Difference between revisions of "MAT1073"

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= College Algebra for Scientists and Engineers - MAT 1073 =
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==Course Catalog==
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[https://catalog.utsa.edu/search/?P=MAT%201073 MAT 1073. Algebra for Scientists and Engineers]. (1-4) 3 Credit Hours. (TCCN = MATH 1314).
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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==
 
==Topics List==
 
{| class="wikitable sortable"
 
{| class="wikitable sortable"
! Date !! Sections !! Topics !! Prerequisite Skills !! Student Learning Outcomes !! Examples/Activities
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! Week !! Sections !! Topics !! Prerequisite Skills !! Student Learning Outcomes
 
|-                 
 
|-                 
|
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|Week 1
 +
||
 +
Fundamentals
 
||
 
||
R
+
* [[Algebraic Properties]]
 
||
 
||
[[OrderOfOperations|Order of Operations]] and [[Radicals|Simplifying Radicals]] ||
+
* Basic mathematical symbols and terminology
Basic mathematical symbols and terminology
+
* Basic arithmetic skills
  
Basic arithmetic skills
+
||
 
+
Students will be able to correctly identify the algebraic properties:
Basic prime factorization
+
* Additive & Multiplicative identity
 
+
* Additive & Multiplicative inverse
Basic understanding of order of operations
+
* Commutative property
 +
* Associative property
 +
* Distributive property
  
Basic understanding of radicals
 
||
 
Review order of operations
 
  
Review the following radical expression concepts:
+
Students will be able to correctly explain the algebraic properties of numbers and correctly apply these properties in procedural explanations of:
* evaluate square roots
+
* Solving mathematical equations
* use the product rule to simplify square roots
+
* Simplifying/evaluating mathematical expressions
* use the quotient rule to simplify square roots
 
* add and subtract square roots
 
||
 
Edit soon
 
 
|-
 
|-
|
+
|Week 2
 
||
 
||
R
+
Fundamentals
 
||
 
||
[[SimplifyingExponents|Simplifying Exponents]] and [[FactoringPolynomials|Factoring Polynomials]]
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* [[Fractions]]
 
||
 
||
Basic mathematical symbols and terminology
+
* Basic mathematical symbols and terminology
 
+
* Basic arithmetic skills
Basic arithmetic skills
+
* Basic understanding of [[Algebraic Properties]]
 
 
Basic prime factorization
 
  
Basic understanding of order of operations
 
  
Basic understanding of exponents
 
 
Basic understanding of factoring
 
 
||
 
||
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
 
  
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
 
||
 
edit soon
 
 
|-
 
|-
|
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|Week 2
 
||
 
||
R
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Fundamentals
 
||
 
||
Solving [[Equations|Equations]] and [[Inequalities|Inequalities]]
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* [[Factoring]]
 
||
 
||
Basic mathematical symbols and terminology
+
* Basic mathematical symbols and terminology
 
+
* Basic arithmetic skills  
Basic arithmetic skills
+
* Basic understanding of [[Algebraic Properties]]
 
 
Basic prime factorization
 
  
Basic understanding of order of operations
 
  
Basic understanding of exponents
 
 
Basic understanding of factoring
 
 
||
 
||
Review the following linear equation topics:
+
Students will be able to:  
solving linear equations in one variable
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* Identify factored vs non-factored forms of a polynomial.
finding a linear equation
+
* Successfully factor binomials & trinomials and difference of squares into two binomial terms.
write and interpret a linear equation
+
* Factor out GCF.
 +
* Multiply and/or distribute to check their factors are correct.
 +
* Differentiate between factors and terms of a polynomial expression.
  
Review the following linear inequality topics:
 
use interval notation
 
use properties of inequalities
 
solve inequalities in one variable algebraically
 
||
 
Edit soon
 
 
|-
 
|-
|
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|Week 3
 
||
 
||
R
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Module 1.1
 
||
 
||
[[LinearEquations|Linear Equations]] and [[Graphs|Graphs]]
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* [[Linear Equations]]
 
||
 
||
Basic mathematical symbols and terminology
+
* Basic mathematical symbols and terminology
 
+
* Basic arithmetic skills  
Basic arithmetic skills
+
* Basic understanding of [[Algebraic Properties]]
 
+
* Understanding of the Cartesian coordinate system
Basic understanding of order of operations
 
 
 
Basic understand of a Cartesian Coordinate System
 
  
Basic understand of graphing ordered pairs
 
||
 
Review the following linear equation topics:
 
graph a linear equation
 
 
||
 
||
edit soon
+
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.
 
|-
 
|-
|
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|Week 3
 
||
 
||
1
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Module 1.2
 
||
 
||
[[Functions|Functions]] and [[FunctionNotation|Function Notation]]
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* [[Systems of Equations in Two Variables]]
 
||
 
||
edit soon
+
* Basic mathematical symbols and terminology
 +
* Basic arithmetic skills
 +
* Basic understanding of [[Algebraic Properties]]
 +
* Basic understanding of [[Linear Equations]]
 
||
 
||
Determine whether a relation represents a function
+
Students will be able to:
 
+
* Solve systems of equations by graphing.
Find the value of a function
+
* Solve systems of equations by substitution.
 
+
* Solve systems of equations by elimination.
Determine whether a function is one-to-one
+
* Identify inconsistent systems of equations containing two variables.
 
+
* Express the solution of a system of dependent equations containing two variables.
Use the vertical line test to identify functions
 
||
 
edit soon
 
 
|-
 
|-
|
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|Week 4
||
 
1
 
 
||
 
||
[[Domain|Domain]] and [[Range|Range]]
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Module 2.1
 
||
 
||
edit soon
+
* [[Functions]]
 
||
 
||
Find the domain and range of a function defined by an equation
+
* Basic understanding of [[Linear Equations]]
 
||
 
||
edit soon
+
Students will be able to:
 +
* Determine whether a relation represents a function.
 
|-
 
|-
|
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|Week 4
||
 
1
 
 
||
 
||
[[ToolkitFunctions|Toolkit Functions]]
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Module 2.2
 
||
 
||
edit soon
+
* [[Function Notation]]
 
||
 
||
Identify the basic toolkit functions
+
* Basic understanding of [[Functions]]
 
 
Determine domain and range for the basic toolkit functions
 
 
 
Graph the basic toolkit functions
 
 
||
 
||
edit soon
+
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.
 
|-
 
|-
|
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|Week 4
 
||
 
||
2
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Module 2.2
 
||
 
||
Intro to [[PowerFunctions|Power]] and [[PolynomialFunctions|Polynomial Functions]]
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* [[Domain of a Function]]
 
||
 
||
edit soon
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* An understanding of [[Function Notation]]
 
||
 
||
Identify power functions
+
Students will be able to:
 +
* Find the domain of a function defined by an equation.
  
Identify polynomial functions
 
||
 
edit soon
 
 
|-
 
|-
|
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|Week 4
 
||
 
||
2
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Module 2.2
 
||
 
||
[[QuadraticFunctions|Quadratic Functions]]
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* [[Range of a Function]]
 
||
 
||
edit soon
+
* An understanding of [[Function Notation]]
||
 
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
 
 
||
 
||
edit soon
+
Students will be able to:
 +
* Find the range of a function defined by an equation.
 
|-
 
|-
|
+
|Week 4
 
||
 
||
3
+
Module 2.2
 
||
 
||
[[DividingPolynomials|Dividing Polynomials]]
+
* [[Toolkit Functions]]
 
||
 
||
edit soon
+
* Basic understanding of [[Functions]]
 
||
 
||
Use long division to divide polynomials
+
Students will be able to:
 +
* Identify the basic toolkit functions.
 +
* Determine [[Domain of a Function|Domain]] and [[Range of a Function| Range]] for the basic toolkit functions.
  
Use synthetic division to divide polynomials
 
||
 
edit soon
 
 
|-
 
|-
|
+
|Week 5
 
||
 
||
3
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Module 3.1
 
||
 
||
[[ZerosOfPolynomials|Zeros of Polynomials]]
+
* [[Composition of Functions]]
 
||
 
||
edit soon
+
* Basic understanding of [[Functions]]
 +
* Basic understanding of [[Function Notation]]
 +
* Basic understanding of [[Domain of a Function|Domain]] and [[Range of a Function| Range]]
 
||
 
||
Evaluate a polynomial using the Remainder Theorem
+
Students will be able to:
 
+
* Combine functions using [[Algebraic Properties]].
Use the Factor Theorem to solve a polynomial equation
+
* Create a new function by composition of functions.
 
+
* Evaluate composite functions.
Use the Rational Zero Theorem to find rational zeros
+
* Find the domain of a composite function.
 
+
* Decompose a composite function into its component functions.
Find zeros of a polynomial function
 
 
 
Solve real-world applications of polynomial equations
 
||
 
edit soon
 
 
|-
 
|-
|
+
|Week 5
 
||
 
||
3
+
Module 3.2
 
||
 
||
More [[PolynomialFunctions|Polynomial Functions]]
+
* [[Inverse Functions]]
 
||
 
||
edit soon
+
* Basic understanding of [[Functions]]
 +
* Basic understanding of [[Function Notation]]
 +
* Basic understanding of [[Domain of a Function|Domain]] and [[Range of a Function| Range]]
 +
* Basic understanding of [[Composition of Functions]]
 
||
 
||
Identify end behavior of power functions
+
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.
  
Identify the degree and leading coefficient of polynomial functions
 
||
 
edit soon
 
 
|-
 
|-
|
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|Week 6
 
||
 
||
4
+
Module 4.1
 
||
 
||
[[RationalFunctions|Rational Functions]]
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* [[Exponential Properties]]
 
||
 
||
edit soon
+
* Basic mathematical symbols and terminology
 +
* Basic arithmetic skills
 +
* Basic understanding of [[Algebraic Properties]]
 
||
 
||
Use arrow notation
+
Students will be able to:
 
+
* Use the product rule for exponents.
Solve applied problems involving rational functions
+
* Use the quotient rule for exponents.
 
+
* Use the power rule for exponents.
Find the domains of rational functions
 
 
 
Identify vertical asymptotes
 
 
 
Identify horizontal asymptotes
 
||
 
edit soon
 
 
|-
 
|-
|
+
|Week 6
 
||
 
||
5
+
Module 4.2
 
||
 
||
Graphs of [[Polynomials|Polynomials]]
+
* [[Exponential Functions]]
 
||
 
||
edit soon
+
* Understanding the [[Domain of a Function|Domain]] and [[Range of a Function| Range]] of the [[Toolkit Functions]] for exponential functions
 +
* Basic understanding of [[Exponential Properties]]
 
||
 
||
Recognize characteristics of graphs of polynomial functions
+
Students will be able to:
 +
* Determine the difference between [[Linear Equations|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.
  
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
 
||
 
edit soon
 
 
|-
 
|-
|
+
|Week 7
 
||
 
||
5
+
Module 5.1
 
||
 
||
Graphs of [[RationalFunctions|Rational Functions]]
+
* [[Logarithmic Properties]]
 
||
 
||
edit soon
+
* Basic understanding of [[Exponential Properties]]
 
||
 
||
Identify and graph vertical asymptotes
+
Students will be to able to:
 
+
* Rewrite from exponential form to logarithmic form and vice versa.
Identify and graph horizontal asymptotes
+
* Use the product rule for logarithms.
 
+
* Use the quotient rule for logarithms.
Determine behavior of rational functions around vertical asymptotes
+
* Use the power rule for logarithms.
 +
* Expand logarithmic expressions.
 +
* Condense logarithmic expressions.
 +
* Use the change-of-base formula for logarithms.
  
Graph rational functions
 
||
 
edit soon
 
 
|-
 
|-
|
+
|Week 7
 
||
 
||
6
+
Module 5.2
 
||
 
||
[[Transformation|Transformation]]
+
* [[Logarithmic Functions]]
 
||
 
||
edit soon
+
* Basic understanding of [[Inverse Functions]]
 +
* Understanding the [[Domain of a Function|Domain]] and [[Range of a Function| Range]] of [[Toolkit Functions]] for logarithmic functions
 +
* Basic understanding of [[Exponential Properties]]
 +
 
 
||
 
||
Graph functions using vertical and horizontal shifts
+
Students will be able to:
 
+
* Evaluate logarithms.
Graph functions using reflections about the x-axis and the y-axis
+
* Use common logarithms.
 +
* Use natural logarithms.
 +
* Graph logarithmic functions.
  
Determine whether a function is even, odd, or neither from it's graph
 
 
Graph functions using compressions and stretches
 
 
Combine transformations
 
||
 
edit soon
 
 
|-
 
|-
|
+
|Week 8
 
||
 
||
7
+
Module 6.2
 
||
 
||
[[CompositionOfFunctions|Composition of Functions]]
+
* [[Quadratic Equations]]
 
||
 
||
edit soon
+
* Basic arithmetic skills
 +
* Basic understanding of [[Algebraic Properties]]
 +
* Basic understanding of [[Factoring]]
 
||
 
||
Combine functions using algebraic operations
+
Students will be able to:
 
+
* Determine complex number solutions.
Create a new function by composition of functions
+
* Determine solutions of quadratic equations using factoring techniques.
 
+
* Determine solutions of quadratic equations using Quadratic Formula.
Evaluate composite functions
 
 
 
Find the domain of a composite function
 
  
Decompose a composite function into its component functions
 
||
 
edit soon
 
 
|-
 
|-
|
+
|Week 8
 
||
 
||
7
+
Module 6.2
 
||
 
||
[[InverseFunctions|Inverse Functions]]
+
* [[Quadratic Functions]]
 
||
 
||
edit soon
+
* Basic understanding of [[Quadratic Equations]]
 +
 
 
||
 
||
Verify inverse functions
+
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.
  
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
 
||
 
edit soon
 
 
|-
 
|-
|
+
|Week 9
 
||
 
||
8
+
Module 7.1
 
||
 
||
[[ExponentialFunctions|Exponential Functions]]
+
* [[Dividing Polynomials]]
 
||
 
||
edit soon
+
* Basic understanding of  [[Fractions]]
||
+
* Basic understanding of [[Factoring]]
Evaluate exponential 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]]
 
+
* Basic understanding of [[Quadratic Functions]]
Find the equation of an exponential function
 
 
 
Use compound interest formulas
 
  
Evaluate exponential functions with base e
 
 
||
 
||
edit soon
+
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
 
||
 
||
8
+
Module 7.2
 
||
 
||
[[LogarithmicFunctions|Logarithmic Functions]]
+
* [[Factoring Polynomials|Zeros of Polynomials]]
 
||
 
||
edit soon
+
* Basic understanding of  [[Fractions]]
 +
* Basic understanding of [[Functions]]
 +
* Basic understanding of [[Dividing Polynomials]]
 
||
 
||
Convert from logarithmic to exponential form
+
Students will be able to:
 
+
* Evaluate a polynomial using the Remainder Theorem.
Convert from exponential to logarithmic form
+
* Use the Factor Theorem to solve a polynomial equation.
 
+
* Use the Rational Zero Theorem to find rational zeros.
Evaluate logarithms
+
* Find zeros of a polynomial function.
 
+
* Solve real-world applications of polynomial equations.
Use common logarithms
 
  
Use natural logarithms
 
||
 
edit soon
 
 
|-
 
|-
|
+
|Week 10
 
||
 
||
9
+
Module 8.1
 
||
 
||
[[LogarithmicProperties|Logarithmic Properties]]
+
* [[Power and Polynomial Functions]]
 
||
 
||
edit soon
+
* Basic understanding of [[Factoring]]
 +
* Basic understanding of [[Quadratic Functions]]
 +
* Basic understanding of [[Dividing Polynomials]]
 +
* Basic understanding of [[Factoring Polynomials|Zeros of Polynomials]]
 
||
 
||
Use the product rule for logarithms
+
Students will be able to:
 
+
* Find the average rate of change of a function.
Use the quotient rule for logarithms
+
* Use a graph to determine where a function is increasing, decreasing, or constant.
 
+
* Use a graph to locate local maxima and local minima.
Use the power rule for logarithms
+
* Use a graph to locate the absolute maximum and absolute minimum.
 +
* Identify end behavior of power functions.
  
Expand logarithmic expressions
 
  
Condense logarithmic expressions
 
  
Use the change-of-base formula for logarithms
 
||
 
edit soon
 
 
|-
 
|-
|
+
|Week 10
 
||
 
||
9
+
Module 8.2
 
||
 
||
[[ExponentialEquations|Exponential]] and [[LogarithmicEquations|Logarithmic Equations]]
+
* [[Graphs of Polynomials]]
 
||
 
||
edit soon
+
* Basic understanding of [[Dividing Polynomials]]
 +
* Basic understanding of [[Factoring Polynomials|Zeros of Polynomials]]
 
||
 
||
Use like bases to solve exponential equations
+
Students will be able to:
 
+
* Recognize characteristics of graphs of polynomial functions.
Use logarithms to solve exponential equations
+
* Use [[Factoring]] to find zeros of polynomial functions.
 
+
* Identify zeros and their multiplicities.
Use the definition of a logarithm to solve logarithmic equations
+
* Determine end behavior of polynomial functions.
 
+
* Understand the relationship between degree and turning points.
Use the one-to-one property of logarithms to solve logarithmic equations
+
* Graph polynomial functions.
  
Solve applied problems involving exponential and logarithmic equations
 
||
 
edit soon
 
 
|-
 
|-
|
+
|Week 11
 
||
 
||
10
+
Module 9.1
 
||
 
||
[[ExponentialModels|Exponential]] and [[LogarithmicModels|Logarithmic Models]]
+
* [[Rational Expressions]]
 
||
 
||
edit soon
+
* The student understands that zero in the denominator of a fraction is undefined
 +
* Basic understanding of  [[Fractions]]
 
||
 
||
Model exponential growth and decay
+
Students will be able to:
 +
* Simplify rational expressions.
 +
* Multiply rational expressions.
 +
* Divide rational expressions.
 +
* Add and subtract rational expressions.
  
Use Newton's Law of Cooling
 
 
Use logistic-growth models
 
 
Choose an appropriate model for data
 
 
Express an exponential model in base e
 
||
 
edit soon
 
 
|-
 
|-
|
+
|Week 11
 
||
 
||
11
+
Module 9.2
 
||
 
||
[[ModelingUsingVariation|Modeling using Variation]]
+
* [[Graphs of Rational Functions]]
 
||
 
||
edit soon
+
* Basic understanding of [[Rational Expressions]]
 
||
 
||
Solve direct variation problems
+
Students will be able to:
 
+
* Identify and graph vertical asymptotes.
Solve inverse variation problems
+
* Identify and graph horizontal asymptotes.
 +
* Determine behavior of rational functions around vertical asymptotes.
 +
* Find the domains of rational functions.
 +
* Graph rational functions.
  
Solve problems involving joint variation
 
||
 
edit soon
 
 
|-
 
|-
|
+
|Week 12
 
||
 
||
12
+
Module 10.1
 
||
 
||
Solving [[SystemsOfEquations|Systems of Equations]] in Two Variables
+
* [[Single Transformations of Functions]]
 
||
 
||
edit soon
+
* Understanding of [[Function Notation]]
 
||
 
||
Solve systems of equations by graphing
+
Students will be able to:
 +
* Graph functions using vertical and horizontal shifts.
 +
* Graph functions using reflections about the x-axis and the y-axis.
  
Solve systems of equations by substitution
 
 
Solve system of equations by elimination
 
 
Identity inconsistent systems of equations containing two variables
 
 
Express the solution of a system of dependent equations containing two variables
 
||
 
edit soon
 
 
|-
 
|-
|
+
|Week 12
 
||
 
||
12
+
Module 10.2
 
||
 
||
Solving [[SystemsOfEquations|Systems of Equations]] in Three Variables
+
* [[Multiple Transformations of Functions]]
 
||
 
||
edit soon
+
* Understanding of [[Single Transformations of Functions]]
 
||
 
||
Solve systems of equations in three varaibles
+
Students will be able to:
 +
* Determine whether a function is even, odd, or neither.
 +
* Graph functions using compressions and stretches.
 +
* Combine transformations.
 +
 
  
Identify inconsistent systems of equations containing three variables
 
  
Express solutions of a system of dependent equations containing three variables
 
||
 
edit soon
 
 
|}
 
|}

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.