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Table of contents
  1. Preface
  2. 1 Sets
    1. Introduction
    2. 1.1 Basic Set Concepts
    3. 1.2 Subsets
    4. 1.3 Understanding Venn Diagrams
    5. 1.4 Set Operations with Two Sets
    6. 1.5 Set Operations with Three Sets
    7. Chapter Summary
      1. Key Terms
      2. Key Concepts
      3. Videos
      4. Formula Review
      5. Projects
      6. Chapter Review
      7. Chapter Test
  3. 2 Logic
    1. Introduction
    2. 2.1 Statements and Quantifiers
    3. 2.2 Compound Statements
    4. 2.3 Constructing Truth Tables
    5. 2.4 Truth Tables for the Conditional and Biconditional
    6. 2.5 Equivalent Statements
    7. 2.6 De Morgan’s Laws
    8. 2.7 Logical Arguments
    9. Chapter Summary
      1. Key Terms
      2. Key Concepts
      3. Videos
      4. Projects
      5. Chapter Review
      6. Chapter Test
  4. 3 Real Number Systems and Number Theory
    1. Introduction
    2. 3.1 Prime and Composite Numbers
    3. 3.2 The Integers
    4. 3.3 Order of Operations
    5. 3.4 Rational Numbers
    6. 3.5 Irrational Numbers
    7. 3.6 Real Numbers
    8. 3.7 Clock Arithmetic
    9. 3.8 Exponents
    10. 3.9 Scientific Notation
    11. 3.10 Arithmetic Sequences
    12. 3.11 Geometric Sequences
    13. Chapter Summary
      1. Key Terms
      2. Key Concepts
      3. Videos
      4. Formula Review
      5. Projects
      6. Chapter Review
      7. Chapter Test
  5. 4 Number Representation and Calculation
    1. Introduction
    2. 4.1 Hindu-Arabic Positional System
    3. 4.2 Early Numeration Systems
    4. 4.3 Converting with Base Systems
    5. 4.4 Addition and Subtraction in Base Systems
    6. 4.5 Multiplication and Division in Base Systems
    7. Chapter Summary
      1. Key Terms
      2. Key Concepts
      3. Videos
      4. Projects
      5. Chapter Review
      6. Chapter Test
  6. 5 Algebra
    1. Introduction
    2. 5.1 Algebraic Expressions
    3. 5.2 Linear Equations in One Variable with Applications
    4. 5.3 Linear Inequalities in One Variable with Applications
    5. 5.4 Ratios and Proportions
    6. 5.5 Graphing Linear Equations and Inequalities
    7. 5.6 Quadratic Equations with Two Variables with Applications
    8. 5.7 Functions
    9. 5.8 Graphing Functions
    10. 5.9 Systems of Linear Equations in Two Variables
    11. 5.10 Systems of Linear Inequalities in Two Variables
    12. 5.11 Linear Programming
    13. Chapter Summary
      1. Key Terms
      2. Key Concepts
      3. Videos
      4. Formula Review
      5. Projects
      6. Chapter Review
      7. Chapter Test
  7. 6 Money Management
    1. Introduction
    2. 6.1 Understanding Percent
    3. 6.2 Discounts, Markups, and Sales Tax
    4. 6.3 Simple Interest
    5. 6.4 Compound Interest
    6. 6.5 Making a Personal Budget
    7. 6.6 Methods of Savings
    8. 6.7 Investments
    9. 6.8 The Basics of Loans
    10. 6.9 Understanding Student Loans
    11. 6.10 Credit Cards
    12. 6.11 Buying or Leasing a Car
    13. 6.12 Renting and Homeownership
    14. 6.13 Income Tax
    15. Chapter Summary
      1. Key Terms
      2. Key Concepts
      3. Videos
      4. Formula Review
      5. Projects
      6. Chapter Review
      7. Chapter Test
  8. 7 Probability
    1. Introduction
    2. 7.1 The Multiplication Rule for Counting
    3. 7.2 Permutations
    4. 7.3 Combinations
    5. 7.4 Tree Diagrams, Tables, and Outcomes
    6. 7.5 Basic Concepts of Probability
    7. 7.6 Probability with Permutations and Combinations
    8. 7.7 What Are the Odds?
    9. 7.8 The Addition Rule for Probability
    10. 7.9 Conditional Probability and the Multiplication Rule
    11. 7.10 The Binomial Distribution
    12. 7.11 Expected Value
    13. Chapter Summary
      1. Key Terms
      2. Key Concepts
      3. Formula Review
      4. Projects
      5. Chapter Review
      6. Chapter Test
  9. 8 Statistics
    1. Introduction
    2. 8.1 Gathering and Organizing Data
    3. 8.2 Visualizing Data
    4. 8.3 Mean, Median and Mode
    5. 8.4 Range and Standard Deviation
    6. 8.5 Percentiles
    7. 8.6 The Normal Distribution
    8. 8.7 Applications of the Normal Distribution
    9. 8.8 Scatter Plots, Correlation, and Regression Lines
    10. Chapter Summary
      1. Key Terms
      2. Key Concepts
      3. Videos
      4. Formula Review
      5. Projects
      6. Chapter Review
      7. Chapter Test
  10. 9 Metric Measurement
    1. Introduction
    2. 9.1 The Metric System
    3. 9.2 Measuring Area
    4. 9.3 Measuring Volume
    5. 9.4 Measuring Weight
    6. 9.5 Measuring Temperature
    7. Chapter Summary
      1. Key Terms
      2. Key Concepts
      3. Videos
      4. Formula Review
      5. Projects
      6. Chapter Review
      7. Chapter Test
  11. 10 Geometry
    1. Introduction
    2. 10.1 Points, Lines, and Planes
    3. 10.2 Angles
    4. 10.3 Triangles
    5. 10.4 Polygons, Perimeter, and Circumference
    6. 10.5 Tessellations
    7. 10.6 Area
    8. 10.7 Volume and Surface Area
    9. 10.8 Right Triangle Trigonometry
    10. Chapter Summary
      1. Key Terms
      2. Key Concepts
      3. Videos
      4. Formula Review
      5. Projects
      6. Chapter Review
      7. Chapter Test
  12. 11 Voting and Apportionment
    1. Introduction
    2. 11.1 Voting Methods
    3. 11.2 Fairness in Voting Methods
    4. 11.3 Standard Divisors, Standard Quotas, and the Apportionment Problem
    5. 11.4 Apportionment Methods
    6. 11.5 Fairness in Apportionment Methods
    7. Chapter Summary
      1. Key Terms
      2. Key Concepts
      3. Videos
      4. Formula Review
      5. Projects
      6. Chapter Review
      7. Chapter Test
  13. 12 Graph Theory
    1. Introduction
    2. 12.1 Graph Basics
    3. 12.2 Graph Structures
    4. 12.3 Comparing Graphs
    5. 12.4 Navigating Graphs
    6. 12.5 Euler Circuits
    7. 12.6 Euler Trails
    8. 12.7 Hamilton Cycles
    9. 12.8 Hamilton Paths
    10. 12.9 Traveling Salesperson Problem
    11. 12.10 Trees
    12. Chapter Summary
      1. Key Terms
      2. Key Concepts
      3. Videos
      4. Formula Review
      5. Projects
      6. Chapter Review
      7. Chapter Test
  14. 13 Math and...
    1. Introduction
    2. 13.1 Math and Art
    3. 13.2 Math and the Environment
    4. 13.3 Math and Medicine
    5. 13.4 Math and Music
    6. 13.5 Math and Sports
    7. Chapter Summary
      1. Key Terms
      2. Key Concepts
      3. Formula Review
      4. Projects
      5. Chapter Review
      6. Chapter Test
  15. A | Co-Req Appendix: Integer Powers of 10
  16. Answer Key
    1. Chapter 1
    2. Chapter 2
    3. Chapter 3
    4. Chapter 4
    5. Chapter 5
    6. Chapter 6
    7. Chapter 7
    8. Chapter 8
    9. Chapter 9
    10. Chapter 10
    11. Chapter 11
    12. Chapter 12
    13. Chapter 13
  17. Index

Key Concepts

5.1 Algebraic Expressions

  • Algebra is useful because it allows us to understand many situations in real life by modeling them with expressions.
  • Algebraic expressions are the building blocks of algebra. From algebraic expressions we can create algebraic equations.
  • Algebraic expressions are the building blocks of algebra. From algebraic expressions we can create algebraic equations.
  • Algebraic expressions are often simplified and evaluated using the four arithmetic operations.

5.2 Linear Equations in One Variable with Applications

  • Solving linear equations means discovering what the value of the variable in a linear equation represents in the given conditions.
  • When solving a linear equation, most often you will have one solution; however, a linear equation may have no solutions or infinitely many solutions.

5.3 Linear Inequalities in One Variable with Applications

  • Inequalities can be used when the possible values (answers) in a certain situation are numerous, or when the exact value (answer) is not known, but it is known to be within a range of possible values.
  • Linear inequalities can be represented using a number line or using interval notation.

5.4 Ratios and Proportions

  • A ratio is a comparison of two numbers. The ratio of two numbers aa and bb can be written as: aa to bb OR aa:bb OR the fraction aa/bb.
  • All fractions are ratios, but not all ratios are fractions. Ratios make part to part, part to whole, and whole to part comparisons. Fractions make part to whole comparisons only.
  • When two ratios are equal, we say they are in proportion or are proportional.
  • Setting up proportions allows us to solve many various situations where three of the four values of the proportion are known.

5.5 Graphing Linear Equations and Inequalities

  • Linear equations can be represented graphically on a rectangular coordinate system.
  • Solving linear equations in two variables means finding the point where two lines intersect. There are three possibilities: The lines intersect at exactly one point; the lines do not intersect (they are parallel); or the lines intersect everywhere (they are the same line).
  • Solving linear inequalities in two variables means finding a region of possible answers. Every point in this region will make both inequalities true statements.
  • Plotting points is a standard way to help graph linear equations and linear inequalities.

5.6 Quadratic Equations with Two Variables with Applications

  • A quadratic equation is an algebraic equation where the highest power (degree) of the equation is two.
  • To solve a quadratic equation is to find the value(s) that when substituted in for the variables, will make the equation equal to zero.
  • There can be two, one, or no solutions to any quadratic equation.
  • There are several methods to solve a quadratic equation. These methods include factoring quadratic equations, graphic quadratic equations, using the square root method, and using the quadratic formula.

5.7 Functions

  • A relation is any set of ordered pairs (x,y)(x,y). All of the xx-values of the set are the domain, and all of the yy-values of the set are the range.
  • A relation is a function if each xx-value in the domain is assigned to exactly one element in the range. A yy-value in the range can have more than one xx-value assigned to it; but each xx-value can only be assigned to one yy-value.
  • For the function y=f(x),fy=f(x),f is the name of the function, xx is the domain value variable, and y=f(x)y=f(x) is the range value variable.
  • The vertical line test is a test that can be done on the graph of a relation to determine if it is a function.

5.8 Graphing Functions

  • Every linear function can be graphically represented by a unique line that shows all the solutions of the equation.
  • The points where the graph of a line intersects the xx-axis and yy-axis are called the intercepts of the line.
  • Most lines will have one xx-intercept and one yy-intercept. Only if the line is straight vertical (no yy-intercept) or straight horizontal (no xx-intercept) will it not have both intercepts. Note that a line that is straight vertical is not a function, but a line that is straight horizontal is a function.
  • Since any two points determine a straight line, any linear function can be graphed if both intercepts are known.
  • The slope of a linear function is the ratio of the vertical change divided by the horizontal change. It is often referred to as riserunriserun.
  • A formula for finding the slope of linear functions is y2y1x2x1,y2y1x2x1, for any two points of the linear function (x1,y1)(x1,y1) and (x2,y2)(x2,y2).

5.9 Systems of Linear Equations in Two Variables

  • To solve a system of linear equations means finding the point or points where the two linear equations intersect.
  • Two lines can intersect at one point, no points if they are parallel, or every point if they are the same equation.
  • Systems of linear equations can be solved by graphing, by using substitution, or by using the elimination method.

5.10 Systems of Linear Inequalities in Two Variables

  • To solve a system of linear inequalities means to find the area(s) where the points in that area make all the linear inequalities true.
  • Systems of linear inequalities can be solved by graphing the linear equations associated with the inequalities, then 'testing' points to see whether the values of the point make the equation true or not.

5.11 Linear Programming

  • Linear programming is a mathematical technique to solve problems involving finding maximums or minimums where a linear function is limited by various constraints.
  • An objective function is a linear function in two or more variables that describes the quantity that needs to be maximized or minimized.
  • In linear programming, a constraint is a restriction that affects the maximum or minimum values of an objective function.
  • Through the creation of objective functions and restraints, a linear system can be developed and solved through linear programming.
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