common core ©2012 - pearson

COMMON

CORE

Common Core ©2012Pearson Algebra 1 • Geometry • Algebra 2

2 3

Custom, Flexible Solutions for EVERY Classroom

Get to the CoreThe Common Core Initiative is raising the bar to help ensure that all students acquire the critical knowledge and skills necessary to succeed in college—and in their careers—regardless of the state or district they live in, or the school they attend. Pearson is proud to announce a NEW Common Core Edition of its High School Algebra 1, Geometry, and Algebra 2 program. Proven effective by an independent research study, the new edition ensures that you can confidently teach the new standards.

Built for the Common CoreComplete and comprehensive coverage of the Common Core Content Standards with the Standards for Mathematical Practice infused throughout every lesson.

Implementation and Transition SupportTargeted support ensures successful transition to a Common Core State Standards-based curriculum. Resources include a Common Core Implementation Guide with Teaching Resources, Correlations, Assessment Support, and an Observational Protocol for the Standards for Mathematical Practice.

Professional DevelopmentTailored professional development offerings and online video tutorials support you through the implementation of the Common Core Edition in your mathematics classroom.

* Foundations Series Table of Contents varies slightly.

Common Core Edition ©2012

Pearson Algebra 1, Geometry, and Algebra 2

AlgebrA 1 1. Foundations for Algebra 2. Solving Equations 3. Solving Inequalities 4. An Introduction to Functions 5. Linear Functions 6. Systems of Equations and Inequalities 7. Exponents and Exponential Functions

Equations 8. Polynomials and Factoring 9. Quadratic Functions and Equations 10. Radical Expressions and Equations 11. Rational Expressions and Functions 12. Data Analysis and Probability

AlgebrA 2 1. Expressions, Equations, and Inequalities 2. Functions, Equations, and Graphs 3. Linear Systems 4. Quadratic Functions and Equations 5. Polynomials and Polynomial Functions 6. Radical Functions and Rational Exponents 7. Exponential and Logarithmic Functions 8. Rational Functions 9. Sequences and Series 10. Quadratic Relations and Conic Sections 11. Probability and Statistics 12. Matrices 13. Periodic Functions and Trigonometry 14. Trigonometric Identities and Equations

geometry 1. Tools of Geometry 2. Reasoning and Proof 3. Parallel and Perpendicular Lines 4. Congruent Triangles 5. Relationships Within Triangles 6. Polygons and Quadrilaterals 7. Similarity 8. Right Triangles and Trigonometry 9. Transformations 10. Area 11. Surface Area and Volume 12. Circles 13. Probability

On-Level Table of Contents*

Complete Digital

Program(iPad version also available)

Foundations Series

Comprehensive On-Level Program

(see pages 14–15)

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Teaching the Common Core State Standards

Problem 2

Got It?

Got It?

110 Chapter 2 Solving Equations

1. a. Solve the equation 4 5 2m 2 5n for m. What are the values of m when

n 5 22, 0, and 2?

b. Reasoning Solve Problem 1 by substituting x 5 3 and x 5 6 into the

equation 10x 1 5y 5 80 and then solving for y in each case. Do you

prefer this method or the method shown in Problem 1? Explain.When you rewrite literal equations, you may have to divide by a variable or variable

expression. When you do so in this lesson, assume that the variable or variable

expression is not equal to zero because division by zero is not ned.Rewriting a Literal Equation With Only Variables

What equation do you get when you solve ax 2 bx 5 c for x?ax 2 bx 5 c

x(a 2 b) 5 c Distributive Propertyx(a 2 b)a 2 b 5 c

a 2 b Divide each side by a 2 b , where a 2 b 2 0.x 5 ca 2 b Simplify.

2. What equation do you get when you solve 2t 5 r 1 px for x?

A formula is an equation that states a relationship among quantities. Formulas are

special types of literal equations. Some common formulas are given below. Notice

that some of the formulas use the same variables, but the nitions of the variables

are erent.

How can you solve a literal equation for a variable? When a literal equation contains only variables, treat the variables you are not solving for as constants.

Formula NameFormula Defi nitions of Variables

Perimeter of a rectangleCircumference of a circle

Area of a rectangleArea of a triangle

Area of a circleDistance traveled

Temperature

P 5 2/ 1 2w

C 5 2pr

A 5 /w

A 5 12 bh

A 5 pr2

d 5 rt

C 5 59 (F 2 32)

P 5 perimeter, / 5 length, w 5 widthC 5 circumference, r 5 radiusA 5 area, / 5 length, w 5 widthA 5 area, b 5 base, h 5 height

A 5 area, r 5 radiusd 5 distance, r 5 rate, t 5 timeC 5 degrees Celsius, F 5 degrees Fahrenheit

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Lesson 2-5 109

UbD

Lesson 2-5 109

S

OLVE IT!

AC T I V I T I E

S

DY

NAMIC

Problem 1

Lesson 2-5 Literal Equations and Formulas 109

Literal Equations

and Formulas2-5

Objective To rewrite and use literal equations and formulas

In this lesson, you will learn to solve problems using equations in more than

one variable. A literal equation is an equation that involves two or more variables.

Essential Understanding When you work with literal equations, you can use

the methods you have learned in this chapter to isolate any particular variable.

You are ordering pizzas and sandwiches.

You have a budget of $80. How many

sandwiches can you buy if you buy

4 pizzas? 5 pizzas? Explain your answer.

Lesson Vocabulary

•literal equation

•formula

Rewriting a Literal Equation

The equation 10x 1 5y 5 80, where x is the number of pizzas and y is the

number of sandwiches, models the problem in the Solve It. How many

sandwiches can you buy if you buy 3 pizzas? 6 pizzas?

Step 1 Solve the equation 10x 1 5y 5 80 for y.

10x 1 5y 5 80

10x 1 5y 2 10x 5 80 2 10x Subtract 10x from each side.

5y 5 80 2 10x Simplify.

5y5 5

80 2 10x5

Divide each side by 5.

y 5 16 2 2x Simplify.

Step 2 Use the rewritten equation to find y when x 5 3 and when x 5 6.

y 5 16 2 2x y 5 16 2 2x

y 5 16 2 2(3) Substitute for x. y 5 16 2 2(6)

y 5 10 Simplify. y 5 4

If you buy 3 pizzas, you can buy 10 sandwiches. If you buy 6 pizzas, you can buy

4 sandwiches.Dynamic Activity

Solving Formulas

for Any Variable

AC T I V I T I

E S

DY

NAMIC

Why should you

rewrite the equation?

If you rewrite the

equation, you have to

isolate y only once. Then

substitute for x. If you

substitute for x first,

you must isolate y twice

(once for each x-value).

Sandwich $5

Pizza $10MENU

What happens to

the number of sandwiches as the

number of pizzas

increases?

Content Standards

A.CED.4 Rearrange formulas to highlight a quantity

of interest, using the same reasoning as in solving

equations . . .

Also N.Q.1, A.CED.1, A.REI.1, A.REI.3

MATHEMATICAL

PRACTICES

2-51 Interactive Learning

Solve It!Step out how to solve the Problem

with helpful hints and an online

question. Other questions are listed

above in Interactive Learning.

Dynamic Activity Explore

literal equations by choosing the

appropriate solution steps. Students

who learn better from step-by-step

instructions will benefit from this

activity.

FAcILItAte

q What is the relationship between the number of

pizzas and the number of sandwiches you can

buy? [As the number of pizzas increases, the

number of sandwiches decreases.]

q How does knowing how to solve a one-

variable linear equation help you solve a literal

equation? [Solving the literal equation involves

the same steps as solving a one-variable, linear

equation.]

Preparing to teach

Big ideas equivalence Solving equations &

Inequalities

EssEntial UndErstandings

•Aliteralequationisanequationthat

involves two or more variables.

•Thesolutionofaliteralequationcanb

e

found using the properties of equality

and inverse operations to form a series of

simpler equations.

•Thepropertiesofequalitycanbeused

repeatedly to isolate any particular

variable.

Math Background

When solving literal equations, students

can use the same properties of equality

and inverse operations that they have used

throughout this chapter. Students can treat

all variables that they are not solving for as

constants.Thisskillisparticularlyuseful

in

working with math and science formulas.

For example, the uniform motion formula

d 5 rt (distance 5 rate 3 time) can be

solve for r, yielding a specific formula for

speed (rate 5 distance/time).

Mathematical Practice

Model with mathematics Students

will be able to interpret verbal mathematical

situations, such as Problem 4, and will put

their solutions in context. Students will also

label solutions with appropriate units of

measure.

1 Interactive Learning

Solve It!PUrPosE Toseehowliteralequationscan

beused

to model real-world situations

ProcEss Students may

•buildachart.

•usethenumberofpizzasrequiredtocalculate

the money remaining for sandwiches.

•useanequation.

answEr SeeSolveitinAnswersonnextpage.

connEct thE Math In this Solve It, the amount

of money spent depends on two variables, the

number of pizzas and the number of sandwiches.

In this lesson, students will learn to use algebra to

model situations with multiple variables.

2 Guided Instruction

Problem 1 Once a value for one variable has been given, the

equation is a one-variable linear equation.

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Problem 1


Literal Equations and Formulas2-5

Objective To rewrite and use literal equations and formulas

In this lesson, you will learn to solve problems using equations in more than

one variable. A literal equation is an equation that involves two or more variables.

Essential Understanding When you work with literal equations, you can use

the methods you have learned in this chapter to isolate any particular variable.

You are ordering pizzas and sand

wiches.

You have a budget of $80. How many

sandwiches can you buy if you buy

4 pizzas? 5 pizzas? Explain your

answer.

Lesson Vocabulary literal equation

formula

VV

Rewriting a Literal Equation

e equation 10x 1 5y 5 80, where x is the number of pizzas and y is the

number of sandwiches, models the problem in the Solve It. How many

sandwiches can you buy if you buy 3 pizzas? 6 pizzas?

Step 1 Solve the equation 10x 1 5y 5 80 for y.

10x 1 5y 5 80

10x 1 5y 2 10x 5 80 2 10x Subtract 10x from each side.

5y 5 80 2 10x Simplify.

5y5 5

80 2 10x5

Divide each side by 5.

y 5 16 2 2x Simplify.

Step 2 Use the rewritten equation to nd y when x 5 3 and when x 5 6.

y 5 16 2 2x y 5 16 2 2x

y 5 16 2 2(3) Substitute for x. y 5 16 2 2(6)

y 5 10 Simplify. y 5 4

If you buy 3 pizzas, you can buy 10 sandwiches. If you buy 6 pizzas, you can buy

4 sandwiches.

Dynamic Activity

Solving Formulas

for Any Variablef

AC T I V I T I

E S

AAAAAAAAC

ACC I E

SSSSSSSS

DYNAMIC

S

S

Why should you

rewrite the equation?

If you rewrite the

equation, you have to

isolate y only once. Then

substitute for x. If you

substitute for x fi rst,

you must isolate y twice

(once for each x-value).

.

r. Sandwich $5

Pizza $10

MENU

Content Standards

A.CED.4 Rearrange formulas to highlight

a quantity of interest, using the same

reasoning as in solving equations…

Also N.Q.1, A.CED.1, A.REI.1, A.REI.3

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As the number of pizzas increases, what do you expect to happen to the number of sandwiches?

“Think” and “Plan” callouts model mathematical reasoning and problem solving for every problem in a lesson.

MATHEMATICAL PRACTICES

This program incorporates the groundbreaking

Understanding by Design® framework. Within each

lesson, students will develop answers to the

Essential Questions posed and make

connections around the Big Ideas.

The Solve It! develops content understanding

and multiple mathematical practices as students are

actively involved in doing mathematics at the beginning of every lesson.


Dynamic Activities provide an interactive way for students to explore lesson concepts.


Built-in professional development supports the Standards for Mathematical Practice.

P R O F E S S I O N A L DEVELOPMENT

Common Core Content Standards and Standards for Mathematical Practice are listed at point of use in every lesson for easy reference.

Take a closer look at how Pearson Algebra 1, Geometry, and Algebra 2 Common Core Edition fully addresses the Common Core Content Standards and infuses the Standards for Mathematical Practice throughout every lesson. C O N T E N T

STANDARDS

Essential Understanding

6 7

Lesson Check


Practice and Problem-Solving Exercises

Solve each equation for y. en nd the value of y for each value of x.

11. y 1 2x 5 5; x 5 21, 0, 3

12. 2y 1 4x 5 8; x 5 22, 1, 3

13. 3x 2 5y 5 9; x 5 21, 0, 1

14. 4x 5 3y 2 7; x 5 4, 5, 6

15. 5x 5 24y 1 4; x 5 1, 2, 3

16. 2y 1 7x 5 4; x 5 5, 10, 15

17. x 2 4y 5 24; x 5 22, 4, 6

18. 6x 5 7 2 4y; x 5 22, 21, 0

Solve each equation for x.

19. mx 1 nx 5 p

20. ax 2 x 5 c 21. rx 1 sx

t 5 1

22. y 5 x 2 v

b

23. S 5 C 1 xC 24. x

a 5y

b

25. A 5 Bxt 1 C

26. 4(x 2 b) 5 x 27. x 1 2

y 2 1 5 2

Solve each problem. Round to the nearest tenth, if necessary. Use 3.14 for p.

28. What is the radius of a circle with circumference 22 m?

29. What is the length of a rectangle with width 10 in. and area 45 in.2?

30. A triangle has height 4 ft and area 32 ft2. What is the length of its base?

31. A rectangle has perimeter 84 cm and length 35 cm. What is its width?

32. Parks A public park is in the shape of a triangle. e side of the

park that forms the base of the triangle is 200 yd long, and the area

of the park is 7500 yd2. What is the length of the side of the park

that forms the height of the triangle?

PracticeA

See Problem 1.

See Problem 2.

See Problem 3.

200 yd

?

Do you know HOW?Solve each equation for the given variable. 1. 22x 1 5y 5 12 for y 2. a 2 2b 5 210 for b

3. mx 1 2nx 5 p for x 4. C 5 59 (F 2 32) for F

5. Gardening Jonah is planting a rectangular garden.

e perimeter of the garden is 120 yd, and the width

is 20 yd. What is the length of the garden?

Do you UNDERSTAND?Vocabulary Classify each equation below as a formula,

a literal equation, or both. 6. c 5 2d 7. y 5 2x 2 1

8. A 5 12bh

9. P 5 2/ 1 2w 10. Compare and Contrast How is the process of

rewriting literal equations similar to the process of

solving equations in one variable? How is it erent?

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Leveled Assignments Practice, Apply, and Challenge exercises provide practice opportunities for all learners.

The Practice and Problem Solving Workbook provides additional practice opportunities. Every lesson contains two pages of practice, one page of test prep, and one page of problem solving.

The Lesson Check is a formative assessment of the new content from the lesson. Almost all of the tasks in the UNDERSTAND part of this assessment elicit the use of one or more Common Core Standards for Mathematical Practice.

ASSESSMENT

Problem 4

Problem 3

Got It?

Got It?


Problem 4

Got It?

Indiana

Mexico

Indiana

1700 miles

Rewriting a Geometric Formula

What is the radius of a circle with circumference 64 ft? Round to the nearest tenth.

Use 3.14 for p.

C 5 2pr Write the appropriate formula.

C2p 5

2pr2p Divide each side by 2p.

C2p 5

r Simplify.

642p 5

r Substitute 64 for C.

10.2 < r Simplify. Use 3.14 for p.

e radius of the circle is about 10.2 ft.

3. What is the height of a triangle that has an area of 24 in.2 and a base with a

length of 8 in.?

Rewriting a Formula

Biology e monarch y is the only y

that migrates annually north and south. e

distance that a particular group of monarch

ies travels is shown. It takes a typical

y about 120 days to travel one way.

What is the average rate at which a y

travels in miles per day? Round to the

nearest mile per day.

d 5 rt Write the appropriate formula.

dt 5

rtt Divide each side by t.

dt 5

r Simplify.

1700120

5 r Substitute 1700 for d and 120 for t.

14 < r Simplify.

e ies travel at an average rate of about

14 mi per day.

4. c gray whales migrate annually from

the waters near Alaska to the waters near Baja

California, Mexico, and back. e whales travel a distance of about 5000 mi

each way at an average rate of 91 mi per day. About how many days does it

take the whales to migrate one way?

Choose an appropriate

formula and solve it for

the variable you need to

fi nd. Substitute what you

know into the rewritten

formula. Simplify.

How do you know

which formula to use?

Read the information

given in the problem.

This problem gives you

a measure of time and a

distance. You need to fi nd

the rate, so use d 5 rt.

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STEM

The Got It? following each problem checks for

understanding. Students can work through each

Got It? in the Student Companion worktext.


Visual instruction supports students as they

analyze complex word problems. Visuals clarify

important concepts, engage students, and

encourage them to make connections with

real-life situations.

PowerAlgebra.com and PowerGeometry.com

serve as the portals into the digital world of

Pearson Algebra 1, Geometry, and Algebra 2

Common Core Edition.

Show the student-produced video demonstrating relevant and engaging applications of the new concepts in the chapter.

Find online definitions for the new terms with audio explanations in both English and Spanish.

Start each lesson with an attention-getting problem. View the problem online with helpful hints.

Increase students’ depth of knowledge with interactive online activities.

Show Problems from each lesson solved step by step. Instant replay allows students to go at their own pace when studying online.

View homework exercises online for easy access anywhere.

Prepare students for the Mid-Chapter Quiz and Chapter Test with online practice and review.

ONLINE

HO

M E W O RK

AC T I V I T I

E S

DYNAMIC

FO

R S C H OOL

MathXL

VIDEO

9


Solve each problem. Round to the nearest tenth, if necessary. 33. Travel A vehicle travels on a highway at a rate of 65 mi/h. How long does it take the vehicle to travel 25 mi? 34. Baseball You can use the formula a 5 h

n to nd the batting average a of a batter who has h hits in n times at bat. Solve the formula for h. If a batter has a batting average of .290 and has been at bat 300 times, how many hits does the batter have?

35. Construction Bricklayers use the formula n 5 7/h to estimate the number n of bricks needed to build a wall of length / and height h, where / and h are in feet. Solve the formula for h. Estimate the height of a wall 28 ft long that requires 1568 bricks.

Solve each equation for the given variable. 36. 2m 2 nx 5 x 1 4 for x 37. xa 2 1 5

yb for x 38. ax 1 2xy 5 14 for y

39. V 5 13pr

2h for h 40. A 5 Q f 1 g2 Rh for g 41. 2(x 1 a) 5 4b for a

42. Think About a Plan e interior angles of a polygon are the angles formed inside a polygon by two adjacent sides. e sum S of the measures of the interior angles of a polygon with n sides can be found using the formula S 5 180(n 2 2). e sum of a polygon’s interior angle measures is 12608. How many sides does the polygon have?

What information are you given in the problem?

What variable do you need to solve for in the formula? 43. Weather Polar stratospheric clouds are colorful clouds that form

when temperatures fall below 2788C. What is this temperature in degrees Fahrenheit? 44. Science e energy E of a moving object is called its kinetic energy. It is calculated using the formula E 5 12 mv2, where m is the object’s mass in kilograms and v is its speed in meters per second. e units of kinetic energy are

kilograms ? meters2

second2 , abbreviated as kg ? m2>s2. a. Solve the given formula for m. b. What is the mass of an object moving at 10 m/s with a kinetic energy of 2500 kg ? m2>s2? 45. Error Analysis Describe and correct the error made in solving the literal

equation at the right for n. 46. Geometry e formula for the volume of a cylinder is V 5 pr2h, where r is the cylinder’s radius and h is its height. Solve the equation for h. What is the height of a cylinder with volume 502.4 cm3 and radius 4 cm? Use 3.14 for p.

47. Density e density of an object is calculated using the formula D 5 mV , where m

is the object’s mass and V is its volume. Gold has a density of 19.3 g>cm3. What is the volume of an amount of gold that has a mass of 96.5 g?

See Problem 4.

ApplyB

-62m + 3 = n

2m = -6n + 32m + 3 = -6n

Polar stratospheric clouds

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STEM


48. Open-Ended Write an equation in three variables. Solve the equation for each

variable. Show all your steps.

49. Surface Area A rectangular prism with height h and with square bases with side

length s is shown.

a. Write a formula for the surface area A of the prism.

b.

nd h in terms of A and s. If s is 10 cm and A is 760 cm2,

what is the height of the prism?

c. Writing Suppose h is equal to s. Write a formula for A in terms of s only.

50. Midpoints Suppose a segment on a number line has endpoints with coordinates

a and b e coordinate of the segment’s midpoint m is given by the formula

m 5a 1 b

2 .

a. Find the midpoint of a segment with endpoints at 9.3 and 2.1.

b.

nd b in terms of a and m.

c. e midpoint of a segment is at 3.5. One endpoint is at 8.9. Find the

other endpoint.

ChallengeCs

s

h

Mixed Review

Solve each equation. If the equation is an identity, write identity. If it has no

solution, write no solution.

54. 3x 2 3 5 x 1 7 55. 2b 2 10 5 23b 1 5

56. 4 1 12a 5 22(6 2 4a) 57. 2(y 2 4) 5 24y 1 10

58. 4c 2 10 5 2(2c 2 5) 59. 5 1 4p 5 2(2p 1 1)

Evaluate each expression for b 5 3 and c 5 7.

60. bc2 61. b2 2 c2 62. (3b)2c 63. (b 1 c)2

Get Ready! To prepare for Lesson 2-6, do Exercises 64–66.

Simplify each product.

64. 3525 3

3014

65. 99108 3

9655

66. 2181 3

63105

See Lesson 2-4.

See Lesson 1-2.

See p. 792.

Standardized Test Prep

51. What is the value of the expression 234m 1 15 when m 5 12?

52. What is the solution of 9p 1 6 2 3p 5 45?

53. e formula F 5n4 1 37 relates the number of chirps n a cricket makes in 1 min to

the outside temperature F in degrees Fahrenheit. How many chirps can you expect

a cricket to make in 1 min when the outside temperature is 608F?

SAT/ACT

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Application problems with the STEM label require students to

apply their knowledge to solve real-world

problems that focus on science, technology, and

engineering topics.

Test Prep and Mixed Review after every lesson ensure students are prepared for standardized assessments and final exams.

Red headings such as Reasoning, Writing, Think About a Plan, Compare and Contrast, and Error Analysis are examples of higher order thinking questions that provide students the opportunity to demonstrate understanding.


8

“Concept Byte” Algebra Labs are found throughout the textbook. Additional lesson resources can be found within the Teaching Resources—in print, online, or on DVD—including hands-on activities, games, puzzles, projects, and more.


“Concept Byte” Graphing Calculator Labsare found throughout the textbook.

Additional graphing calculator labs for the TI-83/84 can be found within the Teaching

with TI Technology Handbook and accompanying CD-ROM. See page 17 for

more information about TI-Nspire™ files for every lesson.


366 Concept Byte Solving Systems Using Tables and Graphs

Concept ByteUse With Lesson 6-1

T E C H N O L O G Y

Solve the system using a table. y 5 3x 2 7 y 5 20.5x 1 7

Step 1Enter the equations in they= screen.

Step 2Use the tblset function. Set TblStart to 0 and nTbl to 1.

Step 3Press table to show the table on the screen.

Plot1 Plot2 Plot3\Y1\Y2\Y3\Y4\Y5\Y6\Y7

= 3X – 7= –0.5X + 7= 5= 0= 1= 1= 1

TABLE SETUPTblStart = 0

Tbl = 1Indpnt : Auto AskDepend : Auto Ask

–7–4–125811

76.565.554.54X 0

X Y1 Y20123456

1. Which x-value gives the same value for Y1 and Y2? 2. What ordered pair is the solution of the system?

Solve the system using a graph. y 5 25x 1 6 y 5 2x 2 2

Step 1 Enter the equations in the y= screen.Step 2 Graph the equations. Use a standard graphing window.Step 3 Use the calc feature. Choose INTERSECT to nd the point where the lines intersect.

3. Copy and complete: e lines intersect at ( 9 , 9 ), so this point is the solution of the system.

ExercisesUse a table and a graph to solve each system. Sketch your graph. 4. y 5 5x 2 3

5. y 5 2x 2 13 6. 2x 2 y 5 1.5

y 5 3x 1 1 y 5 x 2 9

y 5 212x 2 1.5

S l h

S l h

Solving Systems Using Tables and GraphsContent Standard

A.REI.11 Explain why the x-coordinates of the points where the graphs of the equations y=f(x) and y=g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately…

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Concept Byte Equations With Variables on Both Sides 101

Concept ByteUse With Lesson 2-4

A C T I V I T Y

Algebra tiles can help you understand how to solve equations with variables on

both sides.

Model and solve 3b 2 4 5 b 1 2.

Equation Algebra tiles

Step

3b 2 4 5 b 1 2

Model the equation using tiles.

3b 2 4 2 b 5 b 1 2 2 b

2b 2 4 5 2

Remove one green tile from each side of

the equation so that all remaining green

tiles are on one side.

2b 2 4 1 4 5 2 1 4

2b 5 6

Add four yellow tiles to each side of the

equation to form zero pairs that can

be removed.

2b25

62

Notice that two green tiles equal six

yellow tiles. You can divide the tiles

on each side of the equation into two

identical groups, as shown.

b 5 3

So, one green tile equals three yellow

tiles. The solution of 3b 2 4 5 b 1 2

is b 5 3. You can substitute 3 for b

to check.

Exercises

Write the equation modeled by the algebra tiles.

1.

2.

Use algebra tiles to model and solve each equation.

3. 3x 2 5 5 x 1 3 4. 6x 2 4 5 3x 1 2 5. 5x 2 3 5 3x 1 1 6. 4x 1 4 5 1 1 x

M d l d

Modeling Equations With

Variables on Both Sides

Content Standard

Prepares for A.REI.1 Explain each

step in solving a simple equation as

following from the equality of numbers

asserted at the previous step, starting

from the assumption that the original

equation has a solution…

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10 11

Additional ELL SupportTeaching suggestions and activities

within the Teacher’s Edition promote language development

and comprehension for English Language Learners. The Multilingual Handbook in the online Student and

Teacher Resources includes a visual glossary in ten different languages.

Additional resources for Spanish-

speaking students include a Spanish Visual Glossary with audio,

Spanish Homework Video Tutors, and Spanish worksheets and

assessment resources.

Intervention• Reteaching (2 pages)

provides reteaching and practice exercises for the key lesson concepts.

• English Language Learner Support helps students develop and reinforce mathematical vocabulary and key concepts.

Extension • Enrichment sections

provide students with interesting problems and activities that extend the concepts of the lesson.

• Activities, Games, and Puzzles can be used for concepts development, enrichment, and for fun!

On-Level • Practice (2 pages) provides

extra practice for each lesson.

• Think About a Plan helps students develop specific problem-solving skills and strategies by providing scaffolded guiding.

• Standardized Test Prep helps students prepare for the high-stakes assessments.

Points Differentiated Remediation InterventionOn-levelExtension

5 Assess & RemediateAssign the Lesson Quiz. Appropriate intervention, practice, or enrichment is automatically generated based on student performance.

Lesson Resources 419B

Prentice Hall Algebra 1 • Teaching ResourcesCopyright © by Pearson Education, Inc., or its affiliates. All Rights Reserved. 2

Name Class Date

Manufacturing A company is making metal rods with a target diameter of 1.5 mm. A rod is acceptable when its diameter is within 1023 mm of the target diameter. Write an inequality for the acceptable range of diameters.

Understanding the Problem 1. What is the target diameter for the metal rods?

2. How do you know if a rod is acceptable?

3. What is the problem asking you to determine?

Planning the Solution 4. What does the word “within” tell you about the acceptable range of diameters?

5. What does this tell you about the type of inequality that you should use?

Getting an Answer 6. Write 1023 as a fraction and as a decimal.

7. Find the acceptable range for the diameters of the rods.

8. Write your answer as a single inequality.

7-1 Think About a PlanZero and Negative Exponents

1.5 mm

an inequality for the acceptable

110, 0.1

14.99 R d R 15.001

between 14.999 and 15.001 mm

The inequality will use the symbols R and S.

The diameter may not be greater than 1.50 1 0.001 mm or less than

within 1023 of 1.5 mm

range of diameters

1.5 2 0.001 mm.


Name Class Date

Multiple ChoiceFor Exercises 1–6, choose the correct letter. 1. What is the simplifi ed form of 3a4b22c3? A.

81a4c3

b2 B. 81a4

b2c3 C. 3a4

b2c3 D. 3a4c3

b2 2. What is2a22 if a 5 25 ? F. 225 G. 25 H. 2

125

I. 1

25 3. Which of the following simplifi es to a negative number? A. 2424 B. (24)24 C. 424 D.

1

424 4. What is the simplifi ed form of2(14x)0 y27 z ? F. 2

14zy7 G.

14zy7 H.

z

y7 I. 2

z

y7 5. What is (2m)23n if m 5 2 and n 5 224? A. 3 B. 23 C. 4 D. 24 6. What is the simplifi ed form of a2

5a3b23

?

F. 27

125a3 G. 227

125a3 H. 125a3

27 I. 2

125a3

27

Short Response 7. Th e number of bacteria in a culture quadruples every hour. Th ere were 65,536 bacteria in the culture at 8:00 a.m. Th e expression 65,536 ? 4h models the number of bacteria in the culture h hours after 8:00 a.m. a. What is the value of the expression for h 5 24? b. What does the value of the expression in part a represent?

7-1 Standardized Test PrepZero and Negative Exponents

D

H

A

I

A

G

256; the number of bacteria in the culture at 4:00 A.M.

Prentice Hall Algebra 1 • Activities, Games, and PuzzlesCopyright © by Pearson Education, Inc., or its affiliates. All Rights Reserved. 61

Name Class Date

7-1 Puzzle: Find the Power of 2Zero and Negative Exponents

Answer each of the 12 clues below. Each time you fi nd an answer, use an X to cross out the numbers in the fi gure below.

222 and its reciprocal 1022 and 1122 24 and

116

72 and 1

62225 and 1 4 34 34 and 321 223 and 226 82 and

1

721 4 225 and 1 4 322 1 4 2 and 1 4 221 1 4 521 and 1 4 522 62 and

1

321

After you follow all the clues, only two fractions should remain. Circle these fractions. When you rearrange the digits of their denominators, you will fi nd a positive power of 2. What is it? (Hint: Every power of 2 has an even digit as its ones digit.)Puzzle answer: ___________________

49

3

64

4

81 5

16

32

36

2

925

14

116

132

136

149

164

181

1100

1121

1128

13 1

8

12 1

9

8192 or 213

Name Class Date

Prentice Hall Gold Algebra 1 • Teaching ResourcesCopyright © by Pearson Education, Inc., or its affiliates. All Rights Reserved. 3

Simplify each expression. 1. 130

2. 523

3. 3

324 4.

2

421

5. 2(7)22 6. 4621

7. 260 8. 2(12x)22

9. 1

80 10. 6bc0

11. 2(11x)0 12. a2

9b22

13. 3m28 p0 14.

5a24

2c

15. 23k23(mn)3

p28 16. a2m

3nb23

17. 822 q3 r25 18. 2(10a)24 b0

19. 11xy21z0

v23 20.

5m21

9(ab)24 c7

7-1 Practice Form GZero and Negative Exponents

1

243

1

1

21

3m8

23p8m3n3

k3

52a4c

27n3

8m3

5a4b4

9mc7

2110,000a4

q3

64r 5

11xv3y

6b

2 1

49

2 1

144 x

2

20 14

8

146

1125

Name Class Date

Prentice Hall Gold Algebra 1 • Teaching ResourcesCopyright © by Pearson Education, Inc., or its affiliates. All Rights Reserved. 4

Evaluate each expression for a 5 24, b 5 3, and c 5 2 . 21. 3a21

22. b23

23. 4a2 b22 c3 24. 9a0 c4

25. 2a22 26. (2c)22

Write each number as a power of 10 using negative exponents. 27.

11000

28.

110

Write each expression as a decimal. 29. 1023

30. 8 ? 1024 31. Th e number of people who vote early doubles every week leading up to an election. Th is week 1200 people voted early. Th e expression 1200 ? 2w models the number of people who will vote early w weeks after this week. Evaluate the expression for w 5 23. Describe what the value of the expression represents in the situation.

32. A pizza shop makes large pizzas with a target diameter of 16 inches. A pizza is acceptable if its diameter is within 3 ? 222 in. of the target diameter. Let d represent the diameter of a pizza. Write an inequality for the range of acceptable large pizza diameters in inches.

33. Open-Ended Choose a fraction to use as a value for the variable c. Find the values of c21, c23, and c3.

7-1 Practice (continued) Form GZero and Negative Exponents

2 34

2 1

16

5129

127

14

144

1023

0.0010.0008

150; The expression 1200 ? 2 represents the number of people who voted early three weeks ago.

1514 R d R 163

4

Answers may vary. Sample: c 5 23 , c

21 5 32 , R c23 5 27

8 , c3 5 827

1021


Name Class Date

For each exercise below, a student’s answer is below shown. Indicate below each exercise whether each answer is correct or incorrect. For each incorrect answer, indicate where the student made an error, and describe how to correct it. Th en write the correct answer.

1. Simplify 1

3? (2y)0 x23. 2. Simplify 25 ?

8b28cd24

120 .

1

3? (2y)0x23 5

(2)(1)x23

3 25 ?

8b28cd24

120 5240b28cd24

1 5

2

3x3 5

240b8cd4

3. Simplify 2xy24 ?

3z23

18

4. Simplify 2(5a3)22.

2xy24 ?

3z23

185

2x(3z23)y24(18)

2(5a3)22 5 2522 a29

56xy4

18z3 5 2

1

25a9

5xy4

3z3

5. Simplify 9p

7q22 42r23

5.

9p

7q22 42r23

55

9p

7q22 ?5

2r23

545p

14q22 r23

545pq22r23

14

7-1 EnrichmentZero and Negative Exponents

incorrect; The student simplifi ed (2y)0 as 2 instead of 1. correct answer is 1

3x3 .

correct

incorrect; The student simplifi ed 45p14q22r23 as

45pq22r23

14 instead of 45pq2r3

14 . The correct answer is

45pq2r3

14 .

incorrect; The student simplifi ed (5a3)22 as 522a29 instead of 522a26. The correct answer is 2 1

25a6

incorrect; The student simplifi ed cd24 as 1cd

4instead of c

d 4 . The correct answer is 240c

b8d 4 .

Differentiated Remediation continued

On-Level• Practice(2pages)Providesextrapracticeforeachlesson.Forsimplerpracticeexercises,usetheFormKPracticepagesfoundintheAll-in-OneTeachingResourcesandonline.

• Think About a PlanHelpsstudentsdevelopspecificproblem-solvingskillsandstrategiesbyprovidingscaffoldedguidingquestions.• Standardized Test PrepFocusesonallmajorexercises,allmajorquestiontypes,andhelpsstudentsprepareforthehigh-stakesassessments.

Extension• EnrichmentProvidesstudentswithinterestingproblemsandactivitiesthatextendtheconceptsofthelesson.•Activities, Games, and PuzzlesWorksheetsthatcanbeusedforconceptsdevelopment,enrichment,andforfun!

All-in-One Resources/OnlineEnrichment

Online Teacher Resource CenterActivities, Games, and Puzzles

Practice and Problem Solving Wkbk/ All-in-One Resources/OnlineStandardized Test Prep

Practice and Problem Solving Wkbk/ All-in-One Resources/OnlineThink About a Plan

Practice and Problem Solving Wkbk/ All-in-One Resources/OnlinePractice page 2

Practice and Problem Solving Wkbk/ All-in-One Resources/OnlinePractice page 1

0419A_hsm11a1te_FL_07_01_lr.indd 420

3/2/09 1:47:46 PM

Points Differentiated Remediation

InterventionOn-levelExtension

5 Assess & RemediateAssign the Lesson Quiz.

Appropriate intervention, practice,

or enrichment is automatically

generated based on student

performance.

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Now Iget it!Need to

review0 2 4 6 8 10

Math Success

Lesson Check

=

= undefined

xn

a-nb0anxn

b0

anxn

0

197 Lesson 7-1

Check off the vocabulary words that you understand.

exponent zero exponent negative exponent

Rate how well you can simplify zero and negative exponents.

• Do you UNDERSTAND?

Error Analysis A student incorrectly simplifi ed xn

a2nb0 as

shown at the right. Find and correct the student’s error.

25. Did the student work correctly with —

base x? Yes / No base a? Yes / No base b? Yes / No

26. What error did the student make?

_____________________________

_____________________________

23. Now solve the problem.

24. What does each value represent?

For w 5 22, the value For w 5 0, the value For w 5 1, the value

represents the number represents the number represents the number

of insects 9. of insects 9. of insects 9.

27. Now simplify the expression correctly.

Solutions may vary. Sample:

For w 522: For w 5 0: For w 5 1:

5400 ? 3w 5 5400 ? 322 5400 ? 3w 5 5400 ? 30 5400 ? 3w 5 5400 ? 31

5 5400 ? 19 5 5400 ? 1 5 5400 ? 3

5 600 5 5400 5 16,200

600 5400 16,200

2 weeks before the when the population 1 week after the

population was measured was measured population was measured

The student simplified b0 as

0 instead of as 1.


xn

a2n b0 5xnan

b0 5xnan

1 5 xnan

HSM11A1MC_0701.indd 197

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Vocabulary

Chapter 7 194

7-1 Zero and Negative Exponents

Review Circle the exponent in each equation.

1. 35 5 243 2. 72 5 49 3. 27 5 128

Write an equivalent expression using an exponent.

4. 35 ? 35 ? 35 5 5. 19 ? 19 ? 19 ? 19 ? 19 ? 19 ? 19 ? 19 ? 19 5

6. In the expression 43, identify the base and the exponent.

base = exponent =

Vocabulary Builder

negative (adjective) NEG uh tiv

Definition: A negative quantity has a value less than zero.

Examples: 23,212, and 2p are all negative numbers.

Use Your Vocabulary

7. Write a number to represent each situation.

The temperature is 4 degrees You owe your brother A worker’s hourly pay

below zero. eight dollars. increases by $.50.

Draw a line from each negative number in Column A to its opposite in Column B.

Column A Column B

8. 212 17

9. 2335

12

10. 217 335

The symbol for

is

negative

353199

4

24

3

2$ 8 $.50


2/20/09 12:23:27 PM

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Properties Zero and Negative Exponents

11. Complete the table.

Exponent Property Examples

Zero

For every nonzero

number a,(a)0 1 ( 24)0 1

60 1

Negative

7 3 173

1343

4 2 142

1

16

( 3) 5 1

( 3)51

243

For every nonzero

number a and integer n,1an(a) n

Write T for true or F for false.

12. 922 51

81 13. (29)0 5 21

14. 921 5 219

15. 923 51

27

Problem 1

Problem 2

195 Lesson 7-1

Simplifying Powers

Got It? What is the simplified form of 423?

16. Complete each step to simplify 423.

423 51

4

Move the power to the denominator and

make the exponent positive.

51

Evaluate the power to simplify the expression.

Simplifying Exponential Expressions

Got It? What is the simplified form of each expression?

x29 1

n23 4c23b 2

a23 n25

m2

Underline the correct word to complete each sentence.

17. To simplify a base in the numerator that has a negative exponent, move the base to

the denominator and write a positive / negative exponent.

18. To simplify a base in the denominator that has a negative exponent, move the base

to the numerator and write a positive / negative exponent.

T F F F

3

64


2/14/09 5:56:36 AM

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Vocabulary

Chapter 7 194

7-1 Zero and Negative Exponents


1. 35 5 243 2. 72 5 49 3. 27 5 128


4. 35 ? 35 ? 35 5 5. 19 ? 19 ? 19 ? 19 ? 19 ? 19 ? 19 ? 19 ? 19 5


base = exponent =

Vocabulary Builder




Use Your Vocabulary





Column A Column B

8. 212 17

9. 2335

12

10. 217 335

The symbol for

is

negative

353199

4

24

3

2$ 8 $.50


2/14/09 5:56:30 AM

Prentice Hall Algebra 1 • Teaching Resources

Copyright © by Pearson Education, Inc., or its affiliates. All Rights Reserved.

9

Name Class Date

For every nonzero number a, a0 5 1.

For every nonzero number a and integer n, a2n 51

an. In other words, when the

exponent is negative, raise the reciprocal of the base to the opposite of the

exponent.

Problem

What is the simplifi ed form of each expression?

a. 3.90 5 1 Since the exponent is 0 but the base of the expression is 3.9, which is not

0, the expression has a value of 1.

b. 922 51

92 The exponent is negative, so raise the reciprocal of 9, or 19, to the

exponent 2(22), or 2.

51

81 Simplify.

Problem

What is the simplifi ed form of 7b23

a2 using only positive exponents?

7b23

a2 57

a2 ? b23 Rewrite the expression as a product of factors with positive exponents and

factors with negative exponents.

57

a2 ?1

b3 Rewrite the factor with the negative exponent by raising the reciprocal of

the base to a positive exponent.

57

a2 b3 Simplify by multiplying.

7-1 ReteachingZero and Negative Exponents



1

Name Class Date

7-1 ELL Support

Zero and Negative Exponents

Complete the vocabulary chart by fi lling in the missing information.

Word or Word Phrase

Defi nition Picture or Example

base A number used as a repeated factor. 63 5 6 3 6 3 6

Th e base is 6.

exponent63 5 6 3 6 3 6

Th e exponent is 3.

zero as an exponent


negative exponent

For every nonzero number a and

integer n, a2n 51an

.

exponential expression

5x

reciprocal1x3, x3

23, 32

simplest form An algebraic expression is in simplest

form when it is has no like terms,

negative exponents, or parentheses.

The number that tells how many

times a base is to be used as a

repeated factor.

A mathematical expression

consisting of a constant raised to

a power.

50 5 1

622 5162

4a22b4 54b4

a2

3a2 1 2a 2 5ab

A number and its reciprocal

have a product of 1.

Intervention

•Reteaching(2pages)Providesreteaching

andpracticeexercisesforthekeylesson

concepts.Usewithstrugglingstudentsor

absentstudents.

• English Language Learner SupportHelps

studentsdevelopandreinforcemathematical

vocabularyandkeyconcepts.

Differentiated Remediation

0–234

All-in-One Resources/Online

English Language Learner Support


Reteaching

419A Lesson Resources

Additional Instructional Support

Algebra 1 CompanionStudentscanusetheAlgebra 1 Companion

worktext(4pages)asyouteachthelesson.

UsetheCompaniontosupport

• NewVocabulary

• KeyConcepts

• GotItforeachProblem

• LessonCheck

ELL SupportFocus on CommunicationHavestudents

makeatwo-columntable.Labelonecolumn

“ZeroExponent”andtheother“Negative

Exponent.”Havestudentswriteanexample

ofeachinthecolumns.Askvolunteersfor

theirexamplestoputontheboard.Repeatthe

propertyeachtimeyousimplifythepower.For

example,say:Avaluewithazeroexponent

alwaysequals1so290 5 1.Continuewith

examples,allowingstudentsachanceto

explainthepropertyusedtosimplifythe

powers.Usebothnumericandalgebraicbases.

5 Assess & Remediate

Lesson Quiz 1. Whatisthesimplifiedformofeach

expression?

a.223

b.(5.5)0

2. Whatisthesimplifiedformofeach

expression?

a.26a2b21

b. 5y23

3. Whatisthevalueof26a23b2fora 5 22

andb 5 4?

4. Do you unDERStAnD? Thenumberof

hitsonawebsitedoubleseverymonth.

About10,600peoplevisitedthewebsite

duringMay.Theexpression10,600•2t

modelsthenumberofvisitorsafter

tmonths.Evaluatetheexpressionfort 5 0

andt 5 22.Describewhateachvalueof

theexpressionrepresentsinthesituation.

ANSWERS to lESSoN quiz

1. a. 18b.1

2. a. 26a2

b b.5y3

3. 12

4. 10,600;2,650;About10,600people

visitedthewebsiteinMay.About2,650

peoplevisitedthewebsiteinMarch.

7-1 Lesson Resources

PREScRiPtioN foR REmEdiAtioN

UsethestudentworkontheLessonQuizto

prescribeadifferentiatedreviewassignment.


3/2/09 1:47:25 PM

The Lesson Quiz, available in print and online, assesses

lesson skills and concepts. The prescription for remediation

helps teachers make instructional decisions about appropriate

review assignments.

The Student Companion is a worktext that provides support for

math vocabulary and key concepts. Scaffolded support for Got It! and Lesson Check problems reinforces

problem-solving skills.

Built-in Intervention and EnrichmentLeveled resources are included within the Teacher Edition at the end of each lesson. These lesson resources provide a detailed blueprint for instruction, assessment, and remediation.

12 13

Lesson Check

Problem 4

Got It?

Lesson 2-8 Proportions and Similar Figures 133

Do you know HOW? 1. Photocopies You use a photocopier to enlarge a drawing of a right triangle with a base of 13 cm and a height of 7 cm. e enlarged triangle has a height of 17.5 cm. a. What is the base of the enlarged triangle? b. What is the scale of the enlargement? 2. Maps e scale of a map is 1 cm : 75 km. What is the actual distance between two towns that are 3 cm apart on the map?

Do you UNDERSTAND? 3. Vocabulary Suppose nMNP ,nRST. How can you identify corresponding parts? 4. Reasoning Suppose nABC ,nTUV. Determine whether each pair of measures is equal. a. the measures of /A and /T b. the perimeters of the two triangles c. the ratios of the sides BC

UV and ACTV

5. Reasoning e scale of a map is 1 in. : 100 mi. Is the actual distance between two towns 100 times the map distance between the two towns? Explain.

Using Scale ModelsScience A giant model heart is shown below. e heart is the ideal size for a person who is 170 ft tall. About what size would you expect the heart of a man who is 6 ft tall to be?

height of giant heartheight of man’s heart

height of giant personheight of man Write a proportion.

14x 5 170

6 Substitute.14(6) 5 170x Cross Products Property

0.49 < x Divide each side by 170 and simplify. e size of the man’s heart would be about 0.49 ft, or 5.9 in.

4. A scale model of a building is 6 in. tall. e scale of the model is 1 in. : 50 ft. How tall is the actual building?

Is this problem like ones you have seen?Yes. Scale model problems are like scale drawing problems, so you can write a proportion like you did to fi nd the height of the building in Problem 2.

h i hto

f i t h t h i hto

f i t

14 ft

6 ft

x ft

0132_hsm11a1se_0208.indd 133

1/8/09 1:13:31 PM

STEM

Check for Understanding

Following each problem, the Got It? provides instant

assessment of understanding. Within the Lesson Check,

Do you know HOW? and Do you UNDERSTAND? assess how well students

can apply the lesson skills.

ONGOING

STRATEGIC

Data-Driven DifferentiationLesson Resources in the Teacher’s Edition provide a Lesson Quiz to be used as a tool to differentiate remediation. Resources to meet student needs are listed at point of use.

INTENSIVE

Intensive InterventionThe Success Tracker™ online assessment

system provides instant analysis of student performance. It includes benchmark

assessments correlated to the Common Core State Standards. Success Tracker™ diagnoses

student success, prescribes automatic remediation, and reports on student

and class progress.

Differentiate InstructionStudents learn in different ways and at different paces. Unique, built-in resources differentiate instruction to support all levels of learners in becoming successful problem solvers. Differentiating instruction helps all students develop conceptual understanding, foster mathematical reasoning, and refine problem-solving strategies. Options are available to differentiate instruction at the start of each chapter and throughout the lessons.


Intervention

On-levelExtension





performance.

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Now Iget it!Need to

review0 2 4 6 8 10

Math Success

Lesson Check

=

= undefined

xn

a-nb0anxn

b0

anxn

0

197 Lesson 7-1






a2nb0 as





_____________________________

_____________________________








For w 522: For w 5 0: For w 5 1:

5400 ? 3w 5 5400 ? 322 5400 ? 3w 5 5400 ? 30 5400 ? 3w 5 5400 ? 31

5 5400 ? 19 5 5400 ? 1 5 5400 ? 3

5 600 5 5400 5 16,200

6005400

16,200




0 instead of as 1.


xn

a2n b0 5xnan

b0 5xnan

1 5 xnan


2/14/09 5:56:45 AM

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aff

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Res

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d.

Vocabulary

Chapter 7 194

7-1 Zero and Negative

Exponents


1. 35 5 243 2. 72 5 49 3. 27 5 128


4. 35 ? 35 ? 35 5 5. 19 ? 19 ? 19 ? 19 ? 19 ? 19 ? 19 ? 19 ? 19 5


base = exponent =

Vocabulary Builder




Use Your Vocabulary





Column A Column B

8. 212

17

9. 2335

12

10. 217 33

5

The symbol for

isnegative

353199

4

24

3

2$ 8$.50


2/20/09 12:23:27 PM

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d.




Zero

For every nonzero

number a,(a)0 1 ( 24)0 1

60 1

Negative

7 3 173

1343

4 2 142

1

16

( 3) 5 1

( 3)51

243

For every nonzero



12. 922 5181

13. (29)0 5 21 14. 921 5 2

19

15. 923 5127

Problem 1

Problem 2

195 Lesson 7-1

Simplifying Powers



423 51

4



51




x29 1

n23 4c23b 2

a23 n25

m2






TF

F F

3

64


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Vocabulary

Chapter 7 194


Exponents


1. 35 5 243 2. 72 5 49 3. 27 5 128


4. 35 ? 35 ? 35 5 5. 19 ? 19 ? 19 ? 19 ? 19 ? 19 ? 19 ? 19 ? 19 5


base = exponent =

Vocabulary Builder




Use Your Vocabulary





Column A Column B

8. 212

17

9. 2335

12

10. 217 33

5

The symbol for

isnegative

353199

4

24

3

2$ 8$.50


2/14/09 5:56:30 AM



9

Name Class Date





exponent.

Problem




b. 922 51



51

81 Simplify.

Problem



7b23

a25

7



57

a2 ?1



57


7-1 Reteaching




1

Name Class Date

7-1 ELL Support



Word or Word Phrase

Defi nitionPicture or Example


Th e base is 6.

exponent63 5 6 3 6 3 6

Th e exponent is 3.

zero as an exponent


negative exponent


integer n, a2n 51an

.

exponential

expression

5x

reciprocal1x3, x3

23, 32






repeated factor.



a power.

50 5 1

622 5162

4a22b4 54b4

a2

3a2 1 2a 2 5ab



Intervention




absentstudents.





0–234




Reteaching






• NewVocabulary

• KeyConcepts


• LessonCheck















expression?

a.223

b.(5.5)0


expression?

a.26a2b21

b.5

y23


andb 5 4?










1. a. 18b.1

2. a. 26a2

b b.5y3

3. 12

4. 10,600;2,650;About10,600people








3/2/09 1:47:25 PM


Intervention

On-levelExtension





performance.

Lesson Resources 419BPrentice Hall Algebra 1 • Teaching Resources


2

Name Class Date

Manufacturing A company is making metal rods with a target diameter of

1.5 mm. A rod is acceptable when its diameter is within 1023 mm of the target

diameter. Write an inequality for the acceptable range of diameters.

Understanding the Problem

1. What is the target diameter for the metal rods?

2. How do you know if a rod is acceptable?

3. What is the problem asking you to determine?

Planning the Solution

4. What does the word “within” tell you about the acceptable range of

diameters?

5. What does this tell you about the type of inequality that you should use?

Getting an Answer

6. Write 1023 as a fraction and as a decimal.

7. Find the acceptable range for the diameters of the rods.

8. Write your answer as a single inequality.

7-1 Think About a Plan


1.5 mm

an inequality for the acceptable

110, 0.1

14.99 R d R 15.001

between 14.999 and 15.001 mm

The inequality will use the symbols R and S.

The diameter may not be greater than 1.50 1 0.001 mm or less than

within 1023 of 1.5 mm

range of diameters

1.5 2 0.001 mm.



7

Name Class Date

Multiple Choice

For Exercises 1–6, choose the correct letter.

1. What is the simplifi ed form of 3a4b22c3 ?

A. 81a4c3

b2 B.

81a4

b2c3 C. 3a4

b2c3 D. 3a4c3

b2

2. What is2a22 if a 5 25 ?

F. 225 G. 25 H. 2

1

25 I.

1

25

3. Which of the following simplifi es to a negative number?

A. 2424 B. (24)24 C. 424 D. 1

424

4. What is the simplifi ed form of2(14x)0 y27 z ?

F. 214z

y7 G. 14z

y7 H. z

y7 I. 2

z

y7

5. What is (2m)23n if m 5 2 and n 5 224?

A. 3 B. 23 C. 4 D. 24

6. What is the simplifi ed form of a2

5a

3b23

?

F. 27

125a3 G. 227

125a3 H. 125a3

27 I. 2

125a3

27

Short Response

7. Th e number of bacteria in a culture quadruples every hour. Th ere were

65,536 bacteria in the culture at 8:00 a.m. Th e expression 65,536 ? 4h models

the number of bacteria in the culture h hours after 8:00 a.m.

a. What is the value of the expression for h 5 24?

b. What does the value of the expression in part a represent?

7-1 Standardized Test Prep


D

H

A

I

A

G

256; the number of bacteria in the culture at 4:00 A.M.

Prentice Hall Algebra 1 • Activities, Games, and Puzzles


61

Name Class Date

7-1 Puzzle: Find the Power of 2


Answer each of the 12 clues below. Each time you fi nd an answer, use an X to cross

out the numbers in the fi gure below.

222 and its reciprocal 1022 and 1122 24 and

1

16 72 and

1

62

225 and 1 4 34 34 and 321 223 and 226 82 and 1

72

1 4 225 and 1 4 322 1 4 2 and 1 4 221 1 4 521 and 1 4 522 62 and 1

321

After you follow all the clues, only two fractions should remain. Circle these fractions. When

you rearrange the digits of their denominators, you will fi nd a positive power of 2. What is it?

(Hint: Every power of 2 has an even digit as its ones digit.)

Puzzle answer: ___________________

49

3

64

4

81 5

16

32

36

2

925

14

116

132

136

149

164

181

1100

11211

128

13

18

12

19

8192 or 213

Name Class Date

Prentice Hall Gold Algebra 1 • Teaching Resources


3

Simplify each expression.

1. 130 2. 523

3. 3

324 4.

2

421

5. 2(7)22 6. 4621

7. 260 8. 2(12x)22

9. 1

80 10. 6bc0

11. 2(11x)0 12. a2

9b22

13. 3m28 p0 14.

5a24

2c

15. 23k23(mn)3

p28

16. a2m

3nb23

17. 822 q3 r25 18. 2(10a)24 b0

19. 11xy21z0

v23

20. 5m21

9(ab)24 c7

7-1 Practice Form G


1

243

1

1

21

3m8

23p8m3n3

k3

52a4c

27n3

8m3

5a4b4

9mc7

2110,000a4

q3

64r 5

11xv3

y

6b

2 149

2 1

144 x

2

20 14

8

146

1125

Name Class Date



4

Evaluate each expression for a 5 24, b 5 3, and c 5 2 .

21. 3a21 22. b23

23. 4a2 b22 c3 24. 9a0 c4

25. 2a22 26. (2c)22

Write each number as a power of 10 using negative exponents.

27. 1

1000

28. 1

10

Write each expression as a decimal.

29. 1023 30. 8 ? 1024

31. Th e number of people who vote early doubles every week leading up to an

election. Th is week 1200 people voted early. Th e expression 1200 ? 2w models

the number of people who will vote early w weeks after this week. Evaluate the

expression for w 5 23. Describe what the value of the expression represents

in the situation.

32. A pizza shop makes large pizzas with a target diameter of 16 inches. A pizza

is acceptable if its diameter is within 3 ? 222 in. of the target diameter. Let

d represent the diameter of a pizza. Write an inequality for the range of

acceptable large pizza diameters in inches.

33. Open-Ended Choose a fraction to use as a value for the variable c. Find the

values of c21, c23, and c3.

7-1 Practice (continued) Form G


2 34

2 116

5129

127

14

144

1023

0.0010.0008

150; The expression 1200 ? 2 represents the number of people who voted

early three weeks ago.

1514 R d R 163

4

Answers may vary. Sample: c 523 , c

21 532 , R c23 5

278 , c3 5

827

1021



8

Name Class Date

For each exercise below, a student’s answer is below shown. Indicate below each

exercise whether each answer is correct or incorrect. For each incorrect answer,

indicate where the student made an error, and describe how to correct it. Th en

write the correct answer.

1. Simplify 1

3? (2y)0 x23. 2. Simplify 25 ?

8b28cd24

120.

1

3? (2y)0x23 5

(2)(1)x23

3 25 ?

8b28cd24

1205240b28cd24

1

52

3x3 5

240

b8cd4

3. Simplify 2x

y24 ?3z23

18 4. Simplify 2(5a3)22.

2x

y24 ?3z23

185

2x(3z23)

y24(18) 2(5a3)22 5 2522 a29

56xy4

18z3 5 2

1

25a9

5xy4

3z3

5. Simplify 9p

7q22 42r23

5.

9p

7q22 42r23

55

9p

7q22 ?5

2r23

545p

14q22 r23

545pq22r23

14

7-1 Enrichment


incorrect; The student simplifi ed (2y)0 as 2

instead of 1. correct answer is 13x3 .

correct

incorrect; The student simplifi ed 45p

14q22r23 as

45pq22r23

14 instead of

45pq2r3

14. The correct answer

is 45pq2r3

14.

incorrect; The student simplifi ed (5a3)22

as 522a29 instead of 522a26. The

correct answer is 2 125a6

incorrect; The student simplifi ed cd24 as 1cd

4

instead of cd

4 . The correct answer is 240c b8d

4 .

Differentiated Remediation continued

On-Level

• Practice(2pages)Providesextrapractice

foreachlesson.Forsimplerpractice

exercises,usetheFormKPracticepages

foundintheAll-in-OneTeachingResources

andonline.

• Think About a PlanHelpsstudents

developspecificproblem-solvingskillsand

strategiesbyprovidingscaffoldedguiding

questions.

• Standardized Test PrepFocusesonall

majorexercises,allmajorquestiontypes,

andhelpsstudentsprepareforthe

high-stakesassessments.

Extension

• EnrichmentProvidesstudentswith

interestingproblemsandactivitiesthat

extendtheconceptsofthelesson.

•Activities, Games, and Puzzles

Worksheetsthatcanbeusedforconcepts

development,enrichment,andforfun!


Enrichment

Online Teacher Resource Center

Activities, Games, and PuzzlesPractice and Problem Solving Wkbk/


Standardized Test PrepPractice and Problem Solving Wkbk/


Think About a Plan

Practice and Problem Solving Wkbk/


Practice page 2Practice and Problem Solving Wkbk/


Practice page 1


3/2/09 1:47:46 PM


Intervention

On-levelExtension





performance.

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Res

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d.

Now Iget it!Need to

review0 2 4 6 8 10

Math Success

Lesson Check

=

= undefined

xn

a-nb0anxn

b0

anxn

0

197 Lesson 7-1






a2nb0 as





_____________________________

_____________________________








For w 522: For w 5 0: For w 5 1:

5400 ? 3w 5 5400 ? 322 5400 ? 3w 5 5400 ? 30 5400 ? 3w 5 5400 ? 31

5 5400 ? 19 5 5400 ? 1 5 5400 ? 3

5 600 5 5400 5 16,200

6005400

16,200




0 instead of as 1.


xn

a2n b0 5xnan

b0 5xnan

1 5 xnan


2/14/09 5:56:45 AM

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Res

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d.

Vocabulary

Chapter 7 194


Exponents


1. 35 5 243 2. 72 5 49 3. 27 5 128


4. 35 ? 35 ? 35 5 5. 19 ? 19 ? 19 ? 19 ? 19 ? 19 ? 19 ? 19 ? 19 5


base = exponent =

Vocabulary Builder




Use Your Vocabulary





Column A Column B

8. 212

17

9. 2335

12

10. 217 33

5

The symbol for

isnegative

353199

4

24

3

2$ 8$.50


2/20/09 12:23:27 PM

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Res

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d.




Zero

For every nonzero

number a,(a)0 1 ( 24)0 1

60 1

Negative

7 3 173

1343

4 2 142

1

16

( 3) 5 1

( 3)51

243

For every nonzero



12. 922 5181

13. (29)0 5 21 14. 921 5 2

19

15. 923 5127

Problem 1

Problem 2

195 Lesson 7-1

Simplifying Powers



423 51

4



51




x29 1

n23 4c23b 2

a23 n25

m2






TF

F F

3

64


2/14/09 5:56:36 AM

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d.

Vocabulary

Chapter 7 194


Exponents


1. 35 5 243 2. 72 5 49 3. 27 5 128


4. 35 ? 35 ? 35 5 5. 19 ? 19 ? 19 ? 19 ? 19 ? 19 ? 19 ? 19 ? 19 5


base = exponent =

Vocabulary Builder




Use Your Vocabulary





Column A Column B

8. 212

17

9. 2335

12

10. 217 33

5

The symbol for

isnegative

353199

4

24

3

2$ 8$.50


2/14/09 5:56:30 AM



9

Name Class Date





exponent.

Problem




b. 922 51



51

81 Simplify.

Problem



7b23

a25

7



57

a2 ?1



57


7-1 Reteaching




1

Name Class Date

7-1 ELL Support



Word or Word Phrase

Defi nitionPicture or Example


Th e base is 6.

exponent63 5 6 3 6 3 6

Th e exponent is 3.

zero as an exponent


negative exponent


integer n, a2n 51an

.

exponential

expression

5x

reciprocal1x3, x3

23, 32






repeated factor.



a power.

50 5 1

622 5162

4a22b4 54b4

a2

3a2 1 2a 2 5ab



Intervention




absentstudents.





0–234




Reteaching






• NewVocabulary

• KeyConcepts


• LessonCheck















expression?

a.223

b.(5.5)0


expression?

a.26a2b21

b.5

y23


andb 5 4?










1. a. 18b.1

2. a. 26a2

b b.5y3

3. 12

4. 10,600;2,650;About10,600people








3/2/09 1:47:25 PM

14 15

xxvi Contents

5 Linear FunctionsGet Ready!

311My Math Video 313PART A

5-1 Rate of Change and Slope 3145-2 Direct Variation 321 Concept Byte: Investigating y 5 mx 1 b 3285-3 Slope-Intercept Form 329 Part 1 329–333, Part 2 334–337 5-4 Point-Slope Form 338 Part 1 338–340, Part 2 341–344 Chapter 5A Review and Test 345PART B

5-5 Standard Form 3495-6 Parallel and Perpendicular Lines 3575-7 Scatter Plots and Trend Lines 364 Concept Byte: Collecting Linear Data 371Assessment and Test Prep

Pull It All Together 372 Chapter 5B Review and Test 373 Cumulative Test Prep 376

R022_hsm11a1se_fmtoc_LLNA.indd xxvi

4/27/09 11:49:45 AM

Model ThinkingThroughout the text the thinking and reasoning on the left is modeled before the math on the right. Students benefit from reading the reasoning before they see the math.

Prentice Hall Algebra 1, Geometry, Algebra 2, Foundations Series ensures full coverage of the Common Core State Standards by delivering comprehensive and rigorous content, but in an alternate approach that makes it accessible to all students. The unique method of content delivery within separate Student and Teacher Editions improves self-sufficiency and guarantees success. Some of these changes are described below.

More Scaffolded Support More support in problems and exercises helps students connect to what they already know, break down complex steps, and model the thinking before the math.

336 Chapter 5 Linear Functions

336 Chapter 5 Linear Functions

Practice and Problem-Solving Exercises

Graph each equation.

PracticeA

See Problem 5. 3. y 5 3x 1 4 The y-intercept is 4. So plot a point at (0, 4).

GuidedPractice

To start, find the y-intercept.

GuidedPractice

4. y 5 x 1 5

5. y 5 22x 1 1 6. y 5 24x 2 1

7. y 5 2x 2 4

8. y 5 6x 2 3 9. y 5 23x 1 3

10. y 5 7x

11. y 5 5x 1 1 12. y 5 2x 1 10

13. Retail Sales Suppose you have a $5-off coupon at a fabric store. You buy fabric

that costs $7.50 per yard. Write an equation that models the total amount of

money you pay if you buy x yards of fabric. What is the graph of the equation?

To start, identify the slope and the y-intercept. The slope is the cost per yard,

$7.50 per yard.

The y-intercept is the amount of the

coupon, 2$5.00.

14. Temperature The temperature at sunrise is 658F. Each hour, the temperature rises

58F. Write an equation that models the temperature y, in degrees Fahrenheit, after

x hours. What is the graph of the equation?

15. Think About a Plan Polar bears are listed as a threatened species. In 2005, there

were about 25,000 polar bears in the world. If the number of polar bears declines by

1000 each year, in what year will polar bears become extinct?

• What equation models the number of polar bears?

• How can graphing the equation help you solve the problem?

16. Error Analysis A student drew the graph at the right for the equation

y 5 22x 1 1. What error did the student make? Draw the correct graph.

17. Computers A computer repair service charges $50 for diagnosis and

$35 per hour for repairs. Let x be the number of hours it takes to repair a

computer. Let y be the total cost of the repair.

a. Write an equation in slope-intercept form that relates x and y.

b. Graph the equation.

c. Reasoning Explain why you should draw the line only in Quadrant I.

Use the slope and y-intercept to graph each equation.

18. y 5 7 2 3x

19. 2y 1 4x 5 0 20. 3y 1 6 5 22x

21. y 1 2 5 5x 2 4

22. 4x 1 3y 5 2x 2 1 23. 22(3x 1 4) 1 y 5 0

See Problem 6.

ApplyB

202

2

2

y

x

0334_hsm11a1ls_0503-2.indd 336

2/24/09 5:57:50 PM

Weight on Mars

50 lb

Weight on Earth

130 lb

Problem 3

Got It?

Lesson 5-2 Direct Variation

323

3. a. Weight on the moon y varies directly with weight on Earth x. A person

who weighs 100 lb on Earth weighs 16.6 lb on the moon. What is an

equation that relates weight on Earth x and weight on the moon y? What

is the graph of this equation?

b. Reasoning What is the slope of the graph of y 5 0.38x in Problem 3?

How is the slope related to the equation?

Have you graphed

equations like

y 5 0.38x before?

Yes. In Chapter 4, you

graphed linear functions

by making a table of

values and plotting

points.

Concept Summary Graphs of Direct Variations

The graph of a direct variation equation y 5 kx is

a line with the following properties.

• Thelinepassesthrough(0, 0).

• Theslopeofthelineisk.

x

y

k 0

x

y

k 0

Graphing a Direct Variation

Space Exploration Weight on Mars y varies

directly with weight on Earth x. The weights of the

science instruments onboard the Phoenix Mars

Lander on Earth and Mars are shown.

A What is an equation that relates weight, in

pounds, on Earth x and on Mars y?

Start with the function form of a direct variation. y 5 kx

Substitute 130 for x and 50 for y. 50 5 k(130)

Divide each side by 130 to solve for k. 0.38 < k

Write an equation. Substitute 0.38 for k in y 5 kx. y 5 0.38x

The equation y 5 0.38x gives the weight y on

Mars, in pounds, of an object that weighs

x pounds on Earth.

B What is the graph of the equation in part (A)?

Make a table of values. Then draw the graph.

x y

0

50

100

150

0.38(0) 5 0

0.38(50) 5 19

0.38(100) 5 38

0.38(150) 5 57 O 100 15050

20

40

60y

x

The points form a linear

pattern. Draw a line

through them.

0321_hsm11a1ls_0502.indd 323

3/11/09 3:25:29 PMShorter Lessons and ChaptersSome lessons and chapters are divided into parts to help students who might be overwhelmed by denser content. This also allows for more frequent assessment.

Prentice Hall Algebra 1 • Practice and Problem Solving WorkbookCopyright © by Pearson Education, Inc., or its affiliates. All Rights Reserved. 215

Name Class Date

7-6 Practice Form GExponential Functions

Determine whether each table or rule represents an exponential function. Explain why or why not. 1.

2. x 1 2 3 4y 3 9 15 21

3. y 5 5 ? 2x 4. y 5 6 ? x3

5. y 5 3x 2 8 6. y 5 4 ? 0.3x

Evaluate each function for the given value. 7. f (x) 5 5x for x 5 4 8. h(t) 5 3 ? 4t for t 523 9. y 5 8 ? 0.7x for x 5 3Graph each exponential function.

10. f (x) 5 3x 11. y 5 0.25x 12. y 5 8 ? 1.2x

13. An investment of $8000 in a certain Certifi cate of Deposit (CD) doubles in value every seven years. Th e function that models the growth of this investment is f (x) 5 8000 ? 2x, where x is the number of doubling periods. If the investor does not withdraw any money from this CD, how much money will be available for withdrawal after 28 years? 14. A population of amoebas in a petri dish will triple in size every 20 minutes. At

the start of an experiment the population is 800. Th e function y 5 800 ? 3x, where x is the number of 20 minute periods, models the population growth. How many amoebas are in the petri dish after 3 hours? 15. A new car costs $15,000 to build in 2010. Th e company’s fi nancial analysts

expect costs to rise by 6% per year for the 10 years they are planning to build the car. Th e cost to build the car can be modeled by the function f (t) 5 15,000 (1.06)t , where t is the number of years after 2010. How much

will it cost the company to build the car in 2017?

x 1 2 3 4y 3 6 12 24

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VocabularyReview

Chapter 7

206

More MultiplicationProperties of Exponents

7-4

1. Circle the equation that illustrates the Commutative Property of Addition.

3 1 5 5 5 1 3 (2 1 3) 1 4 5 2 1 (3 1 4)

7 1 0 5 7

2. Circle the equation that illustrates the Commutative Property of Multiplication.

xyz 5 yxz x ? 1 5 x

a(bc) 5 (ab)c

Vocabulary Builder

simplify (verb) SIM pluh fyRelated Words: simple (adjective), simplified (adjective, verb)Main Idea: You simplify an expression to make it less complicated.Definition: To simplify an expression means to replace it with a simplified form.

Use Your Vocabulary 3. Draw a line from each expression in Column A to its simplified form in Column B.

Column A Column B x3 ? x5

x15 x6 ? x

x8 x4 ? x11

x7Complete each statement with the appropriate word from the list. Use each word only once.

simplify simplified

simplifying 4. The first step in 9 the expression 10a ? (8 2 3)a2 is to subtract

within parentheses.

5. The 9 form of the expression (17 2 14)h ? 6h5 is 18h6. 6. To 9 the expression z ? 2z3 ? 6z4 means to replace it with 12z8.


4/7/09 2:04:18 PM

In-Class Support For Plus Complete Daily Support

For Every Lesson

ISBN-13:ISBN-10:

978-0-7854-6913-10-7854-6913-3

9 7 8 0 7 8 5 4 6 9 1 3 1

9 0 0 0 0

Leveled ResourcesThe Student Companion with Practice and Problem Solving fits the unique needs of each student with daily support all in one place.

F O U N D A T I O N S S E R I E S

16 17

Engage Today’s StudentsIntroducing PowerAlgebra.com and PowerGeometry.com—the gateway for teachers and students to all digital components of the program. Teachers can enrich instruction with interactive lesson content and video that makes real-world connections, and can model thinking and reasoning using interactive tools. Students can complete lessons independently using the online content to support in-class instruction.

eText with AudioThe online Student Edition contains audio explanations of every lesson and live links to all workbook pages and video tutors. The eText is also available on the iPad.

Interactive Digital PathThe Interactive Digital Path is the ideal presentation and study tool. It contains interactive lesson openers, animated problems with audio, extra practice, self-assessments and an interactive glossary.

MathXL® for SchoolMathXL® for School includes interactive

step-by-step tutorials for problems similar to homework and chapter

assessments. Each problem regenerates to a new problem, so students have

unlimited practice and homework help. Most problems are short answer

problems that require students to actually “do the math”.

Homework Video Tutors(in English and Spanish)Teachers walk students through step-by-step explanations of every concept and sample homework exercises.

TI-Nspire™ LessonsExclusive Partnership!For every lesson, three types of TI-Nspire™ documents guide students from interactive exploration through self-assessment.

• Content Explorations• Lesson Quizzes• Standardized Test Prep

Compatible with TI Navigator System

Math ToolsMath Tools help students explore and visualize concepts.

• Online Graphing Utility• Interactive Number Line• Algebra Tiles• 2D Geometric Constructor• 3D Geometric Constructor

18

Assess Student ProgressPearson Algebra 1, Geometry, and Algebra 2 Common Core Edition features a rich array of diagnostic, formative, and summative assessment tools so that you can assess and remediate your students’ progress every step of the way. These assessments, available in print and online, support the transition to new state-wide assessments that will be aligned to the Common Core Standards.

19

Success Tracker™ diagnoses students’ readiness to learn new skills, benchmarks their progress, provides individualized remediation and enrichment, and reports on mastery of the Common Core Standards.

ASSESSMENT

Standards for Mathematical Practice Observational ProtocolEasily monitor students’ ongoing development of the mathematical practices with rubrics designed to assess proficiency of the Standards for Mathematical Practice.

All-in-One Teaching Resources• Editable Tests and Quizzes• Standardized Test Prep • Chapter Projects• Performance Tasks• Cumulative Review

Progress MonitoringThis resource ensures a clear path to adequate yearly progress through systematic testing and recommendations for remediation. A screening test, benchmark tests, quarter tests, mid-course tests, end-of-course tests, and standardized test prep are all included.

Additional Assessment Resources

The most powerful test generator available—with the most comprehensive test banks correlated to the Common Core State Standards.

• QuickTest Wizard helps you build assessments in seconds.• Test items can be translated into Spanish.• Provides support for modifying tests quickly and easily.• Import images into your assessments using the Math Art Gallery.• Test banks allow you to edit and modify existing practice

worksheets and chapter assessments.

Embedded Program Assessment

Diagnostic

• Entry-Level Assessment

• Get Ready!

• Got It?

• Lesson Check

• Lesson Quiz

• Mid-Chapter Quiz

Formative

• Pull it All Together

• Chapter Test

• Cumulative Standards Review

• End-of-Course Assessment

Summative

ASSESSMENT

20 2120 21

Exceptional Teacher SupportPearson Algebra 1, Geometry, and Algebra 2 Common Core Edition provides a wealth of teaching resources that not only makes teaching easier but also supports the transition from a curriculum, based on current state standards, to a curriculum that embraces all of the concepts and skills that make up the Common Core State Standards.

Common Core Implementation GuideAll the support you need to make the transition to a Common Core curriculum!

• Overview of Common Core Content Standards• Overview of Standards for Mathematical Practice• Common Core Content Correlations• Standards for Mathematical Practice Observational Protocol• Common Core Assessment Resources• Parent Letter

Name

ClassDate

5-4Practice

Form G

Point-Slope Form

Write an equation of the line in slope-intercept form through the given point and with the

given slope m.

1. (2, 1); m = 3

2. (–3, –5); m = –2

3. (−4, 11); m=34

4. (0, −3); 23m = −

Graph each equation.

5. y − 2 = 2(x + 3) 6. y + 3 = –2(x + 1)

7.

Write an equation in point-slope form for each line.

8. 9.

10.

Write an equation in point-slope form of the line through the given points. Then

write the equation in slope-intercept form.

11. (4, 0), (−2, 1) 12. (−3, −2), (5, 3) 13. (−5, 1), (3, 4)

14. Open-Ended Write an equation of a line that has a slope of 12

− in each form.

a. point-slope formb. slope-intercept form



33

Choose your path!All Teaching Resources are available for you in print, online, and on DVD.

ISBN-13:ISBN-10:

978-0-13-318563-80-13-318563-X

9 7 8 0 1 3 3 1 8 5 6 3 8

9 0 0 0 0

1 2 3 4 5 6 7 8 9 10 V0E4 15 14 13 12 11

Easy access to editable and printable Teacher Resources

• Worksheets• Assessments• Homework Video Tutors• Additional Vocabulary Support • Answers

Teaching Resources DVD

Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

NOT FOR RESALE

IMPORTANT! READ THIS NOTICE BEFORE OPENING. This product contains a DVD that is subject to a Terms of Use. The Terms of Use are contained on the DVD and may be printed in the instructions or other accompanying documentati on. You must read and accept the Terms of Use before using the DVD.

Minimum System RequirementsSystem requirements subject to change. For full, up-to-date system requirements, please visit support.pearsonschool.com/contactus.

support.pearsonschool.com/contactusCustomer Service 800-848-9500

TEACHING RESOURCES is a new suite of instructional tools on DVD to help teachers teach and assess at the click of a mouse. Powerful resource management makes class preparation quick and easy!Pearson has developed teaching materials that include worksheets, assessments, and other resources in electronic format and easily accessible on the Teaching Resources DVD. You can browse, open, read, and print information more easily using this electronic resource than ever before!

Teaching Resources Include:• Student Companion• Additional Vocabulary

Support*• Activities, Games, and

Puzzles*• Think About a Plan*• Teaching with TI Technology• Practice Form G*• Practice Form K*

• Quizzes and Tests Form G*• Quizzes and Tests For K*• Homework Video Tutors• Spanish Homework

Video Tutors• Progress Monitoring

Assessments• Standardized Test Prep

• Reteaching*• Enrichment*• Chapter Project• Performance Tasks• Cumulative Review• Answers*denotes editable resource

Algebra 1Common Core

Windows• Windows 98, ME, 2000, XP• DVD drive• At least 100 MB hard disk space available• 32 MB available RAM (64 MB RAM recommended)

Macintosh• Systems OSX 10.2, 10.3, and 10.4• DVD drive• At least 100 MB hard disk space available• 32 MB available RAM (64 MB RAM recommended)

Classroom Management Resources• Lesson Planner helps you create editable

lesson plans correlated to the Common Core Standards.

• Classes can be updated manually or by importing a class roster.

• Content is created and pre-loaded, and includes Common Core benchmark assessments, diagnostic assessments for each chapter, chapter tests, and lesson quizzes—or create your own!

• Reports track student and class performance by test scores, item analysis, and mastery of Common Core Standards.

Answers and Solutions CD-ROMEasy access to all textbook answers and solutions. Choose formats for printing or whiteboard display. Personalize and save answer files for all classes.

ISBN-13:ISBN-10:

978-0-13-318566-90-13-318566-4

9 7 8 0 1 3 3 1 8 5 6 6 9

9 0 0 0 0

1 2 3 4 5 6 7 8 9 10 V0E4 15 14 13 12 11

Algebra 1 • Geometry • Algebra 2Easy access to all textbook answers and solutions• Choose formats for printing or for

whiteboard display• Personalize and save answer files for

all your classes• Use at home or at school—transfer files

onto your USB drive

Answers and Solutions CD-ROM

Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

NOT FOR RESALE

IMPORTANT! READ THIS NOTICE BEFORE OPENING. This product contains a CD-ROM that is subject to a Terms of Use. The Terms of Use are contained on the CD-ROM and/or printed in the instructions or other accompanying documentation. You must read and accept the Terms of Use before using the CD-ROM.Minimum System Requirements System requirements subject to change. For full, up-to-date system requirements, please visit support.pearsonschool.com/contactus.

support.pearsonschool.com/contactusCustomer Support 800-848-9500

High School Mathematics Common Core EditionAlgebra 1 • Geometry • Algebra 2

Easy access to all textbook answers and solutions

• Solve It!• Concept Byte• Chapter Review• Got It?

• Get Ready!• Chapter Test• Lesson Check• Mid-Chapter Quiz

• Cumulative Standards Review

• Practice and Problem Solving

• Pull It All Together

Windows• Windows 2000, XP, 7• CD-ROM Drive• Hard Drive Space: 750 MB• RAM: 256 MB

Macintosh• Mac OS 10.2, 10.3 or 10.4• CD-ROM Drive• Hard Drive Space: 750 MB• RAM: 256 MB

Other Requirements• Display size (in pixels):

1024 x 768• Macromedia Flash

High School

MathematicsCommon Core

Self-paced video tutorials and webinars help educators identify all program

components and begin integrating the material into their classroom.

Editable Word

Documents!

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Cross-Out

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Callout

Suggested Revision: Pearson Algebra 1, Geometry, and Algebra 2 Common Core Edition provides a wealth of teaching resources that make teaching easier and support the transition from a state standards-based curriculum to one that embraces all the concepts and skills that comprise the Common Core State Standards.

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Proven EffectiveBuilt around the Common Core State Standards, Pearson Algebra 1, Geometry, and Algebra 2 Common Core Edition is based on critical foundational research and proven classroom results.

Prentice Hall Algebra 1 students demonstrated greater improvement on the Algebra 1 multiple-choice and open-response tests as compared to students using other Algebra 1 programs. Study data from research in five states confirmed that these students improved their assessment scores by 38 percentile points on both a multiple-choice test and an open-response test.

Prentice Hall Algebra 1, Geometry, and Algebra 2 students of all ability levels showed significant growth on the open-response test. In addition, Prentice Hall math students in all subgroups—females and males, special education students and non-special education, students of various ethnic/racial backgrounds, and students receiving free/reduced lunch and those not—showed significant learning gains, according to study data.

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Assessment PeriodPre Post

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High

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Algebra 1 Multiple-Choice

Pre Post Pre Post

Algebra 1 Open Response

Pearson

Control

41.8

37.4

27.6

29.5

36.5

29.8

19.319.6

“the technology helps to

enhance what I am learning.

When I look at the technology I am able to

really understand the material I am being taught.”

—Rhode Island Student

{“I really liked the opening Solve It; I thought they were really great at getting the kids thinking and bringing out divergent answers.”

– Idaho Teacher}Behind the Research

“I think it [Prentice Hall Algebra 1, Geometry, Algebra 2] has enough material to be

challenging to students of all levels and meet them where they are.” —Ohio Teacher

“I wasn’t sure I would like this program [Prentice Hall Algebra 1, Geometry, Algebra 2] at the beginning of the year, but I love it now and can’t imagine teaching without it!” —New Jersey Teacher

“I like the Pearson High School Math program

better than other programs, because it

is easier to understand;

it’s also more interesting.” —Washington Student

}“I’m glad that you have

made this program for Algebra I, because

now I have a better understanding of what I’m working on. rather

than just doing work out of the textbook all the time, I can have fun with math finally!”

—New Jersey Student

{PRES Associates conducted the randomized control trial study during the 2009–2010 school year, studying 1069 students

in grades 8-12 and 32 math teachers. The full report of first-year results can be accessed at www.pearsoned.com.

Program Components

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PearsonSchool.com800-848-9500International customers: visitPearsonGlobalSchools.com

Copyright Pearson Education, Inc., or its affiliates. All rights reserved.

ADV: 978-0-328-69382-5SAM: 978-0-1332-0678-4

Common Core Student Edition• Standardsdocumentedonthepage• Mathematicalpracticesinfusedthroughout

eachlesson• UnderstandingbyDesignFramework• Visuallearningstrategies• Interactivelessonopeners• “Think”and“Plan”Call-outsmodeleffective

problemsolving• Balanceofskillandhigherorderthinking• CumulativeTestPrepaftereverychapter

Common Core Teacher’s Edition• MathematicalBackgroundprovidedatthe

chapterandlessonlevel• Scaffoldingquestionsthroughouteverylesson

engagestudentsinhigherorderthinking• Alternativeteachingstrategiesforalllearners• Data–drivendifferentiatedremediationafter

everylesson• Answersatpointofuseonthesamepage

Common CoreImplementation Guide• OverviewofCommonCoreContentStandards• OverviewofStandardsforMathematicalPractice• CommonCoreContentCorrelations• CommonCoreAssessmentResources• StandardsforMathematicalPracticeObservationalTool• ParentLetter

Common Core Editable Teaching Resources available in print, online, and on DVD

• StudentCompanion• ThinkAboutaPlan• PracticeFormGandK• StandardizedTestPrep• SolveIt• LessonQuiz• FindtheErrors• AdditionalProblems• Reteaching• AdditionalVocabularySupport• Activities,Games,andPuzzles• Enrichment• TeachingwithTITechnology• ChapterQuizFormGandK• ChapterTestFormGandK• FindtheErrors!• PerformanceTasks• ChapterProject• CumulativeReview• SpanishResources• AnswerKeys

Common Core Progress Monitoring Assessments • Availableinprint,online,andonDVD• Diagnostic,Formative,andSummative• BenchmarkTests• SATandACTTestPrep• Quarter,Mid-Course,andFinalTests• StandardsReports

Common Core Practice and Problem Solving Workbook (Three-In-One)

• Availableinprintandonlineforstudentuse• Containstwopagesofpractice,onepageoftestprep,

andonepageofproblemsolvingforeverylesson

Common Core Student Companion • Availableinprintandonlineforstudentuse• Fourpagesofsupportforeverylesson

Online Common Core eText• TeacherEdition• StudentEditionwithaudioandlinkedresources• eTextavailableontheiPad

Common Core Interactive Digital Path• MathVideosforeverychapter• SolveItlessonopenerwithdynamic

step-by-stepsolutions• DynamicActivities—digitalconceptexplorations• Animatedproblemswithstep-by-stepsolutions

andaudioexplanations• VocabularywithaudioinEnglishandSpanish• SelfCheckQuizzes• MathTools—OnlineGraphingUtility,Interactive

NumberLine,AlgebraTiles,2DGeometricConstructor,3DGeometricConstructor

• MathXL®forSchool—unlimitedpracticeandremediationwithtutoringandguidedassistanceforeveryconcept

• MultilingualGlossary

Common Core TI-Nspire™ Lesson Support CD-ROM• TI-Nspiredocumentsforeverylesson• Conceptexplorations,testprep,andquizzes

InteractMath.com—unlimited homework help with step-by-step tutorials

Homework Video Tutors in English and Spanish

ExamView® Assessment Suite with Common Core Standards

Success Tracker™ Online Intervention, with Common Core Tests and Standards

• Diagnosesstudentsuccess,prescribesautomaticremediation,andreportsonstudentandclassprogress

• DiagnosticTests,BenchmarkTests,ChapterTests,LessonQuizzes,Mid-ChapterQuizzes

Online Lesson Planner, with Common Core Standards• Pre-madeplansforeverylesson• Completelyeditablelessonplans

Common Core Answers and Solutions CD-ROM• Easilydisplayallthetextbook

answersandsolutions• Chooseformatsforprintingor

forwhiteboarddisplay

To learn more about our Common Core Edition visit PearsonSchool.com/HSMath2012