Year 4 Final Exam Review Fall 2011



Year 4 Final Exam Review Fall 2011

2A

1. Convert 25 gallons to quarts.

2. Convert 80 miles per hour to units of miles per minute.

3. Find the area in square feet of a rectangular yard that measures 15 yards by 30 yards.

4. As you leave Paris, you convert 6700 euros to dollars. How many dollars do you receive?

5. You return from Mexico with 4500 pesos. How much are they worth in U.S. dollars?

6. A hose fills a hot tub at a rate of 4.2 gallons per minute. How many hours will it take to fill a 400-gallon hot tub?

7. Convert 275 centimeters to inches.

8. Convert 26 meters per second to miles per hour.

2B

9. Convert 53ºF to Celsius.

10. Convert 78ºC to Kelvin.

11. Assume that running consumes 120 Calories per mile. If you run 12-minute miles, what is your average power output, in watts, during a 1-hour run?

12. A typical glass of wine contains about 20 grams of alcohol. Consider a 120-pound woman, with approximately 4 liters (4000 milliliters) of blood, who drinks two glasses of wine. If all the alcohol were immediately absorbed onto her bloodstream, what would her blood alcohol content be?

13. A meter is __________times as large as a millimeter.

14. A cube of wood measures 3 centimeters on a side and it weighs 20 grams. What is its density?

15. How many quarts does a 20-gallon gasoline tank hold? How many pints? How many ounces?

3A

16. Express the first number as a percentage of the second number. 32.3 Arizonans per square mile in 1990 and 45.2 Arizonans per square mile in 2000.

17. The gestation period of dogs (62 days) is ________percent longer than the gestation period of gerbils (24 days).

18. The height of the Statue of Liberty (305 ft) is ______percent shorter than the Empire State building (1250 feet).

19. You purchase a bicycle with a retail (pre-tax) price of $340. The local sales tax rate is 7.8%. What is the final cost?

20. Your dinner bill is $37.98. You leave $45. What percent tip did you leave? (Ignore taxes in this question)

21. Betsy’s salary increased from $60,000 to $67,000 over a three-year period. Stanley’s salary increased from $65,000 to 74,000 over the same period. Whose salary increased more in absolute terms? In relative terms?

22. Find the absolute change and the percentage change. The number of daily newspapers in the United States was 2226 in 1900 and 1420 in 2010.

23. The annual interest rate for Jaycee’s savings account increased from 3.4% to 3.6%. Find the absolute change in terms of percentage points and as a relative change in terms of a percentage.

3B

24. Convert each of the following numbers from scientific to ordinary notation a) 3 x 103 b) 2 x 10-2

25. Write each of the following numbers in scientific notation a) 233 b) .11

26. Rewrite the following statement using a number in scientific notation: As of 2009, U.S. consumer credit (total amount borrowed) was $2564 billion.

27. Estimate the following quantities using scientific notation a) 400,000 x 100 b) 6.1 million x 1.2 thousand c) 3 x 109 ÷ 4.1 x 105 d) 3,456,367 ÷ 6271 e) (6.129894 x 108) ÷ (3.643 x 103)

28. Find the scale ratio for: 2 centimeters on the map represents 100 kilometers.

3C

29. Describe possible sources of random and systematic errors in: running times at a 10-kilometer race.

30. State which is more accurate and which is more precise? Your true height is 70.50 inches. A tape measure that can be read to the nearest ⅛ inch gives your height as 70⅜ inches. A new laser device at the doctor’s office that gives readings to the nearest 0.05 inch gives your height as 70.90 inches.

3E

31. The table below shows the batting records of two baseball players in the first half (first 81 games) and last half of a season. a) Which player had the higher batting average in the first half of the season? b) Which player had the higher batting average in the second half of the season? c) Which player had the higher overall batting average for the season?

|First Half |

|Player |Hits |At-bats |Batting Average |

|Brian |50 |150 |.333 |

|Robert |10 |50 |.200 |

|Second Half |

|Player |Hits |At-bats |Batting Average |

|Brian |35 |70 |.500 |

|Robert |70 |150 |.467 |

| |Tumor is Malignant |Tumor is Benign |Total |

|Positive Mammogram |90 |990 |1080 |

| |true positives |false positives | |

|Negative Mammogram |10 |8910 |8920 |

| |false negatives |true negatives | |

|Total |100 |9900 |10,000 |

32. One percent of breast tumors are malignant. However, the table above assumes that mammogram screening is 90% accurate. Suppose a patient has a positive mammogram. What is the chance that she really has cancer? What is the chance of a positive mammogram, given that the patient has cancer? Suppose a patient has a negative mammogram. What is the chance that she actually does have cancer?

4A

33. Compute the total cost per year of the following pairs of expenses. Then complete the sentence: On an annual basis, the phone bill is ____% of student health insurance. Suzanne’s cell phone bill is $75 per month, and she spends $180 per year on student health insurance.

34. Find the monthly interest payments; assume that monthly interest rates are 1/12 of annual interest rates. You maintain an average balance of $550 on your credit card, which carries a 21% annual interest rate.

35. Prorate the expenses and find the corresponding monthly expense. Vic pays a semiannual premium of $540 for automobile insurance, a monthly premium of $150 for health insurance, and an annual premium of $500 for life insurance.

36. The following table shows expenses and income. Find the net monthly cash flow.

|Income |Expenses |

|Part-time job: $800/month |Car Payment: $120/month |

|Allowance: $50/week |Food: $40/week |

|College fund from grandparents: |Gas: $80/month |

|$3000/year | |

| |Insurance: $1200/year |

37. Which option is less expensive? You currently drive 200 miles per week in a car that gets 20 miles per gallon of gas. You are considering buying a new fuel-efficient car for $18,000 (after trade-in on your current car) that gets 40 miles per gallon. Insurance premiums for the new and old car are $900 and $500 per year, respectively. You anticipate spending $1700 per year on repairs for the old car and having no repairs on the new car. Assume gas costs $3.30 per gallon. Over a five-year period, is it less expensive to keep your old car or buy the new car?

38. You could take a 16-week, three credit college course, which requires 12 hours per week of your time and costs $400 per credit-hour in tuition. Or during those hours you could have a job paying $10 per hour. What is the net cost of the class compared to working? Given that the average college graduate earns nearly $20,000 per year more than a high school graduate, is paying for the college course a worth while expense?

39. Assume the following insurance plan: Office visits require a co-payment of $25. Emergency room visits have a $300 deductible (you pay the first $300), surgical operations have a $1200 deductible (you pay the first $1200). You pay a monthly premium of $400. During a one-year period, you had the following expenses.

Expense Total Cost (before insurance)

Office visit $150

Surgery $8050

Office visit $150

Emergency room $1200

4B

40. You deposit $2600 in an account with an annual interest rate of 3.65%. Calculate the amount of money you will have in that account after five years, assuming that you earn simple interest.

41. Compute the balance in the account assuming interest is compounded annually. $12,580 is invested at an APR of 5% for 12 years.

42. Compute the balance in the account where $32,000 is invested for 30 years with an APR of 4.9% with quarterly compounding.

43. Find the annual percentage yield (APY) for a bank that offers an APR of 6.55% compounded daily.

44. Compute the balance in the following account: A $14,400 deposit with an APR of 9% compounded continuously for 5 years.

45. How much must you deposit today into the following account in order to have $39,000 in 14 years for a down payment on a house? The account has monthly compounding and an APR of 7.2%. Assume no additional deposits are made.

46. How much must you deposit today into an account with an APR of 5%, compounded daily in order to have a $150,000 college fund in 18 years? Assume no additional deposits are made.

4C

47. Find the savings plan balance after 12 months with an APR of 4.85% and monthly payments of $175. Assume monthly deposits and monthly compounding.

48. You put $490 per month in an investment plan that pays an APR of 4.8%. How much money will you have after 18 years? Compare this amount to the total deposits made over the time period.

49. You want to purchase a new car in 2 years and expect the car to cost $12,500. Your bank offers a plan with a guaranteed APR of 4.7% if you make regular monthly deposits. How much should you deposit each month to end up with $12,500 in 2 years?

50. Compute the total and annual returns. Four years after paying $5600 for shares in a startup company, you sell the shares for $3800 (at a loss)

51. Using the following Chipotle stock from a quote you looked at last night.

|Chipotle (CMG) |

|Last |Change |Volume |P/E Ratio |Dividend Yield |

|334.74 | 2.01 |587,435 |52.14 |1.09 |

a) What was the price per share at the end of the day yesterday?

b) Based on the current price, what is the total value of the shares that have been traded so far today?

c) Suppose you won 100 shares of Chipotle. Bases on the current price and dividend yield, what total dividend should you expect to receive this year?

d) What were the earnings per share for Chipotle?

52. Compute the current yield on the following bond: A $1500 Treasure bond with a coupon rate of 3.0% that has a market value of $1250.

53. Compute the annual interest that you would earn on the following bond: A $1500 Treasury bond with a current yield of 2.7% that is quoted at 118 points.

54. Use the following Mutual fund growth.

|Vanguard Limited-Term Tax-Exempt Fund (VMLTX) | | | |

| |1-Yr |3-Yr |5-Yr |

|NAV $9.80 |1.25% |-0.98% |2.6% |

a) Suppose you invest $6000 in this fund today. How many shares will you buy?

b) Suppose you had invested $6000 in this fund 1 year ago? How much would your investment be worth now? 3 years ago? How much would your investment be worth now?

4D

55. You borrowed $90,400 at an APR of 8%, which you are paying off with monthly payments of $757 for 20 years. Identify the a) loan principal, b) the annual interest rate, c) the number of payments per year, d) the loan term, and e) the payment amount. f) How many total payments does the loan require? g) What is the total amount paid over the full term of the loan? h) Of the total amount paid, what percentage is paid for interest?

56. A home mortgage of $180,000 with a fixed APR of 8% for 15 years. a) Calculate the monthly payment. b) Determine the total amount paid over the term of the loan. c) Of the total amount paid, what percentage is paid toward the principal and what percentage is paid for interest?

57. You need to borrow $15,000 to buy a car and you determine that you can afford monthly payments of $315. The bank offers three choices: a 3-year loan at 6.5%, a 4-year loan at 7.5%, or a 5-year loan at 8.5%. Which loan best meets your needs?

58. Suppose that on January 1, you have a balance of $4700 on a credit card with an APR of 19.5%, which you want to pay off in 4 years. Assume that you make no additional purchases. a) Calculate your monthly payments. b) When the card is paid off, how much will you have paid since January 1? c) What percentage of your total payment (part b) is interest?

59. Complete the table for the next 3 months. The initial balance is $500 and the interest rate is 2% per month (24% APR) and that interest for a given month is charged on the balance for the previous month.

|Month |Payment |Expenses |Interest |Balance |

|0 |- |- |- |$500 |

|1 |400 |250 | | |

|2 |300 |180 | | |

|3 |350 |260 | | |

60. Compare the monthly payments and total loan costs for the following pair of loan options. Assume that both loans are fixed rate and have the same closing costs. You need a $150,000 loan. Option 1: a 30-year loan at an APR of 7%. Option 2: a 15-year loan at 6.5%.

61. Consider the following pairs of loan options for a $160,000 mortgage. Calculate the monthly payments and total closing costs for each option. Choice 1: 30-year fixed rate at 7% with closing costs of $100 and no points. Option 2: 30-year fixed rate at 6.5% with closing costs of $1000 and 2 points.

4E

62. Find the gross income, adjusted gross income, and taxable income: Phil earned wages of $56,900, received $2000 in interest from a savings account, and contributed $2400 to a tax-deferred retirement plan. He was entitled to a personal exemption of $3650 and had deductions totaling $6800

63. Your deductible expenditures are $4100 for interest on a home mortgage, $290 for contributions to charity, and $165 for state income taxes. Your filing status entitles you to a standard deduction of $5700. Decide whether you should itemize your deductions or take the standard deduction.

64. Jill is married filing separately with a taxable income of $61,200. Use the marginal tax rates in Table 4.9 to compute the tax owed.

65. Determine how much Rosa will save in taxes with the specified tax credits or deductions. She is in the 15% tax bracket and claims the standard deduction. How much will her tax bill be reduced if she makes a $1000 contribution to charity?

66. You are in the 33% tax bracket. Your apartment rents for $850 per month. Your monthly mortgage payments would be $1000, of which an average of $900 per month goes toward interest during the first year. Determine whether the monthly rent is greater than or less than the monthly house payments during the first year. In both cases, assume you itemize deductions.

67. Allison earned $47,300 in salary and $1580 in interest and made $1600 in tax-deferred contributions to a retirement fund. Calculate the FICA taxes and income taxes to obtain a total tax bill. Then find the overall tax rate on the gross income, including both FICA and income taxes. Assume single status and take the standard deduction. Use the tax rates in Table 4.9.

68. Calculate the total tax owed by each individual in the following pairs (FICA and income taxes). Compare their overall tax rates. Assume each person is single and takes the standard deduction. Use the tax rates in Table 4.9 and the special rates for dividends and capital gains given in the notes for 4E. Wayne earned $100,000 in wages. Vicky earned $100,000, all in dividends and long-term capital gains.

69. Calculate the change in monthly take-home pay when the following tax-deferred contributions are made. You are married filing jointly and have a taxable income of $95,300. You make monthly contributions of $1100 to a tax-deferred savings plan.

70. Write each English phrase as an algebraic expression. Then simplify the expression. A number decreased by the sum of the number and four.

P

71. Simplify [pic]

72. Simplify [pic]

73. Rationalize the denominator [pic]

74. Simplify [pic]

75. Find the product [pic]

76. Factor [pic]

77. Factor [pic]

78. Factor [pic]

79. Simplify [pic]

80. Find all numbers that must be excluded from the domain of the rational expression in #79.

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