Difference between revisions of "MAT1073"

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= College Algebra for Scientists and Engineers - MAT 1073 =
 +
 
==Course Catalog==
 
==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).  
 
[https://catalog.utsa.edu/search/?P=MAT%201073 MAT 1073. Algebra for Scientists and Engineers]. (1-4) 3 Credit Hours. (TCCN = MATH 1314).  
Line 6: Line 8:
 
==Topics List==
 
==Topics List==
 
{| class="wikitable sortable"
 
{| class="wikitable sortable"
! Date !! Sections !! Topics !! Prerequisite Skills !! Student Learning Outcomes
+
! Week !! Sections !! Topics !! Prerequisite Skills !! Student Learning Outcomes
 
|-                 
 
|-                 
 
|Week 1
 
|Week 1
 
||
 
||
Module R
+
Fundamentals
 
||
 
||
* [[Order of Operations]]
+
* [[Algebraic Properties]]
 
||
 
||
 
* Basic mathematical symbols and terminology
 
* Basic mathematical symbols and terminology
 
* Basic arithmetic skills
 
* Basic arithmetic skills
* Basic understanding of order of operations
+
 
 
||
 
||
'''Review of:'''
+
Students will be able to correctly identify the algebraic properties:
* PEMDAS
+
* Additive & Multiplicative identity
 +
* Additive & Multiplicative inverse
 +
* Commutative property
 +
* Associative property
 +
* Distributive property
 +
 
 +
 
 +
Students will be able to correctly explain the algebraic properties of numbers and correctly apply these properties in procedural explanations of:
 +
* Solving mathematical equations
 +
* Simplifying/evaluating mathematical expressions
 
|-
 
|-
|Week 1
+
|Week 2
||
 
Module R
 
||
 
* [[Simplifying Radicals]]
 
 
||
 
||
* Basic mathematical symbols and terminology
+
Fundamentals
* Basic understanding of [[Order of Operations]] (Module R)
 
* 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:'''
+
* [[Fractions]]
* 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 mathematical symbols and terminology
 
* Basic arithmetic skills
 
* Basic arithmetic skills
* Basic understanding of [[Order of Operations]] (Module R)
+
* Basic understanding of [[Algebraic Properties]]
* Basic understanding of exponents
+
 
 +
 
 
||
 
||
'''Review the following rules of exponents:'''
+
Students will be able to:
* product rule
+
* Add and subtract fractions.
* quotient rule
+
* Determine common denominators and equivalent fractions.
* power rule
+
* Work with proper and improper fractions.
* zero exponent rule
+
* Simplify to lowest terms.
* negative rule
+
* Multiply and divide fractions.
'''Review how to find the power of a product and a quotient'''
+
 
'''Review how to simplify exponential expressions'''
 
 
|-
 
|-
|Week 1
+
|Week 2
 
||
 
||
Module R
+
Fundamentals
 
||
 
||
* [[Factoring Polynomials]]
+
* [[Factoring]]
 
||
 
||
 
* Basic mathematical symbols and terminology
 
* Basic mathematical symbols and terminology
* Basic arithmetic skills
+
* Basic arithmetic skills  
* Basic understanding of [[Order of Operations]] (Module R)
+
* Basic understanding of [[Algebraic Properties]]
* Basic prime factorization
+
 
* Basic understanding of factoring
+
 
 
||
 
||
'''Review factoring techniques for the following type of polynomials:'''
+
Students will be able to:  
* factor the greatest common factor of a polynomial
+
* Identify factored vs non-factored forms of a polynomial.
* factor a trinomial
+
* Successfully factor binomials & trinomials and difference of squares into two binomial terms.
* factor by grouping
+
* Factor out GCF.
* factor a perfect square trinomial
+
* Multiply and/or distribute to check their factors are correct.
* factor a difference of squares
+
* Differentiate between factors and terms of a polynomial expression.
 +
 
 
|-
 
|-
|Week 1
+
|Week 3
 
||
 
||
Module R
+
Module 1.1
||
 
* [[Solving Equations]]
 
||
 
* Basic mathematical symbols and terminology
 
* Basic arithmetic skills
 
* Basic understanding of [[Order of Operations]] (Module R)
 
* 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]] (Module R)
 
* 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]]
 
* [[Linear Equations]]
 
||
 
||
 
* Basic mathematical symbols and terminology
 
* Basic mathematical symbols and terminology
* Basic arithmetic skills
+
* Basic arithmetic skills  
* Basic understanding of [[Order of Operations]] (Module R)
+
* Basic understanding of [[Algebraic Properties]]
* Basic understanding of factoring
+
* Understanding of the Cartesian coordinate system
* Basic understanding of [[Solving Equations]] (Module R)
+
 
 
||
 
||
* Solving and constructing [[Linear Equations]]
+
Students will be able to:
 +
* Solve linear equations in one variable.
 +
* Determine a linear equation.
 +
* Write and interpret a linear equation.
 +
* Graph a linear equation.
 
|-
 
|-
|Week 1
+
|Week 3
 
||
 
||
Module R
+
Module 1.2
 
||
 
||
* [[Graphs]]
+
* [[Systems of Equations in Two Variables]]
 
||
 
||
 
* Basic mathematical symbols and terminology
 
* Basic mathematical symbols and terminology
* Basic arithmetic skills
+
* Basic arithmetic skills  
* Basic understanding of order of operations
+
* Basic understanding of [[Algebraic Properties]]
* Basic understanding of factoring
+
* Basic understanding of [[Linear Equations]]  
* Basic understanding of solving [[Linear Equations]] (Module R)
 
* Understanding of the Cartesian coordinate system
 
 
||
 
||
* Being able to graph a [[Linear Equations]]
+
Students will be able to:
 +
* 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 2
+
|Week 4
 
||
 
||
Module 1.1
+
Module 2.1
 
||
 
||
 
* [[Functions]]
 
* [[Functions]]
 
||
 
||
* Basic understanding of [[Linear Equations]] (Module R)
+
* Basic understanding of [[Linear Equations]]  
* Basic understanding of [[Equations]] (Module R)
 
 
||
 
||
 +
Students will be able to:
 
* Determine whether a relation represents a function.
 
* Determine whether a relation represents a function.
 
|-
 
|-
|Week 2
+
|Week 4
 
||
 
||
Module 1.1
+
Module 2.2
 
||
 
||
 
* [[Function Notation]]
 
* [[Function Notation]]
 
||
 
||
* Basic understanding of [[Linear Equations]] (Module R)
+
* Basic understanding of [[Functions]]  
* Basic understanding of [[Equations]] (Module R)
 
* Basic understanding of [[Graphs]] (Module R)
 
 
||
 
||
* Find the value of a [[Functions]]
+
Students will be able to:
 +
* Find the value of [[Functions]].
 
* Graph the functions listed in the library of functions.
 
* Graph the functions listed in the library of functions.
 
* Determine whether a function is one-to-one.
 
* Determine whether a function is one-to-one.
 
* Use the vertical line test to identify functions.
 
* Use the vertical line test to identify functions.
 
|-
 
|-
|Week 2
+
|Week 4
 
||
 
||
Module 1.2
+
Module 2.2
 
||
 
||
* [[Domain|Domain]] of a Function
+
* [[Domain of a Function]]
 
||
 
||
* Basic understanding of interval notation (Module R: [[Solving Inequalities]])
+
* An understanding of [[Function Notation]]
 
||
 
||
 +
Students will be able to:
 
* Find the domain of a function defined by an equation.
 
* Find the domain of a function defined by an equation.
* Graph piecewise-defined functions.
+
 
 
|-
 
|-
|Week 2
+
|Week 4
 
||
 
||
Module 1.2
+
Module 2.2
 
||
 
||
* [[Range|Range]] of a Function
+
* [[Range of a Function]]
 
||
 
||
* Basic understanding of interval notation (Module R: [[Solving Inequalities]])
+
* An understanding of [[Function Notation]]
 
||
 
||
* Find the domain of a function defined by an equation.
+
Students will be able to:
* Graph piecewise-defined functions.
+
* Find the range of a function defined by an equation.
 
|-
 
|-
|Week 2
+
|Week 4
 
||
 
||
Module 1.2
+
Module 2.2
 
||
 
||
 
* [[Toolkit Functions]]
 
* [[Toolkit Functions]]
 
||
 
||
* Basic understanding of Cartesian coordinate system (Module R: [[Graphs]])
+
* Basic understanding of [[Functions]]
* Basic understanding of interval notation (Module R: [[Solving Inequalities]])
 
 
||
 
||
* Identify the basic toolkit functions
+
Students will be able to:
* Determine [[Domain]] and [[Range]] for the basic toolkit functions (Module 1.2)
+
* Identify the basic toolkit functions.
* [[Graphs|Graph]] the basic toolkit functions. (Module R)
+
* Determine [[Domain of a Function|Domain]] and [[Range of a Function| Range]] for the basic toolkit functions.
 +
 
 
|-
 
|-
|Week 3
+
|Week 5
||
 
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|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 [[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 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]] (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 4
 
 
||
 
||
 
Module 3.1
 
Module 3.1
 
||
 
||
* [[Dividing Polynomials]]
+
* [[Composition of Functions]]
 
||
 
||
* Basic understanding of multiplying and dividing fractions.
+
* Basic understanding of [[Functions]]
* Basic understanding of simplifying fractions by common factors.
+
* Basic understanding of [[Function Notation]]
* Basic understanding of the rules of exponents. (Module R: [[Simplifying Exponents]])
+
* Basic understanding of [[Domain of a Function|Domain]] and [[Range of a Function| Range]]  
* Basic understanding of [[Factoring Polynomials]] (Module R)
 
 
||
 
||
* Use long division to divide polynomials
+
Students will be able to:
* Use synthetic division to divide polynomials
+
* Combine functions using [[Algebraic Properties]].
 +
* 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 4
+
|Week 5
 
||
 
||
 
Module 3.2
 
Module 3.2
 
||
 
||
* [[Zeros of Polynomials]]
+
* [[Inverse Functions]]
 
||
 
||
* Basic understanding of multiplying and dividing fractions.
+
* Basic understanding of [[Functions]]
* Basic understanding of simplifying fractions by common factors.
+
* Basic understanding of [[Function Notation]]
* Basic understanding of [[Factoring Polynomials]] (Module R)
+
* Basic understanding of [[Domain of a Function|Domain]] and [[Range of a Function| Range]]  
* Basic understanding of [[Functions]] (Module 1.1)
+
* Basic understanding of [[Composition of Functions]]
* Basic understanding of [[Solving Equations]] (Module R)
 
 
||
 
||
* Evaluate a polynomial using the Remainder Theorem
+
Students will be able to:
* Use the Factor Theorem to solve a polynomial equation
+
* Verify inverse functions using [[Algebraic Properties]].
* Use the Rational Zero Theorem to find rational zeros
+
* Determine the domain and range of an inverse function, and restrict the domain of a function to make it one-to-one.
* Find zeros of a polynomial function
+
* Find or evaluate the inverse of a function.
* Solve real-world applications of polynomial equations
+
* Use the graph of a one-to-one function to graph its inverse function on the same axes.
 +
 
 
|-
 
|-
|Week 5
+
|Week 6
 
||
 
||
 
Module 4.1
 
Module 4.1
 
||
 
||
* [[More on Polynomial Functions]]
+
* [[Exponential Properties]]
 
||
 
||
* The student understands that zero in the denominator of a fraction is undefined.
+
* Basic mathematical symbols and terminology
* Basic understanding of [[Intro to Polynomial Functions|Polynomial Functions]]
+
* Basic arithmetic skills
* The student recalls the [[Graphs]] and equations of [[Toolkit Functions]], and their associated [[Domain]] and [[Range]] (Module 1.2 & R).
+
* Basic understanding of [[Algebraic Properties]]
 
||
 
||
* Solving applied problems involving [[Intro to Polynomial Functions|Polynomial Functions]].
+
Students will be able to:
* Use arrow notation.
+
* Use the product rule for exponents.
 +
* Use the quotient rule for exponents.
 +
* Use the power rule for exponents.
 
|-
 
|-
|Week 5
+
|Week 6
 
||
 
||
 
Module 4.2
 
Module 4.2
 
||
 
||
* [[Rational Functions]]
+
* [[Exponential Functions]]
 
||
 
||
* [[Rational Expressions]].
+
* Understanding the [[Domain of a Function|Domain]] and [[Range of a Function| Range]] of the [[Toolkit Functions]] for exponential functions
* The student understands that zero in the denominator of a fraction is undefined.
+
* Basic understanding of [[Exponential Properties]]  
* The student recalls the [[Graphs]] and equations of [[Toolkit Functions]], and their associated [[Domain]] and [[Range]] (Module 1.2 & R).
 
 
||
 
||
* Solving applied problems involving [[Intro to Polynomial Functions|Polynomial Functions]]. (Module 2.1)
+
Students will be able to:
* Use arrow notation.
+
* Determine the difference between [[Linear Equations|Linear]] and Exponential Functions.
* Solve applied problems involving rational functions.
+
* Evaluate exponential functions.
* Find the [[Domain|Domain]] of rational functions.
+
* Find the equation of an exponential function.
* Identify vertical asymptotes.
+
* Evaluate exponential functions with base e.
* Identify horizontal asymptotes.
+
* Evaluate exponential functions with base 10.
 +
* Graph exponential functions.
 +
 
 
|-
 
|-
|Week 6
+
|Week 7
 
||
 
||
 
Module 5.1
 
Module 5.1
 
||
 
||
* [[Graphs of Polynomials]]
+
* [[Logarithmic Properties]]
 
||
 
||
* Basic understanding of [[Graphs]] (Module R)
+
* Basic understanding of [[Exponential Properties]]  
* Basic understanding of [[Intro to Polynomial Functions|Polynomial Functions]] (Module 2.1)
 
 
||
 
||
* Recognize characteristics of graphs of polynomial functions
+
Students will be to able to:
* Use factoring to find zeros of polynomial functions
+
* Rewrite from exponential form to logarithmic form and vice versa.
* Identify zeros and their multiplicities
+
* Use the product rule for logarithms.
* Determine end behavior
+
* Use the quotient rule for logarithms.
* Understand the relationship between degree and turning points
+
* Use the power rule for logarithms.
* Graph polynomial functions
+
* Expand logarithmic expressions.
 +
* Condense logarithmic expressions.
 +
* Use the change-of-base formula for logarithms.
 +
 
 
|-
 
|-
|Week 6
+
|Week 7
 
||
 
||
 
Module 5.2
 
Module 5.2
 
||
 
||
* [[Graphs of Rational Functions]]
+
* [[Logarithmic Functions]]
 
||
 
||
* Basic understanding of [[Graphs]] (Module R)
+
* Basic understanding of [[Inverse Functions]]  
* Basic understanding of [[Rational Functions]] (Module 4.1)
+
* Understanding the [[Domain of a Function|Domain]] and [[Range of a Function| Range]] of [[Toolkit Functions]] for logarithmic functions
 +
* Basic understanding of [[Exponential Properties]]  
 +
 
 
||
 
||
* Identify and graph vertical asymptotes
+
Students will be able to:
* Identify and graph horizontal asymptotes
+
* Evaluate logarithms.
* Determine behavior of rational functions around vertical asymptotes
+
* Use common logarithms.
* Graph rational functions
+
* Use natural logarithms.
|-
+
* Graph logarithmic functions.
|Week 7
+
 
||
 
Module 6
 
||
 
* [[Transformations of Functions]]
 
||
 
* Understanding of [[Functions]] (Module R)
 
* Understanding of [[Function Notation]] (Module R)
 
||
 
* 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 8
 
|Week 8
 
||
 
||
Module 7.1
+
Module 6.2
 
||
 
||
* [[Composition of Functions]]
+
* [[Quadratic Equations]]
 
||
 
||
* Understanding of [[Function Notation]] (Module R)
+
* Basic arithmetic skills
* Understanding of [[Functions]] (Module R)
+
* Basic understanding of [[Algebraic Properties]]
 +
* Basic understanding of [[Factoring]]
 
||
 
||
* Combine functions using algebraic operations
+
Students will be able to:
* Create a new function by composition of functions
+
* Determine complex number solutions.
* Evaluate composite functions
+
* Determine solutions of quadratic equations using factoring techniques.
* Find the domain of a composite function
+
* Determine solutions of quadratic equations using Quadratic Formula.
* Decompose a composite function into its component functions
+
 
 
|-
 
|-
 
|Week 8
 
|Week 8
 
||
 
||
Module 7.2
+
Module 6.2
 
||
 
||
* [[Inverse Functions]]
+
* [[Quadratic Functions]]
 
||
 
||
* Understanding of [[Function Notation]] (Module R)
+
* Basic understanding of [[Quadratic Equations]]
* Understanding of [[Functions]] (Module R)
+
 
* Understanding of [[Composition of Functions]] (Module 7.1)
 
 
||
 
||
* Verify inverse functions
+
Students will be able to:
* Determine the domain and range of an inverse function, and restrict the domain of a function to make it one-to-one
+
* Understand a polynomial expression.
* Find or evaluate the inverse of a function
+
* Recognize characteristics of parabolas.
* Use the graph of a one-to-one function to graph its inverse function on the same axes
+
* 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 9
 
|Week 9
 
||
 
||
Module 8.1
+
Module 7.1
 
||
 
||
* [[Exponential Functions]]
+
* [[Dividing Polynomials]]
 
||
 
||
* Understanding the [[Toolkit Functions]] for exponential functions (Module 1)
+
* Basic understanding of  [[Fractions]]
* Understanding the [[Domain]] and [[Range]] for exponential functions (Module 1)
+
* Basic understanding of [[Factoring]]
* Understanding of [[Simplifying Exponents]] (Module R)
+
* The student recalls the graphs and equations of [[Toolkit Functions]], and their associated [[Domain of a Function|Domain]] and [[Range of a Function| Range]]  
 +
* Basic understanding of [[Quadratic Functions]]  
 +
 
 
||
 
||
* Evaluate exponential functions.
+
Students will be able to:
* Find the equation of an exponential function.
+
* Identify polynomial functions.
* Use compound interest formulas.
+
* Identify the degree and leading coefficients of polynomial functions.
* Evaluate exponential functions with base e.
+
* Use long division to divide polynomials.
 +
* Use synthetic division to divide polynomials.
 
|-
 
|-
 
|Week 9
 
|Week 9
 
||
 
||
Module 8.2
+
Module 7.2
 
||
 
||
* [[Logarithmic Functions]]
+
* [[Factoring Polynomials|Zeros of Polynomials]]
 
||
 
||
* Understanding the [[Toolkit Functions]] for logarithmic functions
+
* Basic understanding of  [[Fractions]]  
* Understanding the [[Domain]] and [[Range]] for logarithmic functions (Module 1)
+
* Basic understanding of [[Functions]]  
* Difference between [[Linear Equations|Linear]] and [[Exponential Functions]] (Module R & 8.1)
+
* Basic understanding of [[Dividing Polynomials]]  
 
||
 
||
* Rewriting from exponential form to logarithmic form and vice versa
+
Students will be able to:  
:-y=b^x\equiv\log_b(y)=x
+
* Evaluate a polynomial using the Remainder Theorem.
* Evaluate logarithms.
+
* Use the Factor Theorem to solve a polynomial equation.
* Use common logarithms.
+
* Use the Rational Zero Theorem to find rational zeros.
* Use natural logarithms.
+
* Find zeros of a polynomial function.
 +
* Solve real-world applications of polynomial equations.
 +
 
 
|-
 
|-
 
|Week 10
 
|Week 10
 
||
 
||
Module 9.1
+
Module 8.1
 
||
 
||
* [[Logarithmic Properties]]
+
* [[Power and Polynomial Functions]]
 
||
 
||
* Understanding how to convert between [[Logarithmic Functions|logarithm]] and [[Exponential Functions|exponential]] forms. (Module 8.1 & 8.2)
+
* Basic understanding of [[Factoring]]  
* Understanding [[Order of Operations]]. (Module R)
+
* Basic understanding of [[Quadratic Functions]]  
* Understanding of [[Simplifying Exponents]] (Module R)
+
* Basic understanding of [[Dividing Polynomials]]  
 +
* Basic understanding of [[Factoring Polynomials|Zeros of Polynomials]]  
 
||
 
||
* Use the product rule for logarithms.
+
Students will be able to:
* Use the quotient rule for logarithms.
+
* Find the average rate of change of a function.
* Use the power rule for logarithms.
+
* Use a graph to determine where a function is increasing, decreasing, or constant.
* Expand logarithmic expressions.
+
* Use a graph to locate local maxima and local minima.
* Condense logarithmic expressions.
+
* Use a graph to locate the absolute maximum and absolute minimum.
* Use the change-of-base formula for logarithms.
+
* Identify end behavior of power functions.
 +
 
 +
 
 +
 
 
|-
 
|-
 
|Week 10
 
|Week 10
 
||
 
||
Module 9.2
+
Module 8.2
 
||
 
||
* [[Exponential Equations]]  
+
* [[Graphs of Polynomials]]
 
||
 
||
* Understanding rules for solving [[Linear Equations]] (Module R)
+
* Basic understanding of [[Dividing Polynomials]]  
* Understanding how to check a solution to an [[Solving Equations|equations]] (Module R)
+
* Basic understanding of [[Factoring Polynomials|Zeros of Polynomials]]  
* Understanding rules for solving [[Quadratic Equations]] (Module 2.1)
 
* Understanding of [[Logarithmic Properties]] (Module 9.1)
 
 
||
 
||
* Use like bases to solve exponential equations.
+
Students will be able to:
* Use logarithms to solve exponential equations.
+
* Recognize characteristics of graphs of polynomial functions.
|-
+
* Use [[Factoring]] to find zeros of polynomial functions.
|Week 10
+
* Identify zeros and their multiplicities.
||
+
* Determine end behavior of polynomial functions.
Module 9.2
+
* Understand the relationship between degree and turning points.
||
+
* Graph polynomial functions.
* [[Logarithmic Equations]]
+
 
||
 
* Understanding rules for solving [[Linear Equations]] (Module R)
 
* Understanding how to check a solution to an [[Solving Equations|equations]] (Module R)
 
* Understanding rules for solving [[Quadratic Equations]] (Module 2.1)
 
* Understanding of [[Logarithmic Properties]] (Module 9.1)
 
||
 
* 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 11
 
|Week 11
 
||
 
||
Module 10
+
Module 9.1
 
||
 
||
* [[Exponential Models]]
+
* [[Rational Expressions]]
 
||
 
||
* Understanding of [[Simplifying Exponents]] (Module R)
+
* The student understands that zero in the denominator of a fraction is undefined
* Understanding of [[Exponential Functions]] (Module 8.1)
+
* Basic understanding of [[Fractions]]  
* Understanding of [[Exponential Equations]] (Module 9.2)
 
 
||
 
||
* Model exponential growth and decay
+
Students will be able to:
* Use Newton's Law of Cooling
+
* Simplify rational expressions.
* Choose an appropriate model for data
+
* Multiply rational expressions.
* Express an exponential model in base e
+
* Divide rational expressions.
 +
* Add and subtract rational expressions.
 +
 
 
|-
 
|-
 
|Week 11
 
|Week 11
 
||
 
||
Module 10
+
Module 9.2
 
||
 
||
* [[Logarithmic Models]]
+
* [[Graphs of Rational Functions]]
 
||
 
||
* Understanding of [[Logarithmic Functions]] (Module 8.2)
+
* Basic understanding of [[Rational Expressions]]  
* Understanding of [[Logarithmic Properties]] (Module 9.1)
 
* Understanding of [[Logarithmic Equations]] (Module 9.2)
 
 
||
 
||
* Use logistic-growth models
+
Students will be able to:
* Choose an appropriate model for data
+
* Identify and graph vertical asymptotes.
 +
* Identify and graph horizontal asymptotes.
 +
* Determine behavior of rational functions around vertical asymptotes.
 +
* Find the domains of rational functions.
 +
* Graph rational functions.
 +
 
 
|-
 
|-
 
|Week 12
 
|Week 12
 
||
 
||
Module 11
+
Module 10.1
 
||
 
||
* [[Modeling using Variation]]
+
* [[Single Transformations of Functions]]
 
||
 
||
* Understanding of [[Simplifying Exponents]] (Module R)
+
* Understanding of [[Function Notation]]  
* Understanding of [[Exponential Functions]] (Module 8.1)
 
* Understanding of [[Logarithmic Functions]] (Module 8.2)
 
* Understanding of [[Logarithmic Properties]] (Module 9.1)
 
* Understanding of [[Exponential Equations]] (Module 9.2)
 
* Understanding of [[Logarithmic Equations]] (Module 9.2)
 
* Understanding of [[Exponential]] (Module 10)
 
* Understanding of [[Logarithmic Models]] (Module 10)
 
 
||
 
||
* Solve direct variation problems
+
Students will be able to:
* Solve inverse variation problems
+
* Graph functions using vertical and horizontal shifts.
* Solve problems involving joint variation
+
* Graph functions using reflections about the x-axis and the y-axis.
 +
 
 
|-
 
|-
|Week 13
+
|Week 12
 
||
 
||
Module 12.1
+
Module 10.2
 
||
 
||
* [[Systems of Equations in Two Variables]]
+
* [[Multiple Transformations of Functions]]
 
||
 
||
* Solving and Graphing [[Linear Equations|linear equations]] in 2 variables. (Module R)
+
* Understanding of [[Single Transformations of Functions]]  
* Understanding [[Order of Operations]] (Module R)
 
 
||
 
||
* Solve systems of equations by graphing.
+
Students will be able to:
* Solve systems of equations by substitution.
+
* Determine whether a function is even, odd, or neither.
* Solve systems of equations by elimination
+
* Graph functions using compressions and stretches.
* Identify inconsistent systems of equations containing two variables.
+
* Combine transformations.
* Express the solution of a system of dependent equations containing two variables.
+
 
|-
+
 
|Week 13
+
 
||
 
Module 12.2
 
||
 
* [[Systems of Equations in Three Variables]]
 
||
 
* Solving [[Systems of Equations in Two Variables]] (Module 12.1)
 
||
 
* 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
 
 
|}
 
|}

Latest revision as of 08:04, 23 June 2023

College Algebra for Scientists and Engineers - MAT 1073

Course Catalog

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

Week Sections Topics Prerequisite Skills Student Learning Outcomes
Week 1

Fundamentals

  • Basic mathematical symbols and terminology
  • Basic arithmetic skills

Students will be able to correctly identify the algebraic properties:

  • Additive & Multiplicative identity
  • Additive & Multiplicative inverse
  • Commutative property
  • Associative property
  • Distributive property


Students will be able to correctly explain the algebraic properties of numbers and correctly apply these properties in procedural explanations of:

  • Solving mathematical equations
  • Simplifying/evaluating mathematical expressions
Week 2

Fundamentals

  • Basic mathematical symbols and terminology
  • Basic arithmetic skills
  • Basic understanding of Algebraic Properties


Students will be able to:

  • Add and subtract fractions.
  • Determine common denominators and equivalent fractions.
  • Work with proper and improper fractions.
  • Simplify to lowest terms.
  • Multiply and divide fractions.
Week 2

Fundamentals

  • Basic mathematical symbols and terminology
  • Basic arithmetic skills
  • Basic understanding of Algebraic Properties


Students will be able to:

  • Identify factored vs non-factored forms of a polynomial.
  • Successfully factor binomials & trinomials and difference of squares into two binomial terms.
  • Factor out GCF.
  • Multiply and/or distribute to check their factors are correct.
  • Differentiate between factors and terms of a polynomial expression.
Week 3

Module 1.1

  • Basic mathematical symbols and terminology
  • Basic arithmetic skills
  • Basic understanding of Algebraic Properties
  • Understanding of the Cartesian coordinate system

Students will be able to:

  • Solve linear equations in one variable.
  • Determine a linear equation.
  • Write and interpret a linear equation.
  • Graph a linear equation.
Week 3

Module 1.2

Students will be able to:

  • 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 2.1

Students will be able to:

  • Determine whether a relation represents a function.
Week 4

Module 2.2

Students will be able to:

  • Find the value of 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 4

Module 2.2

Students will be able to:

  • Find the domain of a function defined by an equation.
Week 4

Module 2.2

Students will be able to:

  • Find the range of a function defined by an equation.
Week 4

Module 2.2

Students will be able to:

  • Identify the basic toolkit functions.
  • Determine Domain and Range for the basic toolkit functions.
Week 5

Module 3.1

Students will be able to:

  • Combine functions using Algebraic Properties.
  • 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 5

Module 3.2

Students will be able to:

  • Verify inverse functions using Algebraic Properties.
  • 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 6

Module 4.1

  • Basic mathematical symbols and terminology
  • Basic arithmetic skills
  • Basic understanding of Algebraic Properties

Students will be able to:

  • Use the product rule for exponents.
  • Use the quotient rule for exponents.
  • Use the power rule for exponents.
Week 6

Module 4.2

Students will be able to:

  • Determine the difference between Linear and Exponential Functions.
  • Evaluate exponential functions.
  • Find the equation of an exponential function.
  • Evaluate exponential functions with base e.
  • Evaluate exponential functions with base 10.
  • Graph exponential functions.
Week 7

Module 5.1

Students will be to able to:

  • Rewrite from exponential form to logarithmic form and vice versa.
  • 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 5.2

Students will be able to:

  • Evaluate logarithms.
  • Use common logarithms.
  • Use natural logarithms.
  • Graph logarithmic functions.
Week 8

Module 6.2

Students will be able to:

  • Determine complex number solutions.
  • Determine solutions of quadratic equations using factoring techniques.
  • Determine solutions of quadratic equations using Quadratic Formula.
Week 8

Module 6.2

Students will be able to:

  • Understand a polynomial expression.
  • 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 9

Module 7.1

Students will be able to:

  • Identify polynomial functions.
  • Identify the degree and leading coefficients of polynomial functions.
  • Use long division to divide polynomials.
  • Use synthetic division to divide polynomials.
Week 9

Module 7.2

Students will be able to:

  • 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 10

Module 8.1

Students will be able to:

  • Find the average rate of change of a function.
  • Use a graph to determine where a function is increasing, decreasing, or constant.
  • Use a graph to locate local maxima and local minima.
  • Use a graph to locate the absolute maximum and absolute minimum.
  • Identify end behavior of power functions.


Week 10

Module 8.2

Students will be able to:

  • Recognize characteristics of graphs of polynomial functions.
  • Use Factoring to find zeros of polynomial functions.
  • Identify zeros and their multiplicities.
  • Determine end behavior of polynomial functions.
  • Understand the relationship between degree and turning points.
  • Graph polynomial functions.
Week 11

Module 9.1

  • The student understands that zero in the denominator of a fraction is undefined
  • Basic understanding of Fractions

Students will be able to:

  • Simplify rational expressions.
  • Multiply rational expressions.
  • Divide rational expressions.
  • Add and subtract rational expressions.
Week 11

Module 9.2

Students will be able to:

  • Identify and graph vertical asymptotes.
  • Identify and graph horizontal asymptotes.
  • Determine behavior of rational functions around vertical asymptotes.
  • Find the domains of rational functions.
  • Graph rational functions.
Week 12

Module 10.1

Students will be able to:

  • Graph functions using vertical and horizontal shifts.
  • Graph functions using reflections about the x-axis and the y-axis.
Week 12

Module 10.2

Students will be able to:

  • Determine whether a function is even, odd, or neither.
  • Graph functions using compressions and stretches.
  • Combine transformations.