Study guide

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Study guide

Multiple Choice
Identify the choice that best completes the statement or answers the question.

Write an algebraic expression for the phrase.

the sum of b and 11

b – 11

b + 11

11b

Define a variable and write an expression for the phrase.

4 minus a number

4 – n

You can use the formula

to convert temperature in degrees Fahrenheit, F, to temperature in degrees Celsius, C. What is 62°F in degrees Celsius? Round your answer to the nearest tenth.

30°C

16.7°C

52.2°C

2.4°C

Simplify the expression.

108

A rational number is ____ a real number.

always

sometimes

never

Name the set(s) of numbers to which 1.68 belongs.

a.	rational numbers
b.	natural numbers, whole numbers, integers, rational numbers
c.	rational numbers, irrational numbers
d.	none of the above

Which set of numbers is the most reasonable to describe the number of desks in a classroom?

a.	whole numbers	c.	rational numbers
b.	irrational numbers	d.	integers

The opposite of a negative number is ____ negative.

always

sometimes

never

Over the first five years of owning her car, Gina drove about 12,700 miles the first year, 15,478 miles the second year, 12,675 the third year, 11,850 the fourth year, and 13,075 the fifth year.

a. Find the mean, median, and mode of this data.
b. Explain which measure of central tendency will best predict how many miles Gina will drive in the sixth year.

a.	mean = 12,700; median = 13,156; no mode; the mean is the best choice because it is representative of the entire data set.
b.	mean = 13,156; median = 12,700; mode = 3,628; the median is the best choice because it is not skewed by the high outlier.
c.	mean = 13,156; median = 12,700; no mode; the mean is the best choice because it is representative of the entire data set.
d.	mean = 13,156; median = 12,700; no mode; the median is the best choice because it is not skewed by the high outlier.

10.

Angela’s average for six math tests is 87. On her first four tests she had scores of 93, 87, 82, and 86. On her last test, she scored 4 points lower than she did on her fifth test. What scores did Angela receive on her fifth and sixth tests?

a.	fifth test = 85; sixth test = 89	c.	fifth test = 90; sixth test = 86
b.	fifth test = 85; sixth test = 81	d.	fifth test = 89; sixth test = 85

Find the range.

11.

3 –9 7 –1 5 –4 2

–1

12.

The french club is holding a car wash fundraiser. They are going to charge $10 per car, and expect between 50 and 75 cars. Identify the independent and dependent quantity in the situation, and find reasonable domain and range values.

a.	number of cars; money raised; 50 to 75 cars; $500 to $750	c.	number of cars; money raised; $500 to $750; 50 to 75 cars
b.	money raised; number of cars; $500 to $750; 50 to 75 cars	d.	money raised; number of cars; 50 to 75 cars; $500 to $750

Solve the equation.

13.

x + 5 = 8

14.

11 = –d + 15

–4

15.

–8

–10

–4

16.

5x – 5 = 3x – 9

–2

–1

–3

17.

Steven wants to buy a $565 bicycle. Steven has no money saved, but will be able to deposit $30 into a savings account when he receives his paycheck each Friday. However, before Steven can buy the bike, he must give his sister $65 that he owes her. For how many weeks will Steven need to deposit money into his savings account before he can pay back his sister and buy the bike?

25 weeks

19 weeks

22 weeks

21 weeks

18.

Find the measure of

. (Hint: The sum of the measures of the angles in a triangle is

19.

a. Find the value of a.
b. Find the value of the marked angles.

22; 100º

19; 88º

20; 92º

24; 108º

20.

Which equation is an identity?

a.		c.
b.		d.

21.

Find the unit rate for number of parts manufactured per hour if 1630 parts are made in 6 hours. Round to the nearest integer.

325 parts/h

272 parts/h

237 parts/h

291 parts/h

22.

A car is driving at a speed of 60 mi/h. What is the speed of the car in feet per minute?

a.	5,280 ft/min	c.	316,800 ft/min
b.	3,600 ft/min	d.	2,580 ft/min

Solve the proportion.

23.

2.2

110

1.8

24.

A package delivery company has determined that they can meet their schedules if they have 4 drivers for every 30 square miles of area they cover. If they want to offer service to a county of 75 square miles, how many drivers must they have?

12 drivers

10 drivers

15 drivers

9 drivers

25.

The cross products of a proportion are ____ equal.

always

sometimes

never

26.

Two rectangles are similar. One has a length of 10 cm and a width of 8 cm, and the other has a width of 7 cm. Find the length of the second rectangle. Round to the nearest tenth if necessary.

8.8 cm

6.6 cm

10.1 cm

5.6 cm

27.

A tree casts a shadow 10 ft long. A boy standing next to the tree casts a shadow 2.5 ft. long. The triangle shown for the tree and its shadow is similar to the triangle shown for the boy and his shadow. If the boy is 5 ft. tall, how tall is the tree?

18 ft

12.5 ft

15 ft

20 ft

28.

In similar triangles, corresponding angles are ____ congruent.

always

sometimes

never

29.

Use the scale and map measurements to find the actual distance from New Wilmington to Sharon through Mercer. What is the actual distance if you travel from New Wilmington to Sharon through Volant?

a.	27 mi; 42 mi	c.	13.5 mi; 21 mi
b.	40.5 mi; 63 mi	d.	54 mi; 84 mi

30.

At 9:00 on Saturday morning, two bicyclists heading in opposite directions pass each other on a bicycle path.The bicyclist heading north is riding 6 km/hour faster than the bicyclist heading south. At 10:15, they are 42.5 km apart. Find the two bicyclists’ rates.

a.	northbound bicyclist = 20 km/h; southbound bicyclist = 14 km/h
b.	northbound bicyclist = 23 km/h; southbound bicyclist = 17 km/h
c.	northbound bicyclist = 18 km/h; southbound bicyclist = 11 km/h
d.	northbound bicyclist = 20 km/h; southbound bicyclist = 13 km/h

31.

During the month of February, Fabulous Feet Shoe Mart sold 50 pairs of red loafers. After an ad campaign to boost sales, they sold 60 pairs in March. Find the percent of increase in sales.

12%

20%

15%

23%

32.

The percent of change in two numbers is ____ greater than 100%.

always

sometimes

never

33.

You measure the width of a doorway and find that it is 0.93 m wide. Find the greatest possible error of your measurement.

0.05 m

0.005 m

0.01 m

0.001 m

34.

You measure a piece of rope and find its length to be 13 m. Find the percent error of this measurement. Round to the nearest hundredth.

0.92%

3.85%

0.38%

0.15%

35.

Find the minimum and maximum possible areas for a rectangle measuring 4.15 cm by 7.34 cm. Round to the nearest hundredth.

a.	minimum area: 24.97 cm² maximum area 36.46 cm²	c.	minimum area: 30.40 cm² maximum area 30.52 cm²
b.	minimum area: 29.89 cm² maximum area 31.04 cm²	d.	minimum area: 31.76 cm² maximum area 34.98 cm²

36.

Simplify

37.

The principal square root of a positive real number is ________ negative.

always

sometimes

never

38.

rational or irrational?

rational

irrational

39.

The expression

is ________ rational if a and b are integers and

always

sometimes

never

Find the length of the missing side. If necessary, round to the nearest tenth.

40.

361

14.9

Determine whether the given lengths can be sides of a right triangle.

41.

18 m, 24 m, 30 m

yes

Solve using a graphing calculator.

42.

7d + d – 4d – 7 = 5d

–2

Which number is a solution of the inequality?

43.

b > 11.3

–14

44.

–9

45.

x(7 – x) > 8

–1

46.

Graph the inequality.

47.

k >

a.		c.
b.		d.

Write an inequality for the graph.

48.

x < –8

x > –8

x < 8

49.

m £

m >

m ³

Write an inequality to model the situation.

50.

A number exceeds 21.

n > 21

n < 21

Identify the graph of the inequality from the given description.

51.

x is negative.

a.		c.
b.		d.

52.

x is at least –4.5.

a.		c.
b.		d.

Solve the inequality. Then graph your solution.

53.

a.		c.
b.		d.

54.

x – 7 > –3.1

a.	x > –10.1	c.	x > 4.1
b.	x > 3.9	d.	x > –4.1

55.

a.		c.
b.		d.

56.

a.		c.
b.		d.

57.

c – 3 > 6

a.	c < –9	c.	c >3
b.	c > 9	d.	c > –9

58.

a.		c.
b.		d.

59.

a.	–36 < x < 14	c.	–17 > x > 8
b.	–17 < x < 8	d.	–8 < x < 8

Solve the inequality.

60.

c – 12 > –1

c > –13

c > 11

c > 13

c < –13

61.

k ³

k £

62.

+ x +

63.

–

x – 7 <

x >

x <

64.

–5x – 7 < 28

x > –7

x < –7

65.

Jeanette wants to tile the floor of a room in her house. The square tiles measure

ft on each side. The room is 10 ft wide.

a. Write an inequality to describe how many tiles are needed to make one row of tiles across the width of the room.
b. Solve the inequality.
c. How many tiles should Jeanette buy to form one row?

a.	; ; 13	c.	; ;
b.	; ;	d.	; ; 13

66.

Replace

with a number that makes the inequalities equivalent.
–6v <

; v > –0.5

6.5

–5.5

67.

The French club is sponsoring a bake sale. If their goal is to raise at least $140, how many pastries must they sell at $3.50 each in order to meet that goal? Write and solve an inequality.

a.	;	c.	;
b.	;	d.	;

68.

A student scored 83 and 91 on her first two quizzes. Write and solve a compound inequality to find the possible values for a third quiz score that would give her an average between 85 and 90.

a.
b.
c.
d.

Write an inequality for the situation.

69.

all real numbers at most –9.5 or at least 5.5

a.		c.
b.		d.

Solve the equation. If there is no solution, write no solution.

70.

a.	no solution	c.	h = –7, h = 21
b.	h = 21	d.	h = 7, h = –21

71.

a.	x = or	c.	x = or
b.	x =	d.	no solution

72.

Which graph is the most appropriate to describe a quantity decreasing at a steady rate?

a.		c.
b.		d.

73.

The graph below shows how the cost of gasoline changes over one month. According to the graph, the cost of gasoline ________ decreases.

always

sometimes

never

74.

A plane that carries mail makes a round trip each day from Chicago to New York. It makes 3 intermediate stops on the way to New York and 1 intermediate stop on the way back to Chicago. Suppose you make a graph of the altitude of the plane for one day, with time on the horizontal axis and altitude on the vertical axis. How many times will the graph touch the horizontal axis?

75.

A function is ________ a relation.

always

sometimes

never

76.

Identify the mapping diagram that represents the relation and determine whether the relation is a function.

a.	The relation is not a function.	c.	The relation is a function.
b.	The relation is a function.	d.	The relation is not a function.

77.

Identify the mapping diagram that represents the relation and determine whether the relation is a function.

a.	The relation is a function.	c.	The relation is not a function
b.	The relation is a function.	d.	The relation is not a function.

78.

Evaluate

for x = 3.

–11

–6

Graph the function.

79.

a.		c.
b.		d.

80.

a.		c.
b.		d.

Find the constant of variation k for the direct variation.

81.

k =

82.

x	f(x)
–1	2
0	0
2	–4
5	–10

k = –1.5

k = 2

k = –0.5

k = –2

The pair of points is on the graph of an inverse variation. Find the missing value.

83.

(2.4, 3) and (5, y)

1.44

6.25

0.69

84.

(9, 5) and (x, 6)

85.

An enclosed gas exerts a pressure P on the walls of a container. This pressure is directly proportional to the temperature T of the gas. If the pressure is 7 lb per square inch. when the temperature is 420ºF, find the constant of variation.

86.

Find the constant of variation k for the inverse variation. Then write an equation for the inverse variation.
y = 4.5 when x = 3

a.	k = 13.5; 13.5y = x	c.	k = 1.5; y =
b.	k = 1.5; y = 1.5x	d.	k = 13.5; xy = 13.5

Find the common difference of the arithmetic sequence.

87.

The common difference in an arithmetic sequence is ________ a positive number.

sometimes

always

never

The rate of change is constant in each table. Find the rate of change. Explain what the rate of change means for the situation.

88.

Time (days)	Cost ($)
3	75
4	100
5	125
6	150

a.	dollars per day; the cost is $25 for each day.
b.	dollars per day; the cost is $25 for each day.
c.	dollars per day; the cost is $75 for each day.
d.	dollars per day; the costs $1 for 150 days

The rate of change is constant in the graph. Find the rate of change. Explain what the rate of change means for the situation.

89.

a.	–100; value drops $100 every year.
b.	; value drops $100 every 3 years.
c.	–3; value drops $3 every year.
d.	–1; value drops $1 every year.

Find the rate of change for the situation.

90.

You run 7 miles in one hour and 21 miles in three hours.

a.	3 miles per hour	c.	7 miles
b.	3 hours	d.	7 miles per hour

91.

A chef cooks 9 lbs of chicken for 36 people and 17 lbs of chicken for 68 people.

a.	lb per person	c.	lb per person
b.	4 lb per person	d.	36 people

Find the slope of the line.

92.

–

Find the slope of the line that passes through the pair of points.

93.

(–5.5, 6.1), (–2.5, 3.1)

–1

94.

A student finds the slope of the line between (14, 1) and (18, 17). She writes

. What mistake did she make?

a.	She should have added the values, not subtracted them.
b.	She used y-values where she should have used x-values.
c.	She mixed up the x- and y-values.
d.	She did not keep the order of the points the same in numerator and the denominator.

State whether the slope is 0 or undefined.

95.

undefined

Write the slope-intercept form of the equation for the line.

96.

a.	y = x 1	c.	y = x 1
b.	y = x 1	d.	y = x 1

97.

a.	y = x	c.	y = x
b.	y = x	d.	y = x +

Match the equation with its graph.

98.

–7x + 7y = –49

a.		c.
b.		d.

99.

Write y =

x + 7 in standard form using integers.

a.	–2x + 3y = 21	c.	–2x – 3y = 21
b.	3x – 2y = 21	d.	–2x + 3y = 7

Graph the equation.

100.

y = –3

a.		c.
b.		d.

101.

A line passes through (1, –5) and (–3, 7).
a. Write an equation for the line in point-slope form.
b. Rewrite the equation in slope-intercept form.

a.	y – 5 = 3(x + 1); y = 3x + 8	c.
b.	;	d.	y + 5 = –3(x – 1); y = –3x – 2

Are the graphs of the lines in the pair parallel? Explain.

102.

y = 5x + 6
–18x + 3y = –54

a.	No, since the slopes are different.
b.	Yes, since the slopes are the same and the y-intercepts are different.
c.	No, since the y-intercepts are different.
d.	Yes, since the slope are the same and the y-intercepts are the same.

Write an equation for the line that is parallel to the given line and that passes through the given point.

103.

y = –5x + 3; (–6, 3)

a.	y = –5x + 27	c.	y = 5x – 9
b.	y = –5x – 27	d.	y = –5x + 9

Tell whether the lines for each pair of equations are parallel, perpendicular, or neither.

104.

7x – 4y = 4
x – 4y = 3

perpendicular

parallel

neither

105.

Which graph shows the best trend line for the following data.

a.		c.
b.		d.

106.

Graph y = | x | – 5.

a.		c.
b.		d.

Write an equation for each translation of .

107.

16.5 units right

y = | x – 16.5 |

y = | x | + 16.5

y = | x | – 16.5

y = | x + 16.5 |

Graph each equation by translating y = | x |.

108.

y = | x – 3 | – 4

a.		c.
b.		d.

109.

Giselle pays $210 in advance on her account at the athletic club. Each time she uses the club, $15 is deducted from the account. Model the situation with a linear function and a graph.

a.	b = 210 – 15x	c.	b = 195 + 15x
b.	b = 210 + 15x	d.	b = 195 – 15x

110.

Which graph represents the following system of equations?
y = 3x + 3
y = –x – 3

a.		c.
b.		d.

111.

Use a graphing calculator to find the solution of the system.
y =

x +

y =

x +

(0, 0.17)

(5, 6)

(–5, –4)

(–1.5, 0)

Graph each system. Tell whether the system has no solution, one solution, or infinitely many solutions.

112.

y = x + 4
y – 4 = x

a.	infinitely many solutions
b.	no solutions
c.	one solution

Solve the system of equations using substitution.

113.

3y = –

x + 2
y = –x + 9

(3, 6)

(20, –4)

(10, –1)

(–1, 8)

114.

3x + 2y = 7
y = –3x + 11

(6, –3)

(6, –7)

(5, –4)

Solve the system using elimination.

115.

x + 2y = –6
3x + 8y = –20

(–1, –4)

(–4, 4)

(–4, –1)

(3, 1)

116.

5x = –25 + 5y
10y = 42 + 2x

(–1, 2)

(–1, 4)

(4, –1)

(5, 10)

117.

3x – 4y = 9
–3x + 2y = 9

(3, 9)

(–27, –9)

(–3, –6)

(–9, –9)

118.

A jar containing only nickels and dimes contains a total of 60 coins. The value of all the coins in the jar is $4.45. Solve by elimination to find the amount of nickels and dimes that are in the jar.

a.	30 nickels and 28 dimes	c.	29 nickels and 31 dimes
b.	31 nickels and 29 dimes	d.	30 nickels and 32 dimes

119.

By what number should you multiply the first equation to solve using elimination?
–3x – 2y = 2
–9x + 3y = 24

–9

–3

120.

An ice skating arena charges an admission fee for each child plus a rental fee for each pair of ice skates. John paid the admission fees for his six nephews and rented five pairs of ice skates. He was charged $32.00. Juanita paid the admission fees for her seven grandchildren and rented five pairs of ice skates. She was charged $35.25. What is the admission fee? What is the rental fee for a pair of skates?

a.	admission fee: $3.25 skate rental fee: $2.50	c.	admission fee: $3.00 skate rental fee: $2.00
b.	admission fee: $3.50 skate rental fee: $3.00	d.	admission fee: $4.00 skate rental fee: $3.50

121.

Mike and Kim invest $14,000 in equipment to print yearbooks for schools. Each yearbook costs $7 to print and sells for $35. How many yearbooks must they sell before their business breaks even?

650

2,000

500

400

122.

Write the following inequality in slope-intercept form.

Write the linear inequality shown in the graph.

123.

124.

Find a solution of the linear inequality.

(3, 4)

(2, 1)

(3, 0)

(1, 1)

125.

An electronics store makes a profit of $72 for every standard CD player sold and $90 for every portable CD player sold. The manager’s target is to make at least $360 a day on sales from standard and portable CD players.

a.	Write an inequality that represents the numbers of both kinds of CD players that can be sold to reach or exceed the sales target. Let s represent the number of standard CD players and p represent the number of portable CD players.
b.	Write three possible solutions to the problem.
c.	Graph the inequality.

a.		c.
b.		d.

Short Answer

126.

a. Write an equation to show how the amount of money in a jar of nickels is related to the number of nickels in the jar.

b. If the jar contains 40 nickels, how much money is this?

127.

The population of an endangered animal species has been increasing. Make a scatter plot using the data given in the table.

Year	Population
1	230
2	670
3	620
4	840
5	1400
6	1580

128.

Justify each step.

129.

Van Gogh’s painting Starry Night measures 92 cm long by 73 cm high. You buy a poster that shows an enlargement of the painting. The poster measures 120 cm long by 100 cm high. Is the poster an accurate representation of the painting? (Hint: Is the poster similar to the painting?)

130.

A class writes the equation n + n + 1 + n + 2 = 87 to solve the following problem.

The sum of 3 consecutive odd integers is 87. Find the three integers.

What error did they make?

131.

Use a calculator to find

to the nearest hundredth.

132.

What number would you add to each side of the inequality to solve 13 < 4n – 14.4?

133.

Label each section of the graph.

134.

Find the range of

for the domain {–3, –2, –1, 1}.

Use the vertical line test to determine whether the relation is a function.

135.

136.

137.

Model the function rule

with a table of values and a graph.

x	y
–1
0
1

138.

Elaine is in the business of repairing home computers. She charges a base fee of $45 for each visit and $25 per hour for her labor. The total cost c(x) for a home visit and x hours of labor is modeled by the function rule

. Use the function rule to make a table of values and a graph.

x	c(x)
0
1
2
3

139.

An employee receives a weekly salary of $340 and a 6% commission on all sales.
a. Write a rule to describe the function f(d) that gives weekly earnings in terms of d dollars in sales.
b. Find the employee’s earnings for a week with $660 total sales.
c. What were the employee’s total sales for a week in which her earnings were $1300?

For the data in the table, tell whether y varies directly with x. If it does, write an equation for the direct variation.

140.

x	y
0	0
1	4
2	8
3	12

Is the equation a direct variation? If it is, find the constant of variation.

141.

142.

5x = y

143.

A biologist records the number of microbes growing in a culture at the times listed in the table. If the microbes continue to multiply at this rate, how many will there be at 6 P.M. on the second day?

Time of Observation	Number of Microbes
Day 1, 12:00 noon	12,000
Day 1, 6:00 P.M.	18,000
Day 2, 12:00 midnight	27,000
Day 2, 6:00 A.M.	40,500

144.

Suppose you have $20.00 to buy cold cuts for a class picnic. Ham costs $3.99 per pound and turkey costs $4.99 per pound. The equation 3.99x + 4.99y = 20 models this situation. What does the x-intercept of the graph of the equation tell you about the amount of meat you can buy?

145.

Gloria makes and sells handmade greeting cards. The scatter plot shows the number of cards she made over a 10-hour period. Find the equation of a trend line and use it to predict the number of cards Gloria can make in 12 hours.

146.

The population of a small town is shown in the table.

Would you expect the correlation coefficient for the line of best fit to be positive or negative? Explain your answer.

147.

Graph the following linear inequalities on the same coordinate plane. What figure does the solution to all three inequalities make?

148.

Graph the following equation.

149.

A local citizen wants to fence a rectangular community garden. The length of the garden should be at least 110 ft, and the distance around should be no more than 380 ft.

a.	Write a system of inequalities that models the possible dimensions of the garden.
b.	Graph the system to show all possible solutions.

150.

You have a gift certificate to a book store worth $90. Each paperback books is $9 and each hardcover books is $12. You must spend at least $25 in order to use the gift certificate. Write and graph a system of inequalities to model the number of each kind of books you can buy. Let x = the number of paperback books and y = the number of hardback books.