review 3

1.Solve the equation:.

a.x = 9 b.x = 8 c.x = 9 d.x = 8 e.x = 7

2.Find all real solutions of the equation , rounded to two decimal places.

a. b. c. d. e.

3.Solve the equation.a. b. c. d. e.

4.Solve the equation .

a.x = 6 b.x = 6 c.x = 9 d.x = 7 e.x = 7

5.Solve the equation in the interval [0, 6]. Round the answer to two decimal places.

a.x = 3.37, 2.37 b.x = 6.37 c.x = 3.37 d.x = 2.37 e.x = 7.37


a. b. c. d. e.


a.x = 8 b.x = 10 c.x = 5 d.x = 8 e.x = 5

8. Solve the equation

a.x = 4, x = 2 b.x = 3, x = 3 c.x = 2, x = 2 d.x = 3, x = 1 e.x = 2, x = 3

9.Solve the equation

a. b. c. d. e.

10.The figure shows a lever system, similar to a seesaw that you might find in a children's playground. For the system to balance, the product of the weight and its distance from the fulcrum must be the same on each side; that is

x 1 w 1 = x 2 w 2.

This equation is called the law of the lever, and was first discovered by Archimedes. A woman and her son are playing on a seesaw. The boy is at one end, 8 ft from the fulcrum. If the son weighs 80 lb and the mother weighs 125 lb, where should the woman sit so that the seesaw is balanced?

a.8.1 ft b.12.5 ft c.5.1 ft d.8.0 ft e.6.1 ft

11.Candy and Tim share a paper route. It takes Candy 30 minutes to deliver all the papers, whereas Tim takes 60 minutes. How long does it take them when they work together?

a.20 minutes b.30 minutes c.45.0 minutes d.15.0 minutes e.none of these

12.If Ben invests $2,000 at 3% interest per year, how much additional money must he invest at annual interest to ensure that the interest he receives each year is of the total amount invested?

a.$950 b.$1,100 c.$1,000 d.$2,000 e.$1,500

13.An executive in an engineering firm earns a monthly salary plus a Christmas bonus of $8,600. If she earns a total of $97,400 per year, what is her monthly salary?

a.$8,650.00 b.$8,116.67 c.$7,400.00 d.$88,800.00 e.$720.83

14.Craig is saving to buy a vacation home. He inherits some money from a wealthy uncle, then combines this with the $24,000 he has already saved and doubles the total in a lucky investment. He ends up with $142,000, just enough to buy a cabin on the lake. How much did he inherit?

a.$44,000 b.$48,000 c.$46,000 d.$47,000 e.$94,000

15.A pilot flew a jet from Montreal to Los Angeles, a distance of 2,600 miles. On the return trip the average speed was 20% faster than the outbound speed. The round trip took 10 hours 45 minutes. What was the speed from Montreal to Los Angeles?

a.443.41 miles an hour b.493.41 miles an hour c.241.86 miles an hour d.483.72 miles an hour e.none of these

16.A merchant blends tea that sells for $2.85 a pound with tea that sells for $2.60 a pound to produce 80 lb of a mixture that sells for $2.75 a pound. How many pounds of each type of tea does the merchant use in the blend?

a.48 lb of tea that sells for $2.85 and 32 lb of tea that sells for $2.60 b.32 lb of tea that sells for $2.85 and 48 lb of tea that sells for $2.60 c.40 lb of tea that sells for $2.85 and 40 lb of tea that sells for $2.60 d.48 lb of tea that sells for $2.85 and 24 lb of tea that sells for $2.60 e.none of these

17.During his major league career, Hank Aaron hit 30 more home runs than Babe Ruth hit during his career. Together they hit 1,498 home runs. How many home runs did Babe Ruth hit?

a.704 home runs b.764 home runs c.734 home runs d.779 home runs e.749 home runs

18.A man is walking away from a lamppost with a light source b = 10 meters above the ground. The man is 2 meters tall. How far from the lamppost is the man when his shadow is a = 4 meters long? [Hint: Use similar triangles.]

a.14 meters b.15 meters c.20 meters d.17 meters e.16 meters

19.A father is four times as old as his daughter. In 4 years, he will be three times as old as she is. How old is the daughter now?

a.5 years old b.4 years old c.12 years old d.3 years old e.8 years old

20.Al paints with watercolors on a sheet of paper 30 inches wide by 11 inches high. He then places this sheet on a mat so that a uniformly wide strip of the mat shows all around the picture. The perimeter of the mat is 106 inches. How wide is the strip of the mat showing around the picture?

a.4 inches b.2 inches c.6 inches d.8 inches e.3 inches

21.Find the length y in the figure, if the shaded area is 24 in 2.

a.4 in. b.5 in. c.4.90 in. d.12.00 in. e.5.66 in.

22.A storage bin for corn consists of a cylindrical section made of wire mesh, surmounted by a conical tin roof, as shown in the figure. The height of the roof is one third the entire height of the structure. If the total volume of the structure is 1,100 feet 3 and its radius is r = 10 feet, what is its height? Hint: use the formulas for the volume of the solid.

Volume of cone = Volume of cylinder = a.4.5 feet b.15.7 feet c.14.1 feet d.11.0 feet e.none of these

23.Find three consecutive integers whose sum is 345.

a.114, 115, 116 b.113, 114, 115 c.117, 118, 119 d.106, 107, 108 e.none of these

24.After robbing a bank in Dodge City, the robber gallops off at 10 miles an hour. 15 minutes later the marshal leaves in hot pursuit at 11 miles an hour. How long does it take the marshal to catch up with the bank robber?

a.150 minutes b.163 minutes c.140 minutes d.300 minutes e.none of these

25.Write the sum of three consecutive integers using m, where m = the middle integer of the three.

a.3m b.(m 1) m (m + 1) c.m + 3 d.3m + 3 e.none of these

26.Dr. Plath has been raising fruit flies for use in a biology experiment. She has noticed that the number of new baby flies in her colony each day is always half the previous day's total population, but that 100 adult flies die each day. If after three days she has 3,575 fruit flies, how many did she start with?

a.1,200 flies b.1,250 flies c.1,150 flies d.1,210 flies e.none of these

27.It took a crew 4 h 48 min to row 12.8 km upstream and back again. If the rate of flow of the stream was 2 km/h, what was the rowing rate of the crew in still water?

a.6 km/h b.8 km/h c.10 km/h d.9 km/h e.none of these

28.Find all values of k that ensure that the equation has exactly one solution.

25x 2 + kx + 9 = 0

a.k = 30, k = 30 b.k = 30, k c.k = 30, k > 30 d.k = 60, k = 60 e.none of these

29.Find the length x if the shaded area is 4,800 cm2 and y = 20 cm.

a.80 cm b.70 cm c.90 cm d.100 cm e.none of these

30.Find all real solutions of the equation

ax 2 (2a + 1)x + (a + 1) = 0, for a = 4.

a. b. c. d. e.none of these

31.Solve the equation by factoring.

a.x = 18, x = 16 b.x = 18, x = 16 c.x = 18, x = 16 d.x = 18, x = 32 e.none of these

32.A farmer has a rectangular garden plot surrounded by 300 feet of fence. Find the length and width of the garden if its area is 5,400 feet2.

a.width = 60, length = 90 b.width = 55, length = 95 c.width = 50, length = 80 d.width = 50, length = 100 e.none of these

33.Find two numbers whose sum is 30 and whose product is 225.

34.A wire 290 in. long is cut into two pieces. One piece is formed into a square and the other into a circle. If the two figures have the same area, what are the lengths of the two pieces of wire to the nearest tenth of an inch?

35.A box with a square base and no top is to be made from a square piece of cardboard by cutting y in. squares from each corner and folding up the sides, as shown in the figure. The box is to hold 588 in3. What is the length of the starting piece of cardboard, if y = 3 in?

36.Find all real solutions of the equation.



a. b. c. d. e.None of these38.Evaluate the expression

(18 + 19i) + (17 11i)

and write the result in the form a + bi.

a.35 + 8i b.35 8i c.8 + 35i d.18 + 19i e.none of these

39.Evaluate the expression and write the result in the form a + bi.



a.2i b.2i c.2 d.2 e.none of these


a.6 + 3i b.3 + 6i c.6 3i d.3 6i e.none of these

42.Evaluate the expression

(10 + 8i)(8 3i)


a.104 + 34i b.34 + 104i c.80 + 64i d.34 104i e.none of these

43.Evaluate the expression

6(6 + 7i)


a.36 + 42i b.36 42i c.42 36i d.42 + 36i e.none of these

44.Evaluate the expression i79 and write the result in the form a + bi.

a.i b.(i) c.1 d.1 e.none of these


a.138 + 24i b.24 138i c.120 + 60i d.18 + 24i e.none of these


a.32 + 14i b.14 + 32i c.32 10i d.14 32i e.none of these


a.4 5i b.16 20i c.5 4i d.4 + 5i e.none of these


a.20 6i b.20 + 6i c.6 20i d.6 20i e.none of these

49.Find all solutions of the equation and express them in the form a + bi.

a.x = 3i, x = 3i b.x = 3, x = 3 c.x = 3i d.x = 3i, x = 3 e.none of these


a.x = 1 + 3i, x = 1 3i b.x = 3 + 2i, x = 3 2i c.x = 1, x = 1 d.x = 4 + 12i, x = 4 12i e.No solutions.


a.z = 3 + 3i, z = 3 3i b.z = 3 + 4i, z = 3 4i c.z = 3, z = 3 d.z = 12 + 12i, z = 12 12i e.No solutions.




a.15 b.15 c.0 d.5, 0 e.0, 15


x 4 = 64x 2a.x = 0, x = 8, x = 8 b.x = 0, x = 64, x = 64 c.x = 0, x = 64 d.x = 0 e.none of these




(x + 1 ) 2 13( x + 1 ) + 42 = 0


57.A city lot has the shape of a right triangle whose hypotenuse is 34 ft longer than one of the other sides. The perimeter of the lot is 408 ft. How long is the hypotenuse of the lot?

a.340 feet b.170 feet c.102 feet d.136 feet e.85 feet

58.Grain is falling from a chute onto the ground, forming a conical pile whose diameter is always three times its height. How high is the pile to the nearest hundredth of a foot when it contains 2,300 ft 3 of grain?

a.6.25 feet b.14.31 feet c.9.15 feet d.9.92 feet e.31.24 feet

59.A large plywood box has a volume of 385 ft 3. Its length is a ft greater than its height, and its width is b ft less than its height. What is the height of the box if a = 4 and b = 2?

a.7 feet b.14 feet c.8 feet d.3 feet e.6 feet






a.18 b.0, 18 c.18, 18 d.9 e.none of these

63.Find all solutions, real and complex, of the equation.

x 3 = 343

a. b.x = 7, x = 7 c. d.x = 7 e.none of these


a.x = 26, x = 13 b.x = 6 c.x = 13, x = 6 d.x = 10 e.x = 13, x = 6

69.It is estimated that the annual cost of driving a certain new car is given by the formula

C = 0.1m + 2,200

where m represents the number of miles driven per year and C is the cost in dollars. Jane has purchased such a car, and decides to budget between $3,700 and $3,800 for next year's driving costs. What is the corresponding range of miles that she can drive her new car?

a.Between 14,000 mi and 17,000 mi b.Between 15,000 mi and 16,000 mi c.Between 15,000 mi and 17,000 mi d.More than 16,000 mi e.Between 14,000 mi and 16,000 mi

70.Solve the inequality. Express the solution using interval notation.

a. b. c. d. e.


a. b. c. d. e.


a.[ 1, 6 ) b.[ 6, 1 ) c.[ 6, 4 ) d.[ 4, 5 ) e.[ 5, 4 )


a. b. c. d. e.


a. b. c. d. e.

75.A car rental company offers two plans for renting a car.

Plan A:$25 per day and $0.25 per mile.

Plan B:$45 per day with free unlimited mileage.

For what range of miles will plan B save you money?

a.Less than 330 mi b.Less than 80 mi c.More than 330 mi d.More than 80 mi e.Less than 375 mi

76.Solve the inequality.

3x 2 3x < 2x 2 + 18

a. b. c. d. e.


a. b. c. d. e.

78.A gardener has 140 ft of deerresistant fence. She wants to enclose a rectangular vegetable garden in her backyard, and she wants the area enclosed to be at least 1,200 ft 2. What range of values is possible for the length of her garden?

a.Longer than 30 feet b.From 30 to 40 feet c.Shorter than 40 feet d.From 15 to 20 feet e.Shorter than 30 feet

79.Using calculus it can be shown that if a ball is thrown upward with an initial velocity of 32 ft/s from the top of a building 56 ft high, then its height h above the ground t seconds later will be

h = 56 + 32t 16t 2During what time interval will the ball be at least 8 ft above the ground?

a.From 0 to 3 seconds b.From 3 to 5 seconds c.From 3 to 8 seconds d.From 0 to 5 seconds e.none of these


(x 1)(x 6) > 0

a. b. c. d. e.

81.For a certain model of car the distance d required to stop the vehicle if it is traveling at v mi/h is given by the following formula:

where d is measured in feet. Kerry wants her stopping distance not to exceed x = 420 ft. At what range of speeds can she travel?

a.From 0 to 55 mi/h b.From 0 to 65 mi/h c.From 0 to 60 mi/h d.From 60 to 70 mi/h e.From 0 to 70 mi/h


a. b. c. d. e.


a. b. c. d. e.

84.Determine the values of the variable for which the expression is defined as a real number.

a. b. c. d. e.

85.Find the solution of the inequality.

a. b. c. d. e.


a. b. c.[2,2.4] d.(2,2.4) e.[2.4,2.4]

87.Solve the equation.

| x + 8 | = 2.5

a. b. c. d. e.

88.Solve the inequality. Express the answer using interval notation.

a. b. c. d. e.


a. b. c. d. e.


a. b. c. d. e.

91.Solve the equation.

|x + 23| = |4x + 5|

a. b. c. d. e.

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