Difference between revisions of "MAT1053"

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(Testing mathematics notation)
(Adding MAT 1053 Course Map)
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Test page <math>\frac{1}{2}</math>
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==Topics List==
 +
{| class="wikitable sortable"
 +
! Date !! Sections !! Topics !! Prerequisite Skills !! Student Learning Outcomes
 +
|-               
 +
|Week 1
 +
||
 +
Module R – Prerequisite Review
 +
||
 +
Prerequisites
 +
||
 +
* Previous experience with each of the objectives
 +
* Basic understanding of order of operations
 +
* Basic understanding of exponents and radicals
 +
* Basic understanding of factoring polynomials and definition of a factor
 +
* Basic understanding of solving simple equations
 +
* Understanding operations with fractions
 +
* Understanding of the rectangular coordinate system
 +
||
 +
* Review of:
 +
* Order of Operations
 +
* Exponent Rules
 +
* Radicals,
 +
* Linear Expressions
 +
* Graphing Lines
 +
* Factoring
 +
|-
 +
|Week 2
 +
||
 +
Module 1.1 – Functions and Function Notation
 +
||
 +
Functions
 +
||
 +
* Basic understanding of equations (Module R)
 +
||
 +
* 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.
 +
* Graph the functions listed in the library of functions.
 +
|-
 +
|Week 2
 +
||
 +
Module 1.2 – Toolkit Functions and Domain of a Function
 +
||
 +
Functions
 +
||
 +
* Basic understanding of Cartesian coordinate system (Module R)
 +
* Basic understanding of interval notation (Module R)
 +
||
 +
* Find the domain of a function defined by an equation.
 +
* Graph piecewise-defined functions.
 +
|-
 +
|Week 3
 +
||
 +
Module 2.1 – Intro to Power and Polynomial Functions
 +
||
 +
Polynomials
 +
||
 +
* The student understands what a polynomial expression is.
 +
* 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 equation and solve for an unknown.
 +
||
 +
* Identify power functions.
 +
* Identify end behavior of power functions.
 +
* Identify polynomial functions.
 +
* Identify the degree and leading coefficients of polynomial functions.
 +
|-
 +
|Week 3
 +
||
 +
Module 2.2 – Quadratic Functions
 +
||
 +
Polynomials
 +
||
 +
* Fundamentals of polynomials.
 +
* The student understands the difference between a maximum and minimum.
 +
||
 +
* Recognize characteristic 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 – Rational Expressions
 +
||
 +
Polynomials
 +
||
 +
* 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
 +
||
 +
Polynomials
 +
||
 +
* 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
 +
||
 +
Equations
 +
||
 +
* 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
 +
||
 +
Equations
 +
||
 +
* 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
 +
||
 +
Equations
 +
||
 +
* 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
 +
||
 +
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
 +
||
 +
Math of Finance
 +
||
 +
* 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
 +
||
 +
Math of Finance
 +
||
 +
* 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
 +
||
 +
Math of Finance
 +
||
 +
* 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
 +
||
 +
Math of Finance
 +
||
 +
* 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
 +
||
 +
Systems
 +
||
 +
* 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
 +
||
 +
Systems
 +
||
 +
* 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
 +
||
 +
Systems
 +
||
 +
* 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
 +
||
 +
Systems
 +
||
 +
* 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
 +
||
 +
Statistics and Probability
 +
||
 +
* 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
 +
||
 +
Statistics and Probability
 +
||
 +
* 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
 +
||
 +
Statistics and 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
 +
||
 +
Statistics and Probability
 +
||
 +
* Basic operations with real numbers and fractions.
 +
* Conversion between fractions, decimals, and percents.
 +
||
 +
* Expected value
 +
* Fair game
 +
|-
 +
|Week 14
 +
||
 +
Module 13.1 – Conditional Probability
 +
||
 +
Statistics and Probability
 +
||
 +
* Fundamentals of probability.
 +
||
 +
* Conditional probability
 +
* Probability of “and” for conditional events
 +
|-
 +
|Week 14
 +
||
 +
Module 13.2 – Counting Rules
 +
||
 +
Statistics and Probability
 +
||
 +
* Basic operations with real numbers and fractions.
 +
* Fundamentals of probability.
 +
||
 +
* Basic counting techniques and rules
 +
* Factorial, Permutations, and Combinations
 +
|}

Revision as of 13:44, 15 June 2020

Topics List

Date Sections Topics Prerequisite Skills Student Learning Outcomes
Week 1

Module R – Prerequisite Review

Prerequisites

  • Previous experience with each of the objectives
  • Basic understanding of order of operations
  • Basic understanding of exponents and radicals
  • Basic understanding of factoring polynomials and definition of a factor
  • Basic understanding of solving simple equations
  • Understanding operations with fractions
  • Understanding of the rectangular coordinate system
  • Review of:
  • Order of Operations
  • Exponent Rules
  • Radicals,
  • Linear Expressions
  • Graphing Lines
  • Factoring
Week 2

Module 1.1 – Functions and Function Notation

Functions

  • Basic understanding of equations (Module R)
  • 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.
  • Graph the functions listed in the library of functions.
Week 2

Module 1.2 – Toolkit Functions and Domain of a Function

Functions

  • Basic understanding of Cartesian coordinate system (Module R)
  • Basic understanding of interval notation (Module R)
  • Find the domain of a function defined by an equation.
  • Graph piecewise-defined functions.
Week 3

Module 2.1 – Intro to Power and Polynomial Functions

Polynomials

  • The student understands what a polynomial expression is.
  • 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 equation and solve for an unknown.
  • Identify power functions.
  • Identify end behavior of power functions.
  • Identify polynomial functions.
  • Identify the degree and leading coefficients of polynomial functions.
Week 3

Module 2.2 – Quadratic Functions

Polynomials

  • Fundamentals of polynomials.
  • The student understands the difference between a maximum and minimum.
  • Recognize characteristic 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 – Rational Expressions

Polynomials

  • 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

Polynomials

  • 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

Equations

  • 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

Equations

  • 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

Equations

  • 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

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

Math of Finance

  • 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

Math of Finance

  • 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

Math of Finance

  • 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

Math of Finance

  • 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

Systems

  • 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

Systems

  • 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

Systems

  • 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

Systems

  • 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

Statistics and Probability

  • 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

Statistics and Probability

  • 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

Statistics and 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

Statistics and Probability

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

Module 13.1 – Conditional Probability

Statistics and Probability

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

Module 13.2 – Counting Rules

Statistics and Probability

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