Deck 2: Equations and Inequalities

Question 1

The boundary of a city is a circle of diameter L = 4 miles. As shown in the figure, a straight highway runs through the center of the city from A to B. The highway department is planning to build a 5-mile-long freeway from A to a point P on the outskirts and then to B. Find the distance from A to P. (Hint: APB is a right triangle.) Round the answer to the nearest tenth of a mile.

A)
B)
C)
D)
E)

Answer 1

Question 2

Write the expression in the form , where a and b are real numbers.

A)
B)
C)
D)
E)

Answer 2

Question 3

Solve the equation

A)
B)
C)
D)
E)

Answer 3

Question 4

British sterling silver is a copper-silver alloy that is 7.5% copper by weight. How many grams of pure copper and how many grams of British sterling silver should be used to prepare 226 grams of a copper-silver alloy that is 13% copper by weight?

A)192.4 g of British sterling silver and 33.6 g of copper.
B)196.6 g of British sterling silver and 29.4 g of copper.
C)206.5 g of British sterling silver and 19.5 g of copper.
D)213.9 g of British sterling silver and 12.1 g of copper.
E)212.6 g of British sterling silver and 13.4 g of copper.

Question 5

Find the values of x and y, where x and y are real numbers.

A)
B)
C)
D)
E)

Question 6

A bullet is fired horizontally at a target, and the sound of its impact is heard 1.3 seconds later. If the speed of the bullet is 3,000 ft/sec and the speed of sound is 1,100 ft/sec, how far away is the target?

A)1,161.3 ft
B)1,438.0 ft
C)2,853.7 ft
D)1,046.3 ft
E)1,430.0 ft

Question 7

A student in an algebra course has test scores of 68, 79, 74, and 82. What score on the next test will raise the student's average to 80?

A)97
B)75
C)95
D)100
E)76

Question 8

The speed of the current in a stream is 3.3 mi/hr. It takes a canoeist 30 minutes longer to paddle 1.9 miles upstream than to paddle the same distance downstream. What is the canoeist's rate in still water? Round the answer to the nearest tenth of a mile per hour.

A)3.4 mi/hr
B)7.2 mi/hr
C)4.8 mi/hr
D)9.0 mi/hr
E)6.0 mi/hr

Question 9

Find the values of x and y, where x and y are real numbers.

A)
B)
C)
D)
E)

Question 10

Solve the equation

A)
B)
C)
D)
E)no solution

Question 11

Write the expression in the form , where a and b are real numbers.

A)1 + i
B)1
C)- i
D)- 1
E)i

Question 12

Solve the equation.

A)
B)
C)All real numbers except -2
D)All real numbers except 2
E)No solution

Question 13

A person's intelligence quotient (IQ) is determined by multiplying the quotient of his or her mental age and chronological age by 100. Find the mental age of a person 12 years old whose IQ is 140.

A)14.8 years.
B)16.8 years.
C)19.8 years.
D)8.6 years.
E)18.8 years.

Question 14

During a nuclear explosion, a fireball will be produced having a maximum volume V ₀ . For temperatures below 2,000 K and a given explosive force, the volume V of the fireball t seconds after the explosion can be estimated using the given formula. (Note that the kelvin is abbreviated as K, not ^o K.) Approximate t when V is 84% of V ₀ . Round the answer to the nearest thousandth of a second.

A)0.736 sec
B)5.887 sec
C)37.964 sec
D)1.472 sec
E)1.619 sec

Question 15

Solve the equation by factoring.

A)
B)
C)
D)
E)

Question 16

A square vegetable garden is to be tilled and then enclosed with a fence. If the fence costs $1 per foot and the cost of preparing the soil is $0.60 per ft ² , determine the width of the garden that can be enclosed for $582.40.

A)33 ft
B)11 ft
C)30 ft
D)28 ft
E)48 ft

Question 17

Solve the formula for L.

A)
B)
C)
D)
E)none of these

Question 18

Solve the equation.

A)
B)
C)
D)
E)

Question 19

Solve the equation by factoring.

A)
B)
C)
D)
E)

Question 20

A person's intelligence quotient (IQ) is determined by multiplying the quotient of his or her mental age and chronological age by 100. Find the IQ of a 16 - year - old child whose mental age is 21.6.

A)145 points of IQ
B)142 points of IQ
C)125 points of IQ
D)135 points of IQ
E)74 points of IQ

Question 21

Solve the equation.

A)
B)
C)
D)
E)

Question 22

The speed of the current in a stream is 2.4 mi/hr. It takes a canoeist 60 minutes longer to paddle 1.7 miles upstream than to paddle the same distance downstream. What is the canoeist's rate in still water? Round the answer to the nearest tenth of a mile per hour.

A)3.7 mi/hr
B)4.9 mi/hr
C)2.4 mi/hr
D)3.1 mi/hr
E)6.3 mi/hr

Question 23

A bullet is fired horizontally at a target, and the sound of its impact is heard 1.3 seconds later. If the speed of the bullet is 3,000 ft/sec and the speed of sound is 1,100 ft/sec, how far away is the target?

A)1,438.0 ft
B)2,853.7 ft
C)1,046.3 ft
D)1,430.0 ft
E)1,161.3 ft

Question 24

A square vegetable garden is to be tilled and then enclosed with a fence. If the fence costs $1 per foot and the cost of preparing the soil is $0.20 per ft ² , determine the width of the garden that can be enclosed for $403.20.

A)14 ft
B)41 ft
C)79 ft
D)36 ft
E)40 ft

Question 25

Solve the inequality.

A)
B)
C)
D)
E)

Question 26

British sterling silver is a copper-silver alloy that is 7.5% copper by weight. How many grams of pure copper and how many grams of British sterling silver should be used to prepare 222 grams of a copper-silver alloy that is 15% copper by weight?

A)197.9 g of British sterling silver and 24.1 g of copper.
B)204.0 g of British sterling silver and 18.0 g of copper.
C)183.8 g of British sterling silver and 38.2 g of copper.
D)188.7 g of British sterling silver and 33.3 g of copper.
E)205.3 g of British sterling silver and 16.7 g of copper.

Question 27

A person's intelligence quotient (IQ) is determined by multiplying the quotient of his or her mental age and chronological age by 100. Find the IQ of a 18 - year - old child whose mental age is 21.6.

A)110 points of IQ
B)127 points of IQ
C)130 points of IQ
D)120 points of IQ
E)83 points of IQ

Question 28

Solve the equation by factoring.

A)
B)
C)
D)
E)

Question 29

A student in an algebra course has test scores of 69, 79, 75, and 80. What score on the next test will raise the student's average to 80?

A)76
B)97
C)75
D)94
E)99

Question 30

Solve the equation.

A)
B)
C)All real numbers except -4
D)All real numbers except 4
E)No solution

Question 31

A person's intelligence quotient (IQ) is determined by multiplying the quotient of his or her mental age and chronological age by 100. Find the mental age of a person 18 years old whose IQ is 140.

A)27.2 years.
B)23.2 years.
C)25.2 years.
D)28.2 years.
E)12.9 years.

Question 32

The boundary of a city is a circle of diameter L = 7 miles. As shown in the figure, a straight highway runs through the center of the city from A to B. The highway department is planning to build a 8-mile-long freeway from A to a point P on the outskirts and then to B. Find the distance from A to P. (Hint: APB is a right triangle.) Round the answer to the nearest tenth of a mile.

A)
B)
C)
D)
E)

Question 33

Solve the equation

A)
B)
C)
D)
E)

Question 34

A consumer is trying to decide whether to purchase car A or car B. Car A costs $10,000 and has an mpg rating of 30, and insurance is $500 per year. Car B costs $12,600 and has an mpg rating of 50, and insurance is $550 per year. Assume that the consumer drives 15,000 miles per year and that the price of gas remains constant at $1.25 per gallon. Based only on these facts, determine how long it will take for the total cost of car B to become less than that of car A.

A)13 years
B)17 years
C)47 years
D)57 years
E)15 years

Question 35

During a nuclear explosion, a fireball will be produced having a maximum volume V ₀ . For temperatures below 2,000 K and a given explosive force, the volume V of the fireball t seconds after the explosion can be estimated using the given formula. (Note that the kelvin is abbreviated as K, not ^o K.) Approximate t when V is 92% of V ₀ . Round the answer to the nearest thousandth of a second.

A)29.462 sec
B)11.238 sec
C)49.947 sec
D)6.243 sec
E)12.487 sec

Question 36

Solve the equation

A)
B)
C)
D)
E)no solution

Question 37

Solve the equation by factoring.

A)
B)
C)
D)
E)

Question 38

Write the expression in the form , where a and b are real numbers.

A)
B)
C)
D)
E)

Question 39

Solve the inequality.

A)
B)
C)
D)
E)

Question 40

Solve the formula for K.

A)
B)
C)
D)
E)none of these

Question 41

A person's intelligence quotient (IQ) is determined by multiplying the quotient of his or her mental age and chronological age by 100. Find the IQ of a 16 - year - old child whose mental age is 20.

A)132 points of IQ
B)135 points of IQ
C)115 points of IQ
D)125 points of IQ
E)80 points of IQ

Question 42

British sterling silver is a copper-silver alloy that is 7.5% copper by weight. How many grams of pure copper and how many grams of British sterling silver should be used to prepare 157 grams of a copper-silver alloy that is 9% copper by weight?

A)154.5 g of British sterling silver and 2.5 g of copper.
B)148.4 g of British sterling silver and 8.6 g of copper.
C)142.9 g of British sterling silver and 14.1 g of copper.
D)134.3 g of British sterling silver and 22.7 g of copper.
E)155.8 g of British sterling silver and 1.2 g of copper.

Question 43

Solve the equation

A)
B)
C)
D)
E)no solution

Question 44

Solve the equation

A)
B)
C)
D)
E)

Question 45

A student in an algebra course has test scores of 67, 80, 75, and 82. What score on the next test will raise the student's average to 80?

A)99
B)96
C)76
D)94
E)75

Question 46

A square vegetable garden is to be tilled and then enclosed with a fence. If the fence costs $3 per foot and the cost of preparing the soil is $0.60 per ft ² , determine the width of the garden that can be enclosed for $852.60.

A)34 ft
B)33 ft
C)29 ft
D)64 ft
E)12 ft

Question 47

Solve the equation by factoring.

A)
B)
C)
D)
E)

Question 48

A consumer is trying to decide whether to purchase car A or car B. Car A costs $10,000 and has an mpg rating of 30, and insurance is $500 per year. Car B costs $11,600 and has an mpg rating of 50, and insurance is $550 per year. Assume that the consumer drives 15,000 miles per year and that the price of gas remains constant at $1.25 per gallon. Based only on these facts, determine how long it will take for the total cost of car B to become less than that of car A.

A)27 years
B)9 years
C)8 years
D)17 years
E)37 years

Question 49

Find the values of x and y, where x and y are real numbers.

A)
B)
C)
D)
E)

Question 50

Solve the equation

A)
B)
C)
D)
E)

Question 51

Solve the equation.

A)
B)
C)All real numbers except -4
D)All real numbers except 4
E)No solution

Question 52

Find the values of x and y, where x and y are real numbers.

A)
B)
C)
D)
E)

Question 53

Solve the inequality.

A)
B)
C)
D)
E)

Question 54

Solve the equation.

A)
B)
C)
D)
E)

Question 55

Write the expression in the form , where a and b are real numbers.

A)1 + i
B)- 1
C)- i
D)1
E)i

Question 56

Solve the formula for L.

A)
B)
C)
D)
E)none of these

Question 57

A person's intelligence quotient (IQ) is determined by multiplying the quotient of his or her mental age and chronological age by 100. Find the mental age of a person 18 years old whose IQ is 140.

A)23.2 years.
B)12.9 years.
C)25.2 years.
D)28.2 years.
E)27.2 years.

Question 58

A bullet is fired horizontally at a target, and the sound of its impact is heard 1.3 seconds later. If the speed of the bullet is 3,000 ft/sec and the speed of sound is 1,100 ft/sec, how far away is the target?

A)1,430.0 ft
B)1,046.3 ft
C)2,853.7 ft
D)1,438.0 ft
E)1,161.3 ft

Question 59

Solve the equation by factoring.

A)
B)
C)
D)
E)

Question 60

Solve the inequality.

A)
B)
C)
D)
E)

Question 61

During a nuclear explosion, a fireball will be produced having a maximum volume V ₀ . For temperatures below 2,000 K and a given explosive force, the volume V of the fireball t seconds after the explosion can be estimated using the given formula. (Note that the kelvin is abbreviated as K, not ^o K.) Approximate t when V is 88% of V ₀ . Round the answer to the nearest thousandth of a second.

A)3.681 sec
B)29.445 sec
C)33.656 sec
D)6.625 sec
E)7.361 sec

Question 62

Solve the equation

A)
B)
C)
D)
E)

Question 63

The speed of the current in a stream is 2.2 mi/hr. It takes a canoeist 40 minutes longer to paddle 1.9 miles upstream than to paddle the same distance downstream. What is the canoeist's rate in still water? Round the answer to the nearest tenth of a mile per hour.

A)3.3 mi/hr
B)6.3 mi/hr
C)7.1 mi/hr
D)2.2 mi/hr
E)4.2 mi/hr

Question 64

Solve the equation

A)
B)
C)
D)
E)

Question 65

Solve the equation by using the special quadratic equation.

A)
B)
C)
D)
E)

Question 66

Solve the equation

A)
B)
C)
D)
E)

Question 67

Find the values of x and y, where x and y are real numbers.

A)
B)
C)
D)
E)

Question 68

Write the expression in the form , where a and b are real numbers.

A)i
B)1
C)- i
D)1 + i
E)- 1

Question 69

Solve the equation.

A)
B)
C)
D)
E)

Question 70

Solve the inequality.

A)
B)
C)
D)
E)

Question 71

A stained-glass window is being designed in the shape of a rectangle surmounted by a semicircle, as shown in the figure. The width of the window is to be 2 feet, but the height h is yet to be determined. If 22 ft ² of glass is to be used, find the height h.

A) feet
B) feet
C) feet
D) feet
E) feet

Question 72

Write the expression in the form , where a and b are real numbers.

A)
B)
C)
D)
E)

Question 73

A consumer is trying to decide whether to purchase car A or car B. Car A costs $10,000 and has an mpg rating of 30, and insurance is $450 per year. Car B costs $11,800 and has an mpg rating of 50, and insurance is $500 per year. Assume that the consumer drives 15,000 miles per year and that the price of gas remains constant at $1.25 per gallon. Based only on these facts, determine how long it will take for the total cost of car B to become less than that of car A.

A)10 years
B)31 years
C)41 years
D)18 years
E)9 years

Question 74

Solve the inequality.

A)
B)
C)
D)
E)

Question 75

Find the values of x and y, where x and y are real numbers.

A)
B)
C)
D)
E)

Question 76

Solve the equation.

A)
B)
C)
D)
E)no solution

Question 77

Solve the formula for .

A)
B)
C)
D)
E)

Question 78

Solve the equation.

A)
B)
C)
D)
E)

Question 79

The boundary of a city is a circle of diameter L = 9 miles. As shown in the figure, a straight highway runs through the center of the city from A to B. The highway department is planning to build a 10-mile-long freeway from A to a point P on the outskirts and then to B. Find the distance from A to P. (Hint: APB is a right triangle.) Round the answer to the nearest tenth of a mile.

A)
B)
C)
D)
E)

Question 80

Solve the equation.

A)
B)
C)
D)
E)