MA 111 Review for Exam 1 Exam 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 providing 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 sense 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 in context Be able to find different variables in a percentage calculation e g use the base and the 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 this process 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 1 Practice Problems 1 I enjoy riding my recumbent bicycle at 12 miles per hour What is my speed in yards per 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 Your answer 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 federal budget 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 percentage of the class failed the midterm 12 If your income in one year is 65000 and you pay 10000 in income tax what is the tax 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 a percent 2 15 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 was tuition at UK in 2001 17 A computer that usually sells for 830 is on sale for 15 off How much does the computer cost 18 One year ago a gallon of gas sold 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 s population 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 the final result c If a number is decreased by 15 and then the result is increased by 10 resulting in 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 were enrolled in a math class In 2009 the freshman class had 3500 students and 51 of the freshman class were enrolled in a math class a What is change in the number of students in the freshman class who were enrolled in a math class b What is the percent change in the number of students in the freshman class who were enrolled in a math class c What is the change in the percent of students in the freshman class who were enrolled in a math class d What is the percent change in the percent of students in the freshman class who were enrolled in a math class 22 The town council decides to reduce the sales tax from 6 to 5 By what percent did the sales tax decrease 23 In a poll taken in September Governor Jane Citizen was favored by 49 of the respondents In a poll taken in October Gov Citizen was favored by 55 of the respondents 3 How many percentage points did Gov Citizen gain from September to October By what percent did the favorable responses increase 24 Read this excerpt from http threesixty360 wordpress com 2008 11 12 math confusionin the news percent Last week Governor Arnold Schwarzenegger proposed a temporary 3year sales tax increase in California to help close the budget deficit Some newspapers however are mixing up the amount of the increase in an effort to get the news out Error 1 Governor Proposes 1 5 Percent Sales Tax Hike from MyFox Los Angeles The proposed increase isn t actually 1 5 percent which wouldn t be all that much It s 1 5 percentage points which makes it about a 20 increase from the current 7 25 state sales tax I suspect that most people understand what the headline intends however because using percent instead of percentage point is fairly common Kudos to the LA Times for being precise in their story a Explain what calculation is used to arrive at the about 20 increase statement and 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 decimal places 4