DOC PREVIEW
UK MA 111 - MA 111 Review for Exam 1

This preview shows page 1-2 out of 6 pages.

Save
View full document
View full document
Premium Document
Do you want full access? Go Premium and unlock all 6 pages.
Access to all documents
Download any document
Ad free experience
View full document
Premium Document
Do you want full access? Go Premium and unlock all 6 pages.
Access to all documents
Download any document
Ad free experience
Premium Document
Do you want full access? Go Premium and unlock all 6 pages.
Access to all documents
Download any document
Ad free experience

Unformatted text preview:

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?12 miles1 hour×5280 feet1 mile×1 yard3 feet×1 hour60 minutes=352 feet1 minute2. 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.)186, 000 miles1 second×60 seconds1 minute×60 minutes1 hour×24 hours1 day×365.25 days1 year≈3.87 trillion miles1 year3. 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.)$4.57 trillion is about 191 times as large as $23.9 billion, or $4.57 trillion is about19100% of $23.9 billion. $23.9 billion is about1191of $4.57 trillion, or $23.9 billion isabout 0.52% of $4.57 trillion.4. Find an effective way to make sense of the size of Obama’s proposed $3.8 trillion federalbudget.Examples: Using the estimate that the world’s population is about 6.67 billion, with$3.8 trillion you could give each person on earth about $570. Using the estimate thatthe U.S. population is about 312 million, each person’s share of the debt in this countryis about $12,000.5. Find an effective way to make sense of the size of a water molecule, 0.2 nanometers,which equals 0.0000000002 meters.Example: Using the estimate of a human hair being 0.00002 meters wide, it would takeabout 100,000 water molecules to achieve the width of one hair.6. Express each of the following percentages as a decimal.(a) 43%0.43(b) 1.5%.0152(c) 250%2.5(d) 0.13%.00137. If your score on a test was 62 points out of 70, express the score as a percentage.6270=P100, so P =6270× 100 ≈ 89%.8. What is 37% of 56?A56=37100, so A =37100× 56 = 20.72.9. 78 is what percent of 52?7852=P100, so P =7852× 100 = 150%.10. 123 is 17% of what?123N=17100, so N =123×10017≈ 723.5.11. Out of a class of 35 students, 28 students passed the midterm exam. What percentageof the class failed the midterm?If 28 students passed, then 7 students failed.735=P100, so P =735× 100 = 20%.12. If your income in one year is $65000 and you pay $10000 in income tax, what is thetax rate?1000065000=P100, so P =1000065000× 100 ≈ 15.4%.13. If you buy a book that costs $19.95, and the sales tax is 6%, what amount do you owe?A$19.95=6100, so A =6100× $19.95 ≈ $1.20.14. If you read that the income tax is $230 per $1000 in income, what is the tax rate as apercent?2301000=P100, so P =2301000× 100 = 23%.15. Refer to the previous problem. At that tax rate, if you owed $34500 in income tax,how much was your income?$34500N=23100, so N =$34500×10023= $150, 000.316. In 2000, tuition at UK was $6550. In 2001, tuition increased by 7%. How much wastuition at UK in 2001?Use B = A(1 +P100). Here, B = $6550(1 +7100) = $7008.50.17. A computer that usually sells for $830 is on sale for 15% off. How much does thecomputer cost?Use B = A(1 −P100). Here, B = $830(1 −15100) = $705.50.18. 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?Use P =B−AA× 100. Here, P =$2.63−$2.82$2.82× 100 ≈ −6.74%. So the price has decreasedby about 6.74%.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?Use B = A(1 +P100). Here, 5900 = A(1 +3100), so A =59001.03= 5728.20. (a) If 300 is decreased by 5%, what is the result?Use B = A(1 −P100). Here, B = 300(1 −5100) = 285.(b) If 300 is decreased by 15% and then the result is increased by 10%, what is thefinal result?First use B = A(1 −15100). Here, B = 300(1 −15100) = 255. So if 300 is decreasedby 15%, the result is 255. Now increase 255 by 10%, using B = A(1 +P100). Here,B = 255(1 +10100) = 280.5.Alternatively, you can combine the two operations, and calculate 300(1 −15100)(1 +10100) = 280.5.(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?Longer way: First reverse the increase of 10% using B = A(1 +P100). Here,300 = A(1 +10100), so A =3001.1≈ 272.7. Next, reverse the decrease of 15% usingB = A(1 −P100). Here, 272.7 = A(1 −15100), so A =272.70.85≈ 320.8.Shorter way: Combining the two operations, starting with the initial unknownamount A, A(1 −15100)(1 +10100) = 300. So A =3000.85×1.1≈ 320.8.21. 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.4(a) What is change in the number of students in the freshman class who were enrolledin a math class?In 2008 the number of students enrolled in a math class was 42% of 3000, whichequals42100× 3000 = 1260. In 2009 the number of students enrolled in a math classwas 51% of 3500, which equals51100× 3500 = 1785. So the change in the numberof students enrolled in a math


View Full Document
Download MA 111 Review for Exam 1
Our administrator received your request to download this document. We will send you the file to your email shortly.
Loading Unlocking...
Login

Join to view MA 111 Review for Exam 1 and access 3M+ class-specific study document.

or
We will never post anything without your permission.
Don't have an account?
Sign Up

Join to view MA 111 Review for Exam 1 2 2 and access 3M+ class-specific study document.

or

By creating an account you agree to our Privacy Policy and Terms Of Use

Already a member?