MAT1053

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