Algebra Final Practice Test

Algebra Final Practice Test

1 . The grade in a psychology class is determined by three tests and a final exam. The final exam counts twice as much as a test. A student’s three test grades are 78, 82, and 100. What does he need to score on his final exam to bring his average up to 90?

(a) 83

(b) 95

(c) 50

(d) 190

2 . If 2( x – 3) – 4( x + 5) = 7 x + 1, then

4 . (2 x ³ ) ² =

(a) 2 x ⁵

(b) 2 x ⁶

(c) 4 x ⁵

(d) 4 x ⁶

5 . A rectangle’s length is three times its width. The area is 108 square inches. How wide is the rectangle?

(a) 6 inches

(b) 5 inches

(c) 4 inches

(d) 3 inches

6 . If , then

7 . A coin bank contains $1.65 in nickels, dimes, and quarters. There are twice as many nickels as dimes and one more quarter than nickels. How many quarters are there?

(a) 3

(b) 4

(c) 5

(d) 6

(a) x ^1/3

(b) x ^2/3

(c) x ^3/2

(d) x ^–1/3

9 . A small boat traveled five miles upstream and later traveled back downstream. The stream’s current was 4 mph, and the boat spent a total of 1 hour 40 minutes traveling. What was the boat’s speed in still water?

(a) 5 mph

(b) 6 mph

(c) 9 mph

(d) 8 mph

10 . If 2 x ² – x – 2 = 0, then

11 . Melinda walked a six-mile path in 1 hour 45 minutes. At first she walked at the rate of 4 mph then she finished her walk at the rate of 3 mph. How far did she walk at 4 mph?

(a) 1 mile

(c) 2 miles

(d) 3 miles

12 . What is the solution to 4 – x > 1?

(a) (–∞,3)

(b) (–∞,3]

(c) (3,∞)

(d) [3,∞)

14 . A businessman has a choice of two rental cars. One costs $40 per day with unlimited mileage. The other costs $25 per day plus 30 cents per mile. For what mileage is the $40 plan no more expensive than the other plan?

(a) At least 50 miles per day

(b) No more than 50 miles per day

(c) At least 133 miles per day

(d) No more than 133 miles per day

15 . 3 x ⁸ =

(a) 3( x ⁴ ) ²

(b) 3( x ⁴ ) ⁴

(c) (3 x ⁴ ) ²

(d) (3 x ⁴ ) ⁴

16 . If , then

17 . A small group has $100 to spend for lunch. They plan to tip 20% (before tax). The sales tax is . What is the most they can spend on their order?

(a) $72.50

(b) $78.43

(c) $79.52

(d) $77.52

18 . If x ² – 3 x + 2 = 0, then

(a) x = –1, –2

(b) x = 1, 2

(d) No solution

19 . The sum of two consecutive positive integers is 61. What is their product?

(a) 930

(b) 870

(c) 992

(d) 960

20 . ( x + 4)(2 x – 3) =

(a) 2 x ² + 5 x – 12

(b) 2 x ² – 5 x – 12

(c) 7 x – 12

(d) 7 x + 12

22 . One pipe can fill a tank in three hours. A larger pipe can fill the tank in two hours. How long would it take for both pipes, working together, to fill the tank?

(a) 5 hours

(b) 50 minutes

(c) 1 hour 20 minutes

(d) 1 hour 12 minutes

24 . The division problem can be rewritten as

25 . What is the complete factorization of 2 x ³ + 3 x ² – 18 x – 27?

(a) ( x ² – 9) (2 x + 3)

(b) ( x ² + 9) (2 x – 3)

(c) (2 x + 3) ( x – 3) ( x + 3)

(d) cannot be factored

26 . The difference of two positive numbers is 12. Their product is 405. What is the smaller number?

(a) 13

(b) 16

(c) 15

(d) 17

27 . 14 x ² y – 21 xy ² + 7 x =

(a) 7 x (2 xy – 3 y ² )

(b) 7 x (2 xy – 3 y ² + 1)

(c) – 7 x (– 2 xy – 3 y ² + 1)

(d) – 7 x (– 2 xy + 3 y ² + 1)

28 . A small college received a gift of $150,000. The financial officer will deposit some of the money into a CD, which pays 4% annual interest. The rest will go to purchase a bond that pays annual interest. If $7,890 annual income is required, how much should be used to purchase the bond?

(a) $90,000

(b) $74,400

(c) $75,600

(d) $86,000

30 . – 6 x ² – 9 x + 12 =

(a) – 3(2 x ² – 3 x + 4)

(b) – 3(2 x ² + 3 x + 4)

(c) – 3(2 x ² – 3 x – 4)

(d) – 3(2 x ² + 3 x – 4)

31 . A snack machine has $8.75 in nickels, dimes, and quarters. There are five more dimes than nickels and four more quarters than dimes. How many dimes are there?

(a) 15

(b) 24

(c) 19

(d) 20

33 . If 1.18 x – 0.2 = 1.2 x – 0.3, then

34 . A room is five feet longer than it is wide. Its area is 300 square feet. What is the width of the room?

(a) 15 feet

(b) 12 feet

(c) 20 feet

(d) 25 feet

36 . To use the quadratic formula on 2 x ² – x = 4, let

(a) a = 2, b = 0, c = 4

(b) a = 2, b = 1, c = 4

(c) a = 2, b = – 1, c = 4

(d) a = 2, b = – 1, c = –4

37 . An experienced worker can unload a truck in one hour forty minutes. When he works together with a trainee, they can unload the truck in one hour. How long would the trainee need to unload the truck if he works alone?

(a) 1 hour 50 minutes

(b) 40 minutes

(c) 36 minutes

(d) 2 hours 30 minutes

38 . 3(7 x – 4) ⁵ + 8 x (7 x – 4) ⁴ =

(a) 56 x ² – 11 x – 12

(b) (7 x – 4) ⁴ (29 x – 12)

(c) (3 + 8 x ) (7 x – 4) ⁴

(d) (3 + 8 x ) (7 x – 4) ⁵

39 . If the radius of a circle is increased by 4 meters then the circumference is increased to 18π meters. (Recall: C = 2π r .) What is the original radius?

(a) 6 meters

(b) 5 meters

(c) 4 meters

(d) 3 meters

40 . What is the solution for 2 x + 5 ≥ 9?

(a) (2, ∞)

(b) (–∞, 2]

(c) [2, ∞)

(d) (–∞, 2)

41 . 2 x ^{– 3} =

42 . A rectangular box is 10 inches tall. Its width is three-fourths as long as its length. The box’s volume is 1080 cubic inches. What is the box’s width?

(a) 9 inches

(b) 10 inches

(c) 11 inches

(d) 12 inches

45 . A mixture containing 16% of a drug is to be combined with another mixture containing 28% of a drug to obtain 15 ml of a 24% mixture. How much 16% mixture is required?

(a) 5 ml

(b) 7 ml

(c) 10 ml

(d) 12 ml

46 . Reduce .

47 . The sum of two numbers is 14, and their product is 24. What is the smaller number?

(a) 1

(b) 2

(c) 3

(d) 4

48 . If 2 x ² + 4 x – 1 = 0, then

49 . Daniel is twice as old as Jimmy. Terry is one year younger than Daniel. The sum of their ages is 44. How old is Daniel?

(a) 16 years

(b) 18 years

(c) 20 years

(d) 22 years

51 . A jogger left a park at 6:00. He jogged westward at the rate of 5 mph. At the same time a cyclist left the park traveling southward at the rate of 12 mph. When were they miles apart?

(a) 6:20

(b) 6:30

(c) 6:45

(d) 7:00

52 . The manager of an office building can rent all 40 of its offices when the monthly rent is $1600. For each $100 increase in the monthly rent, one tenant is lost and is not likely to be replaced. The manager wants $68,400 in monthly revenue. What rent should he charge?

(a) $1800

(b) $1900

(c) $1700

(d) $2000

53 . If x ² – 3 x = −2, then

54 . The perimeter of a right triangle is 24 inches. One leg is two inches longer than the other leg. The hypotenuse is two inches longer than the longer leg. What is the length of the hypotenuse?

(a) 12 inches

(b) 10 inches

(c) 8 inches

(d) 6 inches

(a) 27 x ² z ³

(b) 27 x ³ yz ³

(c) 27 yz ³

(d) 27 x ² yz ³

56 . When the radius of a circle is increased by two inches, its area is increased by 24π inches ² . What is the radius of the larger circle?

(a) 4 inches

(b) 5 inches

(c) 6 inches

(d) 7 inches

57 . If 4 x ( x – 3) – 5(3 x – 6) = (2 x – 3) ² , then

58 . If – 2( x – 5) = 12, then

(b) x = – 11

(c) x = – 1

(d) x = 11

59 . A math student has a 100 homework average and test grades of 99, 100, and 97. The homework average counts 15%, each test counts 20%, and the final exam counts 25%. What is the lowest grade the student can get on the final exam and still get an A (an average of 90 or better) in the class?

(a) 62

(b) 64

(c) 54

(d) 75

60 . If x ² + 8 x + 1 = 0, then

61 . Linda has $16,000 to invest. She plans to invest part of the money in a bond that pays 5% and the rest in a bond that pays . She wants $937.50 in annual interest payments. How much should she invest in the bond?

(a) $5,000

(b) $7,000

(c) $9,000

(d) $11,000

63 . A woman paid $21.56 (including sales tax) for a book that was marked 20% off. The sales tax was 8%. What was the cover price of the book?

(a) $24.50

(b) $26.95

(c) $24.95

(d) $24.15

65 . The height of a rectangular box is 8 inches. The length is one-andone-half times the width. The volume is 192 cubic inches. What is the box’s width?

(a) 4 inches

(b) 6 inches

(c) 8 inches

(d) 10 inches

67 . 72 increased by 25% is

(a) 97

(b) 90

(c) 18

(d) 72.25

69 . A highway and train track run parallel to each other. At 5:00 a train crosses a river. Fifteen minutes later a car, traveling in the same direction, crosses the river. If the train’s average speed is 52 mph and the car’s average speed is 64 mph, when will the car pass the train?

(a) 6:00

(b) 6:20

(c) 6:30

(d) 6:40

70 . Completely factor 81 – x ⁴ .

(a) (3 – x ) ² (3 + x ) ²

(b) (9 + x ² ) (3 – x ) (3 + x )

(c) (9 + x ² ) (9 – x ² )

(d) Cannot be factored

71 . Peanuts and a nut mixture containing 40% peanuts will be mixed together to produce eight pounds of a 50% peanut mixture. What quantity of peanuts should be used?

72 . (2 x – 1) (3 x + 4) =

(a) 6 x ² – 4

(b) 6 x ² + 11 x − 4

(c) 11 x – 4

(d) 6 x ² + 5 x – 4

73 . (3 x ³ y ² ) ² =

(a) 3 x ⁶ y ⁴

(b) 9 x ⁶ y ⁴

(c) 3 x ⁵ y ⁴

(d) 9 x ⁵ y ⁴

74 . A department store sells 60 personal CD players per week when the price is $40. For each $2 increase in the price, three fewer players per week will be sold. What should the price of the players be if the store manager needs $2346 per week in revenue?

(a) $50

(b) $46

(c) $48

(d) $51

75 . Completely factor x ³ + 3 x ² – 4 x – 12.

(a) ( x + 3) ( x – 3)

(b) ( x ² – 4) ( x + 3)

(c) ( x – 2) ( x + 2) ( x + 3)

(d) Cannot be factored

76 . A man is dividing $15,000 between two investments. One will pay 8% annual interest, and the other will pay annual interest. If he requires at least $1000 in annual interest payments, how much money can he invest at ?

(a) At least $1666.67

(b) At most $1666.67

(c) At least $13,333.33

(d) At most $13,333.33

77 . Factor x ⁴ + 5 x ² – 36.

(a) ( x ² + 9) ( x – 2) ( x + 2)

(b) ( x + 4) ( x – 9)

(c) ( x – 4) ( x + 9)

(d) ( x – 2) ( x + 2) ( x – 3) ( x + 3)

79 . If x ² – x – 2 = 0, then

80 . A pair of boots is sale priced at $78.40, which is 30% off the original price. What is the original price?

(a) $112

(b) $101.92

(c) $104.53

(d) $98

82 . What is the interval notation for x ≥ 4?

(a) (4, ∞)

(b) [4, ∞)

(c) (–∞, 4)

(d) (–∞, 4]

83 . A salesman earns $12,000 annual base salary plus 8% commission on sales. If he wants an annual salary of at least $45,000, what should his annual sales be?

(a) At least $712,500

(b) At most $712,500

(c) At least $412,500

(d) At most $412,500

85 . A real estate agent drove to a remote property. She averaged 50 mph to the property and 48 mph on the return trip. Her total driving time was 4 hours 54 minutes. How far was the property?

(a) 100 miles

(b) 110 miles

(c) 115 miles

(d) 120 miles

86 . (5 x – 2) ² =

(a) 25 x ² – 20 x + 4

(b) 5 x ² + 4

(c) 25 x ² + 4

(d) 25 x ² – 4

87 . A company that manufactures calculators wants $18,000 monthly profit. Each calculator costs $6 to produce. The selling price is $11. Monthly overhead runs to $150,000. How many calculators should be produced and sold each month?

(a) 13,636

(b) 3,600

(c) 26,400

(d) 33,600

88 . 2 x ³ y ^{– 4} ( x ^{– 2} – x ^–1 y ³ + y ⁴ ) =

(a) 2 x ³ y ^{– 4} – 2 x ^{– 3} y ^{– 12} + 2 x ³ y ^{– 16}

(b) 2 xy ^{– 4} – 2 x ² y ^{– 1} + 2 x ³

(c) 2 x ² y ^{– 1} + 2 x ³

(d) – 2 x ² y ^{– 1} + 2 x ³

89 . How much skim milk (0% milk fat) should be added to 4 gallons of 2% milk to obtain milk?

(a) 12 gallons

(b) 8 gallons

(c) 10 gallons

(d) 6 gallons

92 . The diameter of a rectangular room is 20 feet. The room is four feet longer than it is wide. How wide is the room?

(a) 15 feet

(b) 16 feet

(c) 14 feet

(d) 12 feet

94 . Working together, Matt and Juan can restock a store’s shelves in 2 hours 24 minutes. Alone, Juan needs two hours longer than Matt needs. How long does Matt need to restock the shelves when working alone?

(a) 48 minutes

(b) 1 hour

(c) 4 hours

(d) 6 hours

96 . A car and small airplane leave an airport at the same time. The car is traveling northward at an average speed of 64 mph. The plane is flying eastward at an average speed of 120 mph. When will the car and plane be 102 miles apart?

(a) 45 minutes

(b) 30 minutes

(c) 1 hour

(d) 1 hour 15 minutes

97 . The Holt family pays a monthly base charge of $12 for electricity plus 5 cents per kilowatt-hour. If they want to keep monthly electric costs between $80 and $100, how many kilowatt-hours can they use each month to stay within their budget?

(a) Between 1600 and 2000 kilowatt hours

(b) Between 1333 and 1667 kilowatt hours

(c) Between 1840 and 2240 kilowatt hours

(d) Between 1360 and 1760 kilowatt hours

98 . If , then

(b) x = 0

(c) x = 10

(d) x = 5

99 . 150 is what percent of 40?

100 . A small object is dropped from the top of a 40-foot building. How long will it take the object to hit the ground?

(a) About 1.58 seconds

(b) About 0.4 seconds

(c) 2.5 seconds

(d) 1.6 seconds

101 . What is the solution for – 1 ≤ 4 – x ≤ 10?

(a) [5, – 6]

(b) [6, – 5]

(c) [ –6, 5]

(d) [ –5, 6]

Solutions