MA 111 Review for Exam 1Exam 1 (given in class on Tuesday, February 9) will cover Using Numbers and Quantities,and Percent and Percent Change, discussed in Sections 1 and 2 of the text.Can you work each homework, worksheet, and quiz problem correctly and quickly, pro-viding explanations and justifications, without looking at the text or your notes?Have you carefully studied the material in the text?You should be familiar with the following key ideas:• Understand the difference between number and quantity.• Know how to convert units (e.g., miles/hour to feet/sec).• Know how to compare quantities with ratios and with percents.• Know how to understand, or make better se nse, of very large or very small quantities.• Understand the importance of correct units.• Understand what percent means.• Know what the base of a percent is, and be able to identify the base of a percent incontext.• Be able to find different variables in a percentage calculation (e.g., use the base andthe result to find the percent).• Understand how changes in numbers can be measured by percents (percent change).• Know how to increase or decrease a number by a percentage, and how to reverse thisprocess.• Understand the difference between (1) change, (2) percent change, (3) change in percent(percentage points), and (4) percent change of percent.• Be able to interpret a short passage and analyze the given information about numbers,quantities, percents, and percent change.1Practice Problems1. I enjoy riding my recumbent bicycle at 12 miles per hour. What is my speed in yardsper minute?2. If light can travel 186,000 miles per second, how many miles can it travel in one year?(Assume one year has 365.25 days.)3. Compare the numbers $23.9 billion and $4.57 trillion as a ratio and as a percent. (Youranswer should be in the form of complete sentences.)4. Find an effective way to make sense of the size of Obama’s proposed $3.8 trillion federalbudget.5. Find an effective way to make sense of the size of a water molecule, 0.2 nanometers,which equals 0.0000000002 meters.6. Express each of the following percentages as a decimal.(a) 43%(b) 1.5%(c) 250%(d) 0.13%7. If your score on a test was 62 points out of 70, express the score as a percentage.8. What is 37% of 56?9. 78 is what percent of 52?10. 123 is 17% of what?11. Out of a class of 35 students, 28 students passed the midterm exam. What percentageof the class failed the midterm?12. If your income in one year is $65000 and you pay $10000 in income tax, what is thetax rate?13. If you buy a book that costs $19.95, and the sales tax is 6%, what amount do you owe?14. If you read that the income tax is $230 per $1000 in income, what is the tax rate as apercent?215. Refer to the previous problem. At that tax rate, if you owed $34500 in income tax,how much was your income?16. In 2000, tuition at UK was $6550. In 2001, tuition increased by 7%. How much wastuition at UK in 2001?17. A computer that usually sells for $830 is on sale for 15% off. How much doe s thecomputer cost?18. One year ago, a gallon of gas s old for $2.82. Now the price of a gallon of gas is $2.63.By what percent has the price decreased over the past year?19. The population of Pleasantville this year is 5,900. This is a 3% increase over last year’spopulation. What was the size of the population of Pleasantville last year?20. (a) If 300 is decreased by 5%, what is the result?(b) If 300 is decreased by 15% and then the result is increased by 10%, what is thefinal result?(c) If a number is decreased by 15% and then the result is increased by 10%, resultingin a final value of 300, what was the initial number?21. In 2008 the freshman class had 3000 students and 42% of the freshman class wereenrolled in a math class. In 2009 the freshman class had 3500 students and 51% of thefreshman class were enrolled in a math class.(a) What is change in the number of students in the freshman class who were enrolledin a math class?(b) What is the percent change in the number of students in the freshman class whowere enrolled in a math class?(c) What is the change in the percent of students in the freshman class who wereenrolled in a math class?(d) What is the percent change in the percent of students in the freshman class whowere enrolled in a math class?22. The town council decides to reduce the sales tax from 6% to 5%. By what percent didthe sales tax decrease?23. In a poll taken in September, Governor Jane Citizen was favored by 49% of the respon-dents. I n a poll taken in October, Gov. Citizen was favored by 55% of the respondents.3How many percentage points did Gov. Citizen gain from September to October? Bywhat percent did the favorable responses increase?24. Read this excerpt from http://threesixty360.wordpress.com/2008/11/12/math-confusion-in-the-news-percent:Last week Governor Arnold Schwarzenegger proposed a temporary (3-year) sales tax increase in California to help close the budget deficit. Somenewspapers, however, are mixing up the amount of the increase in an effortto get the news out.Error #1: “Governor Proposes 1.5 Percent Sales Tax Hike” from MyFoxLos AngelesThe proposed increase isn’t actually 1.5 percent (which wouldn’t be allthat much). It’s 1.5 percentage points, which makes it about a 20% increasefrom the current 7.25% state sales tax. I suspect that most people under-stand what the headline intends, however, because using “percent” insteadof “percentage point” is fairly common. (Kudos to the LA Times for beingprecise in their story!)(a) Explain what calculation is used to arrive at the “about 20% increase” statementand give a more precise number rounded to one decimal place.(b) What would the new tax rate be if the tax increase were truly a 1.5% increase,rather than increase of 1.5 percentage points? Round your answer to 2