Student Solutions Manual for Using & Understanding Mathematics

<div class="c-section-headers-number-list_container"> <h3>I. LOGIC AND PROBLEM SOLVING</h3> <ul> <li><strong>1. Thinking Critically</strong> <ul> <li>Activity: Bursting Bubble</li> <li><strong>1A. Living in the Media Age</strong></li> <li>In Your World: Fact Checking on the Web</li> <li><strong>1B. Propositions and Truth Values</strong></li> <li><strong>1C. Sets and Venn Diagrams</strong></li> <li>Brief Review: Sets of Numbers</li> <li><strong>1D. Analyzing Arguments</strong></li> <li>Mathematical Insight: Deductive Proof of the Pythagorean Theorem</li> <li><strong>1E. Critical Thinking in Everyday Life</strong></li> <li>In Your World: Beware of “Up to” Deals</li> </ul></li> <li><strong>2. Approaches to Problem Solving</strong> <ul> <li>Activity: Global Melting</li> <li><strong>2A. Understand, Solve, and Explain</strong></li> <li>Brief Review: Common Fractions</li> <li>Brief Review: Decimal Fractions</li> <li>Using Technology: Currency Exchange Rates</li> <li>In Your World: Changing Money in Foreign Countries</li> <li><strong>2B. Extending Unit Analysis</strong></li> <li>In Your World: Gems and Gold Jewelry</li> <li>Brief Review: Powers of 10</li> <li>Using Technology: Metric Conversions</li> <li>In Your World: Save Money and Save the Earth</li> <li><strong>2C. Problem-Solving Hints</strong></li> <li>Mathematical Insight: Zeno’s Paradox</li> </ul></li> </ul> <h3>II. QUANTITATIVE INFORMATION IN EVERYDAY LIFE</h3> <ul> <li><strong>3. Numbers in the Real World</strong> <ul> <li>Activity: Big Numbers</li> <li><strong>3A. Uses and Abuses of Percentages</strong></li> <li>Brief Review: Percentages</li> <li>Brief Review: What Is a Ratio?</li> <li><strong>3B. Putting Numbers in Perspective</strong></li> <li>Brief Review: Working with Scientific Notation</li> <li>Using Technology: Scientific Notation</li> <li><strong>3C. Dealing with Uncertainty</strong></li> <li>Brief Review: Rounding</li> <li>Using Technology: Rounding in Excel</li> <li><strong>3D. Index Numbers: The CPI and Beyond</strong></li> <li>Using Technology: The Inflation Calculator</li> <li>In Your World: The Chained CPI and the Federal Budget</li> <li><strong>3E. How Numbers Can Deceive: Polygraphs, Mammograms, and More</strong></li> </ul></li> <li><strong>4. Managing Money</strong> <ul> <li>Activity: Student Loans</li> <li><strong>4A. Taking Control of Your Finances</strong></li> <li><strong>4B. The Power of Compounding</strong></li> <li>Brief Review: Powers and Roots</li> <li>Using Technology: Powers</li> <li>Using Technology: The Compound Interest Formula</li> <li>Using Technology: The Compound Interest Formula for Interest Paid More Than Once a Year</li> <li>Using Technology: APY in Excel</li> <li>Using Technology: Powers of e</li> <li>Brief Review: Four Basic Rules of Algebra</li> <li>In Your World: Effects of Low Interest Rates</li> <li><strong>4C. Savings Plans and Investments</strong></li> <li>Mathematical Insight: Derivation of the Savings Plan Formula</li> <li>Using Technology: The Savings Plan Formula</li> <li>Using Technology: Fractional Powers (Roots)</li> <li>In Your World: Building a Portfolio</li> <li><strong>4D. Loan Payments, Credit Cards, and Mortgages</strong></li> <li>Using Technology: The Loan Payment Formula (Installment Loans)</li> <li>Mathematical Insight: Derivation of the Loan Payment Formula</li> <li>Using Technology: Principal and Interest Portions of Loan Payments</li> <li>In Your World: Avoiding Credit Card Trouble</li> <li>In Your World: Choosing or Refinancing a Loan</li> <li><strong>4E. Income Taxes</strong></li> <li><strong>4F. Understanding the Federal Budget</strong></li> </ul><h3>III. PROBABILITY AND STATISTICS</h3></li> <li><strong>5. Statistical Reasoning</strong> <ul> <li>Activity: Cell Phones and Driving</li> <li><strong>5A. Fundamentals of Statistics</strong></li> <li>Using Technology: Random Numbers</li> <li><strong>5B. Should You Believe a Statistical Study?</strong></li> <li>In Your World: The Gun Debate: Defensive Gun Use</li> <li><strong>5C. Statistical Tables and Graphs</strong></li> <li>Using Technology: Frequency Tables in Excel</li> <li>Using Technology: Bar Graphs and Pie Charts in Excel</li> <li>Using Technology: Line Charts in Excel</li> <li><strong>5D. Graphics in the Media</strong></li> <li>Using Technology: Graphs with Multiple Data Sets</li> <li><strong>5E. Correlation and Causality</strong></li> <li>Using Technology: Scatterplots in Excel</li> </ul></li> <li><strong>6. Putting Statistics to Work</strong> <ul> <li>Activity: Are We Smarter Than Our Parents?</li> <li><strong>6A. Characterizing Data</strong></li> <li>Using Technology: Mean, Median, and Mode in Excel</li> <li><strong>6B. Measures of Variation</strong></li> <li>Using Technology: Standard Deviation in Excel</li> <li><strong>6C. The Normal Distribution</strong></li> <li>Using Technology: Standard Scores and Percentiles in Excel</li> <li><strong>6D. Statistical Inference</strong></li> <li>In Your World: Is Polling Reliable?</li> </ul></li> <li><strong>7. Probability: Living With The Odds</strong> <ul> <li>Activity: Lotteries</li> <li><strong>7A. Fundamentals of Probability</strong></li> <li>Brief Review: The Multiplication Principle</li> <li><strong>7B. Combining Probabilities</strong></li> <li><strong>7C. The Law of Large Numbers</strong></li> <li><strong>7D. Assessing Risk</strong></li> <li>In Your World: Terrorism, Risk, and Human Psychology</li> <li><strong>7E. Counting and Probability</strong></li> <li>Using Technology: Factorials</li> <li>Brief Review: Factorials</li> <li>Using Technology: Permutations</li> <li>Using Technology: Combinations</li> </ul></li> </ul> <h3>IV. MODELING</h3> <ul> <li><strong>8. Exponential Astonishment</strong> <ul> <li>Activity: Towers of Hanoi</li> <li><strong>8A. Growth: Linear vs. Exponential</strong></li> <li><strong>8B. Doubling Time and Half-Life</strong></li> <li>Using Technology: Logarithms</li> <li>Brief Review: Logarithms</li> <li><strong>8C. Real Population Growth</strong></li> <li>In Your World: Choosing Our Fate</li> <li><strong>8D. Logarithmic Scales: Earthquakes, Sounds, and Acids</strong></li> <li>In Your World: Ocean Acidification</li> </ul></li> <li><strong>9. Modeling Our World</strong> <ul> <li>Activity: Climate Modeling</li> <li><strong>9A. Functions: The Building Blocks of Mathematical Models</strong></li> <li>Brief Review: The Coordinate Plane</li> <li><strong>9B. Linear Modeling</strong></li> <li>Using Technology: Graphing Functions</li> <li>In Your World: Algebra’s Baghdad Connection</li> <li><strong>9C. Exponential Modeling</strong></li> <li>Brief Review: Algebra with Logarithms</li> <li>Mathematical Insight: Doubling Time and Half-Life Formulas</li> <li>In Your World: Changing Rates of Change</li> </ul></li> <li><strong>10. Modeling With Geometry</strong> <ul> <li>Activity: Eyes in the Sky</li> <li><strong>10A. Fundamentals of Geometry</strong></li> <li>Mathematical Insight: Archimedes and Pi</li> <li>In Your World: Plato, Geometry, and Atlantis</li> <li><strong>10B. Problem Solving with Geometry</strong></li> <li><strong>10C. Fractal Geometry</strong></li> </ul></li> </ul> <h3>V. FURTHER APPLICATIONS</h3> <ul> <li><strong>11. Mathematics and The Arts</strong> <ul> <li>Activity: Digital Music Files</li> <li>11A. Mathematics and Music</li> <li>In Your World: Music Just for You</li> <li>11B. Perspective and Symmetry</li> <li>11C. Proportion and the Golden Ratio</li> </ul></li> <li><strong>12. Mathematics and Politics</strong> <ul> <li>Activity: Partisan Redistricting</li> <li><strong>12A. Voting: Does the Majority Always Rule?</strong></li> <li>In Your World: Counting Votes - Not as Easy as It Sounds</li> <li><strong>12B. Theory of Voting</strong></li> <li>In Your World: The Electoral College and the Presidency</li> <li><strong>12C. Apportionment: The House of Representatives and Beyond</strong></li> <li><strong>12D. Dividing the Political Pie</strong></li> </ul></li> </ul> <h4 class="h5">Credits</h4> <h4 class="h5">Answers to Quick Quizzes and Odd-Numbered Exercises</h4> <h4 class="h5">Index</h4> </div>