MAT1053

Topics List

Date	Sections	Topics	Prerequisite Skills	Student Learning Outcomes
Week 1	Module R	Order of Operations	Basic mathematical symbols and terminology Basic arithmetic skills Basic understanding of order of operations	Review of: PEMDAS
Week 1	Module R	Simplifying Radicals	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	Simplifying Exponents	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	Factoring Polynomials	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	Solving Equations	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	Solving Inequalities	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	Linear Equations	Basic mathematical symbols and terminology Basic arithmetic skills Basic understanding of Order of Operations Basic understanding of factoring Basic understanding of Solving Equations	Solving and constructing Linear Equations
Week 1	Module R	Graphs	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	Being able to graph a Linear Equations
Week 2	Module 1.1	Functions	Basic understanding of Linear Equations Basic understanding of Equations	Determine whether a relation represents a function.
Week 2	Module 1.1	Function Notation	Basic understanding of Linear Equations Basic understanding of Equations Basic understanding of Graphs	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	Domain of a Function	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	Range of a Function	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	Toolkit Functions	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	Intro to Power Functions	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	Intro to Polynomial Functions	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	Quadratic Functions	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
Week 4	Module 3	Rational Expressions	Basic understanding of multiplying and dividing fractions. Basic understanding of the rules of exponents Basic understanding of factoring polynomials. Basic understanding of simplifying fractions by 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	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 Polynomials. Graphs of Polynomials. Solving applied problems involving Polynomial Functions. Use arrow notation.
Week 5	Module 4.2	Rational 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 Polynomials. Graphs of Polynomials. Solving applied problems involving Polynomial Functions. 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	Exponential Functions	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 6	Module 5.2	Logarithmic Functions	Understanding the Toolkit Functions for logarithmic functions Understanding the Domain and Range for logarithmic functions (Module 1) Exponential Functions Difference between Linear and Exponential Functions	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 7	Module 6.1	Logarithmic Properties	Understanding how to convert between logarithm and exponential forms. (Module 5.1 & 5.2) Understanding Order of Operations. (Module R) Understanding of Exponential Rules. (Module 5.1)	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 Equations	Understanding rules for solving Linear Equations Understanding rules for solving Quadratic Equations Understanding how to check a solution to an equations Understanding of Logarithmic Properties	Use like bases to solve exponential equations. Use logarithms to solve exponential equations.
Week 7	Module 6.2	Logarithmic Equations	Understanding rules for solving Linear Equations Understanding rules for solving Quadratic Equations Understanding how to check a solution to an equations Understanding of Logarithmic Properties	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 Interest	Understanding percents and percentages Understanding Order of Operations Understanding of Exponential Functions Solving Linear Equations Solving Exponential Equations	Compound interest
Week 8	Module 7.1	Compound Interest	Understanding percents and percentages Understanding Order of Operations Understanding of Exponential Functions Solving Linear Equations Solving Exponential Equations	Compound interest
Week 8	Module 7.2	Annuities	Understanding percents and percentages Understanding Order of Operations Solving Linear Equations Solving Exponential Equations	Ordinary Annuity Future Values Annuity Due Future Values
Week 8	Module 7.2	Payout Annuities	Understanding percents and percentages Understanding Order of Operations Solving Linear Equations Solving Exponential Equations	Ordinary Annuity Future Values Annuity Due Future Values
Week 9	Module 8.1	Loans	Understanding percents and percentages Understanding Simple and Compound Interest Understanding Order of Operations Solving Linear Equations Solving Exponential Equations	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 Order of Operations Solving Linear Equations Solving Exponential Equations	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 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) Basic understanding of graphing lines (Module R / Module 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 10	Module 9.1	Systems of 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). Basic understanding of graphing lines (Module R / Module 1).	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 Two Variables (Module 9) Understanding how to interpret the solution of a system of equations in two variables. (Systems of Equations Module 9) Understanding how to graph linear inequalities in two variables using Cartesian coordinate system (Systems of Equations Module 9) Understanding how to shade linear inequalities in two variables using Cartesian coordinate system (Systems of Equations 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	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 10.1	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 Two Variables (Module 9) Matrices Matrix Operations, emphasis on multiplication	Find the inverse of a matrix. Solve a system of linear equations using inverse matrix.
Week 12	Module 11.1	Sets	None	Sets, elements of sets, and subsets. Union, intersection, and complement of sets Universal set and empty set
Week 12	Module 11.1	Subsets	None	Subsets, elements of sets Union, intersection, and complement of sets Universal set and empty set
Week 12	Module 11.2	Cardinality	Sets and Subsets (Module 11.1) Unions and intersections of sets. (Module 11.1)	Visualizing the union and intersection of sets using Venn Diagrams Cardinality of a set and the properties Finding cardinality using a Venn diagram
Week 12	Module 11.2	Cardinality	Sets and Subsets (Module 11.1) Unions and intersections of sets. (Module 11.1) Venn Diagrams. (Module 11.2)	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	Review of Introduction to Probability. (Module 12.1)	Conditional probability Probability of “and” for conditional events
Week 14	Module 13.2	Counting Rules	Basic operations with real numbers and fractions. Review of Introduction to Probability. (Module 12.1)	Basic counting techniques and rules Factorial, Permutations, and Combinations