MAT1053

From Department of Mathematics at UTSA
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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 4

Module 3

Rational Expressions

  • The student knows how to multiply and divide fractions.
  • The student recalls rules for exponents when multiplying and dividing with variables.
  • The student knows how to factor polynomials.
  • The student knows how to simplify fractions by reducing common factors.
  • Simplify rational expressions.
  • Multiply rational expressions.
  • Divide rational expressions.
  • Add and subtract rational expressions.
  • Simplify complex rational expressions.
Week 5

Module 4.1

More on Polynomial Functions

  • 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).
  • Zeros of polynomial functions.
  • Graphs of polynomial functions.
  • Solving applied problems involving polynomial functions.
  • Use arrow notation.
  • Solve applied problems involving rational functions.
  • Find the domains of rational functions.
  • Identify vertical asymptotes.
  • Identify horizontal asymptotes.
Week 6

Module 5.1

Exponential Functions

  • Understanding the toolkit functions for exponential and logarithmic functions (Module 1)
  • Understanding the domain and range for exponential and logarithmic functions (Module 1)
  • Evaluate exponential functions.
  • Find the equation of an exponential function.
  • Use compound interest formulas.
  • Evaluate exponential functions with base e.
Week 6

Module 5.2

Logarithmic Functions

  • Exponential Functions
  • Rewriting from exponential to logarithmic or vice versa (y=b^x is equivalent to log_b(y)=x)
  • Difference between linear and exponential functions
  • Convert from logarithmic to exponential form.
  • Convert from exponential to logarithmic form.
  • Evaluate logarithms.
  • Use common logarithms.
  • Use natural logarithms.
Week 7

Module 6.1

Logarithmic Properties

  • Understanding how to convert between logarithm and exponential forms and having a firm grasp on how they work together
  • Understanding Order of Operations
  • Understanding 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 7

Module 6.2

Exponential and Logarithmic Equations

  • Logarithmic Properties
  • Understanding rules for solving linear equations
  • Understanding rules for solving quadratic equations
  • Understanding how to check a solution to an equation
  • Will need to understand Log Properties in order to solve Log equations
  • 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.
Week 8

Module 7.1

Simple and Compound Interest

  • Understanding percents and percentages
  • Understanding Order of Operations
  • Understanding usage of formulas
  • Understanding solving equations (linear and exponential) and with fractions
  • Simple interest
  • Compound interest
Week 8

Module 7.2

Annuities and Payout Annuities

  • Understanding percents and percentages
  • Understanding Order of Operations
  • Understanding usage of formulas
  • Understanding solving equations (linear and exponential) and with fractions
  • Definition of Annuities
  • Ordinary Annuity Future Values
  • Annuity Due Future Values
Week 9

Module 8.1

Loans

  • Understanding percents and percentages
  • Understanding simple and compound interest
  • Understanding usage of formulas
  • Understanding Order of Operations
  • Understanding solving equations (linear and exponential) with fractions
  • Find the amount of a loan given the payments.
  • Find the payments required given the loan amount.
Week 9

Module 8.2

Promissory Notes

  • Understanding percents and percentages
  • Understanding simple and compound interest
  • Understanding usage of formulas
  • Understanding Order of Operations
  • Understanding solving equations (linear and exponential) with fractions
  • Define a promissory note.
  • Calculate unknown values for interest bearing promissory notes.
  • Calculate unknown values for non interest bearing promissory notes.
Week 10

Module 9.1

Systems of Equations and Inequalities in Two Variables

  • Solving linear equations in 2 variables.
  • Graphing linear equations in 2 variables.
  • Basic understanding of linear inequalities (Module R)
  • Understanding Order of Operations (Module R)
  • Understanding solving linear equations with fractions (Module R)
  • Basic understanding of graphing lines (Module R / Module 1)
  • Understanding methods used to verify solution of linear inequalities (Module R)
  • Solve systems of equations by graphing.
  • Solve systems of equations by substitution.
  • Solve systems of equations by addition.
  • Identify inconsistent systems of equations containing two variables.
  • Express the solution of a system of dependent equations containing two variables.
  • Identify the solution region of a system of two inequalities.
Week 10

Module 9.2

Linear Programming

  • Understanding Order of Operations (Module R)
  • Understanding how to solve systems of equations in 2 variables (Module 9)
  • Understanding how to interpret the solution of a system of equations in two variables (Module 9)
  • Understanding how to graph linear inequalities in two variables using Cartesian coordinate system (Module 9)
  • Understanding how to shade linear inequalities in two variables using Cartesian coordinate system (Module 9)
  • Define an objective function.
  • Define constraint equations.
  • Define feasible regions and determine corner points.
  • Solve linear programming problems using a graph.
Week 11

Module 10.1

Matrices and Matrix Operations

  • Basic operations with real numbers.
  • Find the sum and difference of two matrices.
  • Find the scalar multiples of a matrix.
  • Find the product of two matrices.
Week 11

Module 10.2

Solving Systems with Inverses

  • Solving systems of equations in 2 variables.
  • Matrices and matrix operations, esp. multiplication.
  • Find the inverse of a matrix.
  • Solve a system of linear equations using inverse matrix.
Week 12

Module 11.1

Sets and Subsets

  • None
  • Sets, elements of sets, and subsets.
  • Union, intersection, and complement of sets
  • Universal set and empty set
Week 12

Module 11.2

Venn Diagrams and Cardinality

  • Sets and subsets.
  • Unions and intersections of sets.
  • nan
  • Visualizing the union and intersection of sets using Venn Diagrams
  • Cardinality of a set and the properties
  • Finding cardinality using a Venn diagram
Week 13

Module 12.1

Introduction to Probability

  • Basic operations with real numbers and fractions.
  • Conversion between fractions, decimals, and percents.
  • Basic probability
  • Complementary events
  • Odds
  • Probability for independent events
Week 13

Module 12.2

Expected Value

  • Basic operations with real numbers and fractions.
  • Conversion between fractions, decimals, and percents.
  • Expected value
  • Fair game
Week 14

Module 13.1

Conditional Probability

  • Fundamentals of probability.
  • Conditional probability
  • Probability of “and” for conditional events
Week 14

Module 13.2

Counting Rules

  • Basic operations with real numbers and fractions.
  • Fundamentals of probability.
  • Basic counting techniques and rules
  • Factorial, Permutations, and Combinations
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