MATH 012 - Brookdale Community College



|MATH 012 |

|TEST 2 |

|REVIEW SHEET |

1. a) Explain how to change a fraction to a percent.

b) Explain how to change a percent to a fraction.

2. Write each of the following as a decimal and as a fraction in lowest terms.

a) 73% b) [pic]% c) 150% d) 205.3%

e) [pic] f) [pic] g) [pic]

3. Write each of the following decimals as percents:

a) 0.19 b) 0.04 c) 1.7 d) 0.003 e) 3

4. Write each of the following as percents:

a) [pic] b) [pic] c) [pic]

d) [pic] (Give the exact percent and also the percent rounded to the nearest hundredth)

5. Do the following mentally.

a) 8 is 10% of . c) 20 is 50 % of .

b) 16 is % of 8. d) 10 is % of 40.

6. a) Multiplying a number by 200% is the same as multiplying by what whole number?

b) Explain how to find 10% of a number mentally.

For problems 7 – 18, set up an equation of the form Amount = percent ( base and solve.

7. What is 59% of $11.00?

8. 0.75 is what percent of 2.5?

9. 5 is 25% of what number?

10. What percent of 54 is 18?

11. 28 is what percent of 80?

12. 12% of 0.036 is what number?

13. 2% of what number is 0.5?

14. 24 is 200% of what number?

15. 6.5% of $175,000 is what number?

16. $12 is [pic]% of what value?

17. 200% of what number is 800?

18. 25% of what number is 1?

19. The 700 employees at a community college fall into three major categories, as shown below.

a) How many employees are in faculty?

b) How many employees are in administration?

20. Workers at a plant belong to a union, and union dues of 1.5% are deducted from their salaries each month. If a worker earns $2,340 in a month, how much will be deducted for union dues?

21. At the ABC Day Care Center, 8 children were absent on Monday. This is 20% of the total enrollment. How many children are enrolled?

22. A sports store discounts skis at the end of the winter. On sale, the skis are selling for $300. If this represents a discount of 25%, what was the original price of the skis? (Hint: the skis are selling for 75% of its regular price.)

23. A store is offering a 25% off sale on all its merchandise. How much will you be charged for 2 items that were originally $10.80 each?

24. a) Miss Smith works on a commission which is 15% of her sales. Last week her sales were $4120. How much did she earn?

b) Her boss offers her the option of changing her plan, in the future, to $100 a week plus 12% commission. Assuming the amount she made last week was typical for her, should she stay on straight commission or go for the new plan?

25. The population of A-town is growing at a rate of 6% a year. If the population at present is 5750, what will it be 1 year from now?

26. The population of B-town rose from 7460 to 8579 in two years. What percent increase was that?

27. A real estate agent charges a fee of 6% for selling a house. If the agent receives $31,800 from the sale of a certain house, what was the selling price of the house?

28. How much will you pay for a purchase of $54.38 if the sales tax is 6%?

29. If the sales tax on an item is $1.50 and the sales tax rate is 6%, what was the selling price of the item, before the tax was added?

30. If you redeem a $0.50 coupon when you purchase a box of cereal priced at $2.50, what is the percent savings?

31. Bill saw a jacket he liked on sale for 20% off. The regular price was $175. He went back a few days later and the store was giving an additional 10% off the sale price. If he buys the jacket, how much will he have to pay for it?

32. Joel deposited $350 in a savings account at the beginning of the year. How much will he have at the end of the year if he makes no withdrawals and the bank pays 5.5% simple interest annually?

33. a) A college student borrowed $2350 for 3 months at an annual simple interest rate of 7.5%. How much interest will the student pay back on the loan?

b) What is his monthly payment?

34. If you borrow $550 from a bank at 7.2% annual simple interest, how much will you repay the bank if you keep the money for 90 days?

35. A car dealer wishes to reduce its inventory, so the dealer offers customers a simple annual interest rate of 10%. If a customer finances a car loan for $8700 over 3 years, how much interest will the customer pay?

36. A movie theater discounts senior citizens tickets by charging $5.25 for a $7 ticket. What percent discount are they giving?

37. The regular selling price of a DVD is $18.90. If you make a purchase on Monday, the store gives a discount of 8%. How much will the DVD cost if you buy it on Monday? Round to the nearest cent.

38. During the holiday season a department store increases its work force by 25%. If they ordinarily have 600 employees, how many will they have during the holidays?

39. A coat that usually sells for $256 is discounted 25%. Then because it is customer appreciation day an additional discount is given. What was the second discount rate if the final price was $172.80?

CUMULATIVE REVIEW

40. Translate the following expressions into math expressions. If you use a variable define it.

a) Three more than seven

b) Twelve decreased by five

c) Four is greater than two

d) The difference between twenty and sixteen

e) The quotient of seven and nine

f) Three-quarters of twenty-one

g) Double the number of phone calls since last year

h) One-fourth of the budgeted amount

41. Find all the factors of the given numbers:

a) 18

b) 100

c) 21

d) 16

42. From the graph below estimate:

a) The beginning salary for a person who took 3 math classes in college.

b) The beginning salary for a person who took 8 math classes in college.

c) The number of math classes taken by a person with a beginning salary of

$50,000.

d) The number of math classes taken by a person with a beginning salary of

$40,000.

43. Estimate the quotient of 1083 and 114

a) List the two approximate values you would use in your estimate.

b) Divide the two approximate values.

c) Use a calculator to find the exact answer using the original numbers.

44. Solve the following:

a) 13 – m = 28

b) [pic]

c) b + 2.17 = –1.04

d) [pic]

e) [pic]

f) [pic]

g) [pic]

h) [pic]

45. A carpenter finds that he must reduce the size of a piece of lumber by 1.06 inches. If he starts with a 5.92 inch piece, find the length of the piece of lumber after the cut.

46. The perimeter of a square tile is 6.4 cm. How long is each side? Show the equation you used to find the answer.

47. How many [pic]-pound packages can be made from 36 pounds of raisins?

48. A car rental agency charges $28 a day plus $0.30 per mile for a rental car. What will the charge be if you rent the car for 5 days, and drive 425 miles?

49. Choose a variable to represent the unknown. Then write and solve an equation to answer the following question.

One serving of Oreo cookies has 7 grams of fat. This is 2.8 times the amount of fat in a serving of oatmeal crisp cereal. How many grams of fat are in a serving of the cereal?

50. For the following right triangle,

a) find the hypotenuse. 5 cm

b) find the perimeter.

c) find the area. 12 cm

51. You have a 12 foot ladder which leans against the top of a wall. The distance along the ground from the base of the wall to the bottom of the ladder is 5 feet. How high is the wall? Round the answer to the nearest tenth. Make sure to include the unit.

52. Use the appropriate symbols “” or “=” to compare the following problems.

a) [pic]

b) [pic]

c) [pic]

d) 2.13 2.1896

e) [pic]

f) [pic]

53. Evaluate the following

a) [pic]

b) [pic]

54. Round 43.5962 to the nearest

a) whole number

b) tenth

c) ten

d) hundredth

e) thousandth

55. Simplify each of the following expressions. Show all work and check answers using a calculator.

a) [pic]

b) [pic]

c) [pic]

d) [pic]

e) [pic]

f) [pic]

g) [pic]

56. A rectangle is 4 inches longer than it is wide.

a) Choose a variable to represent the width. Define it.

b) Write an expression that represents the length.

57. Complete the following table of solutions for [pic]

|x |y |(x, y) |

|0 | | (0, ) |

| |0 |( , 0) |

| |5 |( , 5) |

58. Give the coordinates of each point on the graph.

59. Simplify each of the following algebraic expression.

a) [pic]

b) [pic]

c) [pic]

60. The temperature in New Jersey today is 48(F. The temperature in Egypt is 10(C. Which one has a warmer temperature and by how many degrees Celsius? Use the formula [pic]. Make sure to include units. Round to nearest hundredth of a degree.

61. a) Explain how to multiply a decimal number by 100 by moving the decimal point.

b) Explain how to divide a decimal number by 1000 by moving the decimal point.

MATH 012 Test 2 Review Sheet

Answer Key

1. a) Write the fraction as a decimal by dividing its numerator by its denominator. Multiply the decimal by 100 by moving the decimal point 2 places to the right. Insert a % symbol.

b) Drop the % symbol and write the given number over 100. Then simplify the fraction, if possible.

2. a) [pic]

b) 0.0125 = [pic]

c) [pic]

d) [pic]

e) [pic]

f) [pic]

g) [pic]

3. a) 19 %

b) 4%

c) 170%

d) 0.3%

e) 300%

4. a) 50%

b) 275%

c) 537.5%

d) [pic]% ≈166.67%

5. a) 80

b) 200

c) 40

d) 25

6. a) 2

b) 10% is the same as [pic] of a number or divided by 10 by moving the decimal point one place to the left.

7. x = 0.59(11)

$6.49

8. 0.75 = x(2.5)

30%

9. 5 = 0.25x

20

10. [pic]

11. 35%

12. 0.00432

13. 25

14. 12

15. $11,375

16. $480

17. 400

18. 4

19. a) 322 faculty

b) 105 administration

20. $35.10

21. 40 children

22. $400

23. $16.20

24. a) $618

b) Straight commission as

[pic]

25. 6095

26. 15%

27. $530,000

28. $57.64

29. $25

30. 20%

31. $126

32. $369.25

33. a) $44.06

b) $798.02

34. $559.76

35. $2610

36. 25%

37. $17.39

38. 750 employees

39. 10%

CUMULATIVE REVIEW

40. a) 7 + 3

b) 12 – 5

c) 4 > 2

d) 20 –16

e) [pic]

f) [pic]

g) 2x x = The number of phone calls

h) [pic] b = The budgeted amount

41. a) 1, 2, 3, 6, 9, 18

b) 1, 2, 4, 5, 10, 20, 25, 50, 100

c) 1, 3, 7, 21

d) 1, 2, 4, 8, 16

42. a) $40,000

b) $75,000

c) 5 classes

d) 3 classes

43. Answer will vary. If front-end rounding is used, then

a) 1000 and 100

b) 10

c) 9.5

44. a) m = –15

b) x = 1.2

c) b = –3.21

d) n = –7.571

e) [pic]

f) [pic]

g) n = 1.6

h) x = 6

45. 4.86 inches

46. p = 4s

S = 1.6 cm

47. 84 packages

48. $267.50

49. 2.5 grams

50. a) 13 cm

b) 30 cm

c) 30 square cm.

51. 10.9 ft

52. a) >

b) >

c) <

d) <

e) =

f) >

53. a) 44

b) 13

54. a) 44

b) 43.6

c) 40

d) 43.60

e) 43.596

55. a) 69

b) [pic]

c) –25

d) 6

e) [pic]

f) [pic]

g) [pic]

56. a) x = the width

b) x + 4

57.

|x |y |(x, y) |

|0 |–5 |(0, –5) |

|4 |0 |(4, 0) |

|8 |5 |(8, 5) |

58. A ( –7, 9)

B (–4, 0)

C (5, –3)

D (0, –9)

59. a) y + 10

b) 60y

c) 2x + 7

60. New Jersey 8.89(C

Egypt is warmer by 1.11(C

61. a) move the decimal point two places to the right.

b) move the decimal point to three places to the left.

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