Difference between revisions of "MAT1073"

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Students will be able to:
 
* Solving linear equations in one variable
 
* Solving linear equations in one variable
 
* Determine a linear equation
 
* Determine a linear equation
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* Basic understanding of [[Linear Equations]] (Module 1.1)
 
* Basic understanding of [[Linear Equations]] (Module 1.1)
 
||
 
||
 +
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.
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* Basic understanding of [[Linear Equations]] (Module 0.4)
 
* Basic understanding of [[Linear Equations]] (Module 0.4)
 
||
 
||
 +
Students will be able to:
 
* Determine whether a relation represents a function.
 
* Determine whether a relation represents a function.
 
|-
 
|-
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* Basic understanding of [[Functions]] (Module 2.1)
 
* Basic understanding of [[Functions]] (Module 2.1)
 
||
 
||
 +
Students will be able to:
 
* Find the value of a [[Functions]]
 
* Find the value of a [[Functions]]
 
* Graph the functions listed in the library of functions.
 
* Graph the functions listed in the library of functions.
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* An understanding of [[Function Notation]]
 
* 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.
  
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* An understanding of [[Function Notation]]
 
* An understanding of [[Function Notation]]
 
||
 
||
 +
Students will be able to:
 
* Find the range of a function defined by an equation.
 
* Find the range of a function defined by an equation.
 
|-
 
|-
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* Basic understanding of [[Functions]] (Module 2.1)
 
* Basic understanding of [[Functions]] (Module 2.1)
 
||
 
||
 +
Students will be able to:
 
* Identify the basic toolkit functions
 
* Identify the basic toolkit functions
 
* Determine [[Domain of a Function|Domain]] and [[Range of a Function| Range]] for the basic toolkit functions (Module 2.2)
 
* Determine [[Domain of a Function|Domain]] and [[Range of a Function| Range]] for the basic toolkit functions (Module 2.2)
 +
 +
|-
 +
|Week 5
 +
||
 +
Module 3.1
 +
||
 +
* [[Composition of Functions]]
 +
||
 +
* Basic understanding of [[Functions]] (Module 2.1)
 +
* Basic understanding of [[Function Notation]] (Module 2.2)
 +
* Basic understanding of [[Domain of a Function|Domain]] and [[Range of a Function| Range]] (Module 2.2)
 +
||
 +
Students will be able to:
 +
* Combine functions using algebraic operations
 +
* Create a new function by composition of functions
 +
* Evaluate composite functions
 +
* Find the domain of a composite function
 +
* Decompose a composite function into its component functions
 +
|-
 +
|Week 5
 +
||
 +
Module 3.2
 +
||
 +
* [[Inverse Functions]]
 +
||
 +
* Basic understanding of [[Functions]] (Module 2.1)
 +
* Basic understanding of [[Function Notation]] (Module 2.2)
 +
* Basic understanding of [[Domain of a Function|Domain]] and [[Range of a Function| Range]] (Module 2.2)
 +
* Basic understanding of [[Composition of Functions]] (Module 3.1)
 +
||
 +
* Verify inverse functions
 +
* Determine the domain and range of an inverse function, and restrict the domain of a function to make it one-to-one
 +
* Find or evaluate the inverse of a function
 +
* Use the graph of a one-to-one function to graph its inverse function on the same axes
 +
 +
|-
 +
|Week 6
 +
||
 +
Module 4.1
 +
||
 +
* [[Exponential Properties]]
 +
||
 +
* 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
 +
||
 +
* [[Exponential Functions]]
 +
||
 +
* Understanding the [[Domain of a Function|Domain]] and [[Range of a Function| Range]] of the [[Toolkit Functions]] for exponential functions (Module 2.2)
 +
* Basic understanding of [[Exponential Properties]] (Module 4.1)
 +
||
 +
* Determine the difference between [[Linear Equations|Linear]] and Exponential Functions (Module 1.1)
 +
* 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
 +
||
 +
* [[Logarithmic Properties]]
 +
||
 +
(Module 9.2 & 10.1)
 +
||
 +
Students will be to able:
 +
* Rewriting from exponential form to logarithmic form and vice versa
 +
:-y=b^x\equiv\log_b(y)=x
 +
* 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
 +
||
 +
* [[Logarithmic Functions]]
 +
||
 +
* Basic understanding of [[Inverse Functions]] (Module 3.2)
 +
* Understanding the [[Domain of a Function|Domain]] and [[Range of a Function| Range]] of [[Toolkit Functions]] for logarithmic functions. (Module 2.2)
 +
* Basic understanding of [[Exponential Properties]] (Module 4.1)
 +
 +
||
 +
* Evaluate logarithms.
 +
* Use common logarithms.
 +
* Use natural logarithms.
 +
* Graph logarithmic functions.
 +
 +
 +
 +
 +
 +
 +
  
 
|-
 
|-
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* Identify power functions.
 
* Identify power functions.
 
* Identify end behavior of power functions.
 
* Identify end behavior of power functions.
 +
 
|-
 
|-
 
|Week 6
 
|Week 6
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||
 
||
 
* Combine transformations
 
* Combine transformations
−
|-
+
 
−
|Week 11
+
 
−
||
 
−
Module 8.1
 
−
||
 
−
* [[Composition of Functions]]
 
−
||
 
−
* An understanding of [[Multiple Transformations of Functions]] (Module 7.2)
 
−
||
 
−
* Combine functions using algebraic operations
 
−
* Create a new function by composition of functions
 
−
* Evaluate composite functions
 
−
* Find the domain of a composite function
 
−
* Decompose a composite function into its component functions
 
−
|-
 
−
|Week 11
 
−
||
 
−
Module 8.2
 
−
||
 
−
* [[Inverse Functions]]
 
−
||
 
−
* An understanding of [[Composition of Functions]] (Module 7.1)
 
−
||
 
−
* Verify inverse functions
 
−
* Determine the domain and range of an inverse function, and restrict the domain of a function to make it one-to-one
 
−
* Find or evaluate the inverse of a function
 
−
* Use the graph of a one-to-one function to graph its inverse function on the same axes
 
−
|-
 
−
|Week 12
 
−
||
 
−
Module 9.1
 
−
||
 
−
* [[Exponential Properties]]
 
−
||
 
−
* Understanding [[Order of Operations]]. (Module 0.1)
 
−
* Use the product rule for exponents.
 
−
* Use the quotient rule for exponents.
 
−
* Use the power rule for logarithms.
 
−
|-
 
−
|Week 12
 
−
||
 
−
Module 9.2
 
−
||
 
−
* [[Exponential Functions]]
 
−
||
 
−
* Understanding the [[Domain of a Function|Domain]] and [[Range of a Function| Range]] of the [[Toolkit Functions]] for exponential functions (Module 2.2)
 
−
* An understanding of [[Exponential Properties]] (Module 9.1)
 
−
||
 
−
* Evaluate exponential functions.
 
−
* Find the equation of an exponential function.
 
−
* Use compound interest formulas.
 
−
* Evaluate exponential functions with base e.
 
−
|-
 
−
|Week 13
 
−
||
 
−
Module 10.1
 
−
||
 
−
* [[Logarithmic Functions]]
 
−
||
 
−
* Understanding the [[Domain of a Function|Domain]] and [[Range of a Function| Range]] of [[Toolkit Functions]] for logarithmic functions. (Module 2.2)
 
−
* Difference between [[Linear Equations|Linear]] and [[Exponential Functions]] (Module 0.4 & 9.2)
 
−
||
 
−
* Rewriting from exponential form to logarithmic form and vice versa
 
−
:-y=b^x\equiv\log_b(y)=x
 
−
* Evaluate logarithms.
 
−
* Use common logarithms.
 
−
* Use natural logarithms.
 
−
|-
 
−
|Week 13
 
−
||
 
−
Module 10.2
 
−
||
 
−
* [[Logarithmic Properties]]
 
−
||
 
−
* Understanding how to convert between [[Logarithmic Functions|logarithm]] and [[Exponential Functions|exponential]] forms. (Module 9.2 & 10.1)
 
−
||
 
−
* Use the product rule for logarithms.
 
−
* Use the quotient rule for logarithms.
 
−
* Use the power rule for logarithms.
 
−
* Expand logarithmic expressions.
 
−
* Condense logarithmic expressions.
 
−
* Use the change-of-base formula for logarithms.
 
−
|-
 
−
|Week 14
 
−
||
 
−
Module 11
 
−
||
 
−
* [[Modeling using Variation]]
 
−
||
 
−
* Understanding of [[Logarithmic Properties]] (Module 10.2)
 
−
||
 
−
* Solve direct variation problems
 
−
* Solve inverse variation problems
 
−
* Solve problems involving joint variation
 
 
|}
 
|}

Revision as of 10:59, 22 May 2022

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

Date 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, subtract fractions:

  • Determine common denominators and equivalent fractions
  • Work with proper and improper fractions
  • Simplify to lowest terms

Students will be able to multiply, and divide fractions:

  • Work with proper and improper fractions
  • Simplify to lowest terms
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:

  • Solving 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

  • Basic understanding of Functions (Module 2.1)

Students will be able to:

  • Find the value of a Functions
  • Graph the functions listed in the library of functions.
  • Determine whether a function is one-to-one.
  • Use the vertical line test to identify functions.
Week 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

  • Basic understanding of Functions (Module 2.1)

Students will be able to:

  • Identify the basic toolkit functions
  • Determine Domain and Range for the basic toolkit functions (Module 2.2)
Week 5

Module 3.1

Students will be able to:

  • Combine functions using algebraic operations
  • Create a new function by composition of functions
  • Evaluate composite functions
  • Find the domain of a composite function
  • Decompose a composite function into its component functions
Week 5

Module 3.2

  • Verify inverse functions
  • Determine the domain and range of an inverse function, and restrict the domain of a function to make it one-to-one
  • Find or evaluate the inverse of a function
  • Use the graph of a one-to-one function to graph its inverse function on the same axes
Week 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

  • Determine the difference between Linear and Exponential Functions (Module 1.1)
  • 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 

(Module 9.2 & 10.1)

Students will be to able:

  • Rewriting from exponential form to logarithmic form and vice versa
-y=b^x\equiv\log_b(y)=x
  • 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

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





Week 6

Module 3.1

  • Basic understanding of power expressions.
  • The student recalls the graphs and equations of Toolkit Functions, and their associated Domain and Range (Module 2.2).
  • The student understands where the x-intercept and y-intercept are located given a graph.
  • The student understands interval notation for Domain and Range (Module 2.2).
  • Identify power functions.
  • Identify end behavior of power functions.
Week 6

Module 3.1

  • Basic understanding of a polynomial expression.
  • The student recalls the graphs and equations of Toolkit Functions, and their associated Domain and Range (Module 2.2).
  • The student understands where the x-intercept and y-intercept are located given a graph.
  • The student understands interval notation for Domain and Range (Module 2.2).
  • Identify polynomial functions.
  • Identify the degree and leading coefficients of polynomial functions.
Week 6

Module 3.2

  • Fundamentals of 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

  • Basic understanding of multiplying and dividing fractions.
  • Basic understanding of simplifying fractions by common factors.
  • Basic understanding of Factoring Polynomials (Module 0.2)
  • Use long division to divide polynomials
  • Use synthetic division to divide polynomials
Week 7

Module 4.2

  • Evaluate a polynomial using the Remainder Theorem
  • Use the Factor Theorem to solve a polynomial equation
  • Use the Rational Zero Theorem to find rational zeros
  • Find zeros of a polynomial function
  • Solve real-world applications of polynomial equations
Week 8

Module 5.1

  • The student understands that zero in the denominator of a fraction is undefined.
  • Basic understanding of Polynomial Functions (Module 3.1)
Week 8

Module 5.2

  • The student understands that zero in the denominator of a fraction is undefined.
  • The student recalls the graphs and equations of Toolkit Functions, and their associated Domain and Range (Module 2.2).
  • Solving applied problems involving Polynomial Functions. (Module 2.1)
  • Use arrow notation.
  • Solve applied problems involving rational functions.
  • Find the Domain of rational functions.
  • Identify vertical asymptotes.
  • Identify horizontal asymptotes.
Week 9

Module 6.1

  • Recognize characteristics of graphs of polynomial functions
  • Use factoring to find zeros of polynomial functions
  • Identify zeros and their multiplicities
  • Determine end behavior
  • Understand the relationship between degree and turning points
  • Graph polynomial functions
Week 9

Module 6.2

  • Identify and graph vertical asymptotes
  • Identify and graph horizontal asymptotes
  • Determine behavior of rational functions around vertical asymptotes
  • Graph rational functions
Week 10

Module 7.1

  • Graph functions using vertical and horizontal shifts
  • Graph functions using reflections about the x-axis and the y-axis
  • Determine whether a function is even, odd, or neither from it's graph
  • Graph functions using compressions and stretches
  • Combine transformations
Week 10

Module 7.2

  • Combine transformations


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