Practice Math Test Chapter 6

Transcription

1 lass: _ ate: _ Name: Practice Math Test hapter 6 Multiple hoice Identify the choice that best completes the statement or answers the question. 1. Find the missing ratio or percent equivalent for each letter on the number line. If necessary, round answers to the nearest hundredth. a. b = 1.67%; c = 2 5 ; d = 7.78% b. b = 0.17%; c = 40 1 ; d = 0.78% c. b = 600%; c = 5 2 ; d = % d. b =16.67%; c = 2 5 ; d = 77.78% 2. ompare 0.795?_ 37%. Write <, >, or =. a. = b. < c. > 3. ompare _? 32%. Write <, >, or =. a. < b. = c. > 4. blimp is fully expanded when it contains 35,000 cubic feet of gas. If the blimp is inflated with 11,650 cubic feet of gas, what percent full is it? If necessary, round your answer to the nearest hundredth of a percent. a % b % c. 0.33% d. 3% 5. Estimate 62% of 47. a. 3,000 b. 30 c. 109 d Mike is eating at a restaurant. His total bill comes to $ If Mike decides to leave a tip that is approximately 15% of the total bill, how much should he leave for the tip? a. $3.00 b. $28.75 c. $0.04 d. $3.75 1

2 7. What percent of 171 is 497? If necessary, round your answer to the nearest hundredth of a percent. a. 2.91% b % c % d % 8. The High ridge has a main span of 3,970 feet. The Y- ridge has a main span that is approximately 134% of the main span of the High ridge. What is the length of the main span of the Y-? Round your answer to the nearest foot. a. 53,198 ft b. 5,320 ft c. 2,963 ft d. 6,987 ft is 90% of what number? If necessary, round your answer to the nearest hundredth. a b c d Mr. S wants to sell his house. Ohio charges a 4.5% sales tax on the sale of a house. Summit county charges a 3.6% sales tax, and New Franklin charges a 1.5% sales tax. If Mr. S sells his home for $130,900, what is his total tax bill? a. $5, b. $1, c. $17, d. $12, The Velociraptor dinosaur averaged 6 feet in length. This is 15% of the average length of a Tyrannosaurus dinosaur. What was the average length of the Tyrannosaurus? If necessary, round your answer to the nearest hundredth. a. 40 ft b. 0.9 ft c. 250 ft d. 0.4 ft 12. Find the percent increase or decrease from 32 to 208. a. 550% decrease b. 85% decrease c. 550% increase d. 85% increase 2

3 13. Maddie owns an ice cream shop. On Saturday evening from 6:00 P.M. to 7:00 P.M., 60 people entered her shop. On Tuesday from 4:00 P.M. to 5:00 P.M., 33 people entered her shop. What was the percent decrease in customers from the given hour on Saturday to the given hour on Tuesday? If necessary, round your answer to the nearest hundredth of a percent. a. 67% b % c. 45% d. 0.45% 14. Jimmie works in a music store and earns 10.5% commission on each sale. If Jimmie sells an organ and earns $59.50, what is the price of the organ? Round your answer to the nearest cent. a. $ b. $ c. $5.67 d. $ bank loans a customer $69,000 for a period of 14 years. The simple interest rate of the loan is 5.4%. What is the total amount that the customer will need to pay the bank over the 14 years? a. $121,164 b. $5,285,400 c. $966,000 d. $52, Grant puts $1, into savings bonds that pay a simple interest rate of 7.8%. How much money will the bonds be worth at the end of 3.5 years? a. $6, b. $1, c. $1, d. $ Matching Match each vocabulary term with its definition. a. simple interest d. percent decrease b. commission e. sales tax c. compatible numbers f. percent 17. a ratio comparing a number to a percent of the cost of an item that is charged by governments to raise money 19. a percent change describing a decrease in a quantity 20. numbers that are close to the given numbers that make estimation or mental calculation easier 21. a fee paid to a person for making a sale 22. a fixed percent of the principal using the formula I = P r t, where P represents the principal, r represents the rate of interest, and t represents the time 3

4 Numeric Response 23. hase bank gives you a simple interest loan at a rate of 6.5%. fter 2 years, you have paid the entire principal plus $39.13 in interest. What was the original principal amount of your loan?. Short nswer 24. tree in a forest is 138 feet tall. This is 51.2% as tall as the tallest tree in the forest. pproximately how tall is the tallest tree in the forest? Show your work You earn a base salary of $14, plus a commission of 5% on every sale you make. a. If you sold $73,200.00, what would be your total pay for the year? Show your work. b. If you had to pay 24% in taxes, how much of your total pay would be left after taxes? Show your work. onus (Optional) 26. To make dry concrete mix, mix sand, cement, and stone. The mix must be 24% sand. The remaining amount of mix must be 35% cement and 65% stone. If you required 200 pounds of dry concrete mix, how would you determine the amount of sand, cement, and stone to purchase? (Show work.) 4

5 I: Practice Math Test hapter 6 nswer Section MULTIPLE HOIE 1. NS: To convert a fraction to a percent, divide the numerator by the denominator and multiply by 100. To convert a percent to a fraction, place the percent over 100 and simplify the fraction. heck that the percents are in the correct places on the number line. To convert a percent to a fraction, place the percent over 100 and simplify the fraction. To convert a fraction to a percent, divide the numerator by the denominator and multiply by 100. orrect! PTS: 1 IF: verage REF: Page 274 OJ: Finding Equivalent Ratios and Percents NT: i TOP: 6-1 Relating ecimals Fractions and Percents KEY: fraction number line percent ratio 2. NS: Write the decimal as a percent, and then compare. To convert a decimal to a percent, multiply by 100 and insert the percent symbol. Write the decimal as a percent, and then compare. Write the decimal as a percent, and then compare. orrect! PTS: 1 IF: asic REF: Page 275 OJ: omparing Fractions ecimals and Percents NT: i TOP: 6-1 Relating ecimals Fractions and Percents 3. NS: Write the fraction as a percent, and then compare. To convert a fraction to a percent, first divide the numerator by the denominator to get a decimal. Then, multiply the decimal by 100 and insert the percent symbol. Write the fraction as a percent, and then compare. Write the fraction as a percent, and then compare. orrect! PTS: 1 IF: asic REF: Page 275 OJ: omparing Fractions ecimals and Percents TOP: 6-1 Relating ecimals Fractions and Percents NT: i 1

6 I: 4. NS: ivide the current amount of gas by the total amount of gas allowed, and multiply the result by 100. orrect! ivide the current amount of gas by the total amount of gas allowed. To convert a decimal to a percent, multiply by 100 and insert the percent symbol. Set up a ratio of part to whole and simplify. PTS: 1 IF: verage REF: Page 275 OJ: pplication NT: e TOP: 6-1 Relating ecimals Fractions and Percents KEY: convert decimal fraction percent 5. NS: Use the table of benchmarks to help you estimate percents. Percent ecimal Fraction 5% % % % % % % % Use a compatible number close to the percent to estimate. orrect! Use a compatible number close to the percent to estimate. Use a compatible number close to the percent to estimate. PTS: 1 IF: verage REF: Page 278 OJ: Estimating with Percents NT: d TOP: 6-2 Estimate with Percents KEY: estimate percent 2

7 I: 6. NS: The percent is already a compatible number. Round the price to the nearest $5, multiply the rounded price by the percent, and divide the resulting product by 100. Round the price to the nearest $5. Find the tip only. Set up the percent portion of your equation correctly. orrect! PTS: 1 IF: verage REF: Page 279 OJ: Problem-Solving pplication NT: d TOP: 6-2 Estimate with Percents KEY: estimate percent 7. NS: Set up an equation to find the percent. ivide both sides by 497 to isolate the variable, and simplify. If necessary, round your answer to the nearest hundredth of a percent. x 171 = x 171 = x = Set up an equation to find the percent. You can set up a proportion and solve. orrect! Set up an equation to find the percent. ivide to undo the multiplication, and simplify. PTS: 1 IF: verage REF: Page 284 OJ: Finding the Percent One Number Is of nother TOP: 6-3 Finding Percents KEY: percent 8. NS: Set up a proportion and solve = n 3,970 NT: d Set up a proportion and solve. orrect! Set up a proportion and solve. Set up a proportion and solve. PTS: 1 IF: verage REF: Page 285 OJ: pplication NT: d TOP: 6-3 Finding Percents KEY: percent 3

8 I: 9. NS: Set up an equation to find the number. ivide to undo the multiplication, and simplify. 44 = 90% n 44 = 0.9n = 0.9n = n Set up an equation to find the number. Set up an equation to find the number. Set up an equation to find the number. orrect! PTS: 1 IF: asic REF: Page 288 OJ: Finding a Number When the Percent Is Known TOP: 6-4 Finding a Number When the Percent Is Known 10. NS: sales tax rate sale price = total tax bill NT: d KEY: percent onvert each tax rate to a decimal and multiply by the price. dd to find the total tax bill. Find the total tax bill for all the districts. onvert each tax rate to a decimal before multiplying by the price. First, convert each tax rate to a decimal and multiply by the price. Then, add to find the total tax bill. orrect! PTS: 1 IF: verage REF: Page 298 OJ: Multiplying by Percents to Find Sales Tax mounts NT: d TOP: 6-6 pplications of Percents KEY: multiplication percent 4

9 I: 11. NS: 6 x = 15 Set up a proportion x = 6( 100) Find the cross products. 15x 15 = 6( 100) Since x is multiplied by??, divide both sides by?? to undo the 15 multiplication. x = 40 orrect! Use the proportion: dinosaur 1 is to dinosaur 2 as percent is to 100. Then, find the cross products. Set up a proportion. Then, cross multiply. In your final answer, convert the decimal to a percent. PTS: 1 IF: verage REF: Page 289 OJ: pplication NT: d TOP: 6-4 Finding a Number When the Percent Is Known KEY: percent 12. NS: Percent increase describes how much the original amount increases. Percent decrease describes how much the original amount decreases. The percent change is the ratio of the amount of change to the original amount, or amount of change percent change = original amount. If the change is from a lesser amount to a greater amount, then there is a percent increase. If the change is from a greater amount to a lesser amount, then there is a percent decrease. If the change is from a lesser amount to a greater amount, then there is a percent increase. If the change is from a greater amount to a lesser amount, then there is a percent decrease. orrect! First, find the amount of change. Then, set up a ratio of the amount of change to the original amount and simplify. PTS: 1 IF: asic REF: Page 294 OJ: Finding Percent Increase or ecrease NT: d TOP: 6-5 Percent Increase and ecrease KEY: percent decrease percent increase 5

10 I: 13. NS: The percent decrease is the ratio of the amount of decrease to the original amount, or amount of decrease percent decrease =. original amount First, find the amount of decrease. Then, set up a ratio of the amount of decrease to the original amount and simplify. ivide the amount of decrease by the original amount. orrect! In your final answer, convert the decimal to a percent. PTS: 1 IF: verage REF: Page 294 OJ: pplication NT: d TOP: 6-5 Percent Increase and ecrease KEY: percent decrease percent increase 14. NS: Set up an equation and solve. sale percent = commission orrect! Set up an equation and solve. heck that the answer reasonable. Set up an equation and solve. PTS: 1 IF: verage REF: Page 299 OJ: ividing by Percents to Find Total Sales NT: d TOP: 6-6 pplications of Percents KEY: division percent 15. NS: First, find the interest the customer will pay. Use the formula I = P r t. Then, find the total amount to be repaid by adding the principal to the interest. orrect! onvert the percent to a decimal before using it. Use the formulas I = Prt and P + I =. This is the interest only. Now, find the total amount to be repaid. PTS: 1 IF: verage REF: Page 302 OJ: Finding Interest and Total Payment on a Loan NT: d TOP: 6-7 Simple Interest KEY: interest simple interest 6

11 I: 16. NS: First, find the interest the customer will earn. Use the formula I = P r t. Then, find the total amount in the account by adding the principal to the interest. Use the correct time. orrect! Use the formulas I = Prt and P + I =. This is the interest only. Now, find the total amount in the account. PTS: 1 IF: verage REF: Page 303 OJ: omputing Total Savings NT: d TOP: 6-7 Simple Interest KEY: interest simple interest MTHING 17. NS: F PTS: 1 IF: asic REF: Page 298 TOP: 6-6 pplications of Percents KEY: multiplication percent 18. NS: E PTS: 1 IF: asic REF: Page 298 TOP: 6-6 pplications of Percents KEY: multiplication percent 19. NS: PTS: 1 IF: asic REF: Page 278 TOP: 6-2 Estimate with Percents KEY: estimate percent 20. NS: PTS: 1 IF: asic REF: Page 278 TOP: 6-2 Estimate with Percents KEY: estimate percent 21. NS: PTS: 1 IF: asic REF: Page 298 TOP: 6-6 pplications of Percents 22. NS: PTS: 1 IF: asic REF: Page 278 TOP: 6-2 Estimate with Percents NUMERI RESPONSE 23. NS: $ PTS: 1 IF: verage NT: d TOP: 6-7 Simple Interest 7

12 I: SHORT NSWER 24. NS: 280 feet Round the height of the measured tree to 140 feet. Round the percent to 50% and simplify = 1 2. Solve : tallest tree height = Scoring Rubric: 4 The solution is correct, and all of the work is shown as above. or different logical method is used to find the correct solution. 3 The solution is correct, but not all of the work is shown. 2 The solution is incorrect, but the work shows understanding of the concept. 1 The solution is incorrect, and the work shows no understanding of the concept. PTS: 1 IF: verage REF: Page 279 OJ: Problem-Solving pplication NT: d TOP: 6-2 Estimate with Percents KEY: estimate percent 8

13 I: 25. NS: a. $17, First determine the amount of salary from commission: commission = $ commission = $ Second, add the commission to the base salary: total pay = $4, $12, b. $13, etermine the amount of tax: tax = $17, Tax = $ etermine the pay after taxes: pay after taxes = $17, $ Scoring Rubric: 4 The solution is correct, and all of the work is shown as above. or different logical method is used to find the correct solution. 3 oth solutions are correct, but not all of the work is shown. 2 The solution for part a is correct, but the solution for part b is incorrect or The solution for part a is incorrect, but the work in part b is correct. 1 oth solutions are incorrect, and the work shows no understanding of the concept. PTS: 1 IF: verage REF: Page 299 OJ: Using Proportions to Find the Percent of Earnings NT: d TOP: 6-6 pplications of Percents KEY: multiplication percent 9

14 I: ESSY 26. NS: You can determine the amount of sand by multiplying the total amount of mix needed by 24%. However, to determine the amount of cement and stone required, you must know how much mix is still required. To find that number, subtract the amount of sand you determined above from the total amount of mix. This will tell you how much cement and stone must be added. To determine the amount of cement needed, take the remaining mix needed and multiply it by 35%. To determine the amount of stone required, take the remaining mix needed and multiply it by 65%. Scoring Rubric: 4 The solution is correct, and the explanation is complete as above. or The solution is correct, and a different logical explanation is given. 3 The solution is correct, but the explanation is incomplete. 2 The solution is incorrect, but the explanation shows some understanding of the concept. 1 The solution is incorrect, and the explanation is missing or shows no understanding of the concept. PTS: 1 IF: verage REF: Page 283 OJ: Finding the Percent One Number Is of nother KEY: percent TOP: 6-3 Finding Percents 10