MAT1073

From Department of Mathematics at UTSA
Revision as of 07:55, 23 June 2020 by Johnraymond.yanez (talk | contribs) (Removed the prereqs of Zeros of Polynomials Graphs of Polynomials from More on Polynomial Functions and Rational Functions)
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Topics List

Date Sections Topics Prerequisite Skills Student Learning Outcomes
Week 1

Module R

  • Basic mathematical symbols and terminology
  • Basic arithmetic skills
  • Basic understanding of order of operations

Review of:

  • PEMDAS
Week 1

Module R

  • 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

  • Basic mathematical symbols and terminology
  • Basic arithmetic skills
  • Basic understanding of Order of Operations
  • Basic understanding of exponents

Review the following rules of exponents:

  • product rule
  • quotient rule
  • power rule
  • zero exponent rule
  • negative rule

Review how to find the power of a product and a quotient Review how to simplify exponential expressions

Week 1

Module R

  • Basic mathematical symbols and terminology
  • Basic arithmetic skills
  • Basic understanding of Order of Operations
  • Basic prime factorization
  • Basic understanding of factoring

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
Week 1

Module R

  • Basic mathematical symbols and terminology
  • Basic arithmetic skills
  • Basic understanding of Order of Operations
  • Basic understanding of factoring

Review the following linear equation topics:

  • Basic mathematical symbols and terminology
  • solving linear equations in one variable
  • finding a linear equation
  • write and interpret a linear equation
Week 1

Module R

  • Basic mathematical symbols and terminology
  • 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

  • Basic mathematical symbols and terminology
  • Basic arithmetic skills
  • Basic understanding of Order of Operations
  • Basic understanding of factoring
  • Basic understanding of Solving Equations
Week 1

Module R

  • Basic mathematical symbols and terminology
  • Basic arithmetic skills
  • Basic understanding of order of operations
  • Basic understanding of factoring
  • Basic understanding of solving Linear Equations
  • Understanding of the Cartesian coordinate system
Week 2

Module 1.1

  • Determine whether a relation represents a function.
Week 2

Module 1.1

  • 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 2

Module 1.2

  • Basic understanding of interval notation (Module R: Inequalities)
  • Find the domain of a function defined by an equation.
  • Graph piecewise-defined functions.
Week 2

Module 1.2

  • Basic understanding of interval notation (Module R: Inequalities)
  • Find the domain of a function defined by an equation.
  • Graph piecewise-defined functions.
Week 2

Module 1.2

  • Basic understanding of Cartesian coordinate system (Module R: Graphs)
  • Basic understanding of interval notation (Module R: Inequalities)
  • Identify the basic toolkit functions
  • Determine Domain and Range for the basic toolkit functions (Module 1.2)
  • Graph the basic toolkit functions. (Module R)
Week 3

Module 2.1

  • Basic understanding of power expressions.
  • The student recalls the Graphs and equations of Toolkit Functions, and their associated Domains and Ranges (Module 1).
  • The student understands where the x-intercept and y-intercept are located given a graph.
  • The student understands interval notation for Domain and Range (Module 1).
  • The student can substitute values for variables in an Equations and solve for an unknown (Module R)
  • Identify power functions.
  • Identify end behavior of power functions.
  • Identify polynomial functions.
  • Identify the degree and leading coefficients of polynomial functions.
Week 3

Module 2.1

  • Basic understanding of a polynomial expression.
  • The student recalls the Graphs and equations of Toolkit Functions, and their associated domains and ranges (Module 1).
  • The student understands where the x-intercept and y-intercept are located given a graph.
  • The student understands interval notation for Domain and Range (Module 1).
  • The student can substitute values for variables in an Equations and solve for an unknown (Module R).
  • Identify polynomial functions.
  • Identify the degree and leading coefficients of polynomial functions.
Week 3

Module 2.2

  • 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 4

Module 3.1

  • Basic understanding of multiplying and dividing fractions.
  • Basic understanding of simplifying fractions by common factors.
  • Basic understanding of the rules of exponents. (Module R: Simplifying Exponents)
  • Basic understanding of Factoring Polynomials (Module R)
  • Use long division to divide polynomials
  • Use synthetic division to divide polynomials
Week 4

Module 3.2

  • Basic understanding of multiplying and dividing fractions.
  • Basic understanding of simplifying fractions by common factors.
  • Basic understanding of Factoring Polynomials (Module R)
  • Basic understanding of Functions (Module 1.1)
  • Basic understanding of Solving Equations (Module R)
  • 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 5

Module 4.1

  • 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 Domains and Ranges (Module 1.2 & R).
Week 5

Module 4.2

  • 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 6

Module 5.1

  • 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 6

Module 5.2

  • Identify and graph vertical asymptotes
  • Identify and graph horizontal asymptotes
  • Determine behavior of rational functions around vertical asymptotes
  • Graph rational functions
Week 7

Module 6

  • Graph functions using vertical and horizontal shifts
  • Graph functions using reflections about the x-axis and the y-axis
  • Determine whether a function is even, odd, or neither from it's graph
  • Graph functions using compressions and stretches
  • Combine transformations
Week 8

Module 7.1

  • 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 8

Module 7.2

  • 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 9

Module 8.1

  • Understanding the Toolkit Functions for exponential functions (Module 1)
  • Understanding the Domain and Range for exponential functions (Module 1)
  • Evaluate exponential functions.
  • Find the equation of an exponential function.
  • Use compound interest formulas.
  • Evaluate exponential functions with base e.
Week 9

Module 8.2

  • 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 10

Module 9.1

  • Understanding how to convert between logarithm and exponential forms and having a firm grasp on how they work together
  • Understanding Order of Operations
  • Understanding of Exponential Rules and Exponents in general
  • 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 10

Module 9.2

  • Use like bases to solve exponential equations.
  • Use logarithms to solve exponential equations.
Week 10

Module 9.2

  • Use the definition of a logarithm to solve logarithmic equations.
  • Use the one-to-one property of logarithms to solve logarithmic equations.
  • Solve applied problems involving exponential and logarithmic equations.
Week 11

Module 10

  • Model exponential growth and decay
  • Use Newton's Law of Cooling
  • Choose an appropriate model for data
  • Express an exponential model in base e
Week 11

Module 10

  • Use logistic-growth models
  • Choose an appropriate model for data
Week 12

Module 11

  • Solve direct variation problems
  • Solve inverse variation problems
  • Solve problems involving joint variation
Week 13

Module 12.1

  • 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 13

Module 12.2

  • 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
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