PSAE Algebra Problems

PSAE

PSAE Algebra Problems

Numbering Code: Unit|Section|Problem

A.1.1.1 If x = 3, then x²- 6x - 18 = ?

A. 9

B. 0

C. - 9

D. - 27

E. - 45

A.1.1.2 How many prime numbers are there between 36 and 53 ?

F. 4

G. 5

H. 6

J. 7

K. 8

A.1.1.3 The fare for each taxi ride consists of a $3.00 initial charge and a charge of $1.20 PER HALF MILE. At that rate, how much is the fare for a taxi ride of six miles ?

A. $10.20

B. $17.40

C. $25.20

D. $32.40

E. $35.50

A.1.1.4 If t = 10, which of the following is equal to 7005 ?

A. 5 + 7t

B. 5 + 70t

C. 5 + 7t²

D. 5 + 700t

E. 5 + 7t⁴

A.1.4.1 If a = 10, then which of the following represents 8.003 ?

F. 8a + 3

G. 80a + 3

H. 8a²+ 3

J. 8a³+ 3

K. 8a⁴+ 3

A.1.5.1 An earring manufacturing company has fixed costs of $10,000 per month and production costs of $0.60 for each pair of earrings it makes. If the company produces x pair of earrings in a month, which of the following expressions represents the total of the company’s monthly costs?

A. $10,000

B. $10,000 + x

C. $10,000 + $0.60

D. $10,000 + $0.60x

E. ( $10,000 + $0.60 ) x

A.1.5.2 John Jones has decided to go into the business of producing and selling boats. In order to begin this venture, he must invest $10 million in a boat production plant. The cost to produce each boat will be $7,000, and the selling price will be $20,000. Accounting for the cost of the production plant, which of the following expressions represents the profit, in dollars, that John will realize when x boats are produced and sold ?

F. 13,000x – 10,000,000

G. 27,000x – 10,000,000

H. 9,973,000x

J. 20,000x

K. 13,000x

A.1.5.3 The number 0.75 is 1000 times as large as

A. 0.00075

B. 0.075

C. 7.5

D. 750.00

E. 7500.00

A.1.5.4 You work at a fruit market. Bananas cost 50¢ a pound. A customer hands you a bunch of bananas that weighs 3 pounds. How much should you charge for the bunch of bananas?

F. $0.17

G. $0.50

H. $0.53

J. $1.50

K. $3.50

A.2.1.1 You are standing in line at the cash register to pay for 2 lamps priced at $8.99 each. A sales tax of 7% of the cost of the lamps will be added (rounded to the nearest cent) to the price of the 2 lamps. You have 20 one-dollar bills. How much will you need in coins if you want to have exact change ready?

A. $0.24

B. $0.38

C. $0.62

D. $0.76

E. $0.87

A.2.1.2 The number 0.005 is 100 times as large as which of the following numbers?

A. 0.5

B. 0.05

C. 0.0005

D. 0.00005

E. 0.000005

A.2.1.3 Which of the following is equal to ?

A.2.1.4 On Saturday, Mike received his pay and spent of it. On Sunday he spent of the remaining money, and on Monday he spent of what remained from Sunday. If Mike had $10 left, how much pay did he receive originally?

A. $27

B. $36

C. $45

D. $60

E. $180

A.2.1.5 What number can you add to the numerator and denominator of to get ?

J. 3

K. 6

A.2.1.6 When a = b and c = d, which of the following equations must be true?

F. a + b = c + d

G. a + d = b + c

H. a + c = a + b

J. a – c = d – b

K. ad = cd

A.2.2.1

A. -28

B. -13

C. 13

D. 28

E. 29

A.2.2.2

A. -4

B. -2

C. 2

D. 4

E. 10

A.2.2.3 For real numbers a and b, when is the equation = true?

A. Always

B. Only when a = b

C. Only when a = 0 and b = 0

D. Only when a = 0 or b = 0

E. Never

B.2.6.1 Which of the following is an equivalent form of

B.2.6.2 The expression 8x – 8y is equivalent to which of the following?

F. 8(x – y)

G. 8(x + y)

H. 8xy

J. - 8(x + y)

K. - 8xy

B.2.6.3 Which of the following is an equivalent form of ?

B.2.6.4 Simplify

B.2.6.5 Which property is used to simplify the expression below?

A. associative property

B. commutative property

C. distributive property

D. identity property

E. property of zero

B.2.6.6 Which does not equal 2 + 2(3 + 4)?

C. log₁₆256

E. 16

B.2.6.7 A classroom has (r – 3s) rows of seats and 4t seats in each row. Which of the following is an expression for the number of seats in the entire classroom?

F. r( - 3s ) 4t

G. (4r 12s ) + ( 4 4t )

H. 4t + (r ( - 3s ))

J. r – 3s + 4t

K. ( 4t r ) - ( 4t 3s )

B.3.1.1 If c, d, and f are nonzero real numbers and cd = f, which of the following equations for c must always be true?

F. c = df

G. c =

H. c =

J. c = f – d

K. c =

B.3.1.2 In the formula d = rt, d represents distance in miles, r represents speed in miles per hour, and t represents time in hours. A search helicopter flies in a circle 60 miles in circumference at 90 miles per hour. What is the time in hours it takes the helicopter to make two turns around the circle?

F. hours

G. 3 hours

H. 30 hours

J. 60 hours

K. 120 hours

*B.3.2.1 In the formula d = rt, d represents distance in miles, re represents average speed in miles per hour, and t represents time in hours. What is an automobile’s average speed, in miles per hour, it if travels 60 miles in hours?

F. 30

G. 40

H. 60

J. 90

K. 120

*B.3.2.2 Sally is running a game booth at the school fair. She carefully collect exactly 30 cents from every player. At the end of the fair, she must count the money collected. She counts it for times, getting a different total each time. Which of the following coud be the correct total?

A. $22.45

B. $22.50

C. $22.60

D. $22.65

B.3.2.3 Each month, Wilma earns $25 from a part-time job. She puts $18 of it into a savings account and the remaining $7 of it into her checking account. Suppose she deposits no money from other sources and withdraws no money from either account. By the time she has deposited $126 into her checking account, how much will she have put into her savings account?

A. $ 43

B. $ 49

C. $ 50

D. $ 90

E. $ 126

B.3.3.1 The total cost of renting a car is $30.00 for each day the care is rented plus cents for each mile the care is driven. What is the total cost of renting the care for 5 days and driving 350 miles? (Note: No sales tax is involved.)

A. $ 104. 75

B. $ 159.98

C. $249.75

D. $ 300.00

E. $ 1,147.50

B.3.3.2 For what value of Y is the following equation true? 3(8 – Y ) – Y = 0

F. – 12

G. – 6

H. 6

J. 8

K. 12

B.3.3.3 The balance of Joan’s savings account tripled during the year. Joan then withdrew $500, and the resulting balance was $100. What was the balance in the account before it tripled?

A. $ 200

B. $ 300

C. $ 400

D. $ 500

E. $ 600

B.3.3.4 If, for all x, , then a = ?

F. 1

G. 2

K. 5

B 3.3.1 If , then ?

A. 3

B. 6

C. 10

D. 11

E. 24

B 3.3.2 For what value of a is a solution to the equation ?

A. 1.5

B. 1

C. -1

D. -1.5

E. -3

B 3.3.3 A truck sprang a leak at the bottom of its radiator, which held 480 ounces of fluid when it started to leak, and started loosing radiator fluid at a constant rate of 4 ounces per a minute. Suppose that the radiator continued to leak at this constant rate and that the truck, traveling 35 miles per an hour, could continue traveling at this rate until its radiator is completely empty. In how many miles will the radiator be empty?

A. 13.7

B. 17.5

C. 35.0

D. 70.0

E. 120.0

B 3.3.4 The three individual sections of the fence indicated in the drawing are each 10 feet long and cost $98 each; posts cost $25 - $35 each; about how much would it cost to buy just enough of these sections and posts to build a 150-foot-long fence of the type pictured in the drawing?

A. between $400 - $700

B. between $800 - $1200

C. between $1300 - $1600

D. between $1800 - $2100

E. between $2200 - $2500

B 3.3.5 For what value of x is the equation true?

A. 15

B. 10

C. 8

D. 4

E. 2

B 3.4.1 How many real numbers y satisfy the equation ?

A. 0

B. 1

C. 2

D. 4

E. Infinitely many solutions

B 3.8.1 Amy can run 3 miles in s minutes. At that pace, how many miles can she run in 50 minutes?

B 3.8.2 As a laboratory assistant, you measure chemicals using the metric system. For your current research, you need to measure out 45 grams of sodium chloride. The bottle you are using lists the amount in ounces. About how many ounces of sodium chloride will you need? (the conversion is 1 ounces = 28.350 grams)

A. 0.1

B. 1.6

C. 28.4

D. 720.0

E. 1275.8

B 3.9.1 If 60% of x equals 90, then ?

A. 5.4

B. 15

C. 54

D. 150

E. 1500

B 3.9.2 To keep up with raises expenses, a hotel manager needs to raise the 40 dollar room rate by 22%. What will be the new rate?

A. $40.22

B. $42.20

C. $48.00

D. $48.80

E. $62.00

B 3.9.3 You an urban planner assessing the growth of the city. 10 years ago the cities population was 249, 583. Its current population is 318, 270. By about what percentage has the city grown over the past 10 years?

A. 13%

B. 22%

C. 28%

D. 69%

E. 78%

B 3.9.4 You are a receptionist at a doctors office. A patient’s bill for a checkup totals $85.00. The patient’s health insurance requires the patient to pay 20% of the total bill. How much should the patient pay for the checkup?

A. $4.25

B. $8.50

C. $17.00

D. $42.50

E. $68.00

B 11.1.1 As a sales person your commission is directly proportional to the dollar amount of sales you make. If your sales are $800 your commission is $112. How much commission would you earn if you had $1400 in sales?

A. $210

B. $196

C. $175

D. $128

E. $64

B 11.1.2 A cookie recipe calls for 2/3 cup of sugar to make 24 2-inch cookies. According to this recipe, how many cups of sugar would be used to make 60 2-inch cookies?

A. 5/9

B. 1

C. 1 1/5

D. 1 2/3

E. 3 1/6

B 11.1.3 A road map is drawn to scale so that 1.5 inches represents 90 miles. How many miles does 1.6 inches represent?

A. 91

B. 96

C. 99

D. 100

E. 106

B 11.1.4 On a scale drawing of a soccer field, ¾ of an inch represents 2 yards. What length in yards is represented by of an inch?

B. 1

C. 1 ¾

D. 2

E. 3 ½

B 6.6.1 It costs a dollars for an adult ticket to a reggie concert and s for a student ticket. The difference between the cost 12 adult tickets and 18 student tickets is $36 which of the following equations represents this relationship between a and s?

B 6.1.2 If which of the following is the solution statement when y = -4?

A. x is any real number

B. x > 4

C. x < 4

D. -4 < x < 4