MAT1073

From Department of Mathematics at UTSA
Revision as of 19:18, 18 June 2020 by Johnraymond.yanez (talk | contribs) (Removal of Rational Expressions)
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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

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 simple 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
  • 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

3

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  • Use long division to divide polynomials
  • Use synthetic division to divide polynomials

3

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  • 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).
Week 5

Module 4.2

  • Rational Expressions.
  • 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).

5

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  • 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

5

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

6

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  • 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

7

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  • 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

7

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  • 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

8

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  • Evaluate exponential functions
  • Find the equation of an exponential function
  • Use compound interest formulas
  • Evaluate exponential functions with base e

8

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  • Convert from logarithmic to exponential form
  • Convert from exponential to logarithmic form
  • Evaluate logarithms
  • Use common logarithms
  • Use natural logarithms

9

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  • 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

9

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  • Use like bases to solve exponential equations
  • Use logarithms to solve exponential equations
  • 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

10

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

11

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

12

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  • Solve systems of equations by graphing
  • 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

12

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  • 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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