MAT1073

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	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 simple 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
	3	Dividing Polynomials	edit soon	Use long division to divide polynomials Use synthetic division to divide polynomials
	3	Zeros of Polynomials	edit soon	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 4	Module 3.3	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 4.1	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 4.2	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.
	5	Graphs of Polynomials	edit soon	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	Graphs of Rational Functions	edit soon	Identify and graph vertical asymptotes Identify and graph horizontal asymptotes Determine behavior of rational functions around vertical asymptotes Graph rational functions
	6	Transformation	edit soon	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	Composition of Functions	edit soon	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	Inverse Functions	edit soon	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	Exponential Functions	edit soon	Evaluate exponential functions Find the equation of an exponential function Use compound interest formulas Evaluate exponential functions with base e
	8	Logarithmic Functions	edit soon	Convert from logarithmic to exponential form Convert from exponential to logarithmic form Evaluate logarithms Use common logarithms Use natural logarithms
	9	Logarithmic Properties	edit soon	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	Exponential Logarithmic Equations	edit soon	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	Exponential Logarithmic Models	edit soon	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	Modeling using Variation	edit soon	Solve direct variation problems Solve inverse variation problems Solve problems involving joint variation
	12	Solving Systems of Equations in Two Variables	edit soon	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	Solving Systems of Equations in Three Variables	edit soon	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