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Study Guides

Mathematics for the Liberal Arts Corequisite

Course Contents

Summary: Review Topics
About This Book

Just in Time Review: Chapter 3 Finance

Course Contents at a Glance
Review Topics for Success
Learning Outcomes
Writing and Naming Decimals

Chapter 1: General Problem Solving

Converting Decimals to Fractions or Mixed Numbers
Why It Matters: General Problem Solving
Locating and Ordering Decimals With a Number Line
Percents and Proportional Relationships
Rounding Decimals
Solving Problems with Math
Adding and Subtracting Decimals
Putting It Together: General Problem Solving
Multiplying Decimals

Chapter 2: Growth Models

Dividing Decimals
Why it Matters: Growth Models
Using Decimals in Money Applications
Linear Growth and Exponential Growth
Converting Fractions to Decimals
Logistic Growth
Comparing Decimals and Fractions
Putting It Together: Growth Models
Simplifying Expressions With Decimals and Fractions

Chapter 3: Finance

Using the Properties of Equality to Solve Equations With Decimals
Why It Matters: Finance
Solving Equations By Clearing Decimals
Translating Words to Equations That Contain Decimals
Simple and Compound Interest
Summary: Review
Annuities and Loans

Just in Time Review: Chapter 4 Set Theory and Logic

Which Finance Formula to Use?
Review Topics for Success
Putting It Together: Finance
Identifying Rational and Irrational Numbers

Chapter 4: Logic and Set Theory

Classifying Real Numbers
Why It Matters: Logic and Set Theory
Rewriting Expressions Using the Commutative and Associative Properties
Logical Fallacies in Common Language
Evaluating and Simplifying Expressions Using the Commutative and Associative Properties
Logic Basics
Simplifying Expressions With Different Forms of the Distributive Property
Analyzing Arguments With Logic
Simplifying and Evaluating Expressions Using the Distributive Property
Set Theory Basics
Using the Multiplication and Division Properties of Zero
Putting It Together: Logic and Set Theory
Using the Identity and Inverse Properties of Addition and Subtraction

Chapter 5: Probability

Simplifying Expressions Using the Properties of Identities, Inverses, and Zero
Why It Matters: Probability
Summary: Review Topics
5.2: Calculating the Probability of an Event

Just in Time Review: Chapter 5 Probability

Counting and Probability
Review Topics for Success
Expected Value
Writing Ratios as Fractions
Putting It Together: Probability
Adding Fractions With Common Denominators

Chapter 6: Statistics

Subtracting Fractions With Common Denominators
Why It Matters: Statistics
Finding the Least Common Multiple of Two Numbers
Data Collection Basics
Adding and Subtracting Fractions With Different Denominators
Sampling Methods and Bias
Finding the Probability of an Event
Representing Data Graphically
Summary: Review Topics
Numerical Summaries of Data

Just in Time Review: Chapter 6 Statistics-Collecting Data

Putting It Together: Statistics
Review Topics for Success

Chapter 7: Voting Theory

Writing Percents as Ratios
Why It Matters: Voting Theory
Writing Percents as Fractions and Decimals
Introduction to Voting Methods
Writing Decimals and Fractions as Percents
Voting Methods: Majority Rule, Plurality, Single Run-off
Translating and Solving Basic Percent Equations
Voting Methods: IRV, Borda Count, Pairwise
Calculating the Mean of a Set of Numbers
Introduction to Fairness Criteria
Finding the Median of a Set of Numbers
The Fairness Criteria
Identifying the Mode of a Set of Numbers
Which Method is Fair?
Summary: Review
Introduction to Approval Voting

A1: Graph Theory

Approval Voting
Why It Matters: Graph Theory
Voting in America
Introduction to Graph Theory Basics

Just in Time Review: Chapter 1 General Problem Solving

Elements of Graph Theory
Review Topics for Success
Shortest Path
Introduction to The Language of Algebra
Introduction to Euler and Hamiltonian Paths and Circuits
Real Numbers
Euler Circuits
Using Models to Represent Fractions and Mixed Numbers
Hamiltonian Circuits
Modeling and Finding Equivalent Fractions
Putting It Together: Graph Theory
Simplifying Fractions

A2: Fractals

Adding and Subtracting Fractions
Why It Matters: Fractals
Multiplying Fractions
Introduction to Fractal Basics
Dividing Fractions
Fractal Basics
Fractal Dimension
Summary: Review Topics
Introduction to Fractals Generated by Complex Numbers

Just in Time Review: Chapter 2 Growth Models

Arithmetic With Complex Numbers
Review Topics for Success
Generating Fractals With Complex Numbers
Determining Whether a Number is a Solution to an Equation
Putting It Together: Fractals
Solving Equations Using the Subtraction and Addition Properties of Equality

A3: Measurement

Solving Equations With Integers Using Properties of Equality
Why It Matters: Measurement
Converting Fractions to Equivalent Fractions With the LCD
Introduction to US Units of Measurement
Solving Equations That Contain Fractions Using the Addition and Subtraction Properties of Equality
Units of Length
Solving Equations That Contain Fractions Using the Multiplication Property of Equality
Units of Weight
Translating Words Involving Division and Multiplication Into an Algebraic Equation and Solving
Units of Capacity
Translating Words Involving Addition and Subtraction Into an Algebraic Equation and Solving
Introduction to Systems and Scales of Measurement
Using the Subtraction and Addition Properties for Multi-Step Equations
Metric System Basics
Using the Division and Multiplication Properties of Equality for Multi-Step Equations
Applications of Metric Conversions
Solving Equations With Variables on Both Sides
Temperature Scales
Solving Equations By Clearing Fractions
Putting It Together: Measurement