Compound]] Interest
* Understanding [[Order of Operations]]
* Solving [[Linear Equations]]
* Solving [[Exponential Equations]]
||
* Find the amount of a loan given the payments.
* Find the payments required given the loan amount.
|-
|Week 9
||
Module 8.2
||
* [[Promissory Notes]]
||
* Understanding percents and percentages
* Understanding percents and percentages
* Understanding [[Order of Operations]]
* Solving [[Linear Equations]]
* Solving [[Exponential Equations]]
||
* 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
||
* [[Systems of Linear Equations in Two Variables]]
||
* Solving [[Linear Equations|linear equations]] in 2 variables.
* Understanding [[Order of Operations]] (Module R)
* Basic understanding of [[Graphs|graphing]] lines (Module R / Module 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
||
* [[Systems of Inequalities in Two Variables]]
||
* Solving [[Linear Equations|linear equations]] in 2 variables.
* Basic understanding of linear [[Solving Inequalities|inequalities]] (Module R).
* Understanding [[Order of Operations]] (Module R).
* Basic understanding of [[Graphs|graphing]] lines (Module R / Module 1).
||
* Identify the solution region of a system of two inequalities.
|-
|Week 10
||
Module 9.2
||
* [[Linear Programming]]
||
* Understanding [[Order of Operations]] (Module R)
* Understanding how to solve [[Systems of Linear Equations in Two Variables]] (Module 9)
* Understanding how to interpret the solution of a system of equations in two variables. ([[Systems of Linear Equations]] Module 9)
* Understanding how to graph linear inequalities in two variables using Cartesian coordinate system ([[[Systems of Linear Equations in Two Variables]]] Module 9)
* Understanding how to shade linear inequalities in two variables using Cartesian coordinate system ([[Systems of Linear Equations in Two Variables]]] Module 9)
||
* 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
||
* [[Matrices]]
||
* 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
||
* [[Matrix Operations]]
||
* 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
||
* [[Solving Systems with Inverses]]
||
* Solving [[Systems of Linear Equations in Two Variables]] (Module 9)
* [[Matrices]]
* [[Matrix Operations]], emphasis on multiplication
||
* Find the inverse of a matrix.
* Solve a system of linear equations using inverse matrix.
|-
|Week 12
||
Module 11.1
||
* [[Sets]]
||
* None
||
* Sets, elements of sets, and subsets.
* Union, intersection, and complement of sets
* Universal set and empty set
|-
|Week 12
||
Module 11.1
||
* [[Subsets]]
||
* None
||
* Subsets, elements of sets
* Union, intersection, and complement of sets
* Universal set and empty set
|-
|Week 12
||
Module 11.2
||
* [[Venn Diagrams]]
||
* [[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]]
||
* [[Sets]] and [[Subsets]] (Module 11.1)
* Unions and intersections of sets. (Module 11.1)
* [[Venn Diagrams]]. (Module 11.2)
||
* Cardinality of a set and the properties
* Finding cardinality using a Venn diagram
|-
|Week 13
||
Module 12.1
||
* [[Introduction to Probability]]
||
* 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
||
* [[Expected Value]]
||
* Basic operations with real numbers and fractions.
* Conversion between fractions, decimals, and percents.
||
* Expected value
* Fair game
|-
|Week 14
||
Module 13.1
||
* [[Conditional Probability]]
||
* Review of [[Introduction to Probability]]. (Module 12.1)
||
* Conditional probability
* Probability of “and” for conditional events
|-
|Week 14
||
Module 13.2
||
* [[Counting Rules]]
||
* Basic operations with real numbers and fractions.
* Review of [[Introduction to Probability]]. (Module 12.1)
||
* Basic counting techniques and rules
* Factorial, Permutations, and Combinations
|}

Systems of Linear Equations in Two Variables

2020-08-17T15:06:08Z

Johnraymond.yanez: Created page with "* [https://mathresearch.utsa.edu/wikiFiles/MAT1053/System_of_Linear_Equations_in_Two_Variables/MAT1053_M9.1Systems_of_Linear_Equations_in_Two_Variables.pdf Systems of Linear E..."

* [https://mathresearch.utsa.edu/wikiFiles/MAT1053/System_of_Linear_Equations_in_Two_Variables/MAT1053_M9.1Systems_of_Linear_Equations_in_Two_Variables.pdf Systems of Linear Equations in Two Variables], Book Chapter
* [https://mathresearch.utsa.edu/wikiFiles/MAT1053/System_of_Linear_Equations_in_Two_Variables/MAT1053_M9.1Systems_of_Linear_Equations_in_Two_VariablesGN.pdf Guided Notes]

Systems of Equations in Two Variables

2020-08-17T15:05:13Z

Johnraymond.yanez: Blanked the page

MAT1053

2020-08-17T15:04:48Z

Johnraymond.yanez:

==Course Catalog==

[https://catalog.utsa.edu/undergraduate/sciences/mathematics/#courseinventory 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==
{| class="wikitable sortable"
! Date !! Sections !! Topics !! Prerequisite Skills !! Student Learning Outcomes
|-
|Week 1
||
Module R
||
* [[Order of Operations]]
||
* Basic mathematical symbols and terminology
* Basic arithmetic skills
* Basic understanding of order of operations
||
'''Review of:'''
* PEMDAS
|-
|Week 1
||
Module R
||
* [[Simplifying Radicals]]
||
* 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 R
||
* [[Simplifying Exponents]]
||
* 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 R
||
* [[Factoring Polynomials]]
||
* 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 R
||
* [[Solving Equations]]
||
* 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 R
||
* [[Solving Inequalities]]
||
* 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 R
||
* [[Linear Equations]]
||
* Basic mathematical symbols and terminology
* Basic arithmetic skills
* Basic understanding of [[Order of Operations]]
* Basic understanding of factoring
* Basic understanding of [[Solving Equations]]
||
* Solving and constructing [[Linear Equations]]
|-
|Week 1
||
Module R
||
* [[Graphs]]
||
* 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
||
* Being able to graph a [[Linear Equations]]
|-
|Week 2
||
Module 1.1
||
* [[Functions]]
||
* Basic understanding of [[Linear Equations]]
* Basic understanding of [[Solving Equations]]
||
* Determine whether a relation represents a function.
|-
|Week 2
||
Module 1.1
||
* [[Function Notation]]
||
* Basic understanding of [[Linear Equations]]
* Basic understanding of [[Solving Equations]]
* Basic understanding of [[Graphs]]
||
* 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
||
* [[Domain]]
||
* Basic understanding of interval notation (Module R [[Solving Inequalities]])
||
* Find the domain of a function defined by an equation.
* Graph piecewise-defined functions.
|-
|Week 2
||
Module 1.2
||
* [[Range]]
||
* Basic understanding of interval notation (Module R [[Solving Inequalities]])
||
* Find the domain of a function defined by an equation.
* Graph piecewise-defined functions.
|-
|Week 2
||
Module 1.2
||
* [[Toolkit Functions]]
||
* Basic understanding of Cartesian coordinate system (Module R [[Graphs]])
* Basic understanding of interval notation (Module R [[Solving Inequalities]])
||
* Identify the basic toolkit functions
* Determine [[Domain]] and [[Range]] for the basic toolkit functions (Module 1.2)
* [[Graphs]] the basic toolkit functions. (Module R)
|-
|Week 3
||
Module 2.1
||
* [[Intro to Power Functions]]
||
* 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 [[Solving Equations|Equations]] and solve for an unknown (Module R)
||
* Identify power functions.
* Identify end behavior of power functions.
* Identify polynomial functions.
* Identify the degree and leading coefficients of polynomial functions.
|-
|Week 3
||
Module 2.1
||
* [[Intro to Polynomial Functions]]
||
* 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 [[Solving Equations|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
||
* [[Quadratic Functions]]
||
* Fundamentals of [[Intro to Polynomial Functions|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
||
* [[Rational Expressions]]
||
* 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
||
* [[More on Polynomial Functions]]
||
* 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).
||
* [[Zeros of Polynomials]].
* [[Graphs of Polynomials]].
* Solving applied problems involving [[Intro to Polynomial Functions|Polynomial Functions]].
* Use arrow notation.
|-
|Week 5
||
Module 4.2
||
* [[Rational Functions]]
||
* [[Rational Expressions]].
* 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).
||
* [[Zeros of Polynomials]].
* [[Graphs of Polynomials]].
* Solving applied problems involving [[Intro to Polynomial Functions|Polynomial Functions]].
* Use arrow notation.
* Solve applied problems involving rational functions.
* Find the [[Domain]] of rational functions.
* Identify vertical asymptotes.
* Identify horizontal asymptotes.
|-
|Week 6
||
Module 5.1
||
* [[Exponential Functions]]
||
* 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
||
* [[Logarithmic Functions]]
||
* Understanding the [[Toolkit Functions]] for logarithmic functions
* Understanding the [[Domain]] and [[Range]] for logarithmic functions (Module 1)
* Difference between [[Linear Equations|Linear]] and [[Exponential Functions]]
||
* 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
||
* [[Logarithmic Properties]]
||
* Understanding how to convert between [[Logarithmic Functions|logarithm]] and [[Exponential Functions|exponential]] forms. (Module 5.1 & 5.2)
* Understanding [[Order of Operations]]. (Module R)
* Understanding of [[Simplifying Exponents|Exponential Rules]]. (Module R)
||
* 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
||
* [[Exponential Equations]]
||
* Understanding rules for solving [[Linear Equations]]
* Understanding rules for solving [[Quadratic Equations]]
* Understanding how to check a solution to an [[Solving Equations|equations]]
* Understanding of [[Logarithmic Properties]]
||
* Use like bases to solve exponential equations.
* Use logarithms to solve exponential equations.
|-
|Week 7
||
Module 6.2
||
* [[Logarithmic Equations]]
||
* Understanding rules for solving [[Linear Equations]]
* Understanding rules for solving [[Quadratic Equations]]
* Understanding how to check a solution to an [[Solving Equations|equations]]
* Understanding of [[Logarithmic Properties]]
||
* 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
||
* [[Simple Interest]]
||
* Understanding percents and percentages
* Understanding [[Order of Operations]]
* Understanding of [[Exponential Functions]]
* Solving [[Linear Equations]]
* Solving [[Exponential Equations]]
||
* Compound interest
|-
|Week 8
||
Module 7.1
||
* [[Compound Interest]]
||
* Understanding percents and percentages
* Understanding [[Order of Operations]]
* Understanding of [[Exponential Functions]]
* Solving [[Linear Equations]]
* Solving [[Exponential Equations]]
||
* Compound interest
|-
|Week 8
||
Module 7.2
||
* [[Annuities]]
||
* Understanding percents and percentages
* Understanding [[Order of Operations]]
* Solving [[Linear Equations]]
* Solving [[Exponential Equations]]
||
* Ordinary Annuity Future Values
* Annuity Due Future Values
|-
|Week 8
||
Module 7.2
||
* [[Payout Annuities]]
||
* Understanding percents and percentages
* Understanding [[Order of Operations]]
* Solving [[Linear Equations]]
* Solving [[Exponential Equations]]
||
* Ordinary Annuity Future Values
* Annuity Due Future Values
|-
|Week 9
||
Module 8.1
||
* [[Loans]]
||
* Understanding percents and percentages
* Understanding [[Simple Interest|Simple]] and [[Compound Interest|Compound]] Interest
* Understanding [[Order of Operations]]
* Solving [[Linear Equations]]
* Solving [[Exponential Equations]]
||
* Find the amount of a loan given the payments.
* Find the payments required given the loan amount.
|-
|Week 9
||
Module 8.2
||
* [[Promissory Notes]]
||
* Understanding percents and percentages
* Understanding percents and percentages
* Understanding [[Order of Operations]]
* Solving [[Linear Equations]]
* Solving [[Exponential Equations]]
||
* 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
||
* [[Systems of Equations in Two Variables]]
||
* Solving [[Linear Equations|linear equations]] in 2 variables.
* Understanding [[Order of Operations]] (Module R)
* Basic understanding of [[Graphs|graphing]] lines (Module R / Module 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
||
* [[Systems of Inequalities in Two Variables]]
||
* Solving [[Linear Equations|linear equations]] in 2 variables.
* Basic understanding of linear [[Solving Inequalities|inequalities]] (Module R).
* Understanding [[Order of Operations]] (Module R).
* Basic understanding of [[Graphs|graphing]] lines (Module R / Module 1).
||
* Identify the solution region of a system of two inequalities.
|-
|Week 10
||
Module 9.2
||
* [[Linear Programming]]
||
* Understanding [[Order of Operations]] (Module R)
* Understanding how to solve [[Systems of Linear Equations in Two Variables]] (Module 9)
* Understanding how to interpret the solution of a system of equations in two variables. ([[Systems of Equations]] Module 9)
* Understanding how to graph linear inequalities in two variables using Cartesian coordinate system ([[Systems of Equations]] Module 9)
* Understanding how to shade linear inequalities in two variables using Cartesian coordinate system ([[Systems of Equations]] Module 9)
||
* 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
||
* [[Matrices]]
||
* 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
||
* [[Matrix Operations]]
||
* 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
||
* [[Solving Systems with Inverses]]
||
* Solving [[Systems of Linear Equations in Two Variables]] (Module 9)
* [[Matrices]]
* [[Matrix Operations]], emphasis on multiplication
||
* Find the inverse of a matrix.
* Solve a system of linear equations using inverse matrix.
|-
|Week 12
||
Module 11.1
||
* [[Sets]]
||
* None
||
* Sets, elements of sets, and subsets.
* Union, intersection, and complement of sets
* Universal set and empty set
|-
|Week 12
||
Module 11.1
||
* [[Subsets]]
||
* None
||
* Subsets, elements of sets
* Union, intersection, and complement of sets
* Universal set and empty set
|-
|Week 12
||
Module 11.2
||
* [[Venn Diagrams]]
||
* [[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]]
||
* [[Sets]] and [[Subsets]] (Module 11.1)
* Unions and intersections of sets. (Module 11.1)
* [[Venn Diagrams]]. (Module 11.2)
||
* Cardinality of a set and the properties
* Finding cardinality using a Venn diagram
|-
|Week 13
||
Module 12.1
||
* [[Introduction to Probability]]
||
* 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
||
* [[Expected Value]]
||
* Basic operations with real numbers and fractions.
* Conversion between fractions, decimals, and percents.
||
* Expected value
* Fair game
|-
|Week 14
||
Module 13.1
||
* [[Conditional Probability]]
||
* Review of [[Introduction to Probability]]. (Module 12.1)
||
* Conditional probability
* Probability of “and” for conditional events
|-
|Week 14
||
Module 13.2
||
* [[Counting Rules]]
||
* Basic operations with real numbers and fractions.
* Review of [[Introduction to Probability]]. (Module 12.1)
||
* Basic counting techniques and rules
* Factorial, Permutations, and Combinations
|}

MAT1053

2020-08-17T15:04:13Z

Johnraymond.yanez:

==Course Catalog==

[https://catalog.utsa.edu/undergraduate/sciences/mathematics/#courseinventory 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==
{| class="wikitable sortable"
! Date !! Sections !! Topics !! Prerequisite Skills !! Student Learning Outcomes
|-
|Week 1
||
Module R
||
* [[Order of Operations]]
||
* Basic mathematical symbols and terminology
* Basic arithmetic skills
* Basic understanding of order of operations
||
'''Review of:'''
* PEMDAS
|-
|Week 1
||
Module R
||
* [[Simplifying Radicals]]
||
* 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 R
||
* [[Simplifying Exponents]]
||
* 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 R
||
* [[Factoring Polynomials]]
||
* 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 R
||
* [[Solving Equations]]
||
* 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 R
||
* [[Solving Inequalities]]
||
* 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 R
||
* [[Linear Equations]]
||
* Basic mathematical symbols and terminology
* Basic arithmetic skills
* Basic understanding of [[Order of Operations]]
* Basic understanding of factoring
* Basic understanding of [[Solving Equations]]
||
* Solving and constructing [[Linear Equations]]
|-
|Week 1
||
Module R
||
* [[Graphs]]
||
* 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
||
* Being able to graph a [[Linear Equations]]
|-
|Week 2
||
Module 1.1
||
* [[Functions]]
||
* Basic understanding of [[Linear Equations]]
* Basic understanding of [[Solving Equations]]
||
* Determine whether a relation represents a function.
|-
|Week 2
||
Module 1.1
||
* [[Function Notation]]
||
* Basic understanding of [[Linear Equations]]
* Basic understanding of [[Solving Equations]]
* Basic understanding of [[Graphs]]
||
* 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
||
* [[Domain]]
||
* Basic understanding of interval notation (Module R [[Solving Inequalities]])
||
* Find the domain of a function defined by an equation.
* Graph piecewise-defined functions.
|-
|Week 2
||
Module 1.2
||
* [[Range]]
||
* Basic understanding of interval notation (Module R [[Solving Inequalities]])
||
* Find the domain of a function defined by an equation.
* Graph piecewise-defined functions.
|-
|Week 2
||
Module 1.2
||
* [[Toolkit Functions]]
||
* Basic understanding of Cartesian coordinate system (Module R [[Graphs]])
* Basic understanding of interval notation (Module R [[Solving Inequalities]])
||
* Identify the basic toolkit functions
* Determine [[Domain]] and [[Range]] for the basic toolkit functions (Module 1.2)
* [[Graphs]] the basic toolkit functions. (Module R)
|-
|Week 3
||
Module 2.1
||
* [[Intro to Power Functions]]
||
* 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 [[Solving Equations|Equations]] and solve for an unknown (Module R)
||
* Identify power functions.
* Identify end behavior of power functions.
* Identify polynomial functions.
* Identify the degree and leading coefficients of polynomial functions.
|-
|Week 3
||
Module 2.1
||
* [[Intro to Polynomial Functions]]
||
* 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 [[Solving Equations|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
||
* [[Quadratic Functions]]
||
* Fundamentals of [[Intro to Polynomial Functions|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
||
* [[Rational Expressions]]
||
* 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
||
* [[More on Polynomial Functions]]
||
* 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).
||
* [[Zeros of Polynomials]].
* [[Graphs of Polynomials]].
* Solving applied problems involving [[Intro to Polynomial Functions|Polynomial Functions]].
* Use arrow notation.
|-
|Week 5
||
Module 4.2
||
* [[Rational Functions]]
||
* [[Rational Expressions]].
* 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).
||
* [[Zeros of Polynomials]].
* [[Graphs of Polynomials]].
* Solving applied problems involving [[Intro to Polynomial Functions|Polynomial Functions]].
* Use arrow notation.
* Solve applied problems involving rational functions.
* Find the [[Domain]] of rational functions.
* Identify vertical asymptotes.
* Identify horizontal asymptotes.
|-
|Week 6
||
Module 5.1
||
* [[Exponential Functions]]
||
* 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
||
* [[Logarithmic Functions]]
||
* Understanding the [[Toolkit Functions]] for logarithmic functions
* Understanding the [[Domain]] and [[Range]] for logarithmic functions (Module 1)
* Difference between [[Linear Equations|Linear]] and [[Exponential Functions]]
||
* 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
||
* [[Logarithmic Properties]]
||
* Understanding how to convert between [[Logarithmic Functions|logarithm]] and [[Exponential Functions|exponential]] forms. (Module 5.1 & 5.2)
* Understanding [[Order of Operations]]. (Module R)
* Understanding of [[Simplifying Exponents|Exponential Rules]]. (Module R)
||
* 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
||
* [[Exponential Equations]]
||
* Understanding rules for solving [[Linear Equations]]
* Understanding rules for solving [[Quadratic Equations]]
* Understanding how to check a solution to an [[Solving Equations|equations]]
* Understanding of [[Logarithmic Properties]]
||
* Use like bases to solve exponential equations.
* Use logarithms to solve exponential equations.
|-
|Week 7
||
Module 6.2
||
* [[Logarithmic Equations]]
||
* Understanding rules for solving [[Linear Equations]]
* Understanding rules for solving [[Quadratic Equations]]
* Understanding how to check a solution to an [[Solving Equations|equations]]
* Understanding of [[Logarithmic Properties]]
||
* 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
||
* [[Simple Interest]]
||
* Understanding percents and percentages
* Understanding [[Order of Operations]]
* Understanding of [[Exponential Functions]]
* Solving [[Linear Equations]]
* Solving [[Exponential Equations]]
||
* Compound interest
|-
|Week 8
||
Module 7.1
||
* [[Compound Interest]]
||
* Understanding percents and percentages
* Understanding [[Order of Operations]]
* Understanding of [[Exponential Functions]]
* Solving [[Linear Equations]]
* Solving [[Exponential Equations]]
||
* Compound interest
|-
|Week 8
||
Module 7.2
||
* [[Annuities]]
||
* Understanding percents and percentages
* Understanding [[Order of Operations]]
* Solving [[Linear Equations]]
* Solving [[Exponential Equations]]
||
* Ordinary Annuity Future Values
* Annuity Due Future Values
|-
|Week 8
||
Module 7.2
||
* [[Payout Annuities]]
||
* Understanding percents and percentages
* Understanding [[Order of Operations]]
* Solving [[Linear Equations]]
* Solving [[Exponential Equations]]
||
* Ordinary Annuity Future Values
* Annuity Due Future Values
|-
|Week 9
||
Module 8.1
||
* [[Loans]]
||
* Understanding percents and percentages
* Understanding [[Simple Interest|Simple]] and [[Compound Interest|Compound]] Interest
* Understanding [[Order of Operations]]
* Solving [[Linear Equations]]
* Solving [[Exponential Equations]]
||
* Find the amount of a loan given the payments.
* Find the payments required given the loan amount.
|-
|Week 9
||
Module 8.2
||
* [[Promissory Notes]]
||
* Understanding percents and percentages
* Understanding percents and percentages
* Understanding [[Order of Operations]]
* Solving [[Linear Equations]]
* Solving [[Exponential Equations]]
||
* 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
||
* [[Systems of Linear Equations in Two Variables]]
||
* Solving [[Linear Equations|linear equations]] in 2 variables.
* Understanding [[Order of Operations]] (Module R)
* Basic understanding of [[Graphs|graphing]] lines (Module R / Module 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
||
* [[Systems of Inequalities in Two Variables]]
||
* Solving [[Linear Equations|linear equations]] in 2 variables.
* Basic understanding of linear [[Solving Inequalities|inequalities]] (Module R).
* Understanding [[Order of Operations]] (Module R).
* Basic understanding of [[Graphs|graphing]] lines (Module R / Module 1).
||
* Identify the solution region of a system of two inequalities.
|-
|Week 10
||
Module 9.2
||
* [[Linear Programming]]
||
* Understanding [[Order of Operations]] (Module R)
* Understanding how to solve [[Systems of Linear Equations in Two Variables]] (Module 9)
* Understanding how to interpret the solution of a system of equations in two variables. ([[Systems of Equations]] Module 9)
* Understanding how to graph linear inequalities in two variables using Cartesian coordinate system ([[Systems of Equations]] Module 9)
* Understanding how to shade linear inequalities in two variables using Cartesian coordinate system ([[Systems of Equations]] Module 9)
||
* 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
||
* [[Matrices]]
||
* 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
||
* [[Matrix Operations]]
||
* 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
||
* [[Solving Systems with Inverses]]
||
* Solving [[Systems of Linear Equations in Two Variables]] (Module 9)
* [[Matrices]]
* [[Matrix Operations]], emphasis on multiplication
||
* Find the inverse of a matrix.
* Solve a system of linear equations using inverse matrix.
|-
|Week 12
||
Module 11.1
||
* [[Sets]]
||
* None
||
* Sets, elements of sets, and subsets.
* Union, intersection, and complement of sets
* Universal set and empty set
|-
|Week 12
||
Module 11.1
||
* [[Subsets]]
||
* None
||
* Subsets, elements of sets
* Union, intersection, and complement of sets
* Universal set and empty set
|-
|Week 12
||
Module 11.2
||
* [[Venn Diagrams]]
||
* [[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]]
||
* [[Sets]] and [[Subsets]] (Module 11.1)
* Unions and intersections of sets. (Module 11.1)
* [[Venn Diagrams]]. (Module 11.2)
||
* Cardinality of a set and the properties
* Finding cardinality using a Venn diagram
|-
|Week 13
||
Module 12.1
||
* [[Introduction to Probability]]
||
* 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
||
* [[Expected Value]]
||
* Basic operations with real numbers and fractions.
* Conversion between fractions, decimals, and percents.
||
* Expected value
* Fair game
|-
|Week 14
||
Module 13.1
||
* [[Conditional Probability]]
||
* Review of [[Introduction to Probability]]. (Module 12.1)
||
* Conditional probability
* Probability of “and” for conditional events
|-
|Week 14
||
Module 13.2
||
* [[Counting Rules]]
||
* Basic operations with real numbers and fractions.
* Review of [[Introduction to Probability]]. (Module 12.1)
||
* Basic counting techniques and rules
* Factorial, Permutations, and Combinations
|}

MAT1053

2020-08-17T14:51:05Z

Johnraymond.yanez: Changed Systems of Equations to Systems of Linear Equations

==Course Catalog==

[https://catalog.utsa.edu/undergraduate/sciences/mathematics/#courseinventory 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==
{| class="wikitable sortable"
! Date !! Sections !! Topics !! Prerequisite Skills !! Student Learning Outcomes
|-
|Week 1
||
Module R
||
* [[Order of Operations]]
||
* Basic mathematical symbols and terminology
* Basic arithmetic skills
* Basic understanding of order of operations
||
'''Review of:'''
* PEMDAS
|-
|Week 1
||
Module R
||
* [[Simplifying Radicals]]
||
* 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 R
||
* [[Simplifying Exponents]]
||
* 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 R
||
* [[Factoring Polynomials]]
||
* 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 R
||
* [[Solving Equations]]
||
* 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 R
||
* [[Solving Inequalities]]
||
* 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 R
||
* [[Linear Equations]]
||
* Basic mathematical symbols and terminology
* Basic arithmetic skills
* Basic understanding of [[Order of Operations]]
* Basic understanding of factoring
* Basic understanding of [[Solving Equations]]
||
* Solving and constructing [[Linear Equations]]
|-
|Week 1
||
Module R
||
* [[Graphs]]
||
* 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
||
* Being able to graph a [[Linear Equations]]
|-
|Week 2
||
Module 1.1
||
* [[Functions]]
||
* Basic understanding of [[Linear Equations]]
* Basic understanding of [[Solving Equations]]
||
* Determine whether a relation represents a function.
|-
|Week 2
||
Module 1.1
||
* [[Function Notation]]
||
* Basic understanding of [[Linear Equations]]
* Basic understanding of [[Solving Equations]]
* Basic understanding of [[Graphs]]
||
* 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
||
* [[Domain]]
||
* Basic understanding of interval notation (Module R [[Solving Inequalities]])
||
* Find the domain of a function defined by an equation.
* Graph piecewise-defined functions.
|-
|Week 2
||
Module 1.2
||
* [[Range]]
||
* Basic understanding of interval notation (Module R [[Solving Inequalities]])
||
* Find the domain of a function defined by an equation.
* Graph piecewise-defined functions.
|-
|Week 2
||
Module 1.2
||
* [[Toolkit Functions]]
||
* Basic understanding of Cartesian coordinate system (Module R [[Graphs]])
* Basic understanding of interval notation (Module R [[Solving Inequalities]])
||
* Identify the basic toolkit functions
* Determine [[Domain]] and [[Range]] for the basic toolkit functions (Module 1.2)
* [[Graphs]] the basic toolkit functions. (Module R)
|-
|Week 3
||
Module 2.1
||
* [[Intro to Power Functions]]
||
* 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 [[Solving Equations|Equations]] and solve for an unknown (Module R)
||
* Identify power functions.
* Identify end behavior of power functions.
* Identify polynomial functions.
* Identify the degree and leading coefficients of polynomial functions.
|-
|Week 3
||
Module 2.1
||
* [[Intro to Polynomial Functions]]
||
* 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 [[Solving Equations|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
||
* [[Quadratic Functions]]
||
* Fundamentals of [[Intro to Polynomial Functions|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
||
* [[Rational Expressions]]
||
* 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
||
* [[More on Polynomial Functions]]
||
* 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).
||
* [[Zeros of Polynomials]].
* [[Graphs of Polynomials]].
* Solving applied problems involving [[Intro to Polynomial Functions|Polynomial Functions]].
* Use arrow notation.
|-
|Week 5
||
Module 4.2
||
* [[Rational Functions]]
||
* [[Rational Expressions]].
* 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).
||
* [[Zeros of Polynomials]].
* [[Graphs of Polynomials]].
* Solving applied problems involving [[Intro to Polynomial Functions|Polynomial Functions]].
* Use arrow notation.
* Solve applied problems involving rational functions.
* Find the [[Domain]] of rational functions.
* Identify vertical asymptotes.
* Identify horizontal asymptotes.
|-
|Week 6
||
Module 5.1
||
* [[Exponential Functions]]
||
* 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
||
* [[Logarithmic Functions]]
||
* Understanding the [[Toolkit Functions]] for logarithmic functions
* Understanding the [[Domain]] and [[Range]] for logarithmic functions (Module 1)
* Difference between [[Linear Equations|Linear]] and [[Exponential Functions]]
||
* 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
||
* [[Logarithmic Properties]]
||
* Understanding how to convert between [[Logarithmic Functions|logarithm]] and [[Exponential Functions|exponential]] forms. (Module 5.1 & 5.2)
* Understanding [[Order of Operations]]. (Module R)
* Understanding of [[Simplifying Exponents|Exponential Rules]]. (Module R)
||
* 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
||
* [[Exponential Equations]]
||
* Understanding rules for solving [[Linear Equations]]
* Understanding rules for solving [[Quadratic Equations]]
* Understanding how to check a solution to an [[Solving Equations|equations]]
* Understanding of [[Logarithmic Properties]]
||
* Use like bases to solve exponential equations.
* Use logarithms to solve exponential equations.
|-
|Week 7
||
Module 6.2
||
* [[Logarithmic Equations]]
||
* Understanding rules for solving [[Linear Equations]]
* Understanding rules for solving [[Quadratic Equations]]
* Understanding how to check a solution to an [[Solving Equations|equations]]
* Understanding of [[Logarithmic Properties]]
||
* 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
||
* [[Simple Interest]]
||
* Understanding percents and percentages
* Understanding [[Order of Operations]]
* Understanding of [[Exponential Functions]]
* Solving [[Linear Equations]]
* Solving [[Exponential Equations]]
||
* Compound interest
|-
|Week 8
||
Module 7.1
||
* [[Compound Interest]]
||
* Understanding percents and percentages
* Understanding [[Order of Operations]]
* Understanding of [[Exponential Functions]]
* Solving [[Linear Equations]]
* Solving [[Exponential Equations]]
||
* Compound interest
|-
|Week 8
||
Module 7.2
||
* [[Annuities]]
||
* Understanding percents and percentages
* Understanding [[Order of Operations]]
* Solving [[Linear Equations]]
* Solving [[Exponential Equations]]
||
* Ordinary Annuity Future Values
* Annuity Due Future Values
|-
|Week 8
||
Module 7.2
||
* [[Payout Annuities]]
||
* Understanding percents and percentages
* Understanding [[Order of Operations]]
* Solving [[Linear Equations]]
* Solving [[Exponential Equations]]
||
* Ordinary Annuity Future Values
* Annuity Due Future Values
|-
|Week 9
||
Module 8.1
||
* [[Loans]]
||
* Understanding percents and percentages
* Understanding [[Simple Interest|Simple]] and [[Compound Interest|Compound]] Interest
* Understanding [[Order of Operations]]
* Solving [[Linear Equations]]
* Solving [[Exponential Equations]]
||
* Find the amount of a loan given the payments.
* Find the payments required given the loan amount.
|-
|Week 9
||
Module 8.2
||
* [[Promissory Notes]]
||
* Understanding percents and percentages
* Understanding percents and percentages
* Understanding [[Order of Operations]]
* Solving [[Linear Equations]]
* Solving [[Exponential Equations]]
||
* 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
||
* Systems of Linear Equations in Two Variables]]
||
* Solving [[Linear Equations|linear equations]] in 2 variables.
* Understanding [[Order of Operations]] (Module R)
* Basic understanding of [[Graphs|graphing]] lines (Module R / Module 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
||
* [[Systems of Inequalities in Two Variables]]
||
* Solving [[Linear Equations|linear equations]] in 2 variables.
* Basic understanding of linear [[Solving Inequalities|inequalities]] (Module R).
* Understanding [[Order of Operations]] (Module R).
* Basic understanding of [[Graphs|graphing]] lines (Module R / Module 1).
||
* Identify the solution region of a system of two inequalities.
|-
|Week 10
||
Module 9.2
||
* [[Linear Programming]]
||
* Understanding [[Order of Operations]] (Module R)
* Understanding how to solve Systems of Linear Equations in Two Variables]] (Module 9)
* Understanding how to interpret the solution of a system of equations in two variables. ([[Systems of Equations]] Module 9)
* Understanding how to graph linear inequalities in two variables using Cartesian coordinate system ([[Systems of Equations]] Module 9)
* Understanding how to shade linear inequalities in two variables using Cartesian coordinate system ([[Systems of Equations]] Module 9)
||
* 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
||
* [[Matrices]]
||
* 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
||
* [[Matrix Operations]]
||
* 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
||
* [[Solving Systems with Inverses]]
||
* Solving Systems of Linear Equations in Two Variables]] (Module 9)
* [[Matrices]]
* [[Matrix Operations]], emphasis on multiplication
||
* Find the inverse of a matrix.
* Solve a system of linear equations using inverse matrix.
|-
|Week 12
||
Module 11.1
||
* [[Sets]]
||
* None
||
* Sets, elements of sets, and subsets.
* Union, intersection, and complement of sets
* Universal set and empty set
|-
|Week 12
||
Module 11.1
||
* [[Subsets]]
||
* None
||
* Subsets, elements of sets
* Union, intersection, and complement of sets
* Universal set and empty set
|-
|Week 12
||
Module 11.2
||
* [[Venn Diagrams]]
||
* [[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]]
||
* [[Sets]] and [[Subsets]] (Module 11.1)
* Unions and intersections of sets. (Module 11.1)
* [[Venn Diagrams]]. (Module 11.2)
||
* Cardinality of a set and the properties
* Finding cardinality using a Venn diagram
|-
|Week 13
||
Module 12.1
||
* [[Introduction to Probability]]
||
* 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
||
* [[Expected Value]]
||
* Basic operations with real numbers and fractions.
* Conversion between fractions, decimals, and percents.
||
* Expected value
* Fair game
|-
|Week 14
||
Module 13.1
||
* [[Conditional Probability]]
||
* Review of [[Introduction to Probability]]. (Module 12.1)
||
* Conditional probability
* Probability of “and” for conditional events
|-
|Week 14
||
Module 13.2
||
* [[Counting Rules]]
||
* Basic operations with real numbers and fractions.
* Review of [[Introduction to Probability]]. (Module 12.1)
||
* Basic counting techniques and rules
* Factorial, Permutations, and Combinations
|}

Systems of Equations in Two Variables

2020-08-17T14:50:17Z

Johnraymond.yanez:

Expected Value

2020-08-17T14:45:53Z

Johnraymond.yanez: Added Links to materials

* [https://mathresearch.utsa.edu/wikiFiles/MAT1053/Expected_Value/MAT1053_M12.2Expected_Value.pdf Expected Value], Book Chapter
* [https://mathresearch.utsa.edu/wikiFiles/MAT1053/Expected_Value/MAT1053_M12.2Expected_Value.pdf Guided Notes]

Introduction to Probability

2020-08-17T14:44:47Z

Johnraymond.yanez: Added Links to materials

* [https://mathresearch.utsa.edu/wikiFiles/MAT1053/Introduction_to_Probability/MAT1053_M12.1Introduction_to_Probability.pdf Introduction to Probability], Book Chapter
* [https://mathresearch.utsa.edu/wikiFiles/MAT1053/Introduction_to_Probability/MAT1053_M12.1Introduction_to_ProbabilityGN.pdf Guided Notes]

Cardinality

2020-08-17T14:43:43Z

Johnraymond.yanez: Added Links to materials

* [https://mathresearch.utsa.edu/wikiFiles/MAT1053/Venn_Diagrams_and_Cardinality/MAT1053_M11.2Venn_Diagrams_and_Cardinality.pdf Venn Diagrams and Cardinality], Book Chapter
* [https://mathresearch.utsa.edu/wikiFiles/MAT1053/Venn_Diagrams_and_Cardinality/MAT1053_M11.2Venn_Diagrams_and_CardinalityGN.pdf Guided Notes]

Venn Diagrams

2020-08-17T14:43:29Z

Johnraymond.yanez: Created page with "* [https://mathresearch.utsa.edu/wikiFiles/MAT1053/Venn_Diagrams_and_Cardinality/MAT1053_M11.2Venn_Diagrams_and_Cardinality.pdf Venn Diagrams and Cardinality], Book Chapter *..."

Subsets

2020-08-17T14:41:26Z

Johnraymond.yanez: Added Links to materials

* [https://mathresearch.utsa.edu/wikiFiles/MAT1053/Sets_and_Subsets/MAT1053_M11.1Sets_and_Subsets.pdf Sets and Subsets], Book Chapter
* [https://mathresearch.utsa.edu/wikiFiles/MAT1053/Sets_and_Subsets/MAT1053_M11.1Sets_and_SubsetsGN.pdf Guided Notes]

Sets

2020-08-17T14:41:10Z

Johnraymond.yanez: Added Links to materials

Matrix Operations

2020-08-17T14:40:04Z

Johnraymond.yanez: Added Links to materials

* [https://mathresearch.utsa.edu/wikiFiles/MAT1053/Matrices_and_Matrix_Operations/MAT1053_M10.1Matrices_and_Matrix_Operations.pdf Matrices and Matrix Operations], Book Chapter
* [https://mathresearch.utsa.edu/wikiFiles/MAT1053/Matrices_and_Matrix_Operations/MAT1053_M10.1Matrices_and_Matrix_Operations.pdf Guided Notes]
* [https://www.youtube.com/watch?v=0iDPZolrGpE Matrix Addition]. Produced by TA Catherine Sporer, UTSA

Matrices

2020-08-17T14:38:42Z

Johnraymond.yanez: Added Links to materials

Linear Programming

2020-08-17T14:36:30Z

Johnraymond.yanez: Added Links to materials

* [https://mathresearch.utsa.edu/wikiFiles/MAT1053/Linear_Programming/MAT1053_M9.2Linear_Programming.pdf Linear Programming], Book Chapter
* [https://mathresearch.utsa.edu/wikiFiles/MAT1053/Linear_Programming/MAT1053_M9.2Linear_ProgrammingGN.pdf Guided Notes]

Systems of Equations in Two Variables

2020-08-17T14:35:10Z

* [https://mathresearch.utsa.edu/wikiFiles/MAT1053/System_of_Linear_Equations_in_Two_Variables/MAT1053_M9.1Systems_of_Linear_Equations_in_Two_Variables.pdf Systems of Linear_Equations in Two Variables], Book Chapter
* [https://mathresearch.utsa.edu/wikiFiles/MAT1053/System_of_Linear_Equations_in_Two_Variables/MAT1053_M9.1Systems_of_Linear_Equations_in_Two_VariablesGN.pdf Guided Notes]

Promissory Notes

2020-08-17T14:33:39Z

Johnraymond.yanez: Added Links to materials

* [https://mathresearch.utsa.edu/wikiFiles/MAT1053/Promisory_Notes/MAT1053_M8.2Promisory_Notes.pdf Promissory Notes], Book Chapter
* [https://mathresearch.utsa.edu/wikiFiles/MAT1053/Promisory_Notes/MAT1053_M8.2Promisory_NotesGN.pdf Guided Notes]

Loans

2020-08-17T14:31:34Z

Johnraymond.yanez: Added Links to materials

* [https://mathresearch.utsa.edu/wikiFiles/MAT1053/Loans/MAT1053_M8.1Loans.pdf Loans], Book Chapter
* [https://mathresearch.utsa.edu/wikiFiles/MAT1053/Loans/MAT1053_M8.1LoansGN.pdf Guided Notes]

Annuities

2020-08-17T14:29:57Z

Johnraymond.yanez: Added Links to materials

* [https://mathresearch.utsa.edu/wikiFiles/MAT1053/Annuities/MAT1053_M7.2Annuities.pdf Annuities], Book Chapter
* [https://mathresearch.utsa.edu/wikiFiles/MAT1053/Annuities/MAT1053_M7.2AnnuitiesGN.pdf Guided Notes]

Compound Interest

2020-08-17T14:29:11Z

Johnraymond.yanez: Added Links to materials

* [https://mathresearch.utsa.edu/wikiFiles/MAT1053/Simple_and_Compound_Interest/MAT1053_M7.1Simple_and_Compound_Interest.pdf Simple and Compound Interest], Book Chapter
* [https://mathresearch.utsa.edu/wikiFiles/MAT1053/Simple_and_Compound_Interest/MAT1053_M7.1Simple_and_Compound_InterestGN.pdf Guided Notes]

Simple Interest

2020-08-17T14:28:51Z

Johnraymond.yanez: Added Links to materials

Logarithmic Equations

2020-08-17T14:27:05Z

Johnraymond.yanez: Created page with "* [https://mathresearch.utsa.edu/wikiFiles/MAT1053/Exponential%20and%20Logarithimic%20Equations/MAT1053_M6.2Exponential_and_Logarithmic_Equations.pdf Exponential and Logarithm..."

* [https://mathresearch.utsa.edu/wikiFiles/MAT1053/Exponential%20and%20Logarithimic%20Equations/MAT1053_M6.2Exponential_and_Logarithmic_Equations.pdf Exponential and Logarithmic Equations], Book Chapter
* [https://mathresearch.utsa.edu/wikiFiles/MAT1053/Exponential%20and%20Logarithimic%20Equations/MAT1053_M6.2Exponential_and_Logarithmic_EquationsGN.pdf Guided Notes]

Exponential Equations

2020-08-17T14:26:52Z

Johnraymond.yanez: Added Links to materials

Logarithmic Properties

2020-08-17T14:24:59Z

Johnraymond.yanez: Added Links to materials

* [https://mathresearch.utsa.edu/wikiFiles/MAT1053/Logarithmic%20Properties/MAT1053_M6.1Logarithmic_Properties.pdf Logarithmic Properties], Book Chapter
* [https://mathresearch.utsa.edu/wikiFiles/MAT1053/Logarithmic%20Properties/MAT1053_M6.1Logarithmic_PropertiesGN.pdf Guided Notes]

Logarithmic Functions

2020-08-17T14:24:22Z

Johnraymond.yanez: Created page with "* [https://mathresearch.utsa.edu/wikiFiles/MAT1053/Logarithmic_Functions/MAT1053_M5.2Logarithmic_Functions.pdf Logarithmic Functions], Book Chapter * [https://mathresearch.uts..."

* [https://mathresearch.utsa.edu/wikiFiles/MAT1053/Logarithmic_Functions/MAT1053_M5.2Logarithmic_Functions.pdf Logarithmic Functions], Book Chapter
* [https://mathresearch.utsa.edu/wikiFiles/MAT1053/Logarithmic_Functions/MAT1053_M5.2Logarithmic_FunctionsGN.pdf Guided Notes]

Exponential Functions

2020-08-17T14:23:00Z

Johnraymond.yanez:

* [https://mathresearch.utsa.edu/wikiFiles/MAT1053/Exponential%20Functions/MAT1053_M5.1Exponential_Functions.pdf Exponential Functions], Book Chapter
* [https://mathresearch.utsa.edu/wikiFiles/MAT1053/Exponential%20Functions/MAT1053_M5.1Exponential_FunctionsGN.pdf Guided Notes]

Exponential Functions

2020-08-17T14:22:49Z

Johnraymond.yanez: Added Links to materials

Rational Functions

2020-08-17T14:21:58Z

Johnraymond.yanez: Added Links to materials

* [https://mathresearch.utsa.edu/wikiFiles/MAT1053/Rational_Functions/MAT1053_M4.2Rational_Functions.pdf Rational Functions], Book Chapter
* [https://mathresearch.utsa.edu/wikiFiles/MAT1053/Rational_Functions/MAT1053_M4.2Rational_FunctionsGN.pdf Guided Notes]

More on Polynomial Functions

2020-08-17T14:20:44Z

Johnraymond.yanez: Added Links to materials

* [https://mathresearch.utsa.edu/wikiFiles/MAT1053/More_on_Polynomial_and_Power_Functions/MAT1053_M4.1More_on_Power_Functions_and_Polynomial_Functions.pdf More on Power Functions and Polynomial Functions], Book Chapter
* [https://mathresearch.utsa.edu/wikiFiles/MAT1053/More_on_Polynomial_and_Power_Functions/MAT1053_M4.1More_on_Power_Functions_and_Polynomial_FunctionsGN.pdf, Guided Notes]

Rational Expressions

2020-08-17T14:17:57Z

Johnraymond.yanez: Added Links to materials

* [https://mathresearch.utsa.edu/wikiFiles/MAT1053/Rational_Expressions/MAT1053_M3Rational_Expressions.pdf Rational Expressions], Book Chapter
* [https://mathresearch.utsa.edu/wikiFiles/MAT1053/Rational_Expressions/MAT1053_M3Rational_ExpressionsGN.pdf Guided Notes]

Quadratic Functions

2020-08-17T14:16:14Z

Johnraymond.yanez: Added Links to materials

* [https://mathresearch.utsa.edu/wikiFiles/MAT1053/Quadratic_Functions/MAT1053_M2.2Quadratic_Functions.pdf Quadratic Functions], Book Chapters
* [https://mathresearch.utsa.edu/wikiFiles/MAT1053/Quadratic_Functions/MAT1053_M2.2Quadratic_FunctionsGN.pdf Guided Notes]

Polynomial Functions

2020-08-17T14:14:48Z

Johnraymond.yanez:

* [https://mathresearch.utsa.edu/wikiFiles/MAT1053/Intro_to_Polynomial_and_Power_Functions/MAT1053_M2.1Intro_to_Power_Functions_and_Polynomial_Functions.pdf Intro to Power Functions and Polynomial Functions], Book Chapter
* [https://mathresearch.utsa.edu/wikiFiles/MAT1053/Intro_to_Polynomial_and_Power_Functions/MAT1053_M2.1Intro_to_Power_Functions_and_Polynomial_FunctionsGN.pdf Guided Notes]
* [https://www.youtube.com/watch?v=nJLzFBsSX3o Multiplying Polynomials]. Produced by TA Catherine Sporer, UTSA

Intro to Power Functions

2020-08-17T14:14:27Z

Johnraymond.yanez: Added Links to materials

Toolkit Functions

2020-08-17T14:12:56Z

Johnraymond.yanez: Added Links to materials

* [https://mathresearch.utsa.edu/wikiFiles/MAT1053/Domain_Range_and_Toolkit_Functions/MAT1053_M1.2Domain_Range_and_Toolkit_Functions.pdf Domain Range and Toolkit Functions], Book Chapter
* [https://mathresearch.utsa.edu/wikiFiles/MAT1053/Domain_Range_and_Toolkit_Functions/MAT1053_M1.2Domain_Range_and_Toolkit_FunctionsGN.pdf Guided Notes]

Range

2020-08-17T14:12:43Z

Johnraymond.yanez: Added Links to materials

Domain

2020-08-17T14:12:27Z

Johnraymond.yanez: Added Links to materials

Function Notation

2020-08-17T14:09:46Z

Johnraymond.yanez:

Function Notation

2020-08-17T14:09:02Z

Johnraymond.yanez: Added Links to materials

MAT1073

2020-08-13T16:25:57Z

Johnraymond.yanez:

==Course Catalog==
[https://catalog.utsa.edu/search/?P=MAT%201073 MAT 1073. Algebra for Scientists and Engineers]. (1-4) 3 Credit Hours. (TCCN = MATH 1314).

Prerequisite: Satisfactory performance on a placement examination. This course is designed to prepare the student for [[MAT1093]] Precalculus and [[MAT1214]] Calculus I. Topics may include algebraic expressions; equations; inequalities over the real numbers; relations; functions; polynomial and rational functions; logarithmic and exponential functions; systems of linear equations and inequalities; matrices and determinants; complex numbers; sequences; series binomial expansion; mathematical induction; permutations, and combinations. (Formerly MTC 1073. Credit can be earned for only one of the following: MAT 1073, MTC 1073, [[MAT1063]], MTC 1023, or [[MAT1023]]. NOTE: For the purpose of the Three-Attempt Rule, these courses are considered to be equivalent and additional fees may be charged for the third or subsequent attempt to take any of these courses in any combination.) May apply toward the Core Curriculum requirement in Mathematics. Generally offered: Fall, Spring, Summer. Course Fees: LRC1 $12; LRS1 $45; STSI $21.

==Topics List==
{| class="wikitable sortable"
! Date !! Sections !! Topics !! Prerequisite Skills !! Student Learning Outcomes
|-
|Week 2
||
Module 0.1
||
* [[Order of Operations]]
||
* Basic mathematical symbols and terminology
* Basic arithmetic skills
* Basic understanding of order of operations
||
'''Review of:'''
* PEMDAS
|-
|Week 2
||
Module 0.1
||
* [[Simplifying Radicals]]
||
* Basic mathematical symbols and terminology
* Basic understanding of [[Order of Operations]] (Module 0.1)
* 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 3
||
Module 0.2
||
* [[Factoring Polynomials]]
||
* Basic mathematical symbols and terminology
* Basic arithmetic skills
* Basic understanding of [[Order of Operations]] (Module 0.1)
* 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 3
||
Module 0.3
||
* [[Solving Equations and Inequalities]]
||
* Basic mathematical symbols and terminology
* Basic arithmetic skills
* Basic understanding of [[Order of Operations]] (Module 0.1)
* 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 3
||
Module 0.4
||
* [[Linear Equations]]
||
* Basic mathematical symbols and terminology
* Basic arithmetic skills
* Basic understanding of [[Order of Operations]] (Module 0.1)
* Basic understanding of factoring
* Basic understanding of [[Solving Equations and Inequalities]] (Module 0.3)
||
* Solving and constructing [[Linear Equations]]
|-
|Week 3
||
Module 0.4
||
* [[Graphs]]
||
* Basic mathematical symbols and terminology
* Basic arithmetic skills
* Basic understanding of order of operations
* Basic understanding of factoring
* Basic understanding of solving [[Linear Equations]] (Module 0.4)
* Understanding of the Cartesian coordinate system
||
* Being able to graph a [[Linear Equations]]
|-
|Week 4
||
Module 1.1
||
* [[Systems of Equations in Two Variables]]
||
* Solving and Graphing [[Linear Equations|linear equations]] in 2 variables. (Module 0.4)
* Understanding [[Order of Operations]] (Module 0.1)
||
* 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 4
||
Module 1.2
||
* [[Systems of Equations in Three Variables]]
||
* Solving [[Systems of Equations in Two Variables]] (Module 1.1)
||
* Solve systems of equations in three variables
* Identify inconsistent systems of equations containing three variables
* Express solutions of a system of dependent equations containing three variables
|-
|Week 5
||
Module 2.1
||
* [[Functions]]
||
* Basic understanding of [[Linear Equations]] (Module 0.4)
* Basic understanding of [[Solving Equations and Inequalities]] (Module 0.3)
||
* Determine whether a relation represents a function.
|-
|Week 5
||
Module 2.2
||
* [[Function Notation]]
||
* Basic understanding of [[Linear Equations]] (Module 0.4)
* Basic understanding of [[Graphs]] (Module 0.4)
||
* 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 5
||
Module 2.2
||
* [[Domain of a Function]]
||
* An understanding of [[Solving Equations and Inequalities]]
||
* Find the domain of a function defined by an equation.
* Graph piecewise-defined functions.
|-
|Week 5
||
Module 2.2
||
* [[Range of a Function]]
||
* An understanding of [[Solving Equations and Inequalities]]
||
* Find the domain of a function defined by an equation.
* Graph piecewise-defined functions.
|-
|Week 5
||
Module 2.2
||
* [[Toolkit Functions]]
||
* Basic understanding of Cartesian coordinate system (Module 0.4: [[Graphs]])
||
* Identify the basic toolkit functions
* Determine [[Domain of a Function|Domain]] and [[Range of a Function| Range]] for the basic toolkit functions (Module 1.2)
* [[Graphs|Graph]] the basic toolkit functions. (Module 0.4)
|-
|Week 6
||
Module 3.1
||
* [[Intro to Power Functions]]
||
* Basic understanding of power expressions.
* The student recalls the [[Graphs]] and equations of [[Toolkit Functions]], and their associated [[Domain of a Function|Domain]] and [[Range of a Function| 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 of a Function|Domain]] and [[Range|Range]] (Module 1).
* The student can substitute values for variables in an [[Solving Equations|Equations]] and solve for an unknown (Module 0.3)
||
* Identify power functions.
* Identify end behavior of power functions.
* Identify polynomial functions.
* Identify the degree and leading coefficients of polynomial functions.
|-
|Week 6
||
Module 3.1
||
* [[Intro to Polynomial Functions]]
||
* Basic understanding of a polynomial expression.
* The student recalls the [[Graphs] (Module 0.4) and equations of [[Toolkit Functions]], and their associated [[Domain of a Function|Domain]] and [[Range of a Function| Range]] (Module 2.2).
* The student understands where the x-intercept and y-intercept are located given a graph.
* The student understands interval notation for [[Domain of a Function|Domain]] and [[Range of a Function| Range]] (Module 2.2).
* The student can substitute values for variables in an [[Solving Equations|Equations]] and solve for an unknown (Module 0.3).
||
* Identify polynomial functions.
* Identify the degree and leading coefficients of polynomial functions.
|-
|Week 6
||
Module 3.2
||
* [[Quadratic Functions]]
||
* Fundamentals of [[Intro to Polynomial Functions|Polynomials]] (Module 2.1)
* 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 7
||
Module 4.1
||
* [[Dividing Polynomials]]
||
* Basic understanding of multiplying and dividing fractions.
* Basic understanding of simplifying fractions by common factors.
* Basic understanding of [[Factoring Polynomials]] (Module 0.2)
||
* Use long division to divide polynomials
* Use synthetic division to divide polynomials
|-
|Week 7
||
Module 4.2
||
* [[Zeros of Polynomials]]
||
* Basic understanding of multiplying and dividing fractions.
* Basic understanding of simplifying fractions by common factors.
* Basic understanding of [[Factoring Polynomials]] (Module 0.2)
* Basic understanding of [[Functions]] (Module 1.1)
* Basic understanding of [[Solving Equations and Inequalities]] (Module 0.3)
* An understanding of [[Dividing Polynomials]] (Module 4.1)
||
* Evaluate a polynomial using the Remainder Theorem
* Use the Factor Theorem to solve a polynomial equation
* Use the Rational Zero Theorem to find rational zeros
* Find zeros of a polynomial function
* Solve real-world applications of polynomial equations
|-
|Week 8
||
Module 5.1
||
* [[More on Polynomial Functions]]
||
* The student understands that zero in the denominator of a fraction is undefined.
* Basic understanding of [[Intro to Polynomial Functions|Polynomial Functions]] (Module 3.1)
* The student recalls the [[Graphs]] (Module 0.4) and equations of [[Toolkit Functions]], and their associated [[Domain of a Function|Domain]] and [[Range of a Function| Range]] (Module 2.2).
||
* Solving applied problems involving [[Intro to Polynomial Functions|Polynomial Functions]].
* Use arrow notation.
|-
|Week 8
||
Module 5.2
||
* [[Rational Functions]]
||
* The student understands that zero in the denominator of a fraction is undefined.
* The student recalls the [[Graphs]] (Module 0.4) and equations of [[Toolkit Functions]], and their associated [[Domain of a Function|Domain]] and [[Range of a Function| Range]] (Module 2.2).
||
* Solving applied problems involving [[Intro to Polynomial Functions|Polynomial Functions]]. (Module 2.1)
* Use arrow notation.
* Solve applied problems involving rational functions.
* Find the [[Domain|Domain]] of rational functions.
* Identify vertical asymptotes.
* Identify horizontal asymptotes.
|-
|Week 9
||
Module 6.1
||
* [[Graphs of Polynomials]]
||
* Basic understanding of [[Graphs]] (Module 0.4)
* Basic understanding of [[Intro to Polynomial Functions|Polynomial Functions]] (Module 2.1)
||
* Recognize characteristics of graphs of polynomial functions
* Use factoring to find zeros of polynomial functions
* Identify zeros and their multiplicities
* Determine end behavior
* Understand the relationship between degree and turning points
* Graph polynomial functions
|-
|Week 9
||
Module 6.2
||
* [[Graphs of Rational Functions]]
||
* Basic understanding of [[Graphs]] (Module 0.4)
* Basic understanding of [[Rational Functions]] (Module 4.1)
||
* Identify and graph vertical asymptotes
* Identify and graph horizontal asymptotes
* Determine behavior of rational functions around vertical asymptotes
* Graph rational functions
|-
|Week 10
||
Module 7.1
||
* [[Single Transformations of Functions]]
||
* Understanding of [[Functions]] (Module 5)
* Understanding of [[Function Notation]] (Module 2.1)
||
* Graph functions using vertical and horizontal shifts
* Graph functions using reflections about the x-axis and the y-axis
* Determine whether a function is even, odd, or neither from it's graph
* Graph functions using compressions and stretches
* Combine transformations
|-
|Week 10
||
Module 7.2
||
* [[Multiple Transformations of Functions]]
||
* Understanding of [[Single Transformations of Functions]] (Module 7.1)
||
* Combine transformations
|-
|Week 11
||
Module 8.1
||
* [[Composition of Functions]]
||
* Understanding of [[Function Notation]] (Module 2.1)
* Understanding of [[Functions]] (Module 5)
||
* Combine functions using algebraic operations
* Create a new function by composition of functions
* Evaluate composite functions
* Find the domain of a composite function
* Decompose a composite function into its component functions
|-
|Week 11
||
Module 8.2
||
* [[Inverse Functions]]
||
* Understanding of [[Function Notation]] (Module 2.1)
* Understanding of [[Functions]] (Module 5)
* Understanding of [[Composition of Functions]] (Module 7.1)
||
* Verify inverse functions
* Determine the domain and range of an inverse function, and restrict the domain of a function to make it one-to-one
* Find or evaluate the inverse of a function
* Use the graph of a one-to-one function to graph its inverse function on the same axes
|-
|Week 12
||
Module 9.1
||
* [[Exponential Properties]]
||
* Understanding [[Order of Operations]]. (Module 0.1)||
* Use the product rule for exponents.
* Use the quotient rule for exponents.
* Use the power rule for logarithms.
|-
|Week 12
||
Module 9.2
||
* [[Exponential Functions]]
||
* Understanding the [[Toolkit Functions]] for exponential functions (Module 1)
* Understanding the [[Domain of a Function|Domain]] and [[Range of a Function| Range]] for exponential functions (Module 2.2)
||
* Evaluate exponential functions.
* Find the equation of an exponential function.
* Use compound interest formulas.
* Evaluate exponential functions with base e.
|-
|Week 13
||
Module 10.1
||
* [[Logarithmic Functions]]
||
* Understanding the [[Toolkit Functions]] for logarithmic functions
* Understanding the [[Domain of a Function|Domain]] and [[Range of a Function| Range]] for logarithmic functions (Module 2.2)
* Difference between [[Linear Equations|Linear]] and [[Exponential Functions]] (Module 0.4 & 9.2)
||
* 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 13
||
Module 10.2
||
* [[Logarithmic Properties]]
||
* Understanding how to convert between [[Logarithmic Functions|logarithm]] and [[Exponential Functions|exponential]] forms. (Module 9.2 & 10.1)
* Understanding [[Order of Operations]]. (Module 0.1)
* Understanding of [[Exponential Properties]] (Module 9.1)
||
* 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 14
||
Module 11
||
* [[Modeling using Variation]]
||
* Understanding of [[Exponential Properties]] (Module 9.1)
* Understanding of [[Exponential Functions]] (Module 9.2)
* Understanding of [[Logarithmic Functions]] (Module 10.1)
* Understanding of [[Logarithmic Properties]] (Module 10.2)
||
* Solve direct variation problems
* Solve inverse variation problems
* Solve problems involving joint variation
|}

MAT1073

2020-08-13T16:22:38Z

Johnraymond.yanez:

==Course Catalog==
[https://catalog.utsa.edu/search/?P=MAT%201073 MAT 1073. Algebra for Scientists and Engineers]. (1-4) 3 Credit Hours. (TCCN = MATH 1314).

Prerequisite: Satisfactory performance on a placement examination. This course is designed to prepare the student for [[MAT1093]] Precalculus and [[MAT1214]] Calculus I. Topics may include algebraic expressions; equations; inequalities over the real numbers; relations; functions; polynomial and rational functions; logarithmic and exponential functions; systems of linear equations and inequalities; matrices and determinants; complex numbers; sequences; series binomial expansion; mathematical induction; permutations, and combinations. (Formerly MTC 1073. Credit can be earned for only one of the following: MAT 1073, MTC 1073, [[MAT1063]], MTC 1023, or [[MAT1023]]. NOTE: For the purpose of the Three-Attempt Rule, these courses are considered to be equivalent and additional fees may be charged for the third or subsequent attempt to take any of these courses in any combination.) May apply toward the Core Curriculum requirement in Mathematics. Generally offered: Fall, Spring, Summer. Course Fees: LRC1 $12; LRS1 $45; STSI $21.

==Topics List==
{| class="wikitable sortable"
! Date !! Sections !! Topics !! Prerequisite Skills !! Student Learning Outcomes
|-
|Week 2
||
Module 0.1
||
* [[Order of Operations]]
||
* Basic mathematical symbols and terminology
* Basic arithmetic skills
* Basic understanding of order of operations
||
'''Review of:'''
* PEMDAS
|-
|Week 2
||
Module 0.1
||
* [[Simplifying Radicals]]
||
* Basic mathematical symbols and terminology
* Basic understanding of [[Order of Operations]] (Module 0.1)
* 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 3
||
Module 0.2
||
* [[Factoring Polynomials]]
||
* Basic mathematical symbols and terminology
* Basic arithmetic skills
* Basic understanding of [[Order of Operations]] (Module 0.1)
* 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 3
||
Module 0.3
||
* [[Solving Equations and Inequalities]]
||
* Basic mathematical symbols and terminology
* Basic arithmetic skills
* Basic understanding of [[Order of Operations]] (Module 0.1)
* 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 3
||
Module 0.4
||
* [[Linear Equations]]
||
* Basic mathematical symbols and terminology
* Basic arithmetic skills
* Basic understanding of [[Order of Operations]] (Module 0.1)
* Basic understanding of factoring
* Basic understanding of [[Solving Equations and Inequalities]] (Module 0.3)
||
* Solving and constructing [[Linear Equations]]
|-
|Week 3
||
Module 0.4
||
* [[Graphs]]
||
* Basic mathematical symbols and terminology
* Basic arithmetic skills
* Basic understanding of order of operations
* Basic understanding of factoring
* Basic understanding of solving [[Linear Equations]] (Module 0.4)
* Understanding of the Cartesian coordinate system
||
* Being able to graph a [[Linear Equations]]
|-
|Week 4
||
Module 1.1
||
* [[Systems of Equations in Two Variables]]
||
* Solving and Graphing [[Linear Equations|linear equations]] in 2 variables. (Module 0.4)
* Understanding [[Order of Operations]] (Module 0.1)
||
* 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 4
||
Module 1.2
||
* [[Systems of Equations in Three Variables]]
||
* Solving [[Systems of Equations in Two Variables]] (Module 1.1)
||
* Solve systems of equations in three variables
* Identify inconsistent systems of equations containing three variables
* Express solutions of a system of dependent equations containing three variables
|-
|Week 5
||
Module 2.1
||
* [[Functions]]
||
* Basic understanding of [[Linear Equations]] (Module 0.4)
* Basic understanding of [[Solving Equations and Inequalities]] (Module 0.3)
||
* Determine whether a relation represents a function.
|-
|Week 5
||
Module 2.2
||
* [[Function Notation]]
||
* Basic understanding of [[Linear Equations]] (Module 0.4)
* Basic understanding of [[Graphs]] (Module 0.4)
||
* 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 5
||
Module 2.2
||
* [[Domain of a Function]]
||
* An understanding of [[Solving Equations and Inequalities]]
||
* Find the domain of a function defined by an equation.
* Graph piecewise-defined functions.
|-
|Week 5
||
Module 2.2
||
* [[Range of a Function]]
||
* An understanding of [[Solving Equations and Inequalities]]
||
* Find the domain of a function defined by an equation.
* Graph piecewise-defined functions.
|-
|Week 5
||
Module 2.2
||
* [[Toolkit Functions]]
||
* Basic understanding of Cartesian coordinate system (Module 0.4: [[Graphs]])
||
* Identify the basic toolkit functions
* Determine [[Domain of a Function|Domain]] and [[Range of a Function| Range]] for the basic toolkit functions (Module 1.2)
* [[Graphs|Graph]] the basic toolkit functions. (Module 0.4)
|-
|Week 6
||
Module 3.1
||
* [[Intro to Power Functions]]
||
* Basic understanding of power expressions.
* The student recalls the [[Graphs]] and equations of [[Toolkit Functions]], and their associated [[Domain of a Function|Domain]] and [[Range of a Function| 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 of a Function|Domain]] and [[Range|Range]] (Module 1).
* The student can substitute values for variables in an [[Solving Equations|Equations]] and solve for an unknown (Module 0.3)
||
* Identify power functions.
* Identify end behavior of power functions.
* Identify polynomial functions.
* Identify the degree and leading coefficients of polynomial functions.
|-
|Week 6
||
Module 3.1
||
* [[Intro to Polynomial Functions]]
||
* Basic understanding of a polynomial expression.
* The student recalls the [[Graphs] (Module 0.4) and equations of [[Toolkit Functions]], and their associated [[Domain of a Function|Domain]] and [[Range of a Function| Range]] (Module 2.2).
* The student understands where the x-intercept and y-intercept are located given a graph.
* The student understands interval notation for [[Domain of a Function|Domain]] and [[Range of a Function| Range]] (Module 2.2).
* The student can substitute values for variables in an [[Solving Equations|Equations]] and solve for an unknown (Module 0.3).
||
* Identify polynomial functions.
* Identify the degree and leading coefficients of polynomial functions.
|-
|Week 6
||
Module 3.2
||
* [[Quadratic Functions]]
||
* Fundamentals of [[Intro to Polynomial Functions|Polynomials]] (Module 2.1)
* 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 7
||
Module 4.1
||
* [[Dividing Polynomials]]
||
* Basic understanding of multiplying and dividing fractions.
* Basic understanding of simplifying fractions by common factors.
* Basic understanding of [[Factoring Polynomials]] (Module 0.2)
||
* Use long division to divide polynomials
* Use synthetic division to divide polynomials
|-
|Week 7
||
Module 4.2
||
* [[Zeros of Polynomials]]
||
* Basic understanding of multiplying and dividing fractions.
* Basic understanding of simplifying fractions by common factors.
* Basic understanding of [[Factoring Polynomials]] (Module 0.2)
* Basic understanding of [[Functions]] (Module 1.1)
* Basic understanding of [[Solving Equations and Inequalities]] (Module 0.3)
||
* Evaluate a polynomial using the Remainder Theorem
* Use the Factor Theorem to solve a polynomial equation
* Use the Rational Zero Theorem to find rational zeros
* Find zeros of a polynomial function
* Solve real-world applications of polynomial equations
|-
|Week 8
||
Module 5.1
||
* [[More on Polynomial Functions]]
||
* The student understands that zero in the denominator of a fraction is undefined.
* Basic understanding of [[Intro to Polynomial Functions|Polynomial Functions]]
* The student recalls the [[Graphs]] and equations of [[Toolkit Functions]], and their associated [[Domain of a Function|Domain]] and [[Range of a Function| Range]] (Module 2.2).
||
* Solving applied problems involving [[Intro to Polynomial Functions|Polynomial Functions]].
* Use arrow notation.
|-
|Week 8
||
Module 5.2
||
* [[Rational Functions]]
||
* [[Rational Expressions]].
* 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 of a Function|Domain]] and [[Range of a Function| Range]] (Module 2.2).
||
* Solving applied problems involving [[Intro to Polynomial Functions|Polynomial Functions]]. (Module 2.1)
* Use arrow notation.
* Solve applied problems involving rational functions.
* Find the [[Domain|Domain]] of rational functions.
* Identify vertical asymptotes.
* Identify horizontal asymptotes.
|-
|Week 9
||
Module 6.1
||
* [[Graphs of Polynomials]]
||
* Basic understanding of [[Graphs]] (Module 0.4)
* Basic understanding of [[Intro to Polynomial Functions|Polynomial Functions]] (Module 2.1)
||
* Recognize characteristics of graphs of polynomial functions
* Use factoring to find zeros of polynomial functions
* Identify zeros and their multiplicities
* Determine end behavior
* Understand the relationship between degree and turning points
* Graph polynomial functions
|-
|Week 9
||
Module 6.2
||
* [[Graphs of Rational Functions]]
||
* Basic understanding of [[Graphs]] (Module 0.4)
* Basic understanding of [[Rational Functions]] (Module 4.1)
||
* Identify and graph vertical asymptotes
* Identify and graph horizontal asymptotes
* Determine behavior of rational functions around vertical asymptotes
* Graph rational functions
|-
|Week 10
||
Module 7.1
||
* [[Single Transformations of Functions]]
||
* Understanding of [[Functions]] (Module 5)
* Understanding of [[Function Notation]] (Module 2.1)
||
* Graph functions using vertical and horizontal shifts
* Graph functions using reflections about the x-axis and the y-axis
* Determine whether a function is even, odd, or neither from it's graph
* Graph functions using compressions and stretches
* Combine transformations
|-
|Week 10
||
Module 7.2
||
* [[Multiple Transformations of Functions]]
||
* Understanding of [[Single Transformations of Functions]] (Module 7.1)
||
* Combine transformations
|-
|Week 11
||
Module 8.1
||
* [[Composition of Functions]]
||
* Understanding of [[Function Notation]] (Module 2.1)
* Understanding of [[Functions]] (Module 5)
||
* Combine functions using algebraic operations
* Create a new function by composition of functions
* Evaluate composite functions
* Find the domain of a composite function
* Decompose a composite function into its component functions
|-
|Week 11
||
Module 8.2
||
* [[Inverse Functions]]
||
* Understanding of [[Function Notation]] (Module 2.1)
* Understanding of [[Functions]] (Module 5)
* Understanding of [[Composition of Functions]] (Module 7.1)
||
* Verify inverse functions
* Determine the domain and range of an inverse function, and restrict the domain of a function to make it one-to-one
* Find or evaluate the inverse of a function
* Use the graph of a one-to-one function to graph its inverse function on the same axes
|-
|Week 12
||
Module 9.1
||
* [[Exponential Properties]]
||
* Understanding [[Order of Operations]]. (Module 0.1)||
* Use the product rule for exponents.
* Use the quotient rule for exponents.
* Use the power rule for logarithms.
|-
|Week 12
||
Module 9.2
||
* [[Exponential Functions]]
||
* Understanding the [[Toolkit Functions]] for exponential functions (Module 1)
* Understanding the [[Domain of a Function|Domain]] and [[Range of a Function| Range]] for exponential functions (Module 2.2)
||
* Evaluate exponential functions.
* Find the equation of an exponential function.
* Use compound interest formulas.
* Evaluate exponential functions with base e.
|-
|Week 13
||
Module 10.1
||
* [[Logarithmic Functions]]
||
* Understanding the [[Toolkit Functions]] for logarithmic functions
* Understanding the [[Domain of a Function|Domain]] and [[Range of a Function| Range]] for logarithmic functions (Module 2.2)
* Difference between [[Linear Equations|Linear]] and [[Exponential Functions]] (Module 0.4 & 9.2)
||
* 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 13
||
Module 10.2
||
* [[Logarithmic Properties]]
||
* Understanding how to convert between [[Logarithmic Functions|logarithm]] and [[Exponential Functions|exponential]] forms. (Module 9.2 & 10.1)
* Understanding [[Order of Operations]]. (Module 0.1)
* Understanding of [[Exponential Properties]] (Module 9.1)
||
* 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 14
||
Module 11
||
* [[Modeling using Variation]]
||
* Understanding of [[Exponential Properties]] (Module 9.1)
* Understanding of [[Exponential Functions]] (Module 9.2)
* Understanding of [[Logarithmic Functions]] (Module 10.1)
* Understanding of [[Logarithmic Properties]] (Module 10.2)
||
* Solve direct variation problems
* Solve inverse variation problems
* Solve problems involving joint variation
|}

MAT1073

2020-08-13T16:18:44Z

Johnraymond.yanez:

==Course Catalog==
[https://catalog.utsa.edu/search/?P=MAT%201073 MAT 1073. Algebra for Scientists and Engineers]. (1-4) 3 Credit Hours. (TCCN = MATH 1314).

Prerequisite: Satisfactory performance on a placement examination. This course is designed to prepare the student for [[MAT1093]] Precalculus and [[MAT1214]] Calculus I. Topics may include algebraic expressions; equations; inequalities over the real numbers; relations; functions; polynomial and rational functions; logarithmic and exponential functions; systems of linear equations and inequalities; matrices and determinants; complex numbers; sequences; series binomial expansion; mathematical induction; permutations, and combinations. (Formerly MTC 1073. Credit can be earned for only one of the following: MAT 1073, MTC 1073, [[MAT1063]], MTC 1023, or [[MAT1023]]. NOTE: For the purpose of the Three-Attempt Rule, these courses are considered to be equivalent and additional fees may be charged for the third or subsequent attempt to take any of these courses in any combination.) May apply toward the Core Curriculum requirement in Mathematics. Generally offered: Fall, Spring, Summer. Course Fees: LRC1 $12; LRS1 $45; STSI $21.

==Topics List==
{| class="wikitable sortable"
! Date !! Sections !! Topics !! Prerequisite Skills !! Student Learning Outcomes
|-
|Week 2
||
Module 0.1
||
* [[Order of Operations]]
||
* Basic mathematical symbols and terminology
* Basic arithmetic skills
* Basic understanding of order of operations
||
'''Review of:'''
* PEMDAS
|-
|Week 2
||
Module 0.1
||
* [[Simplifying Radicals]]
||
* Basic mathematical symbols and terminology
* Basic understanding of [[Order of Operations]] (Module 0.1)
* 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 3
||
Module 0.2
||
* [[Factoring Polynomials]]
||
* Basic mathematical symbols and terminology
* Basic arithmetic skills
* Basic understanding of [[Order of Operations]] (Module 0.1)
* 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 3
||
Module 0.3
||
* [[Solving Equations and Inequalities]]
||
* Basic mathematical symbols and terminology
* Basic arithmetic skills
* Basic understanding of [[Order of Operations]] (Module 0.1)
* 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 3
||
Module 0.4
||
* [[Linear Equations]]
||
* Basic mathematical symbols and terminology
* Basic arithmetic skills
* Basic understanding of [[Order of Operations]] (Module 0.1)
* Basic understanding of factoring
* Basic understanding of [[Solving Equations and Inequalities]] (Module 0.3)
||
* Solving and constructing [[Linear Equations]]
|-
|Week 3
||
Module 0.4
||
* [[Graphs]]
||
* Basic mathematical symbols and terminology
* Basic arithmetic skills
* Basic understanding of order of operations
* Basic understanding of factoring
* Basic understanding of solving [[Linear Equations]] (Module 0.4)
* Understanding of the Cartesian coordinate system
||
* Being able to graph a [[Linear Equations]]
|-
|Week 4
||
Module 1.1
||
* [[Systems of Equations in Two Variables]]
||
* Solving and Graphing [[Linear Equations|linear equations]] in 2 variables. (Module 0.4)
* Understanding [[Order of Operations]] (Module 0.1)
||
* 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 4
||
Module 1.2
||
* [[Systems of Equations in Three Variables]]
||
* Solving [[Systems of Equations in Two Variables]] (Module 1.1)
||
* Solve systems of equations in three variables
* Identify inconsistent systems of equations containing three variables
* Express solutions of a system of dependent equations containing three variables
|-
|Week 5
||
Module 2.1
||
* [[Functions]]
||
* Basic understanding of [[Linear Equations]] (Module 0.4)
* Basic understanding of [[Solving Equations and Inequalities]] (Module 0.3)
||
* Determine whether a relation represents a function.
|-
|Week 5
||
Module 2.2
||
* [[Function Notation]]
||
* Basic understanding of [[Linear Equations]] (Module 0.4)
* Basic understanding of [[Equations]] (Module R)
* Basic understanding of [[Graphs]] (Module 0.4)
||
* 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 5
||
Module 2.2
||
* [[Domain of a Function]]
||
* An understanding of [[Solving Equations and Inequalities]]
||
* Find the domain of a function defined by an equation.
* Graph piecewise-defined functions.
|-
|Week 5
||
Module 2.2
||
* [[Range of a Function]]
||
* An understanding of [[Solving Equations and Inequalities]]
||
* Find the domain of a function defined by an equation.
* Graph piecewise-defined functions.
|-
|Week 5
||
Module 2.2
||
* [[Toolkit Functions]]
||
* Basic understanding of Cartesian coordinate system (Module 0.4: [[Graphs]])
||
* Identify the basic toolkit functions
* Determine [[Domain of a Function|Domain]] and [[Range of a Function| Range]] for the basic toolkit functions (Module 1.2)
* [[Graphs|Graph]] the basic toolkit functions. (Module 0.4)
|-
|Week 6
||
Module 3.1
||
* [[Intro to Power Functions]]
||
* Basic understanding of power expressions.
* The student recalls the [[Graphs]] and equations of [[Toolkit Functions]], and their associated [[Domain of a Function|Domain]] and [[Range of a Function| 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 of a Function|Domain]] and [[Range|Range]] (Module 1).
* The student can substitute values for variables in an [[Solving Equations|Equations]] and solve for an unknown (Module R)
||
* Identify power functions.
* Identify end behavior of power functions.
* Identify polynomial functions.
* Identify the degree and leading coefficients of polynomial functions.
|-
|Week 6
||
Module 3.1
||
* [[Intro to Polynomial Functions]]
||
* Basic understanding of a polynomial expression.
* The student recalls the [[Graphs] (Module 0.4) and equations of [[Toolkit Functions]], and their associated [[Domain of a Function|Domain]] and [[Range of a Function| Range]] (Module 2.1 & 2.2).
* The student understands where the x-intercept and y-intercept are located given a graph.
* The student understands interval notation for [[Domain of a Function|Domain]] and [[Range of a Function| Range]] (Module 2.1 & 2.2).
* The student can substitute values for variables in an [[Solving Equations|Equations]] and solve for an unknown (Module 0.3).
||
* Identify polynomial functions.
* Identify the degree and leading coefficients of polynomial functions.
|-
|Week 6
||
Module 3.2
||
* [[Quadratic Functions]]
||
* Fundamentals of [[Intro to Polynomial Functions|Polynomials]] (Module 2.1)
* 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 7
||
Module 4.1
||
* [[Dividing Polynomials]]
||
* Basic understanding of multiplying and dividing fractions.
* Basic understanding of simplifying fractions by common factors.
* Basic understanding of [[Factoring Polynomials]] (Module 0.2)
||
* Use long division to divide polynomials
* Use synthetic division to divide polynomials
|-
|Week 7
||
Module 4.2
||
* [[Zeros of Polynomials]]
||
* Basic understanding of multiplying and dividing fractions.
* Basic understanding of simplifying fractions by common factors.
* Basic understanding of [[Factoring Polynomials]] (Module 0.2)
* Basic understanding of [[Functions]] (Module 1.1)
* Basic understanding of [[Solving Equations and Inequalities]] (Module 0.3)
||
* Evaluate a polynomial using the Remainder Theorem
* Use the Factor Theorem to solve a polynomial equation
* Use the Rational Zero Theorem to find rational zeros
* Find zeros of a polynomial function
* Solve real-world applications of polynomial equations
|-
|Week 8
||
Module 5.1
||
* [[More on Polynomial Functions]]
||
* The student understands that zero in the denominator of a fraction is undefined.
* Basic understanding of [[Intro to Polynomial Functions|Polynomial Functions]]
* The student recalls the [[Graphs]] and equations of [[Toolkit Functions]], and their associated [[Domain of a Function|Domain]] and [[Range of a Function| Range]] (Module 2.1 & 2.2).
||
* Solving applied problems involving [[Intro to Polynomial Functions|Polynomial Functions]].
* Use arrow notation.
|-
|Week 8
||
Module 5.2
||
* [[Rational Functions]]
||
* [[Rational Expressions]].
* 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 of a Function|Domain]] and [[Range of a Function| Range]] (Module 2.1 & 2.2).
||
* Solving applied problems involving [[Intro to Polynomial Functions|Polynomial Functions]]. (Module 2.1)
* Use arrow notation.
* Solve applied problems involving rational functions.
* Find the [[Domain|Domain]] of rational functions.
* Identify vertical asymptotes.
* Identify horizontal asymptotes.
|-
|Week 9
||
Module 6.1
||
* [[Graphs of Polynomials]]
||
* Basic understanding of [[Graphs]] (Module 0.4)
* Basic understanding of [[Intro to Polynomial Functions|Polynomial Functions]] (Module 2.1)
||
* Recognize characteristics of graphs of polynomial functions
* Use factoring to find zeros of polynomial functions
* Identify zeros and their multiplicities
* Determine end behavior
* Understand the relationship between degree and turning points
* Graph polynomial functions
|-
|Week 9
||
Module 6.2
||
* [[Graphs of Rational Functions]]
||
* Basic understanding of [[Graphs]] (Module 0.4)
* Basic understanding of [[Rational Functions]] (Module 4.1)
||
* Identify and graph vertical asymptotes
* Identify and graph horizontal asymptotes
* Determine behavior of rational functions around vertical asymptotes
* Graph rational functions
|-
|Week 10
||
Module 7.1
||
* [[Single Transformations of Functions]]
||
* Understanding of [[Functions]] (Module 5)
* Understanding of [[Function Notation]] (Module 2.1)
||
* Graph functions using vertical and horizontal shifts
* Graph functions using reflections about the x-axis and the y-axis
* Determine whether a function is even, odd, or neither from it's graph
* Graph functions using compressions and stretches
* Combine transformations
|-
|Week 10
||
Module 7.2
||
* [[Multiple Transformations of Functions]]
||
* Understanding of [[Single Transformations of Functions]] (Module 7.1)
||
* Combine transformations
|-
|Week 11
||
Module 8.1
||
* [[Composition of Functions]]
||
* Understanding of [[Function Notation]] (Module 2.1)
* Understanding of [[Functions]] (Module 5)
||
* Combine functions using algebraic operations
* Create a new function by composition of functions
* Evaluate composite functions
* Find the domain of a composite function
* Decompose a composite function into its component functions
|-
|Week 11
||
Module 8.2
||
* [[Inverse Functions]]
||
* Understanding of [[Function Notation]] (Module 2.1)
* Understanding of [[Functions]] (Module 5)
* Understanding of [[Composition of Functions]] (Module 7.1)
||
* Verify inverse functions
* Determine the domain and range of an inverse function, and restrict the domain of a function to make it one-to-one
* Find or evaluate the inverse of a function
* Use the graph of a one-to-one function to graph its inverse function on the same axes
|-
|Week 12
||
Module 9.1
||
* [[Exponential Properties]]
||
* Understanding [[Order of Operations]]. (Module 0.1)||
* Use the product rule for exponents.
* Use the quotient rule for exponents.
* Use the power rule for logarithms.
|-
|Week 12
||
Module 9.2
||
* [[Exponential Functions]]
||
* Understanding the [[Toolkit Functions]] for exponential functions (Module 1)
* Understanding the [[Domain of a Function|Domain]] and [[Range of a Function| Range]] for exponential functions (Module 2.1 & 2.2)
* Understanding of [[Simplifying Exponents]] (Module R)
||
* Evaluate exponential functions.
* Find the equation of an exponential function.
* Use compound interest formulas.
* Evaluate exponential functions with base e.
|-
|Week 13
||
Module 10.1
||
* [[Logarithmic Functions]]
||
* Understanding the [[Toolkit Functions]] for logarithmic functions
* Understanding the [[Domain of a Function|Domain]] and [[Range of a Function| Range]] for logarithmic functions (Module 2.1 & 2.2)
* Difference between [[Linear Equations|Linear]] and [[Exponential Functions]] (Module 0.4 & 9.2)
||
* 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 13
||
Module 10.2
||
* [[Logarithmic Properties]]
||
* Understanding how to convert between [[Logarithmic Functions|logarithm]] and [[Exponential Functions|exponential]] forms. (Module 9.2 & 10.1)
* Understanding [[Order of Operations]]. (Module 0.1)
* Understanding of [[Exponential Properties]] (Module 9.1)
||
* 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 14
||
Module 11
||
* [[Modeling using Variation]]
||
* Understanding of [[Exponential Properties]] (Module 9.1)
* Understanding of [[Exponential Functions]] (Module 9.2)
* Understanding of [[Logarithmic Functions]] (Module 10.1)
* Understanding of [[Logarithmic Properties]] (Module 10.2)
||
* Solve direct variation problems
* Solve inverse variation problems
* Solve problems involving joint variation
|}

MAT1073

2020-08-13T16:17:56Z

Johnraymond.yanez:

==Course Catalog==
[https://catalog.utsa.edu/search/?P=MAT%201073 MAT 1073. Algebra for Scientists and Engineers]. (1-4) 3 Credit Hours. (TCCN = MATH 1314).

Prerequisite: Satisfactory performance on a placement examination. This course is designed to prepare the student for [[MAT1093]] Precalculus and [[MAT1214]] Calculus I. Topics may include algebraic expressions; equations; inequalities over the real numbers; relations; functions; polynomial and rational functions; logarithmic and exponential functions; systems of linear equations and inequalities; matrices and determinants; complex numbers; sequences; series binomial expansion; mathematical induction; permutations, and combinations. (Formerly MTC 1073. Credit can be earned for only one of the following: MAT 1073, MTC 1073, [[MAT1063]], MTC 1023, or [[MAT1023]]. NOTE: For the purpose of the Three-Attempt Rule, these courses are considered to be equivalent and additional fees may be charged for the third or subsequent attempt to take any of these courses in any combination.) May apply toward the Core Curriculum requirement in Mathematics. Generally offered: Fall, Spring, Summer. Course Fees: LRC1 $12; LRS1 $45; STSI $21.

==Topics List==
{| class="wikitable sortable"
! Date !! Sections !! Topics !! Prerequisite Skills !! Student Learning Outcomes
|-
|Week 2
||
Module 0.1
||
* [[Order of Operations]]
||
* Basic mathematical symbols and terminology
* Basic arithmetic skills
* Basic understanding of order of operations
||
'''Review of:'''
* PEMDAS
|-
|Week 2
||
Module 0.1
||
* [[Simplifying Radicals]]
||
* Basic mathematical symbols and terminology
* Basic understanding of [[Order of Operations]] (Module 0.1)
* 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 3
||
Module 0.2
||
* [[Factoring Polynomials]]
||
* Basic mathematical symbols and terminology
* Basic arithmetic skills
* Basic understanding of [[Order of Operations]] (Module 0.1)
* 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 3
||
Module 0.3
||
* [[Solving Equations and Inequalities]]
||
* Basic mathematical symbols and terminology
* Basic arithmetic skills
* Basic understanding of [[Order of Operations]] (Module 0.1)
* 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 3
||
Module 0.4
||
* [[Linear Equations]]
||
* Basic mathematical symbols and terminology
* Basic arithmetic skills
* Basic understanding of [[Order of Operations]] (Module 0.1)
* Basic understanding of factoring
* Basic understanding of [[Solving Equations and Inequalities]] (Module 0.3)
||
* Solving and constructing [[Linear Equations]]
|-
|Week 3
||
Module 0.4
||
* [[Graphs]]
||
* Basic mathematical symbols and terminology
* Basic arithmetic skills
* Basic understanding of order of operations
* Basic understanding of factoring
* Basic understanding of solving [[Linear Equations]] (Module 0.4)
* Understanding of the Cartesian coordinate system
||
* Being able to graph a [[Linear Equations]]
|-
|Week 4
||
Module 1.1
||
* [[Systems of Equations in Two Variables]]
||
* Solving and Graphing [[Linear Equations|linear equations]] in 2 variables. (Module 0.4)
* Understanding [[Order of Operations]] (Module 0.1)
||
* 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 4
||
Module 1.2
||
* [[Systems of Equations in Three Variables]]
||
* Solving [[Systems of Equations in Two Variables]] (Module 1.1)
||
* Solve systems of equations in three variables
* Identify inconsistent systems of equations containing three variables
* Express solutions of a system of dependent equations containing three variables
|-
|Week 5
||
Module 2.1
||
* [[Functions]]
||
* Basic understanding of [[Linear Equations]] (Module 0.4)
* Basic understanding of [[Solving Equations and Inequalities]] (Module 0.3)
||
* Determine whether a relation represents a function.
|-
|Week 5
||
Module 2.2
||
* [[Function Notation]]
||
* Basic understanding of [[Linear Equations]] (Module 0.4)
* Basic understanding of [[Equations]] (Module R)
* Basic understanding of [[Graphs]] (Module 0.4)
||
* 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 5
||
Module 2.2
||
* [[Domain of a Function]]
||
* (Prerequisite)
||
* Find the domain of a function defined by an equation.
* Graph piecewise-defined functions.
|-
|Week 5
||
Module 2.2
||
* [[Range of a Function]]
||
* (Prerequisite)
||
* Find the domain of a function defined by an equation.
* Graph piecewise-defined functions.
|-
|Week 5
||
Module 2.2
||
* [[Toolkit Functions]]
||
* Basic understanding of Cartesian coordinate system (Module 0.4: [[Graphs]])
||
* Identify the basic toolkit functions
* Determine [[Domain of a Function|Domain]] and [[Range of a Function| Range]] for the basic toolkit functions (Module 1.2)
* [[Graphs|Graph]] the basic toolkit functions. (Module 0.4)
|-
|Week 6
||
Module 3.1
||
* [[Intro to Power Functions]]
||
* Basic understanding of power expressions.
* The student recalls the [[Graphs]] and equations of [[Toolkit Functions]], and their associated [[Domain of a Function|Domain]] and [[Range of a Function| 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 of a Function|Domain]] and [[Range|Range]] (Module 1).
* The student can substitute values for variables in an [[Solving Equations|Equations]] and solve for an unknown (Module R)
||
* Identify power functions.
* Identify end behavior of power functions.
* Identify polynomial functions.
* Identify the degree and leading coefficients of polynomial functions.
|-
|Week 6
||
Module 3.1
||
* [[Intro to Polynomial Functions]]
||
* Basic understanding of a polynomial expression.
* The student recalls the [[Graphs] (Module 0.4) and equations of [[Toolkit Functions]], and their associated [[Domain of a Function|Domain]] and [[Range of a Function| Range]] (Module 2.1 & 2.2).
* The student understands where the x-intercept and y-intercept are located given a graph.
* The student understands interval notation for [[Domain of a Function|Domain]] and [[Range of a Function| Range]] (Module 2.1 & 2.2).
* The student can substitute values for variables in an [[Solving Equations|Equations]] and solve for an unknown (Module 0.3).
||
* Identify polynomial functions.
* Identify the degree and leading coefficients of polynomial functions.
|-
|Week 6
||
Module 3.2
||
* [[Quadratic Functions]]
||
* Fundamentals of [[Intro to Polynomial Functions|Polynomials]] (Module 2.1)
* 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 7
||
Module 4.1
||
* [[Dividing Polynomials]]
||
* Basic understanding of multiplying and dividing fractions.
* Basic understanding of simplifying fractions by common factors.
* Basic understanding of [[Factoring Polynomials]] (Module 0.2)
||
* Use long division to divide polynomials
* Use synthetic division to divide polynomials
|-
|Week 7
||
Module 4.2
||
* [[Zeros of Polynomials]]
||
* Basic understanding of multiplying and dividing fractions.
* Basic understanding of simplifying fractions by common factors.
* Basic understanding of [[Factoring Polynomials]] (Module 0.2)
* Basic understanding of [[Functions]] (Module 1.1)
* Basic understanding of [[Solving Equations and Inequalities]] (Module 0.3)
||
* Evaluate a polynomial using the Remainder Theorem
* Use the Factor Theorem to solve a polynomial equation
* Use the Rational Zero Theorem to find rational zeros
* Find zeros of a polynomial function
* Solve real-world applications of polynomial equations
|-
|Week 8
||
Module 5.1
||
* [[More on Polynomial Functions]]
||
* The student understands that zero in the denominator of a fraction is undefined.
* Basic understanding of [[Intro to Polynomial Functions|Polynomial Functions]]
* The student recalls the [[Graphs]] and equations of [[Toolkit Functions]], and their associated [[Domain of a Function|Domain]] and [[Range of a Function| Range]] (Module 2.1 & 2.2).
||
* Solving applied problems involving [[Intro to Polynomial Functions|Polynomial Functions]].
* Use arrow notation.
|-
|Week 8
||
Module 5.2
||
* [[Rational Functions]]
||
* [[Rational Expressions]].
* 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 of a Function|Domain]] and [[Range of a Function| Range]] (Module 2.1 & 2.2).
||
* Solving applied problems involving [[Intro to Polynomial Functions|Polynomial Functions]]. (Module 2.1)
* Use arrow notation.
* Solve applied problems involving rational functions.
* Find the [[Domain|Domain]] of rational functions.
* Identify vertical asymptotes.
* Identify horizontal asymptotes.
|-
|Week 9
||
Module 6.1
||
* [[Graphs of Polynomials]]
||
* Basic understanding of [[Graphs]] (Module 0.4)
* Basic understanding of [[Intro to Polynomial Functions|Polynomial Functions]] (Module 2.1)
||
* Recognize characteristics of graphs of polynomial functions
* Use factoring to find zeros of polynomial functions
* Identify zeros and their multiplicities
* Determine end behavior
* Understand the relationship between degree and turning points
* Graph polynomial functions
|-
|Week 9
||
Module 6.2
||
* [[Graphs of Rational Functions]]
||
* Basic understanding of [[Graphs]] (Module 0.4)
* Basic understanding of [[Rational Functions]] (Module 4.1)
||
* Identify and graph vertical asymptotes
* Identify and graph horizontal asymptotes
* Determine behavior of rational functions around vertical asymptotes
* Graph rational functions
|-
|Week 10
||
Module 7.1
||
* [[Single Transformations of Functions]]
||
* Understanding of [[Functions]] (Module 5)
* Understanding of [[Function Notation]] (Module 2.1)
||
* Graph functions using vertical and horizontal shifts
* Graph functions using reflections about the x-axis and the y-axis
* Determine whether a function is even, odd, or neither from it's graph
* Graph functions using compressions and stretches
* Combine transformations
|-
|Week 10
||
Module 7.2
||
* [[Multiple Transformations of Functions]]
||
* Understanding of [[Single Transformations of Functions]] (Module 7.1)
||
* Combine transformations
|-
|Week 11
||
Module 8.1
||
* [[Composition of Functions]]
||
* Understanding of [[Function Notation]] (Module 2.1)
* Understanding of [[Functions]] (Module 5)
||
* Combine functions using algebraic operations
* Create a new function by composition of functions
* Evaluate composite functions
* Find the domain of a composite function
* Decompose a composite function into its component functions
|-
|Week 11
||
Module 8.2
||
* [[Inverse Functions]]
||
* Understanding of [[Function Notation]] (Module 2.1)
* Understanding of [[Functions]] (Module 5)
* Understanding of [[Composition of Functions]] (Module 7.1)
||
* Verify inverse functions
* Determine the domain and range of an inverse function, and restrict the domain of a function to make it one-to-one
* Find or evaluate the inverse of a function
* Use the graph of a one-to-one function to graph its inverse function on the same axes
|-
|Week 12
||
Module 9.1
||
* [[Exponential Properties]]
||
* Understanding [[Order of Operations]]. (Module 0.1)||
* Use the product rule for exponents.
* Use the quotient rule for exponents.
* Use the power rule for logarithms.
|-
|Week 12
||
Module 9.2
||
* [[Exponential Functions]]
||
* Understanding the [[Toolkit Functions]] for exponential functions (Module 1)
* Understanding the [[Domain of a Function|Domain]] and [[Range of a Function| Range]] for exponential functions (Module 2.1 & 2.2)
* Understanding of [[Simplifying Exponents]] (Module R)
||
* Evaluate exponential functions.
* Find the equation of an exponential function.
* Use compound interest formulas.
* Evaluate exponential functions with base e.
|-
|Week 13
||
Module 10.1
||
* [[Logarithmic Functions]]
||
* Understanding the [[Toolkit Functions]] for logarithmic functions
* Understanding the [[Domain of a Function|Domain]] and [[Range of a Function| Range]] for logarithmic functions (Module 2.1 & 2.2)
* Difference between [[Linear Equations|Linear]] and [[Exponential Functions]] (Module 0.4 & 9.2)
||
* 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 13
||
Module 10.2
||
* [[Logarithmic Properties]]
||
* Understanding how to convert between [[Logarithmic Functions|logarithm]] and [[Exponential Functions|exponential]] forms. (Module 9.2 & 10.1)
* Understanding [[Order of Operations]]. (Module 0.1)
* Understanding of [[Exponential Properties]] (Module 9.1)
||
* 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 14
||
Module 11
||
* [[Modeling using Variation]]
||
* Understanding of [[Exponential Properties]] (Module 9.1)
* Understanding of [[Exponential Functions]] (Module 9.2)
* Understanding of [[Logarithmic Functions]] (Module 10.1)
* Understanding of [[Logarithmic Properties]] (Module 10.2)
||
* Solve direct variation problems
* Solve inverse variation problems
* Solve problems involving joint variation
|}

MAT1073

2020-08-13T16:09:21Z

Johnraymond.yanez: Redefined list to reflect current syllabus

==Course Catalog==
[https://catalog.utsa.edu/search/?P=MAT%201073 MAT 1073. Algebra for Scientists and Engineers]. (1-4) 3 Credit Hours. (TCCN = MATH 1314).

Prerequisite: Satisfactory performance on a placement examination. This course is designed to prepare the student for [[MAT1093]] Precalculus and [[MAT1214]] Calculus I. Topics may include algebraic expressions; equations; inequalities over the real numbers; relations; functions; polynomial and rational functions; logarithmic and exponential functions; systems of linear equations and inequalities; matrices and determinants; complex numbers; sequences; series binomial expansion; mathematical induction; permutations, and combinations. (Formerly MTC 1073. Credit can be earned for only one of the following: MAT 1073, MTC 1073, [[MAT1063]], MTC 1023, or [[MAT1023]]. NOTE: For the purpose of the Three-Attempt Rule, these courses are considered to be equivalent and additional fees may be charged for the third or subsequent attempt to take any of these courses in any combination.) May apply toward the Core Curriculum requirement in Mathematics. Generally offered: Fall, Spring, Summer. Course Fees: LRC1 $12; LRS1 $45; STSI $21.

==Topics List==
{| class="wikitable sortable"
! Date !! Sections !! Topics !! Prerequisite Skills !! Student Learning Outcomes
|-
|Week 2
||
Module 0.1
||
* [[Order of Operations]]
||
* Basic mathematical symbols and terminology
* Basic arithmetic skills
* Basic understanding of order of operations
||
'''Review of:'''
* PEMDAS
|-
|Week 2
||
Module 0.1
||
* [[Simplifying Radicals]]
||
* Basic mathematical symbols and terminology
* Basic understanding of [[Order of Operations]] (Module 0.1)
* 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 3
||
Module 0.2
||
* [[Factoring Polynomials]]
||
* Basic mathematical symbols and terminology
* Basic arithmetic skills
* Basic understanding of [[Order of Operations]] (Module 0.1)
* 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 3
||
Module 0.3
||
* [[Solving Equations]]
||
* Basic mathematical symbols and terminology
* Basic arithmetic skills
* Basic understanding of [[Order of Operations]] (Module 0.1)
* 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 3
||
Module 0.4
||
* [[Linear Equations]]
||
* Basic mathematical symbols and terminology
* Basic arithmetic skills
* Basic understanding of [[Order of Operations]] (Module 0.1)
* Basic understanding of factoring
* Basic understanding of [[Solving Equations]] (Module 0.3)
||
* Solving and constructing [[Linear Equations]]
|-
|Week 3
||
Module 0.4
||
* [[Graphs]]
||
* Basic mathematical symbols and terminology
* Basic arithmetic skills
* Basic understanding of order of operations
* Basic understanding of factoring
* Basic understanding of solving [[Linear Equations]] (Module 0.4)
* Understanding of the Cartesian coordinate system
||
* Being able to graph a [[Linear Equations]]
|-
|Week 4
||
Module 1.1
||
* [[Systems of Equations in Two Variables]]
||
* Solving and Graphing [[Linear Equations|linear equations]] in 2 variables. (Module 0.4)
* Understanding [[Order of Operations]] (Module 0.1)
||
* 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 4
||
Module 1.2
||
* [[Systems of Equations in Three Variables]]
||
* Solving [[Systems of Equations in Two Variables]] (Module 1.1)
||
* Solve systems of equations in three variables
* Identify inconsistent systems of equations containing three variables
* Express solutions of a system of dependent equations containing three variables
|-
|Week 5
||
Module 2.1
||
* [[Functions]]
||
* Basic understanding of [[Linear Equations]] (Module 0.4)
* Basic understanding of [[Solving Equations]] (Module 0.3)
||
* Determine whether a relation represents a function.
|-
|Week 5
||
Module 2.2
||
* [[Function Notation]]
||
* Basic understanding of [[Linear Equations]] (Module 0.4)
* Basic understanding of [[Equations]] (Module R)
* Basic understanding of [[Graphs]] (Module 0.4)
||
* 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 5
||
Module 2.2
||
* [[Domain of a Function]]
||
* (Prerequisite)
||
* Find the domain of a function defined by an equation.
* Graph piecewise-defined functions.
|-
|Week 5
||
Module 2.2
||
* [[Range of a Function]]
||
* (Prerequisite)
||
* Find the domain of a function defined by an equation.
* Graph piecewise-defined functions.
|-
|Week 5
||
Module 2.2
||
* [[Toolkit Functions]]
||
* Basic understanding of Cartesian coordinate system (Module 0.4: [[Graphs]])
||
* Identify the basic toolkit functions
* Determine [[Domain of a Function|Domain]] and [[Range of a Function| Range]] for the basic toolkit functions (Module 1.2)
* [[Graphs|Graph]] the basic toolkit functions. (Module 0.4)
|-
|Week 6
||
Module 3.1
||
* [[Intro to Power Functions]]
||
* Basic understanding of power expressions.
* The student recalls the [[Graphs]] and equations of [[Toolkit Functions]], and their associated [[Domain of a Function|Domain]] and [[Range of a Function| 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 of a Function|Domain]] and [[Range|Range]] (Module 1).
* The student can substitute values for variables in an [[Solving Equations|Equations]] and solve for an unknown (Module R)
||
* Identify power functions.
* Identify end behavior of power functions.
* Identify polynomial functions.
* Identify the degree and leading coefficients of polynomial functions.
|-
|Week 6
||
Module 3.1
||
* [[Intro to Polynomial Functions]]
||
* Basic understanding of a polynomial expression.
* The student recalls the [[Graphs] (Module 0.4) and equations of [[Toolkit Functions]], and their associated [[Domain of a Function|Domain]] and [[Range of a Function| Range]] (Module 2.1 & 2.2).
* The student understands where the x-intercept and y-intercept are located given a graph.
* The student understands interval notation for [[Domain of a Function|Domain]] and [[Range of a Function| Range]] (Module 2.1 & 2.2).
* The student can substitute values for variables in an [[Solving Equations|Equations]] and solve for an unknown (Module 0.3).
||
* Identify polynomial functions.
* Identify the degree and leading coefficients of polynomial functions.
|-
|Week 6
||
Module 3.2
||
* [[Quadratic Functions]]
||
* Fundamentals of [[Intro to Polynomial Functions|Polynomials]] (Module 2.1)
* 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 7
||
Module 4.1
||
* [[Dividing Polynomials]]
||
* Basic understanding of multiplying and dividing fractions.
* Basic understanding of simplifying fractions by common factors.
* Basic understanding of [[Factoring Polynomials]] (Module 0.2)
||
* Use long division to divide polynomials
* Use synthetic division to divide polynomials
|-
|Week 7
||
Module 4.2
||
* [[Zeros of Polynomials]]
||
* Basic understanding of multiplying and dividing fractions.
* Basic understanding of simplifying fractions by common factors.
* Basic understanding of [[Factoring Polynomials]] (Module 0.2)
* Basic understanding of [[Functions]] (Module 1.1)
* Basic understanding of [[Solving Equations]] (Module 0.3)
||
* Evaluate a polynomial using the Remainder Theorem
* Use the Factor Theorem to solve a polynomial equation
* Use the Rational Zero Theorem to find rational zeros
* Find zeros of a polynomial function
* Solve real-world applications of polynomial equations
|-
|Week 8
||
Module 5.1
||
* [[More on Polynomial Functions]]
||
* The student understands that zero in the denominator of a fraction is undefined.
* Basic understanding of [[Intro to Polynomial Functions|Polynomial Functions]]
* The student recalls the [[Graphs]] and equations of [[Toolkit Functions]], and their associated [[Domain of a Function|Domain]] and [[Range of a Function| Range]] (Module 2.1 & 2.2).
||
* Solving applied problems involving [[Intro to Polynomial Functions|Polynomial Functions]].
* Use arrow notation.
|-
|Week 8
||
Module 5.2
||
* [[Rational Functions]]
||
* [[Rational Expressions]].
* 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 of a Function|Domain]] and [[Range of a Function| Range]] (Module 2.1 & 2.2).
||
* Solving applied problems involving [[Intro to Polynomial Functions|Polynomial Functions]]. (Module 2.1)
* Use arrow notation.
* Solve applied problems involving rational functions.
* Find the [[Domain|Domain]] of rational functions.
* Identify vertical asymptotes.
* Identify horizontal asymptotes.
|-
|Week 9
||
Module 6.1
||
* [[Graphs of Polynomials]]
||
* Basic understanding of [[Graphs]] (Module 0.4)
* Basic understanding of [[Intro to Polynomial Functions|Polynomial Functions]] (Module 2.1)
||
* Recognize characteristics of graphs of polynomial functions
* Use factoring to find zeros of polynomial functions
* Identify zeros and their multiplicities
* Determine end behavior
* Understand the relationship between degree and turning points
* Graph polynomial functions
|-
|Week 9
||
Module 6.2
||
* [[Graphs of Rational Functions]]
||
* Basic understanding of [[Graphs]] (Module 0.4)
* Basic understanding of [[Rational Functions]] (Module 4.1)
||
* Identify and graph vertical asymptotes
* Identify and graph horizontal asymptotes
* Determine behavior of rational functions around vertical asymptotes
* Graph rational functions
|-
|Week 10
||
Module 7.1
||
* [[Single Transformations of Functions]]
||
* Understanding of [[Functions]] (Module 5)
* Understanding of [[Function Notation]] (Module 2.1)
||
* Graph functions using vertical and horizontal shifts
* Graph functions using reflections about the x-axis and the y-axis
* Determine whether a function is even, odd, or neither from it's graph
* Graph functions using compressions and stretches
* Combine transformations
|-
|Week 10
||
Module 7.2
||
* [[Multiple Transformations of Functions]]
||
* Understanding of [[Single Transformations of Functions]] (Module 7.1)
||
* Combine transformations
|-
|Week 11
||
Module 8.1
||
* [[Composition of Functions]]
||
* Understanding of [[Function Notation]] (Module 2.1)
* Understanding of [[Functions]] (Module 5)
||
* Combine functions using algebraic operations
* Create a new function by composition of functions
* Evaluate composite functions
* Find the domain of a composite function
* Decompose a composite function into its component functions
|-
|Week 11
||
Module 8.2
||
* [[Inverse Functions]]
||
* Understanding of [[Function Notation]] (Module 2.1)
* Understanding of [[Functions]] (Module 5)
* Understanding of [[Composition of Functions]] (Module 7.1)
||
* Verify inverse functions
* Determine the domain and range of an inverse function, and restrict the domain of a function to make it one-to-one
* Find or evaluate the inverse of a function
* Use the graph of a one-to-one function to graph its inverse function on the same axes
|-
|Week 12
||
Module 9.1
||
* [[Exponential Properties]]
||
* Understanding [[Order of Operations]]. (Module 0.1)||
* Use the product rule for exponents.
* Use the quotient rule for exponents.
* Use the power rule for logarithms.
|-
|Week 12
||
Module 9.2
||
* [[Exponential Functions]]
||
* Understanding the [[Toolkit Functions]] for exponential functions (Module 1)
* Understanding the [[Domain of a Function|Domain]] and [[Range of a Function| Range]] for exponential functions (Module 2.1 & 2.2)
* Understanding of [[Simplifying Exponents]] (Module R)
||
* Evaluate exponential functions.
* Find the equation of an exponential function.
* Use compound interest formulas.
* Evaluate exponential functions with base e.
|-
|Week 13
||
Module 10.1
||
* [[Logarithmic Functions]]
||
* Understanding the [[Toolkit Functions]] for logarithmic functions
* Understanding the [[Domain of a Function|Domain]] and [[Range of a Function| Range]] for logarithmic functions (Module 2.1 & 2.2)
* Difference between [[Linear Equations|Linear]] and [[Exponential Functions]] (Module 0.4 & 9.2)
||
* 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 13
||
Module 10.2
||
* [[Logarithmic Properties]]
||
* Understanding how to convert between [[Logarithmic Functions|logarithm]] and [[Exponential Functions|exponential]] forms. (Module 9.2 & 10.1)
* Understanding [[Order of Operations]]. (Module 0.1)
* Understanding of [[Exponential Properties]] (Module 9.1)
||
* 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 14
||
Module 11
||
* [[Modeling using Variation]]
||
* Understanding of [[Exponential Properties]] (Module 9.1)
* Understanding of [[Exponential Functions]] (Module 9.2)
* Understanding of [[Logarithmic Functions]] (Module 10.1)
* Understanding of [[Logarithmic Properties]] (Module 10.2)
||
* Solve direct variation problems
* Solve inverse variation problems
* Solve problems involving joint variation
|}

Wronskian

2020-08-12T14:34:48Z

Johnraymond.yanez:

[https://tutorial.math.lamar.edu/Classes/DE/Wronskian.aspx Notes on the Wronskian]. Produced by Paul Dawkins, Lamar University

Wronskian

2020-08-12T14:34:20Z

Johnraymond.yanez: Created page with "[https://tutorial.math.lamar.edu/Classes/DE/Wronskian.aspx]. Produced by Paul Dawkins, Lamar University"

[https://tutorial.math.lamar.edu/Classes/DE/Wronskian.aspx]. Produced by Paul Dawkins, Lamar University