name: mrs. miller’s intro to algebra unit 2 homework …...name: _____ mrs. miller’s intro to...

NAME: _______________

Mrs. Miller’s

INTRO TO ALGEBRA

UNIT 2

HOMEWORK PACKET

Please pay attention to assignments

Make sure you do the correct section

SHOW ALL WORK USE PROVIDED LINED PAPER

ATTEMPT ALL PROBLEMS TO RECEIVE FULL CREDIT

Chapter 1 8 Glencoe Algebra 1

Skills Practice

Variables and Expressions

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Write an algebraic expression for each verbal expression.

1. the sum of a number and 10 2. 15 less than k

3. the product of 18 and q 4. 6 more than twice m

5. 8 increased by three times a number 6. the difference of 17 and 5 times a number

7. the product of 2 and the second power of y 8. 9 less than g to the fourth power

Evaluate each expression.

9. 82 10. 34

11. 53 12. 33

13. 102 14. 24

15. 72 16. 44

17. 73 18. 113

Write a verbal expression for each algebraic expression.

19. 9a 20. 52

21. c � 2d 22. 4 � 5h

23. 2b2 24. 7x3� 1

25. p4� 6q 26. 3n2

� x

Pick one of (3) show work on this page: Skills Practice (Odds) Practice (Multiples of 3 & 2 Word Problem) Word Problems: Pick 5

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Lesso

n 1

-1

Practice


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Write an algebraic expression for each verbal expression.

1. the difference of 10 and u 2. the sum of 18 and a number

3. the product of 33 and j 4. 74 increased by 3 times y

5. 15 decreased by twice a number 6. 91 more than the square of a number

7. three fourths the square of b 8. two fifths the cube of a number


9. 112 10. 83 11. 54

12. 45 13. 93 14. 64

15. 105 16. 123 17. 1004

Write a verbal expression for each algebraic expression.

18. 23f 19. 73

20. 5m2� 2 21. 4d3

� 10

22. x3! y4 23. b2

� 3c3

24. 25.

26. BOOKS A used bookstore sells paperback fiction books in excellent condition for $2.50 and in fair condition for $0.50. Write an expression for the cost of buying eexcellent-condition paperbacks and f fair-condition paperbacks.

27. GEOMETRY The surface area of the side of a right cylinder can be found by multiplyingtwice the number � by the radius times the height. If a circular cylinder has radius rand height h, write an expression that represents the surface area of its side.

4n2

�7

k5

�6


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1. SOLAR SYSTEM It takes Earth about

365 days to orbit the sun. It takes

Uranus about 85 times as long. Write a

numerical expression to describe the

number of days it takes Uranus to orbit

the sun.

2. TECHNOLOGY There are 1024 bytes in

a kilobyte. Write an expression that

describes the number of bytes in a

computer chip with n kilobytes.

3. THEATER Howard Hughes, Professor

Emeritus of Texas Wesleyan College,

reportedly attended a record 6136

theatrical shows. Write an expression to

represent the average number of theater

shows attended if he accumulated the

record over y years. Use the expression to

find the average number of shows Mr.

Hughes attended per year if he went to

the theater for 31 years.

4. TIDES The difference between high and

low tides along the Maine coast in

November is 19 feet on Monday and x

feet on Tuesday. Write an expression to

show the average rise and fall of the tide

for Monday and Tuesday.

BLOCKS For Exercises 5–7, use the

following information.

A toy manufacturer produces a set of blocks

that can be used by children to build play

structures. The product packaging team is

analyzing different arrangements for

packaging their blocks. One idea they have

is to arrange the blocks in the shape of a

cube, with b blocks along one edge.

5. Write an expression representing the

total number of blocks packaged in a

cube measuring b blocks on one edge.

6. The packaging team decides to take one

layer of blocks off the top of this package.

Write an expression representing the

number of blocks in the top layer of the

package.

7. The team finally decides that their

favorite package arrangement is to take

2 layers of blocks off the top of a cube

measuring b blocks along one edge. Write

an expression representing the number

of blocks left behind after the top two

layers are removed.

Word Problem Practice


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Skills Practice

Order of Operations

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1-21-2


Lesson 1-2

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1. (5 � 4) 7 2. (9 � 2) 3

3. 4 � 6 3 4. 28 � 5 4

5. 12 � 2 2 6. (3 � 5) 5 � 1

7. 9 � 4(3 � 1) 8. 2 � 3 5 � 4

9. 30 � 5 4 � 2 10. 10 � 2 6 � 4

11. 14 ! 7 5 � 32 12. 6 ! 3 7 � 23

13. 4[30 � (10 � 2) 3] 14. 5 � [30 � (6 � 1)2]

15. 2[12 � (5 � 2)2] 16. [8 2 � (3 � 9)] � [8 � 2 3]

Evaluate each expression if x 6, y 8, and z 3.

17. xy � z 18. yz � x

19. 2x � 3y � z 20. 2(x � z) � y

21. 5z � (y � x) 22. 5x � (y � 2z)

23. x2 � y2 � 10z 24. z3 � ( y2 � 4x)

25. 26.3y � x2

�z

y � xz�

2


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Practice

Order of Operations

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1. (15 � 5) 2 2. 9 (3 � 4) 3. 5 � 7 4

4. 12 � 5 � 6 2 5. 7 9 � 4(6 � 7) 6. 8 ! (2 � 2) 7

7. 4(3 � 5) � 5 4 8. 22 ! 11 9 � 32 9. 62 � 3 7 � 9

10. 3[10 � (27 ! 9)] 11. 2[52 � (36 ! 6)] 12. 162 ! [6(7 � 4)2]

13. 14. 15.

Evaluate each expression if a 12, b 9, and c 4.

16. a2 � b � c2 17. b2 � 2a � c2

18. 2c(a � b) 19. 4a � 2b � c2

20. (a2 ! 4b) � c 21. c2 (2b � a)

22. 23.

24. 25.

CAR RENTAL For Exercises 26 and 27, use the following information.

Ann Carlyle is planning a business trip for which she needs to rent a car. The car rentalcompany charges $36 per day plus $0.50 per mile over 100 miles. Suppose Ms. Carlyle rentsthe car for 5 days and drives 180 miles.

26.Write an expression for how much it will cost Ms. Carlyle to rent the car.

27. Evaluate the expression to determine how much Ms. Carlyle must pay the car rentalcompany.

GEOMETRY For Exercises 28 and 29, use the following information.

The length of a rectangle is 3n � 2 and its width is n � 1. The perimeter of the rectangle istwice the sum of its length and its width.

28.Write an expression that represents the perimeter of the rectangle.

29. Find the perimeter of the rectangle when n � 4 inches.

b2 � 2c2��a � c � b

2(a � b)2��

5c

2c3 � ab��

4

bc2 � a�

c

7 � 32�42 2

(2 5)2 � 4��

32 � 5

52 4 � 5 42��

5(4)


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Order of Operations

NAME ______________________________________________ DATE______________ PERIOD _____

1-21-2


Lesson 1-2

1. SCHOOLS Jefferson High School has100 less than 5 times as many studentsas Taft High School. Write and evaluatean expression to find the number ofstudents at Jefferson High School if TaftHigh School has 300 students.

2. GEOGRAPHY Guadalupe Peak in Texashas an altitude that is 671 feet morethan double the altitude of MountSunflower in Kansas. Write and evaluatean expression for the altitude ofGuadalupe Peak if Mount Sunflower hasan altitude of 4039 feet.

3. TRANSPORTATION The Plaid Taxi CabCompany charges $1.75 per passengerplus $3.45 per mile for trips less than 10miles. Write and evaluate an expressionto find the cost for Max to take a Plaidtaxi 8 miles to the airport.

4. GEOMETRY The area of a circle isrelated to the radius of the circle suchthat the product of the square of theradius and a number gives the area.Write and evaluate an expression for thearea of a circular pizza below.Approximate as 3.14.

5. BIOLOGY Lavania is studying thegrowth of a population of fruit flies inher laboratory. She notices that thenumber of fruit flies in her experiment isfive times as large after any six-dayperiod. She observes 20 fruit flies onOctober 1. Write and evaluate anexpression to predict the population offruit flies Lavania will observe onOctober 31.

CONSUMER SPENDING For Exercises

6–8, use the following information.

During a long weekend, Devon paid a totalof x dollars for a rental car so he could visithis family. He rented the car for 4 days at arate of $36 per day. There was an additionalcharge of $0.20 per mile after the first 200miles driven.

6.Write an algebraic expression torepresent the amount Devon paid foradditional mileage only.

7.Write an algebraic expression torepresent the number of miles over 200miles that Devon drove the rented car.

8. How many miles did Devon drive overallif he paid a total of $174 for the carrental?C

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7 in.


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Skills Practice

The Distributive Property

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Rewrite each expression using the Distributive Property. Then simplify.

1. 4(3 � 5) 2. 2(6 � 10)

3. 5(7 � 4) 4. (6 � 2)8

5. (a � 7)2 6. 7(h � 10)

7. 3(m � n) 8. (x � y)6

9. 2(x � y � 1) 10. 3(a � b � 1)

Use the Distributive Property to find each product.

11. 5 89 12. 9 99

13. 15 104 14. 15�2 �

15. 12�1 � 16. 8�3 �

Simplify each expression. If not possible, write simplified.

17. 2x � 8x 18. 17g � g

19. 16m � 10m 20. 12p � 8p

21. 2x2 � 6x2 22. 7a2 � 2a2

23. 3y2 � 2y 24. 2(n � 2n)

25. 4(2b � b) 26. 3q2 � q � q2

1�8

1�4

1�3

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Practice


1-51-5


Lesson 1-5

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Rewrite each expression using the Distributive Property. Then simplify.

1. 9(7 � 8) 2. 7(6 � 4) 3. 6(b � 4)

4. (9 � p)3 5. (5y � 3)7 6. 15 f � �

7. 16(3b � 0.25) 8. m(n � 4) 9. (c � 4)d

Use the Distributive Property to find each product.

10. 9 499 11. 7 110 12. 21 1004

13. 12 2.5 14. 27 2 � 15. 16 4 �

Simplify each expression. If not possible, write simplified.

16. w � 14w � 6w 17. 3(5 � 6h) 18. 14(2r � 3)

19. 12b2 � 9b2 20. 25t3 � 17t3 21. c2 � 4d2 � d2

22. 3a2 � 6a � 2b2 23. 4(6p � 2q � 2p) 24. x � x �

DINING OUT For Exercises 25 and 26, use the following information.

The Ross family recently dined at an Italian restaurant. Each of the four family membersordered a pasta dish that cost $11.50, a drink that cost $1.50, and dessert that cost $2.75.

25.Write an expression that could be used to calculate the cost of the Ross’ dinner beforeadding tax and a tip.

26.What was the cost of dining out for the Ross family?

ORIENTATION For Exercises 27 and 28, use the following information.

Madison College conducted a three-day orientation for incoming freshmen. Each day, anaverage of 110 students attended the morning session and an average of 160 studentsattended the afternoon session.

27.Write an expression that could be used to determine the total number of incomingfreshmen who attended the orientation.

28.What was the attendance for all three days of orientation?

x�3

2�3

1�4

1�3

1�3

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1. OPERA Mr. Delong’s drama class isplanning a field trip to see Mozart’sfamous opera Don Giovanni. Tickets cost$39 each, and there are 23 students and2 teachers going on the field trip. Writeand evaluate an expression to find thegroup’s total ticket cost.

2. LIBRARY In Cook County Library’schildren’s section there are 7 shelves and4 tables. Each shelf and table displays 12books. Write and evaluate an expressionto find how many books are in thechildren’s section.

3. COSTUMES Isabella’s ballet class isperforming a spring recital for whichthey need butterfly costumes. Each

butterfly costume is made from 3�35� yards

of fabric. Use the Distributive Propertyto find the number of yards of fabricneeded for 5 costumes. (Hint: a mixednumber can be written as the sum of aninteger and a fraction.)

4. FENCES Demonstrate the DistributiveProperty by writing two equivalentexpressions to represent the perimeter ofthe fenced dog pen below.

5.MENTAL MATH During a math factsspeed contest, Jamal calculated thefollowing expression faster than anyoneelse in his class.

197 4

When classmates asked him how he wasable to answer so quickly, he told themhe used the Distributive Property tothink of the problem differently. Writeand evaluate an expression using theDistributive Property that would helpJamal perform the calculation quickly.

INVESTMENTS For Exercises 6 and 7,

use the following information.

Letisha and Noel each opened a checkingaccount, a savings account, and a collegefund. The chart below shows the amountsthat they deposited into each account.

6. If Noel used only $50 bills when hedeposited the money to open hisaccounts, how many $50 bills did hedeposit?

7. If all accounts earn 1.5% interest peryear and no further deposits are made,how much interest will Letisha haveearned one year after her accounts wereopened?



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Checking Savings College

Letisha $125 $75 $50

Noel $250 $50 $50

m

nDog Pen

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Skills Practice

Commutative and Associative Properties

1-6


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3-61-6


1. 16 � 8 � 14 � 12 2. 36 � 23 � 14 � 7 3. 32 � 14 � 18 � 11

4. 5 3 4 3 5. 2 4 5 3 6. 5 7 10 4

7. 1.7 � 0.8 � 1.3 8. 1.6 � 0.9 � 2.4 9. 4 � 6 � 5

Simplify each expression.

10. 2x � 5y � 9x 11. a � 9b � 6a

12. 2p � 3q � 5p � 2q 13. r � 3s � 5r � s

14. 5m2� 3m � m2 15. 6k2 � 6k � k2 � 9k

16. 2a � 3(4 � a) 17. 5(7 � 2g) � 3g

Write an algebraic expression for each verbal expression. Then simplify,

indicating the properties used.

18. three times the sum of a and b increased by a

19. twice the sum of p and q increased by twice the sum of 2p and 3q

1�2

1�2

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Practice


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1. 13 � 23 � 12 � 7 2. 6 5 10 3

3. 7.6 � 3.2 � 9.4 � 1.3 4. 3.6 0.7 5

5. 7 � 2 � 1 6. 3 3 16

Simplify each expression.

7. 9s2 � 3t � s2 � t 8. (p � 2n) � 7p

9. 6y � 2(4y � 6) 10. 2(3x � y) � 5(x � 2y)

11. 3(2c � d) � 4(c � 4d) 12. 6s � 2(t � 3s) � 5(s � 4t)

13. 5(0.6b � 0.4c) � b 14. q � 2 q � r�15.Write an algebraic expression for four times the sum of 2a and b increased by twice the

sum of 6a and 2b. Then simplify, indicating the properties used.

SCHOOL SUPPLIES For Exercises 16 and 17, use the following information.

Kristen purchased two binders that cost $1.25 each, two binders that cost $4.75 each, twopackages of paper that cost $1.50 per package, four blue pens that cost $1.15 each, and fourpencils that cost $.35 each.

16.Write an expression to represent the total cost of supplies before tax.

17.What was the total cost of supplies before tax?

GEOMETRY For Exercises 18 and 19, use the following information.

The lengths of the sides of a pentagon in inches are 1.25, 0.9, 2.5, 1.1, and 0.25.

18. Using the commutative and associative properties to group the terms in a way thatmakes evaluation convenient, write an expression to represent the perimeter of thepentagon.

19.What is the perimeter of the pentagon?

1�2

1�4

1�2

1�3

3�4

2�9

1�9

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1-6


Lesso

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-6

1. SCHOOL SUPPLIES At a local schoolsupply store, a highlighter costs $1.25, aballpoint pen costs $0.80, and a spiralnotebook costs $2.75. Use mental mathand the Associative Property of Additionto find the total cost if one of each item ispurchased.

2. BUS STOPS Mr. McGowan drives a citybus. Occasionally he keeps track of thenumber of riders for market research.The chart below shows a morning route.

How many people are on the bus afterthe fourth stop?

3. MENTAL MATH The triangular bannerhas a base of 9 centimeters and a heightof 6 centimeters. Using the formula forarea of a triangle, the banner’s area can

be expressed as �12� 9 6 . Gabrielle

finds it easier to write and evaluate

��12� 6� 9 to find the area. Is

Gabrielle’s expression equivalent to thearea formula? Explain.

4. ANATOMY The human body has 60bones in the arms and hands, 84 bones inthe upper body and head, and 62 bonesin the legs and feet. Use the AssociativeProperty to write and evaluate anexpression that represents the totalnumber of bones in the human body.

SPORTS For Exercises 5–7, use the

following information.

Kim, Doug, and Conner all run on the crosscountry team. In the last race Doug finishedfirst, Kim finished 3 minutes after Doug, andConner finished with a time that was twiceDoug’s time.

5. What is the sum of their times?

6. What property or properties did you use?

7. Evaluate the expression if Doug ran therace in 27 minutes.

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1-6

Bus Route

First stop 12 people got on

Second stop 4 people off; 15 on

Third stop 16 people off; 7 on

Fourth stop 11 people off; 14 on

b

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Skills Practice

Number Systems


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Find each square root. If necessary, round to the nearest hundredth.

1. 144! 2. � 36!

3. 0.25! 4. �"#5. 17! 6. 2.25!

Name the set or sets of numbers to which each real number belongs.

7. � 8. �

9. 29! 10. 196!

11. 12. 1.8!

Graph each solution set.

13. x ! �1 14. x � 1

15. x " 1.5 16. x # �2.5

Replace each � with , !, or " to make each sentence true.

17. � 0.4! 18. 0.0!9! �

19. 6.2!3! � 39! 20. �

Write each set of numbers in order from least to greatest.

21. 5!, 2.3!6!, 22. , 0.2!1!, 0.05!

23. � 12!, �3.4!8!, � 11! 24. 0.4!3!, ,3�7

6!�5

2�9

7�3

1�

8!1�8

1�90

4�9

�2 �1�4 �3 0 1 2 3 4�2 �1�4 �3 0 1 2 3 4

�2 �1�4 �3 0 1 2 3 4�2 �1 0 1 2 3 4 5 6

9�13

5�6

28�7

49�100

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Practice

Number Systems

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Find each square root. If necessary, round to the nearest hundredth.

1. 324! 2. � 62! 3. 25! 4. � 84!

5. "# 6. �"# 7. � 0.081! 8. 3.06!

Name the set or sets of numbers to which each real number belongs.

9. 93! 10. � 0.062!5! 11. 12. �

Graph each solution set.

13. x ! �0.5 14. x " �3.5

Replace each � with , !, or " to make each sentence true.

15. 0.9!3! � 0.93! 16. 8.1!7! � 66! 17. �

Write each set of numbers in order from least to greatest.

18. 0.03!, , 0.1!7! 19. � , � 8!, � 20. � 8.5!, � , �2

21. SIGHTSEEING The distance you can see to the horizon is given by the formula

d � 1.5h!, where d is the distance in miles and h is the height in feet above the

horizon line. Mt. Whitney is the highest point in the contiguous 48 states. Its elevation

is 14,494 feet. The lowest elevation, at �282 feet, is located near Badwater, California.

With a clear enough sky and no obstructions, could you see from the top of Mt. Whitney

to Badwater if the distance between them is 135 miles? Explain.

22. SEISMIC WAVES A tsunami is a seismic wave caused by an earthquake on the ocean

floor. You can use the formula s � 3.1 d!, where s is the speed in meters per second and

d is the depth of the ocean in meters, to determine the speed of a tsunami. If an

earthquake occurs at a depth of 200 meters, what is the speed of the tsunami generated

by the earthquake?

19�20

35!�2

7!�8

84�30

2!�8

5!�

5�6

�2 �1�4 �3 0 1 2 3 4

144�3

8�7

7�12

4�289

NAME ______________________________________________ DATE______________ PERIOD _____


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Number Systems


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1. MATH CLASS In Mrs. Carson’s mathclass, students draw numbers todetermine the order in which each willsolve a problem on the board. If the orderis least to greatest value, list thestudents in order of their turn.

2. SPORTS Matthew won the 100-yarddash in a photo-finish race with a time of15.83 seconds. Brady’s time was 15.84seconds, and he came in third place. Usea number line to graph Matthew’s time,Brady’s time, and the possible time of theperson who finished in second place.

3. WEATHER The table shows how theaverage temperature for each monthvaried from the normal meantemperature each month for Barrow,Alaska. Graph these values on a number.

Source: World Almanac 2005, pg 185

4. LIGHTING The brightness of a light bulbdepends on the observer’s distance fromthe bulb. For a 200-watt bulb, thedistance D (in inches) from the bulb is

given by the equation D � �3B18�! , where

B is the brightness (in lumens per squareinch). Using a light meter, a productengineer finds the brightness of a 200-watt bulb is 0.244 lumens per square inch. How far is the light meterfrom the bulb?

GEOMETRY For Exercises 5 and 6, use

the following information.

The Pythagorean Theorem is used to findthe length of an unknown side of a righttriangle when two side lengths are known.

Pythagorean Theorem a2 � b2 � c2

The length of side c can be found by usingthe following rearrangement of thePythagorean Theorem: c � "a2 � b#2#.

5. Should c � "a2 � b#2# have a symbol infront of the c?

6. Find the length of the hypotenuse c ifa � 6 centimeters and b � 8 centimeters.

Month Change in Month Change in

Temp. (°F) Temp. (°F)

Jan. –3 Jul. �5

Feb. –2 Aug. –1

Mar. �2 Sep. –8

Apr. �13 Oct. –16

May �21 Nov. –16

Jun. �15 Dec. –10

a

b c

"97# "2.56# �283�

�2.

756� �"49#

Amanda Boyd Celeste

Dominic Eve

15.80 15.81 15.82 15.83 15.84 15.85

NAME ______________________________________________ DATE______________ PERIOD _____


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Chapter 4 44 Glencoe Pre-Algebra

Skills Practice

Scientific Notation

NAME ______________________________________________ DATE ____________ PERIOD _____

4-7

Express each number in standard form.

1. 1.5 103 2. 4.01 104

3. 6.78 102 4. 5.925 106

5. 7.0 108 6. 9.99 107

7. 3.0005 105 8. 2.54 105

9. 1.75 104 10. 1.2 10�6

11. 7.0 10�1 12. 6.3 10�3

13. 5.83 10�2 14. 8.075 10�4

15. 1.1 10�5 16. 7.3458 107

Express each number in scientific notation.

17. 1,000,000 18. 17,400

19. 500 20. 803,000

21. 0.00027 22. 5300

23. 18 24. 0.125

25. 17,000,000,000 26. 0.01

27. 21,800 28. 2,450,000

29. 0.0054 30. 0.000099

31. 8,888,800 32. 0.00912

Choose the greater number in each pair.

33. 8.8 103, 9.1 10�4 34. 5.01 102, 5.02 10�1

35. 6.4 103, 900 36. 1.9 10�2, 0.02

37. 2.2 10�3, 2.1 102 38. 8.4 102, 839


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Practice

Scientific Notation

Chapter 4 45 Glencoe Pre-Algebra

NAME ______________________________________________ DATE ____________ PERIOD _____

4-7

Lesson 4–7

Express each number in standard form.

1. 2.4 104 2. 9.0 103

3. 4.385 107 4. 1.03 108

5. 3.05 102 6. 5.11 1010

7. 6.000032 106 8. 1.0 101

9. 8.75 105 10. 8.49 10�2

11. 7.1 10�6 12. 1.0 10�3

13. 4.39 10�7 14. 1.25 10�4

Express each number in scientific notation.

15. 40,000 16. 16

17. 876,000,000 18. 4500

19. 151 20. 0.00037

21. 83,000,000 22. 919,100

23. 5,000,000,000,000 24. 0.13

25. 0.0000007 26. 0.0067

NIAGARA FALLS For Exercises 27 and 28, use the following information.

Every minute, 840,000,000,000 drops of water flow over Niagara Falls.

27. Write this number in scientific notation.

28. How many drops flow over the falls in a day?


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