Name
1-1
Class
Date
Think About a Plan
Patterns and Expressions
Use the graph shown.
y
15
a. Identify a pattern of the graph by making a table of the
Output
inputs and outputs.
b. What are the outputs for inputs 6, 7, and 8?
1. What are the ordered pairs of the points in the graph?
(1, 3), (2, 6), (3, 9), (4, 12), (5, 15)
12
9
6
3
O
x
1
2
3
4
Input
2. Complete the table of the input and output values shown in the ordered pairs.
Input
Output
1
3
2
6
3
9
4
12
5
15
3. Complete the process column with the process that takes each input value
and gives the corresponding output value.
4. output 5
Input
Process
Column
Output
1
1( 3 )
3
2
2( 3 )
6
3
3( 3 )
9
4
4( 3 )
12
5
5( 3 )
15
input ∙ 3
5. Complete the process column for inputs 6, 7, and 8. Then find the outputs for
inputs 6, 7, and 8.
Input
Process
Column
Output
6
6( 3 )
18
7
7( 3 )
21
8
8( 3 )
24
18, 21, 24
6. The outputs for inputs 6, 7, and 8 are
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5
Name
1-1
Class
Date
Practice
Form K
Patterns and Expressions
Describe each pattern using words. Draw the next figure in each pattern.
1.
Answers may vary. Sample: Start with a row of two squares. Add a row of two squares
below the previous figure for each new figure.
2.
Answers may vary. Sample: Start with one square. Add a row of squares below the
previous figure that has one more square than the row above it for each new figure.
3.
Answers may vary. Sample: Start with an isosceles triangle that points upward. Rotate
the triangle 90° clockwise for each new figure.
Make a table with a process column to represent the pattern. Write an
expression for the number of circles in the nth figure. The table has been started
for you.
4.
The expression for the
number of circles in
the nth figure is 2n.
Figure Number
(Input)
Process
Column
Number of
Circles (Output)
1
1(2)
2
2
2(2)
4
3
3(2)
6
4
4(2)
8
■
■
■
n
n(2)
2n
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Name
Class
Date
Practice (continued)
1-1
Form K
Patterns and Expressions
Number of cups of flour
The graph shows the number of cups of flour needed for
baking cookies.
5. How many cups of flour are needed for baking 4 batches
of cookies?
8 cups
6. How many cups of flour are needed for baking 30 batches
of cookies?
10
Baking Cookies
8
6
4
2
0
0 2 4 6 8 10
Number of batches of cookies
60 cups
7. How many cups of flour are needed for baking n batches
of cookies?
2n cups
Identify a pattern by making a table. Include a process column.
(1, 4), (2, 5), (3, 6), (4, 7)
Hint: To start, list the points on the graph. Make a table of input and
output values shown in the ordered pairs. Use the process column to
figure out the pattern.
10
10
9.
8
8
6
6
Output
Output
8.
4
2
4
Input
6
0
8
2
4
Input
6
8
Identify the pattern and find the next three numbers in the pattern.
10. 1, 4, 16, 64, . . .
11. 3, 6, 12, 24, . . .
Each term is 4 times the previous term;
256, 1024, 4096
Each term is 2 times
the previous term;
48, 96, 192
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Process
Column
(Output)
1
113
4
2
213
5
3
313
6
4
413
7
n
n13
n13
(1, 1.5), (2, 3), (3, 4.5), (4, 6)
2
2
0
4
(Input)
(Input)
Process
Column
(Output)
1
1(1.5)
1.5
2
2(1.5)
3
3
3(1.5)
4.5
4
4(1.5)
6
n
n(1.5)
1.5n
Name
Class
1-1
Date
Standardized Test Prep
Patterns and Expressions
Multiple Choice
For Exercises 1–5, choose the correct letter.
1. What is the next figure in the pattern at the right? C
2. Which is the next number in the table? H
14
15
16
20
Input
Output
1
1
2
3
3
6
4
10
5
■
3. How many toothpicks would be in the tenth figure? A
21
20
4. What is the next number in the pattern?
21
23
2, 7, 12, 17, c G
22
5. What is the next number in the pattern?
23
11
23
27
1, 21, 2, 22, 3, c A
0
3
4
Short Response
6. Ramon has 25 books in his library. Each month, he adds 3 new books to his
collection. How many books will Ramon have after 12 months?
61 books
[2] correct number of books
[1] incorrect number of books
[0] no answer given
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Name
1-2
Class
Date
Think About a Plan
Properties of Real Numbers
Five friends each ordered a sandwich and a drink at a restaurant. Each sandwich
costs the same amount, and each drink costs the same amount. What are two
ways to compute the bill? What property of real numbers is illustrated by the two
methods?
Understanding the Problem
1. There are
5
sandwiches and
5
drinks on the bill.
2. What is the problem asking you to determine?
two ways to represent the cost of 5 sandwiches and 5 drinks, and the property of real
numbers illustrated by the two representations
Planning the Solution
3. How can you represent the cost of five sandwiches?
Answers may vary. Sample: 5s
4. How can you represent the cost of five drinks?
Answers may vary. Sample: 5d
5. How can you represent the cost of the items ordered by one friend?
Answers may vary. Sample: d 1 s
Getting an Answer
6. Write an expression that represents the cost of five drinks and the cost of five
sandwiches.
Answers may vary. Sample: 5d 1 5s
7. Write an expression that represents the cost of the items ordered by five
friends.
Answers may vary. Sample: 5(d 1 s)
8. What property of real numbers tells you that these two expressions are equal?
Explain.
Distributive Property; the Distributive Property states a(b 1 c) 5 ab 1 ac.
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Name
Class
1-2
Date
Practice
Form K
Properties of Real Numbers
Classify each variable according to the set of numbers that best describes
its values.
1. the number of students in your class natural numbers
To start, make a list of some numbers that could describe the number of
students in your class.
2. the area of the circle A found by using the formula A 5 pr2 irrational numbers
To start, make a list of some numbers that could describe the area of a circle.
3. the elevation e of various land points in the United States measured to the nearest foot integers
To start, make a list of some numbers that could describe elevation levels.
Graph each number on a number line.
1
4. 5 2
6. 2.25
5
⫺4
5. 24
1
2
⫺8⫺7⫺6⫺5⫺4⫺3⫺2⫺1 0 1 2
⫺1 0 1 2 3 4 5 6 7 8 9
2.25
1
7. 26 3
⫺1 0 1 2 3 4 5 6 7 8 9
⫺6
1
3
⫺8⫺7⫺6⫺5⫺4⫺3⫺2⫺1 0 1 2
8. !8
√ 8 ⬇ 2.83
To start, use a calculator to approximate the square root.
ⴚ1 0 1 2 3 4 5 6 7 8 9
Compare the two numbers. Use R or S .
9. !50 and 8.8 R
10. 5 and !23 S
11. 6.2 and !40 R
12. 2!3 and 23 S
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Name
1-2
Class
Date
Practice (continued)
Form K
Properties of Real Numbers
Name the property of real numbers illustrated by each equation.
2 3
13. 3 ? 2 5 1
Inverse Property of Multiplication
14. 6(2 1 x) 5 6 ? 2 1 6 ? x
Distributive Property
15. 2 ? 20 5 20 ? 2
Commutative Property of Multiplication
16. 8 1 (28) 5 0
Inverse Property of Addition
17. 2(0.5 ? 4) 5 (2 ? 0.5) ? 4
Associative Property of Multiplication
18. 211 1 5 5 5 1 (211)
Commutative Property of Addition
Estimate the numbers graphed at
the labeled points.
C
A
⫺5 ⫺4 ⫺3 ⫺2 ⫺1
19. point A Answers may vary. Sample: 22
B
0
1
D
2
3
4
5
20. point B Answers may vary. Sample: 1.5
21. point C Answers may vary. Sample: 24.75 22. point D Answers may vary. Sample: 2.25
To find the length of the side b of the square base of a rectangular prism, use the
formula b 5 ÅVh , where V is the volume of the prism and h is the height. Which
set of numbers best describes the value of b for the given values of V and h?
23. V 5 100, h 5 1
24. V 5 100, h 5 10
natural numbers
irrational numbers
Write the numbers in increasing order.
5
5
25. 6, !28, 22, 20.8, 1
2
26. 3, 24, !32, !13, 20.4
24, 20.4, 23, !13, !32
252, 20.8, 56, 1, "28
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Name
Class
1-2
Date
Standardized Test Prep
Properties of Real Numbers
Multiple Choice
For Exercises 1–5, choose the correct letter.
1. Which letter on the graph corresponds to !5? C
2. Which letter on the graph corresponds to 21.5? F
A
⫺1
BC
0
1
F
2
G
⫺3 ⫺2 ⫺1
D
3
H
0
4
5
2
3
I
1
What property of real numbers is illustrated by the equation?
3. 26 1 (6 1 5) 5 (26 1 6) 1 5 D
Identity Property of Addition
Commutative Property of Addition
Inverse Property of Addition
Associative Property of Addition
4. 2(24 1 x) 5 2(24) 1 2 ? x G
Associative Property of Multiplication
Associative Property of Addition
Distributive Property
Closure Property of Multiplication
2
5. Which of the following shows the numbers 13, 1.3, 17, 24, and 2!10 in
order from greatest to least? B
13, 1.3, 127, 24, 2!10
13, 127, 1.3, 2!10, 24
13, 1.3, 127, 2!10, 24
24, 2!10, 127, 1.3, 13
Short Response
Geometry The length c of the hypotenuse of a right triangle with legs having
lengths a and b is found by using the formula c 5 "a2 1 b2 . Which set of
numbers best describes the value of c for the given values of a and b?
6. a 5 3, b 5 4 [2] natural numbers [1] incorrect set of numbers [0] no answer given
1
1
7. a 5 3, b 5 4 [2] rational numbers [1] incorrect set of numbers [0] no answer given
8. a 5 !3, b 5 !4 [2] irrational numbers [1] incorrect set of numbers [0] no answer given
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Name
1-3
Class
Date
Think About a Plan
Algebraic Expressions
Write an algebraic expression to model the situation.
The freshman class will be selling carnations as a class project. What is the class’s
income after it pays the florist a flat fee of $200 and sells x carnations for $2 each?
1. What does the variable represent?
the number of carnations sold
2. How will the class’s income change for each carnation sold?
It will increase by $2.
3. Will paying the florist increase or decrease their income? By how much?
decrease; $200
4. Will the expression include both the income for each carnation and the
florist’s fee? Explain.
Yes; the class’s profit is a function of the proceeds from carnation sales
and the florist’s fee.
5. Write the expression in words.
The
income
z 2200
z
is
and
2 z
z times
x z .
z 6. Write the expression using symbols.
income
5
z 2200
z
1 z
z 2 z
z . z
z x z
z 7. Check your expression by substituting 300 for the number of carnations. Does
your answer make sense? Explain.
2200 1 2(300) 5 2200 1 600 5 400; yes; the class has an income of $400 after they
make $600 and pay the florist $200.
z
z
220012x
8. The algebraic expression models the freshman class income.
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Name
1-3
Class
Date
Practice
Form K
Algebraic Expressions
Write an algebraic expression that models each word phrase.
1. six less than the number r r 2 6
To start, relate what you know. “Less than” means subtraction.
Describe what you need to find. Begin with the number r and subtract 6.
2. twelve more than the number b b 1 12
3. five times the sum of 3 and the number m 5(3 1 m)
Write an algebraic expression that models each situation.
4. Alexis has $250 in her savings account and deposits $20 each week for w weeks. 250 1 20w
5. You have 30 gallons of gas and you use 5 gallons per day for d days. 30 2 5d
Evaluate each expression for the given values of the variables.
6. 22a 1 5b 1 6a 2 2b 1 a; a 5 23 and b 5 2 29
To start, substitute the value
for each variable.
22(23) 1 5(2) 1 6(23) 2 2(2) 1 (23)
7. y(3 2 x) 1 x2; x 5 2 and y 5 12 16
8. 3(4e 2 2f ) 1 2(e 1 8f ); e 5 23 and f 5 10 58
The expression 6s2 represents the surface area of a cube with edges of length s.
What is the surface area of a cube with each edge length?
9. 4 centimeters 96 cm2
10. 2.5 feet 37.5 ft2
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Name
1-3
Class
Date
Practice (continued)
Form K
Algebraic Expressions
Write an algebraic expression to model the total score in each situation.
Then evaluate the expression to find the total score.
11. In the first half, there were fifteen two-point shots, ten three-point shots and
5 one-point free throws. T 5 2w 1 3r 1 1f; 65
To start, define your variables. Let w 5 the number of two-point shots,
r 5 the number of three-point shots, and f 5 the number of one-point free throws.
12. In the first quarter, there were two touchdowns and 1 extra point kick. T 5 6t 1 1e; 13
Hint: A touchdown is worth 6 points. An extra point kick is worth 1 point.
Simplify by combining like terms.
13. 10b 2 b 9b
14. 12 1 8s 2 3s 12 1 5s
15. 3a 1 2b 1 6a 9a 1 2b
16. 5m 1 2n 1 6m 1 4n 11m 1 6n
17. 8r 2 (3s 2 5r) 13r 2 3s
18. 2.5y 2 4y 21.5y
The expression 19.95 1 0.05x models a household’s monthly Internet charges,
where x represents the number of online minutes during the month. What are
the monthly charges for each number of online minutes?
19. 65 minutes $23.20
20. 128 minutes $26.35
Evaluate each expression for the given value of the variable.
21. 3a 1 (2a 1 6); a 5 2 16
22. x 2 5(x 1 2); x 5 25 10
23. 2r 1 (3r2 1 1); r 5 4 45
24. x2 2 5(3x 2 12); x 5 10 10
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Name
Class
1-3
Date
Standardized Test Prep
Algebraic Expressions
Multiple Choice
For Exercises 1–3, choose the correct letter.
1. The expression 2p(rh 1 r2) represents the total surface area of a cylinder with
height h and radius r. What is the surface area of a cylinder with height
6 centimeters and radius 2 centimeters? C
16p cm2
32p cm2
28p cm2
96p cm2
2. Which expression best represents the simplified form of
3(m 2 3) 1 m(5 2 m) 2 m2 ? F
22m2 1 8m 2 9
22m2 2 2m 2 9
8m 2 9
22m 2 9
3. The price of a discount airline ticket starts at $150 and increases by $30 each
week. Which algebraic expression models this situation? D
30 1 150w
30 2 150w
150 2 30w
150 1 30w
Extended Response
4. Members of a club are selling calendars as a fundraiser. The club pays $100
for a box of wall and desk calendars. They sell wall calendars for $12 and desk
calendars for $8.
a. Write an algebraic expression to model the club’s profit from selling w wall
calendars and d desk calendars. Explain in words or show work for how you
determined the expression
b. What is the club’s profit from selling 9 wall calendars and 7 desk calendars?
Show your work.
a. The income from wall calendars is 12w. The income from desk calendars is 8d. The
total income is 12w 1 8d. The club must pay $100 from the total income, so the profit
is 12w 1 8d 2 100. (OR equivalent explanation)
b. 12w 1 8d 2 100 5 12(9) 1 8(7) 2 100 5 108 1 56 2 100 5 64; $64
[4] appropriate methods and correct expression with no computational errors
[3] appropriate methods and correct expression, but minor computational error
[2] incorrect expression or multiple computational errors
[1] correct expression and profit, without work shown
[0] no answer or no attempt made
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27
Name
1-4
Class
Date
Think About a Plan
Solving Equations
Geometry The measure of the supplement of an angle is 208 more
than three times the measure of the original angle. Find the measures
of the angles.
Know
z
z
1808 .
1. The sum of the measures of the two angles is 2. What do you know about the supplemental angle?
It is 208 more than three times the measure of the original angle.
Need
3. To solve the problem, I need to define:
the measure of the original angle 5 x
the measure of the supplemental angle 5 3x 1 20
Plan
4. What equation can you use to find the measure of the original angle?
x 1 (3x 1 20) 5 180
5. Solve the equation.
x 5 40
6. What are the measures of the angles?
original angle: 408; supplemental angle: 1408
7. Are the solutions reasonable? Explain.
Yes; three times the measure of the first angle plus 208 is 1408; the sum of
the measures of the angles is 1808, so they are supplementary.
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Name
1-4
Class
Date
Practice
Form K
Solving Equations
Solve each equation.
1. 5x 1 4 5 2x 1 10 2
2. 10w 2 3 5 8w 1 5 4
To start, subtract 2x from each side.
To start, subtract 8w from each side.
3. 4(d 2 3) 5 2d 6
4. s 1 2 2 3s 2 16 5 0 27
Solve each equation. Check your answer.
5. 9(z 2 3) 5 12z 29
6. 7y 1 5 5 6y 1 11 6
7. 5w 1 8 2 12w 5 16 2 15w 1
8. 3(x 1 1) 5 2(x 1 11) 19
Write an equation to solve each problem.
9. Lisa and Beth have babysitting jobs. Lisa earns $30 per week and Beth earns
$25 per week. How many weeks will it take for them to earn a total of $275?
To start, record what you know.
Describe what you need to find.
Lisa earns $30 per week.
Beth earns $25 per week.
Total earned: $275
an equation to find the number of
weeks it takes to earn $275 together
Variable may vary. Sample: 30w 1 25w 5 275
10. The angles of a triangle are in the ratio 2 : 12 : 16. The sum of all the angles in a
triangle must equal 180 degrees. What is the degree measure of each angle of
the triangle? Let x 5 the common factor.
2x 1 12x 1 16x 5 180
11. What two consecutive numbers have a sum of 53?
Variable may vary. Sample: n 1 (n 1 1) 5 53
Determine whether the equation is always, sometimes, or never true.
12. 3(2x 2 4) 5 6(x 2 2)
always
13. 4(x 1 3) 5 2(2x 1 1)
never
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Name
Class
Date
Practice (continued)
1-4
Form K
Solving Equations
Solve each formula for the indicated variable.
1
14. A 5 2bh, for b
b 5 2A
h
15. P 5 2w 1 2l, for w
1
16. A 5 2h(b1 1 b2), for h
h 5 b 2A
1 b
17. S 5 2prh 1 2pr2 , for h
1
w 5 P 22 2l
2pr2
h 5 S 22pr
2
Solve each equation for y.
18. ry 2 sy 5 t
y 5 r 2t s, r u s
3
19. 7(y 1 2) 5 g
y 5 73 g 2 2
y
20. m 1 3 5 n
y 5 m(n 2 3), m u 0
21.
3y 2 1
5z
2
2z 1 1
y5 3
Solve each equation.
22. (x 2 3) 2 2 5 6 2 2(x 1 1)
3
23. 4(a 1 2) 2 2a 5 10 1 3(a 2 3)
7
24. 2(2c 1 1) 2 c 5 213
25
25. 8u 1 2(u 2 10) 5 0
2
26. The first half of a play is 35 minutes longer than the second half of the play. If
the entire play is 155 minutes long, how long is the first half of the play? Write
an equation to solve the problem.
Variable may vary. Sample: (m 1 35) 1 m 5 155; m 5 60
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Name
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Date
Standardized Test Prep
1-4
Solving Equations
Gridded Response
Solve each exercise and enter your answer in the grid provided.
1. A bookstore owner estimates that her weekly profits p can be described
by the equation p 5 8b 2 560, where b is the number of books sold that
week. Last week the store’s profit was $720. What is the number of books
sold?
2. What is the value of m in the equation 0.6m 2 0.2 5 3.7?
3. Three consecutive even integers have a sum of 168. What is the value of the
largest integer?
4. If 6(x 2 3) 2 2(x 2 2) 5 11, what is the value of x?
5. Your long distance service provider charges you $.06 per minute plus a
monthly access fee of $4.95. For referring a friend, you receive a $10 service
credit this month. If your long-distance bill is $7.85, how many long-distance
minutes did you use?
Answers
1.
–
160
0
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
2.
0
1
2
3
4
5
6
7
8
9
0 0
1 1
2 2
3 3
4 4
5 5
6 6
7 7
8 8
9 9
–
6 . 5
0
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
3.
0
1
2
3
4
5
6
7
8
9
0 0
1 1
2 2
3 3
4 4
5 5
6 6
7 7
8 8
9 9
–
58
0
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
4.
0
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
0 0
1 1
2 2
3 3
4 4
5 5
6 6
7 7
8 8
9 9
–
6 . 25
0
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
5.
0 0
1 1
2 2
3 3
4 4
5 5
6 6
7 7
8 8
9 9
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–
215
0
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
0 0
1 1
2 2
3 3
4 4
5 5
6 6
7 7
8 8
9 9
Name
Class
Date
Think About a Plan
1-5
Solving Inequalities
Your math test scores are 68, 78, 90, and 91. What is the lowest score you can earn
on the next test and still achieve an average of at least 85?
Understanding the Problem
1. What information do you need to find an average of scores? How do you find
an average?
The sum of the scores and the total number of scores;
divide the sum of the scores by the total number of scores.
5
2. How many scores should you include in the average? ___________
z
z z
z
greater than or equal
to what score?
3. You want to achieve an average that is 85
Planning the Solution
4. Assign a variable, x.
x 5 the score on the next test
5. Write an expression for the sum of all of the scores, including the next test.
327 1 x
6. Write an expression for the average of all of the scores.
327 1 x
5
7. Write an inequality that can be used to determine the lowest score you can
earn on the next test and still achieve an average of at least 85.
327 1 x
5
L 85
Getting an Answer
8. Solve your inequality to find the lowest score you can earn on the next test and
still achieve an average of at least 85. What score do you need to earn? at least 98
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Name
Class
Date
Practice
1-5
Form K
Solving Inequalities
Write the inequality that represents the sentence.
1. Five less than a number is at least 228. x 2 5 L 228
2. The product of a number and four is at most 210. 4x K 210
3. Six more than a quotient of a number and three is greater than 14. x3 1 6 S 14
Solve each inequality. Graph the solution.
4. 5a 2 10 . 5 a S 3
5. 25 2 2y $ 33 y K 24
To start, add 10 to each side.
7 6 5 4 3 2 1
1
2
3
4
5
6
7
6. 22(n 1 2) 1 6 # 16 n L 27
7. 2(7a 1 1) . 2a 2 10 a S 21
10 9 8 7 6 5 4
4 3 2 1
0
1
2
Solve the following problem by writing an inequality.
8. The width of a rectangle is 4 cm less than the length. The perimeter is
at most 48 cm. What are the restrictions on the dimensions of the rectangle?
To start, record what you know.
width: length 2 4
perimeter: at most 48 cm
Describe what you need to find.
restrictions on the width and
w S 0, l 2 4 S 0
length of the rectangle
2(l 2 4) 1 2l K 48; 4 R l K 14; 0 R w K 10
The length is more than 4 cm and at most 14 cm.
The width is more than 0 cm and at most 10 cm.
Is the inequality always, sometimes, or never true?
9. 5(x 2 2) $ 2x 1 1 sometimes
10. 2x 1 8 # 2(x 1 1) never
11. 6x 1 1 , 3(2x 2 4) never
12. 2(3x 1 3) . 2(3x 1 1) always
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Name
Class
Date
Practice (continued)
1-5
Form K
Solving Inequalities
Solve each compound inequality. Graph the solution.
13. 2x . 24 and 4x , 12 x S 22 and x R 3
To start, simplify each inequality.
x . 22 and x , 3
2 1
0
1
2
3
4
5 4 3 2 1
0
1
4
5
6
5 4 3 2 1
0
1
5 4 3 2 1
0
1
2 1
3
4
Remember, “and” means that a solution makes BOTH inequalities true.
14. 3x $ 212 and 5x # 5 x L 24 and x K 1
15. 6x . 6 and 9x # 45 x S 1 and x K 5
0
1
2
3
Solve each compound inequality. Graph the solution.
16. 3x , 29 or 8x . 28 x R 23 or x S 21
To start, simplify each inequality.
x , 23 or x . 21
Remember, “or” means that a solution makes EITHER inequality true.
17. 7x # 228 or 2x . 22 x K 24 or x S 21
18. 3x . 3
or
5x , 2x 2 3 x S 1 or x R 21
0
1
Write an inequality to represent each sentence.
19. The average of Shondra’s test scores in Physics is between 88 and 93.
88 R x R 93 OR x S 88 and x R 93
20. The Morgans are buying a new house. They want to buy either a house more
the 75 years old or a house less than 10 years old. x S 75 or x R 10
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2
Name
Class
1-5
Date
Standardized Test Prep
Solving Inequalities
Multiple Choice
For Exercises 1–5, choose the correct letter.
1. What is the solution of 4t 2 (3 1 t) # t 1 7? B
t # 52
t#5
t#2
t#1
r , 24
r . 24
2. What is the solution of 217 2 2r , 3(r 1 1)? I
r.4
r . 220
3
3. Which graph best represents the solution of 4(m 1 4) . m 1 3? A
1
3 2 1
0
1
2
3
1
3 2 1
0
1
2
3
8
9
10 11 12
1
3 2 1
0
1
6
7
4. What is the solution of the compound inequality 4x , 28 or 9x . 18?
x , 2 or x . 22
x.2
x , 22
x , 22 or x . 2
2
3
I
5. What is the solution of the compound inequality 22x # 6 and 23x . 227? C
x # 23 and x . 9
x $ 23 and x , 9
x $ 3 and x , 29
x # 3 and x . 29
Short Response
6. Geometry The lengths of the sides of a triangle are in the ratio 3 : 4 : 5.
Describe the length of the longest side if the perimeter is not more than 72 in.
Solve the inequality 3x 1 4x 1 5x " 72 or 12x " 72 or x " 6. The longest side,
5x, is not more than 5 ∙ 6 5 30 in. [2] All student calculations are correct.
[1] minor incorrect calculation [0] no answer given
7. Between 8.5% and 9.4% of the city’s population uses the municipal transit
system daily. According to the latest census, the city’s population is 785,000.
How many people use the transit system daily?
[2] between 66,725 and 73,790 people [1] minor incorrect miscalculation of
one or both values in the range [0] no answer given
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Name
Class
1-6
Date
Think About a Plan
Absolute Value Equations and Inequalities
Write an absolute value inequality to represent the situation.
Cooking Suppose you used an oven thermometer while baking and discovered
that the oven temperature varied between 15 and 25 degrees from the setting. If
your oven is set to 350°, let t be the actual temperature.
1. How do you have to think to solve this problem?
If I subtract the set temperature from the real temperature, the result
should be between 25° and 5°.
2. Write a compound inequality that represents the actual oven temperature t.
345 K t K 355
3. It often helps to draw a picture. Graph this compound inequality on a
number line.
345
350
355
t
4. What is the definition of tolerance?
Tolerance is the difference between a desired measurement and its
maximum and minimum allowable values. It equals half of the difference
between the maximum and minimum values.
5°
5. What is the tolerance of the oven? _________
6. Use the tolerance to write an inequality without absolute values.
25 K t 2 350 K 5
7. Rewrite the inequality as an absolute value inequality.
»t 2 350… K 5
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Name
Class
1-6
Date
Practice
Form K
Absolute Value Equations and Inequalities
Solve each equation. Check your answers. Graph the solution.
1. u 22x u 5 12 x 5 6 or x 5 26
⫺6 ⫺4 ⫺2
0
2
4
2. u 7y u 5 28 y 5 4 or y 5 24
⫺6 ⫺4 ⫺2
6
0
2
4
6
Solve each equation. Check your answers.
3. u t 1 7 u 5 1 t 5 26 or t 5 28
t 1 7 5 1 or t 1 7 5 21
To start, rewrite the absolute value
equation as two equations.
4. 4u z 1 1 u 5 24 z 5 5 or z 5 27
5. u 2w 1 1 u 5 5 w 5 2 or w 5 23
6. u 2x 2 2 u 5 4 x 5 3 or x 5 21
7. u 5 2 2y u 1 3 5 8 y 5 0 or y 5 5
Solve each equation. Check for extraneous solutions.
8. u 2z 2 9 u 5 z 2 3 z 5 6 or z 5 4
To start, rewrite as two equations.
2z 2 9 5 z 2 3 or 2z 2 9 5 2(z 2 3)
9. u x 1 6 u 5 2x 2 3 x 5 9
10. u 2t 2 5 u 5 3t 2 10 t 5 5
11. 2u 4y 1 1 u 5 4y 1 10 y 5 2 or y 5 21
12. u w 1 1 u 2 5 5 2w w 5 22
Write an absolute value equation to describe each graph.
13.
⫺5 ⫺4 ⫺3 ⫺2 ⫺1 0
1
2
3
14.
4
Variable may vary. Sample: »x… 5 3
⫺5 ⫺4 ⫺3 ⫺2 ⫺1
0
Variable may vary. Sample: »x 1 3… 5 1
Is the absolute value equation always, sometimes, or never true? Explain.
15. u w u 5 22
16. u z u 1 1 5 z 1 1
never; the distance between a number
w and 0 is never negative
sometimes; the equation is true only
for z L 0
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Name
Class
1-6
Date
Practice (continued)
Form K
Absolute Value Equations and Inequalities
Solve each inequality. Graph the solution.
17. 2u x 1 5 u # 8
29 K x K 21
⫺9 ⫺8 ⫺7 ⫺6 ⫺5⫺4 ⫺3 ⫺2 ⫺1
ux 1 5u # 4
To start, divide each side by 2.
x 1 5 is greater than or equal to 24 and less than or equal to 4.
18. u x 1 1 u 2 3 # 1 25 K x K 3
⫺5 ⫺4 ⫺3 ⫺2 ⫺1 0
1
2
0
⫺5 ⫺4 ⫺3 ⫺2 ⫺1 0
3
0
1
2
3
21. u y 2 3 u 1 2 $ 4 y K 1 or y L 5
0
1
22. u 2t 1 2 u 1 5 # 9 23 K t K 1
⫺5 ⫺4 ⫺3 ⫺2 ⫺1
z R 23 or z S 1
19. u 2z 1 2 u 2 1 . 3
20. 2u w 1 3 u 2 1 , 1 24 R w R 22
⫺5 ⫺4 ⫺3 ⫺2 ⫺1
24 # x 1 5 # 4
1
2
3
4
5
6
23. u 2s 1 1 u . 3 s R 22 or s S 1
⫺5 ⫺4 ⫺3 ⫺2 ⫺1 0
1
1
2
3
Write each compound inequality as an absolute value inequality.
24. 1.2 # a # 2.4 »a 2 1.8… K 0.6
To start, find the tolerance.
2.4 2 1.2
1.2
5 2 5 0.6
2
25. 22 , x , 4 »x 2 1… R 3
26. 1 # m # 2 »m 2 1.5… K 0.5
27. 20 # y # 30 »y 2 25… K 5
28. 23 , t , 17 »t 2 7… R 10
Write an absolute value inequality to represent each situation.
29. In order to enter the kiddie rides at the amusement park, a child must be
between the ages of 4 and 10. Let a represent the age of a child who may go
on the kiddie rides.
»a 2 7… K 3
30. The outdoor temperature ranged between 42°F and 60°F in a 24-hour period.
Let t represent the temperature during this time period.
»t 2 51… K 9
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56
Name
Class
1-6
Date
Standardized Test Prep
Absolute Value Equations and Inequalities
Multiple Choice
For Exercises 1–5, choose the correct letter.
1. What is the solution of u 5t 2 3 u 5 8? C
t 5 8 or t 5 28
t 5 11
5 or t 5 21
t 5 1 or t 5 211
5
t 5 5 or t 5 23
8
2. What is the solution of u 3z 2 2 u # 8? F
10
22 # z # 3
10
23 #z#2
8
10
z # 22 or z $ 3
10
z # 2 3 or z $ 2
1
3. What is the solution of 2 u 2x 1 3 u 2 1 . 1? B
7
22 , x , 12
7
x , 22 or x . 12
7
x . 2 or x , 212
7
x , 12 or x . 22
4. Which absolute value inequality is equivalent to the compound inequality
23 # T # 45? I
u T 2 11 u # 34
u T 2 45 u # 22
u T 2 24 u # 1
u T 2 34 u # 11
5. Which is the correct graph for the solution of u 2b 1 1 u 2 3 # 2? C
⫺3 ⫺2 ⫺1
0
1
2
3
⫺3 ⫺2 ⫺1
0
1
2
3
⫺3 ⫺2 ⫺1
0
1
2
3
⫺3 ⫺2 ⫺1
0
1
2
3
Short Response
6. An employee’s monthly earnings at an electronics store are based on a salary
plus commissions on her sales. Her earnings can range from $2500 to $3200,
depending on her commission. Write a compound inequality to describe
E, the amount of her monthly earnings. Then rewrite your inequality as an
absolute value inequality.
2500 K E K 3200,»E 2 2850… K 350
[2] correct compound inequality and correct absolute value inequality
[1] incorrect compound inequality OR incorrect absolute value inequality
[0] no answer given
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