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by Jenny Paden, [email protected]
1A
Give two ways to write each algebra
expression in words.
9+r
the sum of 9 and r
9 increased by r

1B
Lou drives at 65 mi/h. Write an
expression for the number of miles
that Lou drives in t hours.
65t
1C
Evaluate each expression for
a = 4, b =7, and c = 2.
ac
ac = 4 ·2
=8
Substitute 4 for a and 2 for c.
Simplify.
2A
Add.
–5 + (–7)
–5 + (–7) = 5 + 7
5 + 7 = 12
–12
When the signs are the same,
find the sum of the absolute
values.
Both numbers are negative, so
the sum is negative.
2B
Add.
x + (–68) for x = 52
First substitute 52 for x.
x + (–68) = 52 + (–68)
When the signs of the
numbers are different, find the
difference of the absolute
values.
68 – 52
–16
Use the sign of the number
with the greater absolute
value.
The sum is negative.
2C
Subtract.
4
To subtract –3 1 add 3 1 .
2
2
When the signs of the
numbers are the same, find
the sum of the absolute
values: 3 1 + 1 = 4.
2
2
Both numbers are positive
so, the sum is positive.
3A
Find the value of each expression.
12
The quotient of two numbers
with the same sign is positive.
3B
Find the value of each expression.
–6x for x = 7
–6x = –6(7)
= –42
First substitute 7 for x.
The product of two numbers with
different signs is negative.
3C
Divide.
Copy Change Flip
Multiply the numerators and
multiply the denominators.
and
have the same sign,
so the quotient is positive.
4A
Simplify
• (-2)3 =
• -8
• -72 =
• -49
4B
Evaluate the expression.
22
9 9
2  2= 4
9 9 81
Use 2 as a factor 2 times.
9
4C
Write each number as a power of the given base.
81; base –3
(–3)(–3)(–3)(–3)
(–3)4
The product of four –3’s is 81.
5A
Find each square root.
A.
42 = 16
=4
B.
32 = 9
= –3
Think: What number squared equals 16?
Positive square root
positive 4.
Think: What is the opposite of the
square root of 9?
Negative square root
negative 3.
5B
Write all classifications that apply to each
Real number.
–32
32
–32 = –
= –32.0
1
32 can be written as a
fraction and a decimal.
rational number, integer, terminating decimal
5C
Write all classifications that apply to each real
number.
= 3.16227766… The digits continue with no
pattern.
irrational number
6A
Simplify each expression.
15 – 2 · 3 + 1
15 – 2 · 3 + 1
15 – 6 + 1
10
There are no grouping symbols.
Multiply.
Subtract and add from left to right.
6B
Simplify each expression.
12 – 32 + 10 ÷ 2
12 – 32 + 10 ÷ 2
There are no grouping symbols.
12 – 9 + 10 ÷ 2
Evaluate powers. The
exponent applies only to the 3.
Divide.
Subtract and add from left to
right.
12 – 9 + 5
8
6C
Evaluate the expression for the given value of x.
(x · 22) ÷ (2 + 6) for x = 6
(x · 22) ÷ (2 + 6)
(6 · 22) ÷ (2 + 6)
(6 · 4) ÷ (2 + 6)
(24) ÷ (8)
3
First substitute 6 for x.
Square two.
Perform the operations
inside the parentheses.
Divide.
7A
Write the product using the Distributive
Property. Then simplify.
9(52)
9(50 + 2)
9(50) + 9(2)
450 + 18
468
Rewrite 52 as 50 + 2.
Use the Distributive Property.
Multiply.
Add.
7B
Simplify the expression by combining like
terms.
72p – 25p
72p – 25p
47p
72p and 25p are like terms.
Subtract the coefficients.
7C
Simplify the expression by combining like
terms.
0.5m + 2.5n
0.5m + 2.5n
0.5m and 2.5n are not like terms.
0.5m + 2.5n
Do not combine the terms.
8A
Name the quadrant in which each point lies.
A. E
Quadrant ll
B. F
no quadrant (y-axis)
•F
•E
•G
•H
8B
The ordered pair of each point
•F
G (4, 1)
•E
•G
•H
H (-1, -1)
8C
A cable company charges $50 to set up
a movie channel and $3.00 per movie
watched. Write a rule for the company’s
fee. Write ordered pairs for the fee
when a person watches 1, 2, 3, or 4
movies.
y = 50 + 3x
(1, 53), (2, 56), (3, 59), (4, 62)
9A
Solve the equation. Check your answer.
y – 8 = 24
+8 +8
y = 32
Since 8 is subtracted from y, add 8 to both
sides to undo the subtraction.
9B
Solve the equation. Check your answer.
5 =z– 7
7
7
Since
is
subtracted
from
z,
add
to
16
16
16
16
both sides to undo the subtraction.
+ 7
+ 7
16
16
3=z
4
9C
Solve the equation. Check your answer.
4.2 = t + 1.8
–1.8
– 1.8
2.4 = t
Since 1.8 is added to t, subtract 1.8
from both sides to undo the addition.
10A
Solve the equation.
n
= 2.8
6
n = 16.8
Since n is divided by 6,
multiply both sides by 6
to undo the division.
10B
Solve the equation. Check your answer.
9y = 108
y = 12
Since y is multiplied by 9,
divide both sides by 9 to
undo the multiplication.
10C
Solve the equation.
5
w = 20
6
The reciprocal of 5 is 6 . Since w is
6
5
5
multiplied by , multiply both sides
6
6
by
.
w = 24
5
11A
Solve 5t – 2 = –32.
5t – 2 = –32
+2
+2
5t
= –30
5t = –30
5
5
t = –6
First t is multiplied by 5. Then 2 is
subtracted. Work backward: Add 2
to both sides.
Since t is multiplied by 5, divide both
sides by 5 to undo the multiplication.
11B
Solve –4 + 7x = 3.
–4 + 7x = 3
+4
+4
7x = 7
7x = 7
7
7
x=1
First x is multiplied by 7. Then –4 is
added. Work backward: Add 4 to
both sides.
Since x is multiplied by 7, divide both
sides by 7 to undo the multiplication.
11C Solve
2a + 3 – 8a = 8
2a + 3 – 8a = 8
2a – 8a + 3 = 8
–6a + 3 = 8
–3 –3
–6a = 5
Use the Commutative Property of Addition.
Combine like terms.
Since 3 is added to –6a, subtract 3 from
both sides to undo the addition.
Since a is multiplied by –6, divide both
sides by –6 to undo the multiplication.
12A
Solve
4b + 2 = 3b
–3b
–3b
b+2= 0
–2 –2
b = –2
4b + 2 = 3b
To collect the variable terms on one
side, subtract 3b from both sides.
12B Solve
0.5 + 0.3y = 0.7y – 0.3
0.5 + 0.3y = 0.7y – 0.3
–0.3y –0.3y
0.5
= 0.4y – 0.3
+0.3
0.8
+ 0.3
= 0.4y
2=y
To collect the variable terms
on one side, subtract 0.3y
from both sides.
Since 0.3 is subtracted from
0.4y, add 0.3 to both sides
to undo the subtraction.
Since y is multiplied by 0.4,
divide both sides by 0.4 to
undo the multiplication.
12CSolve
3x + 15 – 9 = 2(x + 2)
3x + 15 – 9 = 2(x + 2) Distribute 2 to the expression
in parentheses.
3x + 15 – 9 = 2(x) + 2(2)
3x + 15 – 9 = 2x + 4
3x + 6 = 2x + 4
–2x
–2x
x+6=
–6
x = –2
4
–6
Combine like terms.
To collect the variable terms
on one side, subtract 2x
from both sides.
Since 6 is added to x, subtract
6 from both sides to undo
the addition.
13A
The ratio of the number of bones in a human’s
ears to the number of bones in the skull is 3:11.
There are 22 bones in the skull. How many
bones are in the ears?
Write a ratio comparing bones in ears
to bones in skull.
Write a proportion. Let x be the
number of bones in ears.
Since x is divided by 22, multiply
both sides of the equation by 22.
There are 6 bones in the ears.
13B
Raulf Laue of Germany flipped a pancake 416
times in 120 seconds to set the world record.
Find the unit rate. Round your answer to the
nearest hundredth.
Write a proportion to find an equivalent
ratio with a second quantity of 1.
Divide on the left side to find x.
The unit rate is about 3.47 flips/s.
13C
The ratio of games lost to games won for a
baseball team is 2:3. The team has won 18
games. How many games did the team lose?
Write a ratio comparing games lost to
games won.
Write a proportion. Let x be the
number of games lost.
Since x is divided by 18, multiply
both sides of the equation by 18.
The team lost 12 games.
14A
Solve the proportion.
Use cross
products.
3(m) = 5(9)
3m = 45
Divide both
sides by 3.
m = 15
14B
Solve the proportion.
Use cross
products.
6(7) = 2(y – 3)
42 = 2y – 6
+6
+6 Add 6 to
both sides.
48 = 2y
Divide both
sides by 2.
24 = y
14C
In a school, the ratio of boys to girls is 4:3. There
are 216 boys. How many girls are there?
162
15A
Find the value of x in the diagram if ABCD ~ WXYZ.
ABCD ~ WXYZ
Use cross products.
x = 2.8
Since x is multiplied by 5, divide both
sides by 5 to undo the multiplication.
The length of XY is 2.8 in.
15B
A flagpole casts a shadow that is 75 ft long
at the same time a 6-foot-tall man casts a
shadow that is 9 ft long. Write and solve a
proportion to find the height of the flag pole.
Since h is multiplied by 9, divide both sides
by 9 to undo the multiplication.
The flagpole is 50 feet tall.
15C
A forest ranger who is 150 cm tall casts a
shadow 45 cm long. At the same time, a
nearby tree casts a shadow 195 cm long.
Write and solve a proportion to find the
height of the tree.
45x = 29250
Since x is multiplied by 45, divide both sides
by 45 to undo the multiplication.
x = 650
The tree is 650 centimeters tall.
16A
Find 30% of 80
Method 1 Use a proportion.
Use the percent proportion.
Let x represent the part.
100x = 2400
x = 24
Find the cross products.
Since x is multiplied by 100, divide
both sides by 100 to undo the
multiplication.
16B
What percent of 45 is 35?
Round your answer to the nearest tenth.
Method 1 Use a proportion.
Use the percent proportion.
Let x represent the percent.
45x = 3500
x ≈ 77.8
Find the cross products.
Since x is multiplied by 45, divide
both sides by 45 to undo the
multiplication.
16C
38% of what number is 85?
Round your answer to the nearest tenth.
Method 1 Use a proportion.
Use the percent proportion.
Let x represent the whole.
38x = 8500
x = 223.7
Find the cross products.
Since x is multiplied by 38, divide
both sides by 38 to undo the
multiplication.
17A
Mr. Cortez earns a base salary of $26,000 plus
a sales commission of 5%. His total sales for
one year were $300,000. Find his total pay for
the year.
total pay = base salary + commission
= base + % of total sales
= 26,000 + 5% of 300,000
= 26,000 + (0.05)(300,000)
= 26,000 + 15,000
= 41,000
Mr. Cortez’s total pay was $41,000.
17B
Find the simple interest paid for 3 years on
a $2500 loan at 11.5% per year.
I = Prt
I = (2500)(0.115)(3)
I = 862.50
Write the formula for simple
interest.
Substitute known values.
Write the interest rate as a
decimal.
Multiply.
The amount of interest is $862.50.
17C
Lunch at a restaurant is $27.88. Estimate a
15% tip.
Step 1 First round $27.88 to $30.
Step 2 Think: 15% = 10% + 5% Move the decimal
point one place left.
10% of $30 = $3.00
Step 3 Think 5% = 10% ÷ 2
= $3.00 ÷ 2 = $1.50
Step 4 15 = 10% + 5%
= $3.00 + $1.50 = $4.50
The tip should be about $4.50.
18A
Use the graph to answer each question.
A. Which casserole was
ordered the most? lasagna
B. About how many more tuna
C.
noodle casseroles were
ordered than king ranch
casseroles? 10
18B
Use the graph to answer each question.
A. Which feature received
the same satisfaction
rating for each SUV?
Cargo
Find the two bars that are the
same.
B. Which SUV received a
better rating for mileage?
SUV Y
Find the longest mileage bar.
18C
Use the graph to answer each question.
At what time was the humidity the lowest?
4 A.M. Identify the lowest point.
19A
The numbers of defective widgets in batches
of 1000 are given below. Use the data to
make a stem-and-leaf plot.
14, 12, 8, 9, 13, 20, 15, 9, 21, 8, 13, 19
Number of Defective
Widgets per Batch
0
1
2
8899
233459
01
Key: 1|9 means 19
The tens digits are the stems.
The ones digits are the
leaves. List the leaves
from least to greatest
within each row.
Title the graph and add a key.
19B
The number of runs scored by a softball team
at 19 games is given. Use the data to make a
box-and-whisker plot.
3, 8, 10, 12, 4, 9, 13, 20, 12, 15, 10, 5, 11,
5, 10, 6, 7, 6, 11
3, 4, 5, 5, 6, 6, 7, 8, 9, 10, 10, 10, 11, 11, 12, 12, 13, 15, 20
Minimum
3
Q2
10
Q1
6
First quartile
Minimum
0
20
Third quartile
Maximum
Median
●
Maximum
Q3
12
●
●
8
●
●
16
24
19C
The numbers of pounds of laundry in the
washers at a laundromat are given below. Use
the data to make a cumulative frequency table.
2, 12, 4, 8, 5, 8, 11, 3, 6, 9, 8
20A
Find the mean, median, mode, and range of the
data set.
The number of hours students spent on a
research project: 2, 4, 10, 7, 5
Write the data in numerical
order.
mean:
Add all the values and divide
by the number of values.
median: 2, 4, 5, 7, 10
The median is 5. There are an odd number of
values. Find the middle
mode: none
value.
No value occurs more than
range: 10 – 2 = 8
once.
20B
Find the mean, median, mode, and range of
each data set.
The weight in pounds of six members of a
basketball team: 161, 156, 150, 156, 150, 163
mean:
median: 150, 150, 156, 156, 161, 163
The median is 156.
modes: 150 and 156
range: 163 – 150 = 13
150 and 156 both occur
more often than any other
value.
20C
The following list gives times of Tara’s oneway ride to school (in minutes) for one week:
12, 23, 13, 14, 13. Use the mean, median, and
mode of her times to answer each question.
mean = 15 median = 13 mode = 13
The graph shows customer
satisfaction with different
brands.
Explain why the graph is
misleading.
The scale on the vertical axis
starts at 76. This
exaggerates the difference’s
between the sizes of the
bars.
%
21A
21B
The graph shows the
amount of rainfall by year
in a particular metropolitan
area.
Explain why the graph is
misleading.
The intervals on the vertical
axis are not equal.
21C
The graph shows the
allocation of the county
budget for 2005.
Explain why the graph is
misleading.
The sections of the graph do
not add to 100%, so the
expenditures are not accurately represented.
22A
Identify the sample space and the outcome
shown for each experiment.
Rolling a number cube
Sample space:{1, 2, 3, 4, 5, 6}
Outcome shown: 4
22B
Identify the sample space and the outcome
shown for each experiment.
Spinning a spinner
Sample space:{red, green,
orange, purple}
Outcome shown: green
22C
An experiment consists of
spinning a spinner. Use the
results in the table to find
the experimental
probability of the event.
Spinner lands on orange
Outcome
Frequency
Green
15
Orange
10
Purple
8
Pink
7
23A
An experiment consists of rolling a number
cube. Find the theoretical probability of each
outcome.
rolling a 5
There is one 5
on a number
cube.
23B
An experiment consists of rolling a number
cube. Find the theoretical probability of each
outcome.
rolling an odd number
There 3 odd
numbers on
a cube.
= 0.5 = 50%
23C
A jar has green, blue, purple, and white
marbles. The probability of choosing a green
marble is 0.2, the probability of choosing blue
is 0.3, the probability of choosing purple is 0.1.
What is the probability of choosing white?
Either it will be a white marble or not.
P(green) + P(blue) + P(purple) + P(white) = 1.0
0.2 + 0.3 + 0.1 + P(white) = 1.0
0.6 + P(white) = 1.0
Subtract 0.6 from
– 0.6
– 0.6
both sides.
P(white) = 0.4
24A
Tell whether each set of events is independent
or dependent. Explain you answer.
A number cube lands showing an odd
number. It is rolled a second time and
lands showing a 6.
Independent; the result of rolling the number
cube the 1st time does not affect the result of the
2nd roll.
24B
An experiment consists of randomly selecting a
marble from a bag, replacing it, and then
selecting another marble. The bag contains 3
red marbles and 12 green marbles. What is the
probability of selecting a red marble and then a
green marble?
P(red, green) = P(red)  P(green)
The probability of selecting red
is
, and the probability of
selecting green is
.
24C
A coin is flipped 4 times. What is the
probability of flipping 4 heads in a row.
Because each flip of the coin has an equal
probability of landing heads up, or a tails, the
sample space for each flip is the same. The events
are independent.
P(h, h, h, h) = P(h) • P(h) • P(h) • P(h)
The probability of landing
heads up is with
each event.
25A
A sandwich can be made with 3 different types
of bread, 5 different meats, and 2 types of
cheese. How many types of sandwiches can be
made if each sandwich consists of one bread,
one meat, and one cheese.
Method 2 Use the Fundamental Counting Principle.
There are 3 choices for the first item,
352
5 choices for the second item, and
30
2 choices for the third item.
There are 30 possible types of sandwiches.
25B
A voicemail system password is 1 letter
followed by a 3-digit number less than 600.
How many different voicemail passwords are
possible?
Method 2 Use the Fundamental Counting Principle.
26  600
15,600
There are 26 choices for letters and
600 different numbers (000-599).
There are 15,600 possible combinations of letters
and numbers.
25C
A group of 8 swimmers are swimming in a race.
Prizes are given for first, second, and third place.
How many different outcomes can there be?
The order in which the swimmers finish matters
so use the formula for permutations.
n = 8 and r = 3.
A number divided by itself
is 1, so you can divide
out common factors in
the numerator and
denominator.
There can be 336 different outcomes for the race.
26A
Graph each inequality.
m ≤ –3
Draw a solid circle at –3.
−3
–8 –6 –4 –2
0
2
4
6
8
10 12
Shade in all numbers less than –3
and draw an arrow pointing to the left.
26B
Graph each inequality.
c > 2.5
Draw an empty circle at 2.5.
–4 –3 –2 –1
0
1
2
3
4
5
6
Shade in all the numbers greater
than 2.5 and draw an arrow pointing
to the right.
26C
Graph each inequality.
22 – 4 ≥ w
Draw a solid circle at 0.
22
–4≥w
4–4≥
w 0≥w
–4 –3 –2 –1 0
1
Shade in all numbers less than 0 and
draw an arrow pointing to the left.
2
3
4
5
6
27A
Write the inequality shown by each graph.
x<2
Use any variable. The arrow points to the left, so use
either < or ≤. The empty circle at 2 means that 2 is
not a solution, so use <.
27B
Write the inequality shown by each graph.
x ≥ –0.5
Use any variable. The arrow points to the right, so
use either > or ≥. The solid circle at –0.5 means
that –0.5 is a solution, so use ≥.
27C
Ray’s dad told him not to turn on the air
conditioner unless the temperature is at least
85°F. Define a variable and write an inequality
for the temperatures at which Ray can turn on
the air conditioner. Graph the solutions.
Let t represent the temperatures at which Ray can
turn on the air conditioner.
Turn on the AC when temperature
t
≥
t  85
70
75
80
85
is at least 85°F
90
85
Draw a solid circle at 85. Shade
all numbers greater than 85 and
draw an arrow pointing to the
right.
28A
Solve the inequality and graph the solutions.
x + 12 < 20
x + 12 < 20
–12 –12
x+0 < 8
x < 8
–10 –8 –6 –4 –2
0
2
Since 12 is added to x,
subtract 12 from both sides
to undo the addition.
4
6
8 10
Draw an empty circle at 8.
Shade all numbers less
than 8 and draw an arrow
pointing to the left.
28B
Solve the inequality and graph the solutions.
d – 5 > –7
d – 5 > –7
+5 +5
d + 0 > –2
d > –2
Since 5 is subtracted from
d, add 5 to both sides to
undo the subtraction.
Draw an empty circle at –2.
–10 –8 –6 –4 –2
0
2
4
6
8 10
Shade all numbers greater
than –2 and draw an arrow
pointing to the right.
28C
Solve each inequality and graph the solutions.
> –3 + t
> –3 + t
+3
+3
> 0+t
t<
Since –3 is added to t, add 3 to both
sides to undo the addition.
–10 –8 –6 –4 –2
0
2
4
6
8 10
29A
Solve the inequality and graph the solutions.
7x > –42
7x > –42
Since x is multiplied by 7, divide both
sides by 7 to undo the multiplication.
>
1x > –6
x > –6
–10 –8 –6 –4 –2
0
2
4
6
8 10
29B
Solve the inequality and graph the solutions.
3(2.4) ≤ 3
Since m is divided by 3, multiply both
sides by 3 to undo the division.
7.2 ≤ m(or m ≥ 7.2)
0
2
4
6
8 10 12 14 16 18 20
29C
Solve the inequality and graph the solutions.
–12x > 84
Since x is multiplied by –12, divide
both sides by –12. Change > to <.
x < –7
–7
–14 –12 –10 –8 –6 –4 –2
0
2
4
6
30A
Solve the inequality and graph the solutions.
45 + 2b > 61
45 + 2b > 61
–45
–45
Since 45 is added to 2b,
subtract 45 from both sides
to undo the addition.
2b > 16
b>8
0
2
4
6
Since b is multiplied by 2, divide
both sides by 2 to undo the
multiplication.
8 10 12 14 16 18 20
30B
Solve the inequality and graph the solutions.
8 – 3y ≥ 29
Since 8 is added to –3y, subtract
8 from both sides to undo the
addition.
8 – 3y ≥ 29
–8
–8
–3y ≥ 21
Since y is multiplied by –3,
divide both sides by –3 to
undo the multiplication.
Change ≥ to ≤.
y ≤ –7
–7
–10 –8 –6 –4 –2
0
2
4
6
8 10
30C
Solve the inequality and graph the solutions.
–12 ≥ 3x + 6
Since 6 is added to 3x, subtract 6
from both sides to undo the
addition.
–12 ≥ 3x + 6
–6
–6
–18 ≥ 3x
Since x is multiplied by 3, divide
both sides by 3 to undo the
multiplication.
–6 ≥ x
–10 –8 –6 –4 –2
0
2
4
6
8 10
31A
Solve the inequality and graph the solutions.
–4(2 – x) ≤ 8
−4(2 – x) ≤ 8
−4(2) − 4(−x) ≤
8
–8 + 4x ≤ 8
+8
+8
4x ≤ 16
Distribute –4 on the left side.
Since –8 is added to 4x, add 8 to
both sides.
Since x is multiplied by 4, divide
both sides by 4 to undo the
multiplication.
x≤4
–10 –8 –6 –4 –2
0
2
4
6
8 10
31B
Solve the inequality and graph the solutions.
3 + 2(x + 4) > 3
Distribute 2 on the left side.
x
Combine like terms.
Since 11 is added to 2x, subtract
11 from both sides to undo the
addition.
3 + 2(x + 4) > 3
3 + 2x + 8 > 3
2x + 11 > 3
– 11 – 11
2x
> –8
Since x is multiplied by 2, divide
both sides by 2 to undo the
multiplication.
x > –4
–10 –8 –6 –4 –2
0
2
4
6
8 10
31C
Solve the inequality and graph the solutions.
Multiply both sides by 6, the LCD of
the fractions.
Distribute 6 on the left side.
4f + 3 > 2
–3 –3
4f
> –1
Since 3 is added to 4f, subtract 3
from both sides to undo the
addition.
32A
Solve the inequality and graph the solutions.
y ≤ 4y + 18
y ≤ 4y + 18
–y –y
To collect the variable terms on one
side, subtract y from both sides.
0 ≤ 3y + 18
–18
– 18
Since 18 is added to 3y, subtract 18
from both sides to undo the
addition.
–18 ≤ 3y
Since y is multiplied by 3, divide both
sides by 3 to undo the
multiplication.
–6 ≤ y (or y  –6)
–10 –8 –6 –4 –2
0
2
4
6
8 10
32BSolve the inequality and graph the solutions.
4m – 3 < 2m + 6
4m – 3 < 2m + 6
–2m
– 2m
2m – 3 <
+3
2m
<
+6
+3
9
To collect the variable terms on one
side, subtract 2m from both sides.
Since 3 is subtracted from 2m, add
3 to both sides to undo the
subtraction
Since m is multiplied by 2, divide
both sides by 2 to undo the
multiplication.
4
5
6
32CSolve the inequality and graph the solutions.
2(k – 3) > 6 + 3k – 3
2(k – 3) > 3 + 3k
2k + 2(–3) > 3 + 3k
2k – 6 > 3 + 3k
–2k
– 2k
–6 > 3 + k
–3 –3
–9 > k
Distribute 2 on the left side of
the inequality.
To collect the variable terms,
subtract 2k from both
sides.
Since 3 is added to k, subtract 3
from both sides to undo the
addition.
33A
Solve the compound inequality and graph
the solutions.
–5 < x + 1 < 2
–5 < x + 1 < 2
–1
–1–1
–6 < x < 1
Graph –6 < x.
–10
–6 –4 –2
0
2
4
6
8 10
Graph x < 1.
Graph the intersection by
finding where the two
graphs overlap.
33B
Solve the compound inequality and graph
the solutions.
8 < 3x – 1 ≤ 11
8 < 3x – 1 ≤ 11
+1
+1 +1
9 < 3x ≤ 12
Since 1 is subtracted from 3x, add
1 to each part of the inequality.
Since x is multiplied by 3, divide
each part of the inequality by 3
to undo the multiplication.
3<x≤4
–4 –3 –2 –1
0
1
2
3
4
5
33C
Solve the inequality and graph the solutions.
8 + t ≥ 7 OR 8 + t < 2
8 + t ≥ 7 OR 8 + t < 2
–8
–8
–8
−8
t ≥ –1 OR
t < –6
–10 –8 –6 –4 –2
0
2
4
6
8 10
Solve each simple
inequality.
34A
Each day several leaves fall from a tree. One
day a gust of wind blows off many leaves.
Eventually, there are no more leaves on the
tree. Choose the graph that best represents
the situation.
The correct graph is B.
34B
The air temperature increased steadily for
several hours and then remained constant. At
the end of the day, the temperature increased
slightly before dropping sharply. Choose the
graph that best represents this situation.
The correct graph is graph C.
34C
Sketch a graph for the situation. Tell whether
the graph is continuous or discrete.
•
•
•
•
•
initially increases
remains constant
decreases to a stop
increases
remains constant
Speed
A truck driver enters a street, drives at a
constant speed, stops at a light, and then
continues.
As time passes during the trip
y
(moving left to right along the
x-axis) the truck's speed (y-axis)
does the following:
Time
x
The graph is continuous.
35A
Express the relation {(2, 3), (4, 7), (6, 8)} as a
table, as a graph, and as a mapping diagram.
Table
x
y
Graph
Mapping Diagram
y
x
1
3
2
4
3
5
35B
Give the domain and range of the relation.
6
5
2
1
–4
–1
0
The domain values are all
x-values 1, 2, 5 and 6.
The range values are
y-values 0, –1 and –4.
Domain: {6, 5, 2, 1}
Range: {–4, –1, 0}
35C
Give the domain and range of the relation.
x
y
1
1
4
4
8
1
The domain values are all
x-values 1, 4, and 8.
The range values are
y-values 1 and 4.
Domain: {1, 4, 8}
Range: {1, 4}
36A
Determine a relationship between the x- and
y-values. Write an equation.
x
5
y
1
or
10 15 20
2
3
4
The value of y is one-fifth of x.
36B
Determine a relationship between the x- and
y-values. Write an equation.
{(1, 3), (2, 6), (3, 9), (4, 12)}
y = 3x
1
2
3
4
3
6
9
12
The value of y is 3 times x.
36C
Identify the independent and dependent variables
in the situation.
The height of a candle decrease d centimeters
for every hour it burns.
The height of a candle depends on the number of
hours it burns.
Dependent: height of candle
Independent: time
37A
Evaluate the function for the given input values.
For f(x) = 3x + 2, find f(x) when x = 7 and
when x = –4.
f(x) = 3(x) + 2
f(7) = 3(7) + 2 Substitute
7 for x.
= 21 + 2
Simplify.
= 23
f(x) = 3(x) + 2
f(–4) = 3(–4) + 2 Substitute
–4 for x.
Simplify.
= –12 + 2
= –10
37B
Evaluate the function for the given input values.
For g(t) = 1.5t – 5, find g(t) when t = 6 and
when t = –2.
g(t) = 1.5t – 5
g(t) = 1.5t – 5
g(6) = 1.5(6) – 5
g(–2) = 1.5(–2) – 5
=9–5
= –3 – 5
=4
= –8
37C
Evaluate the function for the given input values.
For h(c) = 2c – 1, find h(c) when c = 1
and when c = –3.
h(c) = 2c – 1
h(1) = 2(1) – 1
h(c) = 2c – 1
h(–3) = 2(–3) – 1
=2–1
= –6 – 1
=1
= –7
38A
A ___________ is a graph with
points plotted to show a possible
relationship between two sets of
data.
A. Bar Graph
B. Circle Graph
C. Line Graph
D. Scatter Plot
D. Scatter Plot
38B
Example 1: Graphing a Scatter Plot from Given Data
The table shows the number of cookies in a
jar from the time since they were baked.
Graph a scatter plot using the given data.
Use the table to make ordered pairs
for the scatter plot.
The x-value represents the time since the cookies were baked and the
y-value represents the number of cookies left in the jar.
Plot the ordered pairs.
38C
The table shows the number of points scored
by a high school football team in the first four
games of a season. Graph a scatter plot using
the given data.
Game
Score
1
6
2 3 4
21 46 34
Use the table to make ordered pairs
for the scatter plot.
The x-value represents the individual games and
the y-value represents the points scored in each
game.
Plot the ordered pairs.
39A
Identify whether the graph represents a function.
Explain. If the graph does represent a function, is
the function linear?
Each domain value is
paired with exactly
one range value. The
graph forms a line.
linear function
39B
Identify whether the graph represents a function.
Explain. If the graph does represent a function, is
the function linear?
Each domain value is
paired with exactly one
range value. The graph
is not a line.
not a linear function
39C
Tell whether the set of ordered pairs satisfies a
linear function. Explain.
{(0, –3), (4, 0), (8, 3), (12, 6), (16, 9)}
x
+4
+4
+4
+4
y
0
–3
4
0
8
3
12
6
16
9
+3
+3
+3
+3
Write the ordered pairs in a table.
Look for a pattern.
A constant change of +4 in x
corresponds to a constant
change of +3 in y.
These points satisfy a linear
function.
40A
Find the x- and y-intercepts.
5x – 2y = 10
5x – 0 = 10
5x = 10
x=2
The x-intercept is 2.
y = –5
The y-intercept is –5.
40B
Find the x- and y-intercepts.
The y-intercept is 1.
The x-intercept is –2.
40C
Use intercepts to GRAPH the line described
by the equation.
3x – 7y = 21
Step 1 Find the intercepts.
Step 2 Graph the line.
3x = 21
x
x=7
y = –3
Plot (7, 0) and (0, –3).
Connect with a straight line.
41A
Tell whether the slope of each line is positive,
negative, zero or undefined.
A.
B.
The line rises from left to right. The line falls from left to
right.
The slope is positive.
The slope is negative.
41B
Find the slope of the line.
2.
41C
Find the slope of the line.
undefined
42A
Find the slope of the line that contains (2, 5)
and (8, 1).
Use the slope formula.
Substitute (2, 5) for (x1, y1) and
(8, 1) for (x2, y2).
Simplify.
42B
Find the slope of the line that
contains (–2, –2) and (7, –2).
Use the slope formula.
Substitute (–2, –2) for (x1, y1) and
(7, –2) for (x2, y2).
Simplify.
=0
42CThe graph shows a linear
relationship. Find the slope.
Let (0, 2) be (x1, y1) and (–2, –2) be (x2, y2).
Use the slope formula.
Substitute (0, 2) for (x1, y1)
and (–2, –2) for (x2, y2).
Simplify.
43A
Write the equation in slope-intercept form. Then
graph the line described by the equation.
y = x + 0 is in the form
y = mx + b.
slope:
y-intercept: b = 0
Step 1 Plot (0, 0).
Step 2 Count 2 units up and 3 units right
and plot another point.
Step 3 Draw the line connecting the two
points.
43B
Graph the line given the slope and y-intercept.
slope = 2, y-intercept = –3
Step 1 The y-intercept is –3, so the line
contains (0, –3). Plot (0, –3).
Step 2 Slope =
Count 2 units up and 1 unit
right from (0, –3) and plot
another point.
Step 3 Draw the line through
the two points.
Run = 1
Rise = 2
43C
Write the equation that describes the line in
slope-intercept form.
slope =
; y-intercept = 4
y = mx + b
y=
x+4
Substitute the given values
for m and b.
Simply if necessary.
44A
Write the trigonometric ratio as a fraction
and as a decimal rounded to the nearest
hundredth.
sin J
44B
Write the trigonometric ratio as a
fraction and as a decimal rounded
to the nearest hundredth.
tan K
44C
Find the measure of angle D
5.3
0
tan D 
 68
2. 1
1
45A
Find BC.
Write a trigonometric ratio.
Substitute the given values.
Multiply both sides by BC
and divide by tan 15°.
BC  38.07 ft
Simplify the expression.
45B
Find the length of QR
Substitute the given values.
12.9(sin 63°) = QR
11.49 cm  QR
Multiply both sides by 12.9.
Simplify the expression.
45C
Find the length of FD
Substitute the given values.
Multiply both sides by FD and
divide by cos 39°.
FD  25.74 m
Simplify the expression.
46A
The Seattle Space Needle casts a 67meter shadow. If the angle of
elevation from the tip of the shadow
to the top of the Space Needle is
70º, how tall is the Space Needle?
Round to the nearest meter.
You are given the side adjacent to
A, and y is the side opposite A.
So write a tangent ratio.
y = 67 tan 70° Multiply both sides by 67.
y  184 m
Simplify the expression.
46B
Use the diagram above to classify
each angle as an angle of elevation
or angle of depression.
1a. 5
1b. 6
1a. Depression
1b. Elevation
46C
A plane is flying at an altitude of 14,500
ft. The angle of elevation from the control
tower to the plane is 15°. What is the
horizontal distance from the plane to the
tower? Round to the nearest foot.
14500
tan 15 
x
54,115 ft
47A
Given the figure, segment JM
is best described as:
a. Chord
b. Secant
c. Tangent
d. Diameter
A. Chord
47B
Given the figure, Line JM is
best described as:
a. Chord
b. Secant
c. Tangent
d. Diameter
B. Secant
47C
Given the figure, line m is
best described as:
a. Chord
b. Secant
c. Tangent
d. Diameter
C. Tangent
48A
Find a.
5a – 32 = 4 + 2a
3a – 32 = 4
3a = 36
a = 12
48B
Find RS
n + 3 = 2n – 1
4=n
RS = 4 + 3
=7
48C
Find RS
x = 4x – 25.2
–3x = –25.2
x = 8.4
= 2.1
49A
Find
mLJN
mLJN = 360° – (40 +
25)°
= 295°
49B
Find n.
9n – 11 = 7n + 11
2n = 22
n = 11
49C C  J, and mGCD  mNJM.
Find NM.
14t – 26 = 5t + 1
9t = 27
t=3
NM = 5(3) + 1
= 16
50A
Find each measure.
mPRU
50B
Find each measure.
mSP
50C
Find each measure.
mDAE
51A
Find each measure.
mEFH
= 65°
51B
Find each measure.
51C
Find each angle measure.
mABD
52A
Find the value of x.
50° = 83° – x
x = 33°
52B
52C
Find the value of x.
ML  JL = KL2
20(5) = x2
100 = x2
±10 = x
53A
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53B
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53C
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54A
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54B
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54C
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55A
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55B
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55C
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56A
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56B
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56C
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57A
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57B
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57C
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58A
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58B
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58C
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59A
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59B
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59C
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60A
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60B
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60C
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61A
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61B
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61C
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62A
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62B
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63A
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63B
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64A
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