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 2
+
|Week 1
 
||
 
||
Module 0.1
+
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 2
 
|Week 2
 
||
 
||
Module 0.1
+
Fundamentals
||
 
* [[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]]
+
* [[Fractions]]
 
||
 
||
 
* Basic mathematical symbols and terminology
 
* Basic mathematical symbols and terminology
 
* Basic arithmetic skills
 
* Basic arithmetic skills
* Basic understanding of [[Order of Operations]] (Module 0.1)
+
* 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
+
* Add and subtract fractions.
* factor a trinomial
+
* Determine common denominators and equivalent fractions.
* factor by grouping
+
* Work with proper and improper fractions.
* factor a perfect square trinomial
+
* Simplify to lowest terms.
* factor a difference of squares
+
* Multiply and divide fractions.
 +
 
 
|-
 
|-
|Week 3
+
|Week 2
 
||
 
||
Module 0.3
+
Fundamentals
 
||
 
||
* [[Solving Equations and Inequalities]]
+
* [[Factoring]]
 
||
 
||
 
* Basic mathematical symbols and terminology
 
* Basic mathematical symbols and terminology
* Basic arithmetic skills
+
* Basic arithmetic skills  
* Basic understanding of [[Order of Operations]] (Module 0.1)
+
* Basic understanding of [[Algebraic Properties]]
* Basic understanding of factoring
+
 
 +
 
 
||
 
||
'''Review the following linear equation topics:'''
+
Students will be able to:  
* Basic mathematical symbols and terminology
+
* Identify factored vs non-factored forms of a polynomial.
* solving linear equations in one variable
+
* Successfully factor binomials & trinomials and difference of squares into two binomial terms.
* finding a linear equation
+
* Factor out GCF.
* write and interpret a linear equation
+
* Multiply and/or distribute to check their factors are correct.
 +
* Differentiate between factors and terms of a polynomial expression.
 +
 
 
|-
 
|-
 
|Week 3
 
|Week 3
 
||
 
||
Module 0.4
+
Module 1.1
 
||
 
||
 
* [[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 0.1)
+
* Basic understanding of [[Algebraic Properties]]
* Basic understanding of factoring
+
* Understanding of the Cartesian coordinate system
* Basic understanding of [[Solving Equations and Inequalities]] (Module 0.3)
+
 
 
||
 
||
* 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 3
 
|Week 3
 
||
 
||
Module 0.4
+
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 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)
 
 
||
 
||
 +
Students will be able to:
 
* Solve systems of equations by graphing.
 
* Solve systems of equations by graphing.
 
* Solve systems of equations by substitution.
 
* Solve systems of equations by substitution.
* Solve systems of equations by elimination
+
* Solve systems of equations by elimination.
 
* Identify inconsistent systems of equations containing two variables.
 
* Identify inconsistent systems of equations containing two variables.
 
* Express the solution of a system of dependent equations containing two variables.
 
* Express the solution of a system of dependent equations containing two variables.
 
|-
 
|-
 
|Week 4
 
|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
 
Module 2.1
Line 137: Line 114:
 
* [[Functions]]
 
* [[Functions]]
 
||
 
||
* Basic understanding of [[Linear Equations]] (Module 0.4)
+
* Basic understanding of [[Linear Equations]]  
* Basic understanding of [[Solving Equations and Inequalities]] (Module 0.3)
 
 
||
 
||
 +
Students will be able to:
 
* Determine whether a relation represents a function.
 
* Determine whether a relation represents a function.
 
|-
 
|-
|Week 5
+
|Week 4
 
||
 
||
 
Module 2.2
 
Module 2.2
Line 148: Line 125:
 
* [[Function Notation]]
 
* [[Function Notation]]
 
||
 
||
* Basic understanding of [[Linear Equations]] (Module 0.4)
+
* Basic understanding of [[Functions]]  
* Basic understanding of [[Equations]] (Module R)
 
* Basic understanding of [[Graphs]] (Module 0.4)
 
 
||
 
||
* 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 5
+
|Week 4
 
||
 
||
 
Module 2.2
 
Module 2.2
Line 163: Line 139:
 
* [[Domain of a Function]]
 
* [[Domain of a Function]]
 
||
 
||
* (Prerequisite)
+
* 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 5
+
|Week 4
 
||
 
||
 
Module 2.2
 
Module 2.2
Line 174: Line 151:
 
* [[Range of a Function]]
 
* [[Range of a Function]]
 
||
 
||
* (Prerequisite)
+
* 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 5
+
|Week 4
 
||
 
||
 
Module 2.2
 
Module 2.2
Line 185: Line 162:
 
* [[Toolkit Functions]]
 
* [[Toolkit Functions]]
 
||
 
||
* Basic understanding of Cartesian coordinate system (Module 0.4: [[Graphs]])
+
* Basic understanding of [[Functions]]
 
||
 
||
* Identify the basic toolkit functions
+
Students will be able to:
* Determine [[Domain of a Function|Domain]] and [[Range of a Function| Range]] for the basic toolkit functions (Module 1.2)
+
* Identify the basic toolkit functions.
* [[Graphs|Graph]] the basic toolkit functions. (Module 0.4)
+
* Determine [[Domain of a Function|Domain]] and [[Range of a Function| Range]] for the basic toolkit functions.
 +
 
 
|-
 
|-
|Week 6
+
|Week 5
 
||
 
||
 
Module 3.1
 
Module 3.1
 
||
 
||
* [[Intro to Power Functions]]
+
* [[Composition of Functions]]
 
||
 
||
* Basic understanding of power expressions.
+
* Basic understanding of [[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 1).
+
* Basic understanding of [[Function Notation]]  
* The student understands where the x-intercept and y-intercept are located given a graph.
+
* Basic understanding of [[Domain of a Function|Domain]] and [[Range of a Function| Range]]  
* 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.
+
Students will be able to:
* Identify end behavior of power functions.
+
* Combine functions using [[Algebraic Properties]].
* Identify polynomial functions.
+
* Create a new function by composition of functions.
* Identify the degree and leading coefficients of polynomial functions.
+
* Evaluate composite functions.
 +
* Find the domain of a composite function.
 +
* Decompose a composite function into its component functions.
 
|-
 
|-
|Week 6
+
|Week 5
 
||
 
||
Module 3.1
+
Module 3.2
 
||
 
||
* [[Intro to Polynomial Functions]]
+
* [[Inverse Functions]]
 
||
 
||
* Basic understanding of a polynomial expression.
+
* Basic understanding of [[Functions]]  
* 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).
+
* Basic understanding of [[Function Notation]]  
* The student understands where the x-intercept and y-intercept are located given a graph.
+
* Basic understanding of [[Domain of a Function|Domain]] and [[Range of a Function| Range]]  
* The student understands interval notation for [[Domain of a Function|Domain]] and [[Range of a Function| Range]] (Module 2.1 & 2.2).
+
* Basic understanding of [[Composition of Functions]]
* The student can substitute values for variables in an [[Solving Equations|Equations]] and solve for an unknown (Module 0.3).
 
 
||
 
||
* Identify polynomial functions.
+
Students will be able to:
* Identify the degree and leading coefficients of polynomial functions.
+
* 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
 
|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
 
Module 4.1
 
||
 
||
* [[Dividing Polynomials]]
+
* [[Exponential Properties]]
 
||
 
||
* Basic understanding of multiplying and dividing fractions.
+
* Basic mathematical symbols and terminology
* Basic understanding of simplifying fractions by common factors.
+
* Basic arithmetic skills
* Basic understanding of [[Factoring Polynomials]] (Module 0.2)
+
* Basic understanding of [[Algebraic Properties]]
 
||
 
||
* Use long division to divide polynomials
+
Students will be able to:
* Use synthetic division to divide polynomials
+
* Use the product rule for exponents.
 +
* Use the quotient rule for exponents.
 +
* Use the power rule for exponents.
 
|-
 
|-
|Week 7
+
|Week 6
 
||
 
||
 
Module 4.2
 
Module 4.2
 
||
 
||
* [[Zeros of Polynomials]]
+
* [[Exponential Functions]]
 
||
 
||
* Basic understanding of multiplying and dividing fractions.
+
* Understanding the [[Domain of a Function|Domain]] and [[Range of a Function| Range]] of the [[Toolkit Functions]] for exponential functions
* Basic understanding of simplifying fractions by common factors.
+
* Basic understanding of [[Exponential Properties]]  
* 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
+
Students will be able to:
* Use the Factor Theorem to solve a polynomial equation
+
* Determine the difference between [[Linear Equations|Linear]] and Exponential Functions.
* Use the Rational Zero Theorem to find rational zeros
+
* Evaluate exponential functions.
* Find zeros of a polynomial function
+
* Find the equation of an exponential function.
* Solve real-world applications of polynomial equations
+
* Evaluate exponential functions with base e.
 +
* Evaluate exponential functions with base 10.
 +
* Graph exponential functions.
 +
 
 
|-
 
|-
|Week 8
+
|Week 7
 
||
 
||
 
Module 5.1
 
Module 5.1
 
||
 
||
* [[More on Polynomial Functions]]
+
* [[Logarithmic Properties]]
 
||
 
||
* The student understands that zero in the denominator of a fraction is undefined.
+
* Basic understanding of [[Exponential Properties]]  
* 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]].
+
Students will be to able to:
* Use arrow notation.
+
* 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 8
+
|Week 7
 
||
 
||
 
Module 5.2
 
Module 5.2
 
||
 
||
* [[Rational Functions]]
+
* [[Logarithmic Functions]]
 
||
 
||
* [[Rational Expressions]].
+
* Basic understanding of [[Inverse Functions]]  
* The student understands that zero in the denominator of a fraction is undefined.
+
* Understanding the [[Domain of a Function|Domain]] and [[Range of a Function| Range]] of [[Toolkit Functions]] for logarithmic 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).
+
* Basic understanding of [[Exponential Properties]]
 +
 
 
||
 
||
* Solving applied problems involving [[Intro to Polynomial Functions|Polynomial Functions]]. (Module 2.1)
+
Students will be able to:
* Use arrow notation.
+
* Evaluate logarithms.
* Solve applied problems involving rational functions.
+
* Use common logarithms.
* Find the [[Domain|Domain]] of rational functions.
+
* Use natural logarithms.
* Identify vertical asymptotes.
+
* Graph logarithmic functions.
* Identify horizontal asymptotes.
+
 
 
|-
 
|-
|Week 9
+
|Week 8
 
||
 
||
Module 6.1
+
Module 6.2
 
||
 
||
* [[Graphs of Polynomials]]
+
* [[Quadratic Equations]]
 
||
 
||
* Basic understanding of [[Graphs]] (Module 0.4)
+
* Basic arithmetic skills
* Basic understanding of [[Intro to Polynomial Functions|Polynomial Functions]] (Module 2.1)
+
* Basic understanding of [[Algebraic Properties]]
 +
* Basic understanding of [[Factoring]]
 
||
 
||
* Recognize characteristics of graphs of polynomial functions
+
Students will be able to:
* Use factoring to find zeros of polynomial functions
+
* Determine complex number solutions.
* Identify zeros and their multiplicities
+
* Determine solutions of quadratic equations using factoring techniques.
* Determine end behavior
+
* Determine solutions of quadratic equations using Quadratic Formula.
* Understand the relationship between degree and turning points
+
 
* Graph polynomial functions
 
 
|-
 
|-
|Week 9
+
|Week 8
 
||
 
||
 
Module 6.2
 
Module 6.2
 
||
 
||
* [[Graphs of Rational Functions]]
+
* [[Quadratic Functions]]
 
||
 
||
* Basic understanding of [[Graphs]] (Module 0.4)
+
* Basic understanding of [[Quadratic Equations]]
* Basic understanding of [[Rational Functions]] (Module 4.1)
+
 
 
||
 
||
* Identify and graph vertical asymptotes
+
Students will be able to:
* Identify and graph horizontal asymptotes
+
* Understand a polynomial expression.
* Determine behavior of rational functions around vertical asymptotes
+
* Recognize characteristics of parabolas.
* Graph rational functions
+
* 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 10
+
|Week 9
 
||
 
||
 
Module 7.1
 
Module 7.1
 
||
 
||
* [[Single Transformations of Functions]]
+
* [[Dividing Polynomials]]
 
||
 
||
* Understanding of [[Functions]] (Module 5)
+
* Basic understanding of [[Fractions]]
* Understanding of [[Function Notation]] (Module 2.1)
+
* Basic understanding of [[Factoring]]
 +
* 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]]  
 +
 
 
||
 
||
* Graph functions using vertical and horizontal shifts
+
Students will be able to:
* Graph functions using reflections about the x-axis and the y-axis
+
* Identify polynomial functions.
* Determine whether a function is even, odd, or neither from it's graph
+
* Identify the degree and leading coefficients of polynomial functions.
* Graph functions using compressions and stretches
+
* Use long division to divide polynomials.
* Combine transformations
+
* Use synthetic division to divide polynomials.
 
|-
 
|-
|Week 10
+
|Week 9
 
||
 
||
 
Module 7.2
 
Module 7.2
 
||
 
||
* [[Multiple Transformations of Functions]]
+
* [[Factoring Polynomials|Zeros of Polynomials]]
 
||
 
||
* Understanding of [[Single Transformations of Functions]] (Module 7.1)
+
* Basic understanding of [[Fractions]]
 +
* Basic understanding of [[Functions]]  
 +
* Basic understanding of [[Dividing Polynomials]]
 
||
 
||
* Combine transformations
+
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 11
+
|Week 10
 
||
 
||
 
Module 8.1
 
Module 8.1
 
||
 
||
* [[Composition of Functions]]
+
* [[Power and Polynomial Functions]]
 
||
 
||
* Understanding of [[Function Notation]] (Module 2.1)
+
* Basic understanding of [[Factoring]]  
* Understanding of [[Functions]] (Module 5)
+
* Basic understanding of [[Quadratic Functions]]  
 +
* Basic understanding of [[Dividing Polynomials]]
 +
* Basic understanding of [[Factoring Polynomials|Zeros of Polynomials]]
 
||
 
||
* Combine functions using algebraic operations
+
Students will be able to:
* Create a new function by composition of functions
+
* Find the average rate of change of a function.
* Evaluate composite functions
+
* Use a graph to determine where a function is increasing, decreasing, or constant.
* Find the domain of a composite function
+
* Use a graph to locate local maxima and local minima.
* Decompose a composite function into its component functions
+
* Use a graph to locate the absolute maximum and absolute minimum.
 +
* Identify end behavior of power functions.
 +
 
 +
 
 +
 
 
|-
 
|-
|Week 11
+
|Week 10
 
||
 
||
 
Module 8.2
 
Module 8.2
 
||
 
||
* [[Inverse Functions]]
+
* [[Graphs of Polynomials]]
 
||
 
||
* Understanding of [[Function Notation]] (Module 2.1)
+
* Basic understanding of [[Dividing Polynomials]]  
* Understanding of [[Functions]] (Module 5)
+
* Basic understanding of [[Factoring Polynomials|Zeros of Polynomials]]  
* 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
+
* Recognize characteristics of graphs of polynomial functions.
* Find or evaluate the inverse of a function
+
* Use [[Factoring]] to find zeros of polynomial functions.
* Use the graph of a one-to-one function to graph its inverse function on the same axes
+
* Identify zeros and their multiplicities.
 +
* Determine end behavior of polynomial functions.
 +
* Understand the relationship between degree and turning points.
 +
* Graph polynomial functions.
 +
 
 
|-
 
|-
|Week 12
+
|Week 11
 
||
 
||
 
Module 9.1
 
Module 9.1
 
||
 
||
* [[Exponential Properties]]
+
* [[Rational Expressions]]
 +
||
 +
* The student understands that zero in the denominator of a fraction is undefined
 +
* Basic understanding of  [[Fractions]]  
 
||
 
||
* Understanding [[Order of Operations]]. (Module 0.1)||
+
Students will be able to:
* Use the product rule for exponents.
+
* Simplify rational expressions.
* Use the quotient rule for exponents.
+
* Multiply rational expressions.
* Use the power rule for logarithms.
+
* Divide rational expressions.
 +
* Add and subtract rational expressions.
 +
 
 
|-
 
|-
|Week 12
+
|Week 11
 
||
 
||
 
Module 9.2
 
Module 9.2
 
||
 
||
* [[Exponential Functions]]
+
* [[Graphs of Rational Functions]]
 
||
 
||
* Understanding the [[Toolkit Functions]] for exponential functions (Module 1)
+
* Basic understanding of [[Rational Expressions]]  
* 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.
+
Students will be able to:
* Find the equation of an exponential function.
+
* Identify and graph vertical asymptotes.
* Use compound interest formulas.
+
* Identify and graph horizontal asymptotes.
* Evaluate exponential functions with base e.
+
* Determine behavior of rational functions around vertical asymptotes.
 +
* Find the domains of rational functions.
 +
* Graph rational functions.
 +
 
 
|-
 
|-
|Week 13
+
|Week 12
 
||
 
||
 
Module 10.1
 
Module 10.1
 
||
 
||
* [[Logarithmic Functions]]
+
* [[Single Transformations of Functions]]
 
||
 
||
* Understanding the [[Toolkit Functions]] for logarithmic functions
+
* Understanding of [[Function Notation]]  
* 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
+
Students will be able to:  
:-y=b^x\equiv\log_b(y)=x
+
* Graph functions using vertical and horizontal shifts.
* Evaluate logarithms.
+
* Graph functions using reflections about the x-axis and the y-axis.
* Use common logarithms.
+
 
* Use natural logarithms.
 
 
|-
 
|-
|Week 13
+
|Week 12
 
||
 
||
 
Module 10.2
 
Module 10.2
 
||
 
||
* [[Logarithmic Properties]]
+
* [[Multiple Transformations of Functions]]
 
||
 
||
* Understanding how to convert between [[Logarithmic Functions|logarithm]] and [[Exponential Functions|exponential]] forms. (Module 9.2 & 10.1)
+
* Understanding of [[Single Transformations of Functions]]  
* Understanding [[Order of Operations]]. (Module 0.1)
 
* Understanding of [[Exponential Properties]] (Module 9.1)
 
 
||
 
||
* Use the product rule for logarithms.
+
Students will be able to:
* Use the quotient rule for logarithms.
+
* Determine whether a function is even, odd, or neither.
* Use the power rule for logarithms.
+
* Graph functions using compressions and stretches.
* Expand logarithmic expressions.
+
* Combine transformations.
* 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
 
 
|}
 
|}

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.