MAT1073

From Department of Mathematics at UTSA
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Topics List

Data Sections Topics Prerequisite Skills Student Learning Outcomes Examples/Activities

R

Order of Operations and Simplifying Radicals || Basic mathematical symbols and terminology

Basic arithmetic skills

Basic prime factorization

Basic understanding of order of operations

Basic understanding of radicals

Review order of operations

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

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R

Simplifying Exponents and Factoring Polynomials

Basic mathematical symbols and terminology

Basic arithmetic skills

Basic prime factorization

Basic understanding of order of operations

Basic understanding of exponents

Basic understanding of factoring

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

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

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R

Solving Equations and Inequalities

Basic mathematical symbols and terminology

Basic arithmetic skills

Basic prime factorization

Basic understanding of order of operations

Basic understanding of exponents

Basic understanding of factoring

Review the following linear equation topics: solving linear equations in one variable finding a linear equation write and interpret a linear equation

Review the following linear inequality topics: use interval notation use properties of inequalities solve inequalities in one variable algebraically

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R

Linear Equations and Graphs

Basic mathematical symbols and terminology

Basic arithmetic skills

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

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1

Functions and Function Notation

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Determine whether a relation represents a function

Find the value of a function

Determine whether a function is one-to-one

Use the vertical line test to identify functions

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1

Domain and Range

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Find the domain and range of a function defined by an equation

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1

Toolkit Functions

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Identify the basic toolkit functions

Determine domain and range for the basic toolkit functions

Graph the basic toolkit functions

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2

Intro to Power and Polynomial Functions

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Identify power functions

Identify polynomial functions

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2

Quadratic Functions

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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

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3

Dividing Polynomials

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Use long division to divide polynomials

Use synthetic division to divide polynomials

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3

Zeros of Polynomials

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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

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3

More Polynomial Functions

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Identify end behavior of power functions

Identify the degree and leading coefficient of polynomial functions

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4

Rational Functions

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Use arrow notation

Solve applied problems involving rational functions

Find the domains of rational functions

Identify vertical asymptotes

Identify horizontal asymptotes

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5

Graphs of Polynomials

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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

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5

Graphs of Rational Functions

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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

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6

Transformation

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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

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7

Composition of Functions

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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

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7

Inverse Functions

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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

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8

Exponential Functions

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Evaluate exponential functions

Find the equation of an exponential function

Use compound interest formulas

Evaluate exponential functions with base e

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8

Logarithmic Functions

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Convert from logarithmic to exponential form

Convert from exponential to logarithmic form

Evaluate logarithms

Use common logarithms

Use natural logarithms

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9

Logarithmic Properties

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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

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9

Exponential and Logarithmic Equations

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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

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10

Exponential and Logarithmic Models

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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

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11

Modeling using Variation

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Solve direct variation problems

Solve inverse variation problems

Solve problems involving joint variation

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12

Solving Systems of Equations in Two Variables

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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

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12

Solving Systems of Equations in Three Variables

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Solve systems of equations in three varaibles

Identify inconsistent systems of equations containing three variables

Express solutions of a system of dependent equations containing three variables

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