USING AND UNDERSTANDING

INSTRUCTOR’S

TESTING MANUAL

DAWN DABNEY

USING AND UNDERSTANDING

MATHEMATICS A QUANTITATIVE REASONING

APPROACH

EIGHTH EDITION

Jeffrey Bennett William Briggs 1 / 4

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Table of Contents

• Thinking Critically

1A Living in the Media Age ....................................................................... 1 1B Propositions and Truth Values ............................................................. 9 1C Sets and Venn Diagrams .................................................................... 17 1D Analyzing Arguments ......................................................................... 29 1E Critical Thinking in Everyday Life .................................................... 37

• Approaches to Problem Solving

2A Understand, Solve, and Explain ......................................................... 46 2B Extending Unit Analysis ..................................................................... 52 2C Problem-Solving Hints ....................................................................... 58

• Numbers in the Real World

3A Uses and Abuses of Percentages ........................................................ 66 3B Putting Numbers in Perspective ......................................................... 74 3C Dealing with Uncertainty ................................................................... 80 3D Index Numbers: The CPI and Beyond ................................................ 88 3E Numerical Surprises: Polygraphs, Mammograms, and More ................................................................... 96

• Managing Money

4A Taking Control of Your Finances ..................................................... 108 4B The Power of Compounding ............................................................ 114 4C Savings Plans and Investments ......................................................... 120 4D Loan Payments, Credit Cards, and Mortgages ................................. 126 4E Personal Income Taxes ..................................................................... 132 4F Understanding the Federal Budget ................................................... 140

• Statistical Reasoning

5A Fundamentals of Statistics ................................................................ 146 5B Should You Believe a Statistical Study? .......................................... 154 5C Statistical Tables and Graphs ........................................................... 162 5D Graphics in the Media ...................................................................... 172 5E Correlation and Causality ................................................................. 180

• Putting Statistics to Work

6A Characterizing Data .......................................................................... 190 6B Measures of Variation ...................................................................... 198 6C The Normal Distribution .................................................................. 206 6D Statistical Inference .......................................................................... 214

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7 Probability: Living with the Odds

7A Fundamentals of Probability ............................................................. 222 7B Combining Probabilities ................................................................... 230 7C The Law of Large Numbers ............................................................. 238 7D Assessing Risk .................................................................................. 246 7E Counting and Probability .................................................................. 254

• Exponential Astonishment

8A Growth: Linear versus Exponential .................................................. 260 8B Doubling Time and Half-Life ........................................................... 268 8C Real Population Growth ................................................................... 274 8D Logarithmic Scales: Earthquakes, Sounds, and Acids ..................... 282

• Modeling Our World

9A Functions: The Building Blocks of Mathematical Models ............... 288

9B Linear Modeling ............................................................................... 294 9C Exponential Modeling ...................................................................... 303

10 Modeling with Geometry 10A Fundamentals of Geometry .............................................................. 313 10B Problem Solving with Geometry ...................................................... 323 10C Fractal Geometry .............................................................................. 330 11 Mathematics and the Arts 11A Mathematics and Music .................................................................... 334 11B Perspective and Symmetry ............................................................... 338 11C Proportion and the Golden Ratio ...................................................... 344 12 Mathematics and Politics 12A Voting: Does the Majority Always Rule? ........................................ 350 12B Theory of Voting .............................................................................. 358 12C Apportionment: The House of Representatives and Beyond ........... 368 12D Dividing the Political Pie .................................................................. 379

Answers to Unit Exams ................................................................................ 387 3 / 4

Unit 1A Test 1

Name:

Date:

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• List the two components of a logical argument.

• Summarize the fallacy of personal attack.

• Summarize the fallacy of false cause.

• Give an example of an argument that involves a straw man.

5. List the premise and the conclusion of the following argument:

The dogs are barking. Someone must be outside.

6. List the premise and the conclusion of the following argument:

People love puppies, so don’t count on there being any puppies at the animal shelter.

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