Difference between revisions of "MAT1073"

From Department of Mathematics at UTSA
Jump to navigation Jump to search
(Added Range to prereq of ToolkitFunctions)
m (→‎Topics List: Sinmi A. "Edited Prerequisite for each topic to follow the same format")
 
(52 intermediate revisions by 6 users not shown)
Line 1: Line 1:
 +
= College Algebra for Scientists and Engineers - MAT 1073 =
 +
 +
==Course Catalog==
 +
[https://catalog.utsa.edu/search/?P=MAT%201073 MAT 1073. Algebra for Scientists and Engineers]. (1-4) 3 Credit Hours. (TCCN = MATH 1314).
 +
 +
Prerequisite: Satisfactory performance on a placement examination. This course is designed to prepare the student for [[MAT1093]] Precalculus and [[MAT1214]] Calculus I. Topics may include algebraic expressions; equations; inequalities over the real numbers; relations; functions; polynomial and rational functions; logarithmic and exponential functions; systems of linear equations and inequalities; matrices and determinants; complex numbers; sequences; series binomial expansion; mathematical induction; permutations, and combinations. (Formerly MTC 1073. Credit can be earned for only one of the following: MAT 1073, MTC 1073, [[MAT1063]], MTC 1023, or [[MAT1023]]. NOTE: For the purpose of the Three-Attempt Rule, these courses are considered to be equivalent and additional fees may be charged for the third or subsequent attempt to take any of these courses in any combination.) May apply toward the Core Curriculum requirement in Mathematics. Generally offered: Fall, Spring, Summer. Course Fees: LRC1 $12; LRS1 $45; STSI $21.
  
 
==Topics List==
 
==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
 
||
 
||
* [[OrderOfOperations|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
+
Fundamentals
 
||
 
||
* [[Radicals|Simplifying Radicals]]
+
* [[Fractions]]
||
 
* Basic mathematical symbols and terminology
 
* Basic understanding of order of operations
 
* Basic understanding of exponents and radicals
 
* Basic understanding of factoring polynomials and definition of a factor
 
* Understanding operations with fractions
 
||
 
'''Review the following radical expression concepts:'''
 
* evaluate square roots
 
* use the product rule to simplify square roots
 
* use the quotient rule to simplify square roots
 
* add and subtract square roots
 
|-
 
|Week 1
 
||
 
Module R
 
||
 
* [[SimplifyingExponents|Simplifying Exponents]]
 
 
||
 
||
 
* 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 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
 
||
 
||
* [[FactoringPolynomials|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
+
* 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|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
+
* Basic understanding of [[Algebraic Properties]]
* Basic understanding of factoring
+
* Understanding of the Cartesian coordinate system
 +
 
 
||
 
||
'''Review the following linear equation topics:'''
+
Students will be able to:
* Basic mathematical symbols and terminology
+
* Solve linear equations in one variable.
* solving linear equations in one variable
+
* Determine a linear equation.
* finding a linear equation
+
* Write and interpret a linear equation.
* write and interpret a linear equation
+
* Graph a linear equation.
 
|-
 
|-
|Week 1
+
|Week 3
 
||
 
||
Module R
+
Module 1.2
 
||
 
||
* Solving [[Inequalities|Inequalities]]
+
* [[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]]
 
||
 
||
'''Review the following linear inequality topics:'''
+
Students will be able to:
* use interval notation
+
* Solve systems of equations by graphing.
* use properties of inequalities
+
* Solve systems of equations by substitution.
* solve inequalities in one variable algebraically
+
* 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 1
+
|Week 4
 
||
 
||
Module R
+
Module 2.1
 
||
 
||
* Solving [[Inequalities|Inequalities]]
+
* [[Functions]]
 
||
 
||
* Basic mathematical symbols and terminology
+
* Basic understanding of [[Linear Equations]]  
* Basic arithmetic skills
 
* Basic understanding of order of operations
 
* Basic understanding of factoring
 
||
 
'''Review the following linear inequality topics:'''
 
* use interval notation
 
* use properties of inequalities
 
* solve inequalities in one variable algebraically
 
|-
 
|Week 1
 
||
 
Module R
 
||
 
* [[LinearEquations|Linear Equations]]
 
||
 
* Basic mathematical symbols and terminology
 
* Basic arithmetic skills
 
* Basic understanding of order of operations
 
* Basic understanding of factoring
 
* Basic understanding of solving simple equations
 
||
 
* Solving and constructing [[LinearEquations|Linear Equations]]
 
|-
 
|Week 1
 
||
 
Module R
 
||
 
* [[Graphs|Graphs]]
 
||
 
* Basic mathematical symbols and terminology
 
* Basic arithmetic skills
 
* Basic understanding of order of operations
 
* Basic understanding of factoring
 
* Basic understanding of solving [[LinearEquations|Linear Equations]]
 
* Understanding of the Cartesian coordinate system
 
||
 
* Being able to graph a [[LinearEquations|Linear Equations]]
 
|-
 
|Week 2
 
||
 
Module 1.1
 
||
 
* [[Functions|Functions]]
 
||
 
* Basic understanding of [[LinearEquations|Linear Equations]]
 
* Basic understanding of [[Equations|Equations]]
 
 
||
 
||
 +
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
 
||
 
||
* [[FunctionNotation|Function Notation]]
+
* [[Function Notation]]
 
||
 
||
* Basic understanding of [[LinearEquations|Linear Equations]]
+
* Basic understanding of [[Functions]]  
* Basic understanding of [[Equations|Equations]]
 
* Basic understanding of [[Graphs|Graphs]]
 
 
||
 
||
* Find the value of a [[Functions|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 [[Inequalities|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
 
||
 
Module 1.2
 
||
 
* [[Range|Range]] of a Function
 
||
 
* Basic understanding of interval notation (Module R [[Inequalities|Inequalities]])
 
||
 
* Find the domain of a function defined by an equation.
 
* Graph piecewise-defined functions.
 
 
|-
 
|-
|Week 2
+
|Week 4
 
||
 
||
Module 1.2
+
Module 2.2
 
||
 
||
* [[ToolkitFunctions|Toolkit Functions]]
+
* [[Range of a Function]]
 
||
 
||
* Basic understanding of Cartesian coordinate system (Module R [[Graphs|Graphs]])
+
* An understanding of [[Function Notation]]
* Basic understanding of interval notation (Module R [[Inequalities|Inequalities]])
 
 
||
 
||
* Identify the basic toolkit functions
+
Students will be able to:
* Determine [[Domain|Domain]] and [[Range|Range]] for the basic toolkit functions (Module 1.2)
+
* Find the range of a function defined by an equation.
* [[Graphs|Graph]] the basic toolkit functions. (Module R)
 
 
|-
 
|-
|
+
|Week 4
 
||
 
||
2
+
Module 2.2
 
||
 
||
Intro to:
+
* [[Toolkit Functions]]
* [[PowerFunctions|Power]]
 
* [[PolynomialFunctions|Polynomial Functions]]
 
 
||
 
||
edit soon
+
* Basic understanding of [[Functions]]
 
||
 
||
* Identify power functions
+
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.
  
* Identify polynomial functions
 
 
|-
 
|-
|
+
|Week 5
 
||
 
||
2
+
Module 3.1
 
||
 
||
* [[QuadraticFunctions|Quadratic Functions]]
+
* [[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]]
 
||
 
||
* Recognize characteristics of parabolas
+
Students will be able to:
 
+
* Combine functions using [[Algebraic Properties]].
* Understand how the graph of a parabola is related to its quadratic function
+
* Create a new function by composition of functions.
 
+
* Evaluate composite functions.
* Determine a quadratic function's minimum or maximum value
+
* Find the domain of a composite function.
 
+
* Decompose a composite function into its component functions.
* Solve problems involving a quadratic function's minimum or maximum value
 
 
|-
 
|-
|
+
|Week 5
 
||
 
||
3
+
Module 3.2
 
||
 
||
* [[DividingPolynomials|Dividing Polynomials]]
+
* [[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]]
 
||
 
||
* Use long division to divide polynomials
+
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.
  
* Use synthetic division to divide polynomials
 
 
|-
 
|-
|
+
|Week 6
 
||
 
||
3
+
Module 4.1
 
||
 
||
* [[ZerosOfPolynomials|Zeros of Polynomials]]
+
* [[Exponential Properties]]
 
||
 
||
edit soon
+
* Basic mathematical symbols and terminology
 +
* Basic arithmetic skills
 +
* Basic understanding of [[Algebraic Properties]]
 
||
 
||
* Evaluate a polynomial using the Remainder Theorem
+
Students will be able to:
 
+
* Use the product rule for exponents.
* Use the Factor Theorem to solve a polynomial equation
+
* Use the quotient rule for exponents.
 
+
* Use the power rule for exponents.
* Use the Rational Zero Theorem to find rational zeros
 
 
 
* Find zeros of a polynomial function
 
 
 
* Solve real-world applications of polynomial equations
 
 
|-
 
|-
|
+
|Week 6
 
||
 
||
3
+
Module 4.2
 
||
 
||
* More [[PolynomialFunctions|Polynomial Functions]]
+
* [[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]]
 
||
 
||
* Identify end behavior of power 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.
  
* Identify the degree and leading coefficient of polynomial functions
 
 
|-
 
|-
|
+
|Week 7
 
||
 
||
4
+
Module 5.1
 
||
 
||
* [[RationalFunctions|Rational Functions]]
+
* [[Logarithmic Properties]]
 
||
 
||
edit soon
+
* Basic understanding of [[Exponential Properties]]
 
||
 
||
* Use arrow notation
+
Students will be to able to:
 
+
* Rewrite from exponential form to logarithmic form and vice versa.
* Solve applied problems involving rational functions
+
* Use the product rule for logarithms.
 
+
* Use the quotient rule for logarithms.
* Find the domains of rational functions
+
* Use the power rule for logarithms.
 
+
* Expand logarithmic expressions.
* Identify vertical asymptotes
+
* Condense logarithmic expressions.
 +
* Use the change-of-base formula for logarithms.
  
* Identify horizontal asymptotes
 
 
|-
 
|-
|
+
|Week 7
 
||
 
||
5
+
Module 5.2
 
||
 
||
* Graphs of [[Polynomials|Polynomials]]
+
* [[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]]
 +
 
 
||
 
||
* Recognize characteristics of graphs of polynomial functions
+
Students will be able to:
 
+
* Evaluate logarithms.
* Use factoring to find zeros of polynomial functions
+
* Use common logarithms.
 
+
* Use natural logarithms.
* Identify zeros and their multiplicities
+
* Graph logarithmic functions.
 
 
* Determine end behavior
 
 
 
* Understand the relationship between degree and turning points
 
  
* Graph polynomial functions
 
 
|-
 
|-
|
+
|Week 8
 
||
 
||
5
+
Module 6.2
 
||
 
||
* Graphs of [[RationalFunctions|Rational Functions]]
+
* [[Quadratic Equations]]
 
||
 
||
edit soon
+
* Basic arithmetic skills
 +
* Basic understanding of [[Algebraic Properties]]
 +
* Basic understanding of [[Factoring]]
 
||
 
||
* Identify and graph vertical asymptotes
+
Students will be able to:
 
+
* Determine complex number solutions.
* Identify and graph horizontal asymptotes
+
* Determine solutions of quadratic equations using factoring techniques.
 
+
* Determine solutions of quadratic equations using Quadratic Formula.
* Determine behavior of rational functions around vertical asymptotes
 
  
* Graph rational functions
 
 
|-
 
|-
|
+
|Week 8
 
||
 
||
6
+
Module 6.2
 
||
 
||
* [[Transformation|Transformation]]
+
* [[Quadratic Functions]]
 
||
 
||
edit soon
+
* Basic understanding of [[Quadratic Equations]]
 +
 
 
||
 
||
* Graph functions using vertical and horizontal shifts
+
Students will be able to:
 
+
* Understand a polynomial expression.
* Graph functions using reflections about the x-axis and the y-axis
+
* Recognize characteristics of parabolas.
 
+
* Understand how the graph of a parabola is related to its quadratic function.
* Determine whether a function is even, odd, or neither from it's graph
+
* Determine a quadratic function's minimum or maximum value.
 +
* Solve problems involving a quadratic function's minimum or maximum value.
  
* Graph functions using compressions and stretches
 
  
* Combine transformations
 
 
|-
 
|-
|
+
|Week 9
 
||
 
||
7
+
Module 7.1
 
||
 
||
* [[CompositionOfFunctions|Composition of Functions]]
+
* [[Dividing Polynomials]]
 
||
 
||
edit soon
+
* Basic understanding of  [[Fractions]]
||
+
* Basic understanding of [[Factoring]]
* Combine functions using algebraic operations
+
* 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]]
  
* 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
 
|-
 
|
 
||
 
7
 
||
 
* [[InverseFunctions|Inverse Functions]]
 
||
 
edit soon
 
 
||
 
||
* Verify inverse functions
+
Students will be able to:
 
+
* Identify polynomial functions.
* Determine the domain and range of an inverse function, and restrict the domain of a function to make it one-to-one
+
* Identify the degree and leading coefficients of polynomial functions.
 
+
* Use long division to divide polynomials.
* Find or evaluate the inverse of a function
+
* Use synthetic division to divide polynomials.
 
 
* Use the graph of a one-to-one function to graph its inverse function on the same axes
 
 
|-
 
|-
|
+
|Week 9
 
||
 
||
8
+
Module 7.2
 
||
 
||
* [[ExponentialFunctions|Exponential Functions]]
+
* [[Factoring Polynomials|Zeros of Polynomials]]
 
||
 
||
edit soon
+
* Basic understanding of  [[Fractions]]
 +
* Basic understanding of [[Functions]]
 +
* Basic understanding of [[Dividing Polynomials]]
 
||
 
||
* Evaluate exponential functions
+
Students will be able to:
 
+
* Evaluate a polynomial using the Remainder Theorem.
* Find the equation of an exponential function
+
* Use the Factor Theorem to solve a polynomial equation.
 
+
* Use the Rational Zero Theorem to find rational zeros.
* Use compound interest formulas
+
* Find zeros of a polynomial function.
 +
* Solve real-world applications of polynomial equations.
  
* Evaluate exponential functions with base e
 
 
|-
 
|-
|
+
|Week 10
 
||
 
||
8
+
Module 8.1
 
||
 
||
* [[LogarithmicFunctions|Logarithmic Functions]]
+
* [[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]]
 
||
 
||
* Convert from logarithmic to exponential form
+
Students will be able to:
 
+
* Find the average rate of change of a function.
* Convert from exponential to logarithmic form
+
* 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.
  
* Evaluate logarithms
 
  
* Use common logarithms
 
  
* Use natural logarithms
 
 
|-
 
|-
|
+
|Week 10
 
||
 
||
9
+
Module 8.2
 
||
 
||
* [[LogarithmicProperties|Logarithmic Properties]]
+
* [[Graphs of Polynomials]]
 
||
 
||
edit soon
+
* Basic understanding of [[Dividing Polynomials]]
 +
* Basic understanding of [[Factoring Polynomials|Zeros of Polynomials]]
 
||
 
||
* Use the product rule for logarithms
+
Students will be able to:
 
+
* Recognize characteristics of graphs of polynomial functions.
* Use the quotient rule for logarithms
+
* Use [[Factoring]] to find zeros of polynomial functions.
 
+
* Identify zeros and their multiplicities.
* Use the power rule for logarithms
+
* Determine end behavior of polynomial functions.
 
+
* Understand the relationship between degree and turning points.
* Expand logarithmic expressions
+
* Graph polynomial functions.
 
 
* Condense logarithmic expressions
 
  
* Use the change-of-base formula for logarithms
 
 
|-
 
|-
|
+
|Week 11
 
||
 
||
9
+
Module 9.1
 
||
 
||
* [[ExponentialEquations|Exponential]]
+
* [[Rational Expressions]]
* [[LogarithmicEquations|Logarithmic Equations]]
 
 
||
 
||
edit soon
+
* The student understands that zero in the denominator of a fraction is undefined
 +
* Basic understanding of  [[Fractions]]
 
||
 
||
* Use like bases to solve exponential equations
+
Students will be able to:
 
+
* Simplify rational expressions.
* Use logarithms to solve exponential equations
+
* Multiply rational expressions.
 
+
* Divide rational expressions.
* Use the definition of a logarithm to solve logarithmic equations
+
* Add and subtract rational expressions.
 
 
* Use the one-to-one property of logarithms to solve logarithmic equations
 
  
* Solve applied problems involving exponential and logarithmic equations
 
 
|-
 
|-
|
+
|Week 11
 
||
 
||
10
+
Module 9.2
 
||
 
||
* [[ExponentialModels|Exponential]]
+
* [[Graphs of Rational Functions]]
* [[LogarithmicModels|Logarithmic Models]]
 
 
||
 
||
edit soon
+
* Basic understanding of [[Rational Expressions]]
 
||
 
||
* Model exponential growth and decay
+
Students will be able to:
 
+
* Identify and graph vertical asymptotes.
* Use Newton's Law of Cooling
+
* Identify and graph horizontal asymptotes.
 
+
* Determine behavior of rational functions around vertical asymptotes.
* Use logistic-growth models
+
* Find the domains of rational functions.
 
+
* Graph rational functions.
* Choose an appropriate model for data
 
  
* Express an exponential model in base e
 
 
|-
 
|-
|
+
|Week 12
 
||
 
||
11
+
Module 10.1
 
||
 
||
* [[ModelingUsingVariation|Modeling using Variation]]
+
* [[Single Transformations of Functions]]
 
||
 
||
edit soon
+
* Understanding of [[Function Notation]]
 
||
 
||
* Solve direct variation problems
+
Students will be able to:
 
+
* Graph functions using vertical and horizontal shifts.
* Solve inverse variation problems
+
* Graph functions using reflections about the x-axis and the y-axis.
  
* Solve problems involving joint variation
 
 
|-
 
|-
|
+
|Week 12
 
||
 
||
12
+
Module 10.2
 
||
 
||
* Solving [[SystemsOfEquations|Systems of Equations]] in Two Variables
+
* [[Multiple Transformations of Functions]]
 
||
 
||
edit soon
+
* Understanding of [[Single Transformations of Functions]]
 
||
 
||
* Solve systems of equations by graphing
+
Students will be able to:
 
+
* Determine whether a function is even, odd, or neither.
* Solve systems of equations by substitution
+
* Graph functions using compressions and stretches.
 
+
* Combine transformations.
* 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
 
|-
 
|
 
||
 
12
 
||
 
* Solving [[SystemsOfEquations|Systems of Equations]] in Three Variables
 
||
 
edit soon
 
||
 
* 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.