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Contents

Algebra: Linear Systems, Matrices, and Vertex-Edge GraphsQuiz for Lessons 1.1-1.6

Performance Taskfor Lessons 1.1-1.6

Performance Task for Lessons 1.1-1.6Quiz for Lessons 1.7-1.12

Performance Task for Lessons 1.7-1.12


Unit Test for Algebra: Linear Systems, Matrices,andVertex-Edge GraphsBenchmark Test for Algebra: Linear Systems, Matrices,and Vertex-Edge Graphs

Performance Task for Algebra: Linear Systems, Matrices,and Vertex-Edge Graphs

1

2

3

4

5

6

7-8

9-10

11

Algebra: Polynomial FunctionsQuiz for Lessons 2.1-2.4



Quiz for Lessons 2.5-2.8

PerformanceTask for Lessons 2.5-2.8


Unit Test for Algebra: Polynomial FunctionsBenchmark Test for Algebra: Polynomial FunctionsPerformance Task for Algebra: Polynomial Functions

Algebra: Rational Exponents and Square Root FunctionsQuiz for Lessons 3.1-3.2




PerformanceTask for Lessons 3.3-3.4


Unit Test for Algebra: Rational Exponents andSquare Root Functions

Benchmark Test for Algebra: Rational Exponents andSquare Root Functions

Performance Task for Algebra: Rational Exponents andSquare Root Functions

12

13

14

15

16

18-19

20-21

22

23

24

25

26

27

28

29-30

31-32

33

lii

BV

Algebra: Exponential and Logarithmic FunctionsQuiz for Lessons 4.1-4.5


Performance Task forLessons 4.1-4.5Quiz for Lessons 4.6-4.9



Unit Test for Algebra: Exponential and Logarithmic FunctionsBenchmark Test for Algebra: Exponential andLogarithmic Functions

Performance Task for Algebra: Exponential andLogarithmicFunctions

Geometry







UnitTest for GeometryBenchmark Test for GeometryPerformance Task for Geometry

Data Analysis and ProbabilityQuiz for Lessons 6.1-6.3






Unit Test for Data Analysis and ProbabilityBenchmark Test for Data Analysis and ProbabilityPerformance Task for Data Analysis and Probability

Assessment Book Answers

34

35

36

37

38

39

40-41

42-43

44

45

46

47

48

49

50

51-52

53-54

55

56

57

58

59

60

61

62-63

64-65

66

A1-A1S

4-s

w

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ft.

i

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•

•

Name Date

Quiz for Lessons 11-16

1. You buy 15 articles of clothing at a local clothing store. Each shirtcosts $3.00 and each pair of pants costs$10.00. The totalcost is$94. How many shirts and pairs of pants did you buy?

Graph the linear system and estimate the solution.

2. 3x+y = 9

x - 2y = 10

j •'1-

! i i

•2

_i-

i1

-

• ™„

_. .....

2_..

-

X

j

3. Ax - 3y = 12 L_

2x + 3y = 18 -

n:

Solve the system. Then classify the system as consistent andindependent, consistent and dependent, or Inconsistent.

4. 3x -5y = 9

6x- 10y= 18

5. 4x-y= 12

y = -8 + 4x

i

£

Solve the system using the substitution method.

6. 3x - 1\y = 16 7. 6x - 12^ = 16

x+y = 3 3*-6y=8

Solve the system using the elimination method.

8. 7jc - 2y= 15 9. 3x + ly= 11

7x + 2y= 13 2x - 3^= -8

Tell whether the given ordered pair is a solution ofthe inequality.

10. y>-2x + 11;(5,1)

Graph the system of inequalities.

12. y<3

x+y>-4 L. L

———ZZZZ~*

—!—I.. I.. J—1—I

11. y<\x +9;(S,3)

13. x-2y<6

x + 5y2l0

" i: j *

14. Find the minimum and maximum values ofthe objective functionC= 3x + 5y subject to the following constraints: x £ 0, y > 0,-3* + 2y< 14,and 5x + y £ 20.

Answers

1.

2. See left.

3. See left.

4.

5.

6.

7.

8.

9.

10.

11.

12. See left.

13. See left.

14.

Copyright © McDougal Lrttell/Houghton Mifflin Company Georgia Assessment Book,Mathematics 3

Name Date

Performance Task for Lessons 11 -16

Wh Georfi'a®m Performance

Standard(s)

MM3P3a,MM3A6a,MM3A6b

A company manufactures two types of cellular phone cases. Case Iyields a profit of $7 per unit, and Case II yields a profit of $10 per unit.The combined production for the cases should not exceed 2700 unitsper month. The demand for Case II is no more than half the demand forCase I and the production level of Case I is less than or equal to 900units plus five times the production level of Case II.

In the following exercises, let x represent the number of unitsof Case I and let y represent the number of units of Case II.

a. Write an objective function that represents the total profit P.

b. Write a system of linear inequalities that represents this situation.

c. Graph the system from part (b).

d. Find the coordinates of the vertices of the feasible region.

e. Evaluate the profit function at each vertex of the feasible region.

f. How much of each type of case should the company produce tomaximize its monthly profit?

g. Does your answer to part (f) change if Case I yields a profit of$10 per unit and Case H yields a profit of $7 per unit? Explain.

Georgia Assessment Book, Mathematics 3 Copyright © McDougal Littell/Houghton Mifflin Company.

•

NameDate

Performance Task for LesSOtIS 11 -16

GeorgiaPerformance

Standard(s)

MM3Pld,MM3P3a,MM3A5c

You and your friend each belong to amusic club. You pay $9.50 per yearto your music club where you can download songs for $.80 per song. Yourfriend pays $4.90 per year to her music club where she can download songsfor $.85 per song.

a. So far this year, you have spent $58.30 while your friend has spent$45.70. Copy and complete the table below. Use the table to estimatehow many songs you and your friend have downloaded so far this year.

b. Write an equation that represents your annual cost y. Let x represent thenumber ofsongs you have downloaded. Then use the equation to findthe number ofsongs you have downloaded sofar this year.

c. Write an equation that represents your friend's annual cost. Then usethe equation to find the number ofsongs she has downloaded so farthis year.

d. Are your estimates from part (a) compatible with the exact answers youfound in parts (b) and (c)? Explain.

e. Graph the system ofequations that represents the amounts you and yourfriend pay annually. Classify the system as consistent and independent,consistent anddependent, or inconsistent.

f. Solve the system in part (e) algebraically. What does the solutionrepresent?

g. Anew music club charges $3.50 per year and $.95 per song. Write anequation that represents the annual cost ofjoining the new club.

h. Graph the system of equations that represents the amount you payannually and the annual cost ofjoining the new club. After how manydownloaded songs will the total costs ofyour music club and the newmusic club be the same? What is the total cost?

i. Graph the system ofequations that represents the amount your friendpays annually and the annual cost ofjoining the new club. After howmany downloaded songs will the total costs ofyour friend's music cluband the new music club be the same? What is the total cost?

j. Explain why itmight be difficult to solve the systems ofequations inparts (h) and (i) by graphing.

k. Suppose one ofyour friends is thinking ofjoining a music club. Yourfriend mentions that he plans ondownloading several hundred songsper year. Whose club would you recommend he joins? Explain yourreasoning.

Copyright © McDougal Uttell/Houghton Mifflin Company Georgia Assessment Book, Mathematics 3

Name Date

Quiz for Lessons 17-112

Solve the system using any algebraic method.

1. 2x - 3y + z = 10

3x - Sy + 2z = 11

-x + 5y + 3z = 15

2. 3* - 7/ + 4z = 11

jc + _y-z = 4

2x- 6y + z=l5

Use matrices 4, B, and C to evaluate the matrix expression,if possible. If not possible, state the reason.

A =5 -7~

B ="-3 11"

C =

" 1 6"

2 9

-3 9. .-4 2. _-4 5_

3. B + A 4. C + /1 5. 2A -B 6. |c

Using the given matrices, evaluate the expression.

A ="2 -5"

5 ="4 -f

C ="-9 -2"

.7 2_ . 1 -3. .5 0.

7. 3,45 8. A(B + C) 9. (/I - 5)C

Evaluate the determinant of the matrix.

10.3 -9"

11.

0

-2

1

-4

-7

2 12.

1

1

-2 3

4 1

4 2J . 3 5 1. . 2 5 2

Use an Inverse matrix to solve the linear system.

13. 3x + 5y = -7 14. -2.x + Sy = 11

x —3.y = 7 3x - 4y = 15

15. You have $33 to spend on 24 balloons. Birthday balloons cost$1.50 each, congratulation balloons cost $1.00 each, and get wellballoons cost $2.00 each. You want twice as many birthday balloonsas the other two types combined. Write and solve a system ofequations to find how many ofeach type you should buy.

16. A set of bridges connect five islands:Akini, Beli, Caya, Dali, and Elise.There are bridges connecting Akiniand Beli, Beli and Dali, Beli and Elise,Caya and Dali, and Dali and Elise.Draw a vertex-edge graph to representthis situation.

Answers

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

13.

14.

15. _:

lg. See left.

Georgia Assessment Book, Mathematics 3 Copyright © McDougal Littell/Houghton Mifflin Company.

™

•

NameDate

Performance Task for Lessons 17-112

M, GeorgiaWMff Performance

Standard(s)

MM3A4a,

MM3A5a,

MM3A5b,MM3A5c

Acompany manufactures three types ofhome theater systems: a 300-wattsystem, an 800-watt system, and a 1000-watt system. The systems areshipped to two warehouses. The numbers ofunits shipped to each warehousethis month and last month are given in matrices shown below.

This month (A) Last month (B)

300W 800W 1000W

3500 7850 7220

300W 800W 1000W

3670 7350 7490

3190 8050 7160

Warehouse 1

Warehouse 2 2980 8310 7450

a.

b.

c.

d.

e.

f.

Write a matrix M that gives the total number of each type ofhome theater system shipped to the each of two warehouses forthe two months.

Write a matrix N thatgives thedifference of thenumber of unitsshipped this month andthe number of units shipped last month.How many more 1000-watt systems were shipped to Warehouse 2this month compared to last month?

Howwould you determine the average number of units shippedto each warehouse for the two months? Write the matrix that

represents the average number of units shipped.

The prices of the hometheatersystems are given in matrix C.

Matrix C

Price

'$149.99300-watt

800-watt

1000-watt

$249.99

$399.99

Use your result from part (a) and a graphingcalculator to writea matrix that gives the total value of the home theater systemsshipped to each warehouse for the two months.

In one month, an electronics store sells 77 home theater systemsfor a total of $22,549.23. There were twice as many 800-wattsystems sold than 300-watt systems. Writea system of equationsto represent this situation.

Rewrite the system you wrote in part (e) as a matrixequation.

Use a graphingcalculatorto solve the equation in part (f).What does the.solution represent?

6 Georgia Assessment Book, Mathematics 3 Copyright© McDougal Littell/HougMon Mifflin Company.

Name Date

^ unit Test for Algebra: Linear SystemsMatrices, and Vertex-Edge Graphs

•

1. You travel onthe highway ata speed of60 miles perhour for2.5 hours. How far did you travel?

2. Aferry connects an island to the mainland. The island is 47 milesaway from the mainland. Aone-way trip to the island on the ferrytakes 2.5 hours. What is theaverage speed of the ferry?

3. Solve the system by graphing. Then classifythe system asconsistent and independent,consistent and dependent, or inconsistent.

y = -x + 1

y = x —1

y

l X

—

Solve the system usingany algebraic method.

4. x + 2y = 5 5. 5x-2y=-l-2x + 3y = -3 -3x + 2v= 5

6. 0.1x-0.1;> = 2 7. -2x - 3y = 7

0.7^ + 0.7^ = 7 4x'+y=l

Graph the inequality.

8. y>-\, y

—

• i X

9. y<2x-3

y

i X

'

Graph the system of inequalities.

10. x-2y<>-2 11. y>2\x+ l|-22x-4v>2 y<-\x+l\-\

, y

—

X

y

— — -——

-1

X

•

Answers

1.

3. See left.

4.

5.

6.

7.

g# See left.

9. See left.

10. See left.

11. See left.

Copyright© McDougal Littell/Houghton Mifflin Company Georgia Assessment Book, Mathematics 3

Name Date

unit Test for Algebra: Linear Systems,Matrices, and Vertex-Edge Graphs com12. Find the minimum and maximum values of the objective function

C - 4x + ly subject to the following constraints: x >. 2,y > 3,and

\x +y<9.13. Solve the system using

any algebraic method.Ax + 2y - z = 4

2x - 3y + 2z = 4

x + y- z= -1

Perform the indicated operation, if possible. If not possible,state the reason. .

"• [l 3 -5] +[! l] "• 2[_3 0 -4]16. Solve the matrix equation for x and y.

(: :H"Ht -i\Find the product. If it is not defined, state the reason.

17.

-1

3

-4

[1 0 -2] 18.

Evaluate the determinant of the matrix.

1 0

-1 -2

3 5 .[-

1 3

5 -1

4 2

-4

-6

-8

19.

21.

2 41-1 -2J

20.

An ant and its cargo weigh 76 milligrams. The cargo is 18 timesheavier than the ant. Use a linear system and Cramer's rule to findthe weight of the ant and the weight of its cargo.

22. On a recent vacation, your uncle spent a total of $680 on airfare,a hotel room, and a rental car. The airfare was twice as much asthe hotel room, and the rental car was one-third as much as thehotel room. Use a linear system and Cramer's rule to find howmuch your uncle paid for each service.

Use an inverse matrix to solve the linear system.

23. 2x - y = 5 24. 2x + 3y = 12

-x + 2y = -1 3x - 2y = 5

25. A ferry system has routes between ports A and B, B and C, B andD, C and D, and A and D. Write a matrix M that represents thevertex-edge graph ofthis situation. Then calculate M2 tofind thenumber of two-route trips there are from port B to port D.

Answers

12.

13.

14.

15.

16.

17.

18.

19.

20.

21.

22.

23.

24.

25.

8 Georgia Assessment Book, Mathematics 3 Copyright © McDougal Littetl/Houghton Mifflin Company.

TT'.

•

Name Date

Benchmark Test for Algebra: Linear SystemsMatrices, and Vertex-Edge Graphs1. Which equation is represented bythe table? MM3P3a

(K) y = 2x + 9 (§) y = 3x + 5(D y = 5x - 3 (§) y = 9x + 2

2. The graph of the linear system shows the profits,in thousands of dollars, of two companies. Howcanyou classify thesystem? MM3A5c

(g) consistent and independent

(D consistent anddependent

CD inconsistent

CD inconsistent andindependent

3. You have $123.50 in quarters and dimes. There are 1202 coins altogether.Which system ofequations can you use to find the number ofeach type'ofcoin you have? MM3A5c

(g> x+y=l2Q2 CD x+y= 123.5O.Ijc + 0.25y = 123.5 O.tx + 0.25y = 1202

(g)x+y=l202 • (§) x+y =12020.1* + 0.25v = 12,350 \0x + 25y = 123.5

4. Which inequality is represented by the graph? MM3A6aCg) j/>-2|jc+l|-4 CD j><-2|x-l|-4<g) j»-2|;c+l| +4 (§).y<-2\x+l\ +4

0 1 2 3

i 2 11 20 29

5. Which system ofinequalities is represented by the graph?MM3A6a

(£) x+y<3 CD x+y>3-4x + 2y > 1 -4x + 2y £ 1

CD x + y>3 CD *+>^3

-4x + 2y>l -4x + 2y£l

6. Your debate team plans to raise money by selling two sizes offruit baskets.Your team plans to buy small baskets for $20 and sell them for $25 andbuy large baskets for $30 and sell them for $40. It is estimated that yourteam will not sell more than 100baskets and can spend up to $2400 forbaskets. How many small baskets and large baskets should your team buyto maximize profit? MM3A6b

(5) 60; 40 CD 50; 40 CD 0; 80 CD 100; 0

\ y hikSji'l y^*;

\ s'*

i ^ s*

/ 1 sJ

f

/tf

Answers

1.

2.

3.

4.

5.

6.

Copyright © McDougal Uttell/Houghton Mifflin Company Georgia Assessment Book, Mathematics 3 9

Name Date

Benchmark Test for Algebra: Linear Systems, ^Matrices, and Vertex-Edge Graphs continued

7. A school has 950 students, which includessophomores, juniors, and seniors.Twice the sophomore enrollment is three times the seniorenrollment. The totalnumberof juniors and seniors is 200 more than the numberof sophomores.How many seniors are enrolled? MM3A5c

CD 250 seniors CD 325 seniors CD 375 seniors CD 400 seniors

8. What is the sum

2 114 3J

|~ 19 32lL32 43 J

9. What is the product

<S>7

12CD

-9

1

-4

11 ]•<D [

? MM3A4a

1

5

2

3

4

3

-1

13

? MM3A4a

[~25 30"1[_32 11J

-ills :t\ ">

CD

CD

[1 -;]

25 14 10

59 26 17

32 16 11

10. What is the solution of l 4 \x= ? MM3A5b

<S>3

-4 -23J CD

• 43

15

52"

15

4

. 51

CDI" -43 52]L-12 15 J

11. Brenda (B), Carrie (C), Elena (£), Patty (/>), and Susan (S) play in a golftournament. Patty and Carrie have each playedeveryone exceptBrenda.Elena has playedeveryone except Susan. Susanhas not played Brenda.Which vertex-edge graph represents this situation? MM3A7a

<s> B CD > © =A ml> »s

: *^zk e^X £^iB. CD B>

12. Which expression can be used to find the value ofx in the solution of thelinear system below? MM3A5c

5x-ly = 2

Ax - 3y = 12

CD

5 -7

4 -3

13 CD

5 2

4 12

13 CD

2 -7

12 -3

13 CD

5 -7

4 -3

13

Answers

7.

8.

9.

10.

11.

12.

10 Georgia Assessment Book, Mathematics 3 Copyright © McDougal Uttell/Houghton Mifflin Company.

•

m!<*-:--

Pfts

IJK.5

sfr

ML

Name Date

performance Task for Algebra: Linear Systems,Matrices, and Vertex-Edge Graphs§?&>, Georgia

Performance

Standard(s)

MM3Pld,MM3P3a,MM3A4a,MM3A4b,MM3A5a,MM3A5b,MM3ASC

Youand four friends, Ken, Sara, Lily, and Alan, participate in yourschool's community service project. You each volunteer a total of40 hours over the course of the school year. The volunteer hours includeserving at a soup kitchen, picking up trash at local parks, and collectingtoys for needy children.

In the following exercises, let s represent the number of hours servingat a soup kitchen, let p represent the number of hours picking uptrash, and let c represent the number of hours collecting toys.

a. You spend4 times as many hours collecting toys as pickinguptrash, and you spend 2 hours less serving at a soup kitchenas picking up trash. Write a system of equations to representthis situation.

b. Solve the system from part (a)using the substitution method.How many hours did you spend doing each volunteer service?

c.

d.

e.

Ken spends 3 times as many hours picking up trash as collectingtoys. He spends as many hours serving at a soup kitchen aspicking up trash and collecting toys combined. Write a systemof equations to represent this situation.

Solve the system from part (c)using the elimination method.How many hours did Ken spend doing each volunteer service?

The number of hours Saraspends serving at a soup kitchen is4 less than the numberof hours she spendspicking up trash andcollecting toys combined. The number of hours she spends pickingup trash is one more than twice the number ofhours she spendscollecting toys. Write a system ofequations to represent thissituation.

f. Solve the system from part (e) using Cramer's rule. How manyhours did Saraspend doing each volunteer service?

The numberof hours Lilyspends collecting toys is Five less thanthenumber of hours she spends serving at a soup kitchen. Thenumber of hours shespends picking up trash is eight more thanthenumber of hours shespends collecting toys. Write a system ofequations to represent this situation.

Write thesystem from part(g)as a matrix equation. Then use agraphing calculator to solve the equation to determine how manyhours Lily spent doing each volunteer service.

The number of hoursAlan spends collecting toys is two less thantwice the number of Hours he spends pickingup trash.The numberof hours he spends serving at a soup kitchen is one less than onehalf the number of hours he spends collecting toys. Write a systemof equations to represent this situation.

Solve the system from part(i) using any methods you havelearned.Which method did you choose?Explain your reasoning.

Copyright ©McDougal Litteii/Houghton Mifflin Company Georgia Assessment Book, Mathematics 3

g-

h.

J.

11

Name

Quiz for Lessons 2.1 -2.4

Graph the polynomial function.

1. /(*) = x3 - 5x + 1

y

2

4— —. — — I •— —*

__ __ | 2 | <

•

2. f(x) = -3.x3 - 2x + 4

y

1 X

Date

Explain how the graphs of f and g are related.

3. /(*) =x\ g{x) = (x - 5)3 4. /(*) = jc4, g(x) =x4 + 3

Factor the polynomial completely.

5. 3x3-81 6. 3*3 + 6x2 + x + 2

7. 4*7-64x3 8. 5x2-20;c-25

9. A wastebasket has the shape ofa rectangular prism. Itsdimensions(in inches) are: length (x - 4), width (jc - 6), and height 2x.If the volume of the wastebasket is 480 cubic inches, find thedimensions of the wastebasket.

Solve the inequality using any method.

10. *3-3x2-4;c>0 11. jc4-5*2 + 4<0

Answers

1. See left.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

See left.

12 Georgia Assessment Book, Mathematics 3 Copyright © McDougal Littell/Houghton Mifflin Company.

*

#

>$'&••''•••'• •• •,-•••. H

;•••.(!'•'' .- ' • r

ii^f" .

&¥$••••*#%'-• VH 'iV-• ,V• !£?•••.•

•: &];&•••• •

Name Date

Performance Task for 2.1-2.

GeorgiaPerformance

Standard(s)

MM3Ald,MM3A3b,

MM3A3c,MM3A3d

From 1990 to 2006, the profit P (in thousands of dollars) ofa localrestaurant chain can be modeled by

P(t) = 2r3 - 2t2 - Atwhere t is the number of years since 1990.

a. Classify the function by degree and type.

b. Evaluate the polynomial function for t = 1. Interpret your answerin the context of the situation.

c. Use the model to predict the profit in the year2010. Is itappropriate to use the model to make this prediction? Explain.

d. Determine when the profit was $0.

e. Describe the end behavior of the graph of the function.

f. Graph the function on the domain0 < t < 16.

g. For what years was the profit greater than $500,000?


Name Date


w!f.'.'.'

GeorgiaPerformance

Standard(s)

MM3Ala,MM3A3b,

MM3A3c,

MM3A3d

Youare making a three-layer mini-cake for your school's bake salesimilar to the one shown in the figure. The dimensions of the middlelayer are to be 1 inch less than the dimensions of the bottom layer.The dimensions of the top layer are to be 2 inches less than thedimensions of the bottom layer.

a. Write a function that represents the volume Vt(x) of thebottom layer.

b. Write a function that represents the volume V2(x) of themiddle layer.

c. Write a function that represents the volume V^x) ofthe top layer.d. What is the total volume of the cake when x = 6 inches?

Graph Vv Vv and Vy

Explain how the graphs of Vx and V2 differ.

Explain how the graphs of Vx and K, differ.

If the volume of the middle layer is 8 cubic inches, what are thedimensions of each layer of the mini-cake?

i. For what values of* is thevolume of thetop layer greater than orequal to 64 cubic inches?

j. If the total volume of the mini-cake is 36 cubic inches, whatarethe dimensionsofeach layerof the mini-cake?

e.

f.

g.

h.

14 Georgia Assessment Book, Mathematics 3 Copyright © McDougal littell/Houghton Mifflin Company.

#

#

#

I \0i.••';*:,

•

'm\

Name Date


Divide using polynomial long division or synthetic division.

1. (x4 + 10x3 + Sx2 - 59* + 40) * (x2 + 3x - 5)2. (2x3 - 25** + S3x - 88) -5- (x - 8)

Find all real zeros of the function.

3. f(x) = x3 - 3x2 - x + 34. /(*) = x3 - 6x2 + 4* - 24

Find all zeros of the polynomial function.

5. g(x) = x3-2x2-x + 26. h{x) = 2xA - 3*3 - 27x2 + 62* - 24

Write a polynomial function f of least degree that has rationalcoefficients, a leading coefficient of 1, and the given zeros/

9. -3, \/2, -V27. -2,5,3 8. 2,i, -i

Graph the function.

10. fix) = (jc - 5)(x + 5Xx - 1)

y

20

; X

•

11. /(*) = x(x - 1)(jc + 2)(* - 3)

. >

-5

X

•

12. You have 432 cubic inches of concrete to make a rectangular prismfor a small bench. You want the width and the height to be 6 inchesless than the length. What should be the dimensions of the bench?

Answers

1.

2.

3.

4.

5.

6.

7.

8.

9.

10. See left.

11. See left.

12.

Copyright® McDougal Littell/Houghton Mifflin Company Georgia Assessment Book, Mathematics 3 15

Name Date


gamm

Georgia^ Performance

Standard(s)

MM3A3a,MM3A3d

You are designing a cylindrical, plastic glasswith an outside layer of waterthat, when frozen,keeps the contents of the glass cold. The outerheight of the glass shouldbe four times its outerradius, and the thickness of the sides and bottomof theglass should be 1 centimeter. Theglass isto hold 1407T cubic centimeters of liquid.

1 cm

cm

r-xH

a. Write a function Vx(x) for the volume ofliquid the glass can hold.Substitute 1407T for Vx{x) and rewrite the resulting equation instandard form.

b. Use the Rational Root Theorem to list the rational possibilitiesfor the outer radius. Use a graphingcalculatorto determinewhichrational possibilities for the outer radius are reasonable.

c. Use the zero (or root) feature ofa graphing calculator and theequation from part (b) to approximate the outer radius of the glassto the nearest whole number.

d. The thickness of the glass (1 cm) includes the thickness of theplastic andthe space for thewater. Write a function V2(x) for thevolume of the sides and bottom of the glass. Use your answer frompart (d) to approximate this volume to the nearest whole number.

e. If the thickness of the plastic is 0.25 centimeter, approximate the .volume of water that can be enclosed in the outside layer of theglass. Explain your answer.


;„?•

i$ ;V,i;\ •

Name Date


^s Georgia3$?^ Performance'*"* Standard(s)

MM3Ald,MM3A3a,MM3A3d

A rectangular package to be sent by a shipping company can havea combined length and girth of 120 inches. Girth is defined as theperimeter of a cross section.

a.

b.

e.

f.

g-

h.

i.

i.

k.

I.

Write an expression for the lengthy of the package.

Write a function that represents the volume Vof the packagein terms ofx.

When x = 5 inches, the volume of the package is 2500cubicinches. What other value ofx gives the same volume?

Suppose thevolume of the package is 116 cubic inches. Write apolynomial equation thatcanbe used to find the value ofx.

List the possible whole number solutions of the equation frompart (d).

Use synthetic division to determine which of the possible solutionsfrom part (e) is anactual solution. What are the dimensions of thepackage?

Approximate the value ofx when the volume of the package is1000 cubic inches.

Find values of x such that V= 13,500cubic inches. Which ofthese values is a physical impossibility in the construction of thepackage? Explain your reasoning.

Graph the function from part (b) using a graphing calculator.

Identify any turning points onthe domain 0 <x < 30. What real-lifemeaning do these points have?

What is the range of the function?

Suppose the shipping company changed its regulations and nowa rectangular package can have a combined length and girth of108 inches. How do your answers from parts (j) and (k) change?

Copyright © McDougal Littell/Houghton Mifflin Company Georgia Assessment Book, Mathematics 3 17

Name Date

unit Test for Algebra: PolynomialFunctions1. Use direct substitution to evaluate -2x3 + 2x2 + 6x - 4 for

x= -1.

2. Use synthetic substitution to evaluate 2x4 - 4x2 + x - 20 forx = 2.

3. Graph/(x) = 4x3 - 4x - 2.

4. Graphg(x) = (x + 4)3-2.Compare the graph with thegraph of/(x) = x3.

y

i X

y

- X

Factor the polynomial completely.

5. ±x4-4

6. y3 + 6y2 - 3y - 18

7. A shipping box is shapedlike a rectangular prism. It has a volumeof 96 cubic inches. The height is two inches less than the widthand the length is eight inches greater than the width. What are thedimensions of the box?

Solve the inequality using any method.

8. x* + lx2 + 6x < 0 9. x4 - 9 > 0

Divide using polynomial long division or synthetic division.

10. (x3 - 13* - 12) -f (x - 4)11. (x3 + 6x2 -9x- 54) + (x - 3)

12. Find the zeros of/(x) = x3 + 5*2 - 18x - 72 given that onezero is 4.

Answers

1.

2.

3. See left.

4. See left.

5.

6.

7.

8.

9.

10.

11.

12.


•

#

^-J":

m

•Mk

m

Name Date

unit Test for Algebra: PolynomialFunctions continued

13. The profitP (in millions of dollars) of a company thatproduceselectric scooters can be modeled by P = -jc3 + 7x where x isthenumber of scooters produced (in millions). Currently, the companyproduces 2 million scooters and makes a profit of$6,000,000.What lesser number of scooters could the company produce andstill yield the same profit?

14. List the possible rational zeros of/(x) = 2x3 + 4x2 - 6x - 6using the Rational RootTheorem.

15. Find all real zeros of/(x) = x3 + 4x2 - 5x - 20.16. Write a polynomial function/of least degree that has rational

coefficients, a leading coefficient of 1,and the zeros 2, -3,and -3j.

17. Determine the possible numbers ofpositive real zeros, negative realzeros, and imaginary zeros for/(x) = x5 - .t4 + 3x3 - 2x - 4x + 5.

Graph the function.

18. /(x) = x(x + l)(x - 2)

. y_

1

4— _ _— — I •— ^*I x

19. f{x) = -(x + IX* " 2)2

y

X

•

Find all the real zeros of the function. Then determine themultiplicity of each zero and the exact number of turning points ofthe graph.

20. g(x) = (x + 3)2(x - 5) 21. f(x) =x2(x + l)3

22. Use agraphing calculator to graph/(x) = (x2 - l)(x - 5).Identify the x-intercepts and the points where the local maximumsor local minimums occur.

23. Agift box has length (16 - 2x) inches, width (12 - 2x) inches,and height x inches. What is the maximum volume ofthe box?

Answers

13.

14.

15.

16.

17.

18.

19.

20.

21.

22.

23.

See left.

See left.

Copyright © McDougal Littell/Houghton Mifflin Company Georgia Assessment Book, Mathematics 3 19

Name Date

Benchmark Test for Algebra: PolynomialFunctions1. The graph of a polynomial function is shown. Which

statement about the function is true? MM3Alb

(R) Thedegree of thefunction is odd.

CD Thedegree of the function iseven.

CD The leading coefficient of the function ispositive.

CD f(x) -»+ooasx->+oo.

2. If the graph of/(x) = 2x4 is shifted left 4 units, what is the equation ofthetranslated graph? MM3Ala

Cg) Sto = 2x4 + 4 (g> g(x) = 2x4 - 4CD g(x) = 2(x + 4)4 Cg) g(x) = 2(x - 4)4

3. What is the degree of the function h(f) = St2 + 5 - 3/3? MM3Alb

Cg) i CD 2

Cg) 3 (g) 4

4. Which numberis a solution of 9x3 + 15x2 = 6x? MM3A3d

CS) -l CD 4

® 5 CD i

tft—tiS--f--zr 3

uti

5. Which number is not a solutionof 3x4 - 3x2 = 0? MM3A3d

(£> -3 CD-i

CD 0 (g) 1

6. The storage space ina moving truck is shaped like a rectangular prism.It has a volume of 16 cubic meters. The length andheight areeach2 meters lessthan the width. What is thewidth of the storage space?MM3A3d

CS) 2m CD 4m

CD 6m CD 8m

7. What is the solution of x3 - 6x2 - 14x £ 2x1 MM3A3c

CD (-»,-2) and (0,8) CD (-», -2]and[0, 8]CD (-2,0) and (8, ») (g) [-2,0] and [8, oo)

8. Ifx + 3 is a factor ofx3 - x2 - 17x - 15, what isanotherfactor? MM3A3a

Cg) x+l CD x-\<S> x + 5 <g) x-3

Answers

1.

2.

3.

4.

5.

6.

7.

8.


#

#

•

. "•i..,.:c-i i

Name Date

Benchmark Test for Algebra: PolynomialFUnCtlOnS continued

9. The volume of the box shown at the right is givenby V= x4 + 3x3 + 2x2. Which expression representsthe missing dimension? MM3A3a

Cg) x CD x2 - 2x

CD x2 + 2x CD x2 + 3x + 2

10. Ifx - 2 is a factor ofa polynomial/(x), which of the following statementsdoes not have to be true? MM3A3a

Cg) /(2) = 0 (D A-2) = 0

CD 2 isa root of/(x). CD 2 isa zero of/(x).

U. Which are not possible rational zeros of/(x) = 3x3 - 1lx2 + 5x - 6?MM3A3a

Cg) ±\ CD ±| .CD ±2 CD ±6

12. Based upon Descartes' Rule of Signs, which of the following isthe only possible classification of the zeros of the functionf{x) = -3x3.+ 5x2 - x + 4? MM3A3a

Cg) 3 positive real zeros, 0 negative real zeros, 0 imaginary zeros

CD 0 positive real zeros, 3 negative real zeros, 0 imaginary zeros

CD 1positive real zero, 1negative real zero, 1 imaginary zero

CD 2 positive real zeros, 1 negative real zero, 0 imaginary zeros

13. From 1990 to 2004, the number N (in millions) of individual tax returnsfiled in the United States can be modeled by the function

N = 0.0012*4 - 0.055*3 + 0.72/2 - 1.6r + 114

where t is the number of years since 1990. In which year did the numberof individual tax returns filed first reach 127,000,000? MM3A3d

Cg) 1999 CD 2000

CD 2001 CD 2005

14. What is (are) the local minimum(s) for v(x) = 2x3 - x2 + 1? MM3AId

x+ 1

Cg) 0

CD Oandj

CDi

CD There are none.

Answers

9.

10.

11.

12.

13.

14.

Copyright ©McDougal Uttell/Houghton Mifflin Company Georgia Assessment Book, Mathematics 3 21

Name Date

Performance Task for Algebra: PolynomialFunctions

GeorgiaPerformance

Standard(s)

MM3Ald,MM3A3a,MM3A3C,MM3A3d

The models below represent the sales of two competing video gamemanufacturers for the years 1996 to 2006. In the models, S representsthe sales (in millions of dollars) and / represents the number of yearssince 1996.

Company A: S = 0.25f3 - t2 + 4Company B: S = 0.02/4 - 0.2r3 + 0.5r2 + 6t + 5

a. Classify each function by degree.

b. In which year(s) was the sales for company A $4 million?Solve the problem algebraically.

c. In which year(s) was the sales for company B $35 million?Solve the problem using a graphing calculator.

d. Make a table of values for each function.

e. Graph each function on the domain 0 £ t < 10.

f. Identify any turning pointsof the graph ofeach function on thedomain. What real-life meaning do these pointshave?

g. Forwhich years were thesales for company B greaterthanthesales for company A?

h. Which company will have the greater sales in 2010? Explain yourreasoning.

Themodels below represent the profit of the two competingvideo game manufacturers. In themodels, P represents the profit(inmillions of dollars) and x represents the number of video game

.,. units produced (in millions).

Company A: P = -x3 + 4x2 + 15x

Company B: P = -x3 + 2x2 + 16x

i. Currently company A produces 6 million video game units andmakes a profitof $18,000,000. What lesser number of video gameunits could company A produce and still make the same profit?

j. Currently company B produces 4 million video game units andmakes a profit of $32,000,000. What lesser number ofvideo gameunits could company B produce and still make the same profit?

22 Georgia Assessment Book, Mathematics 3 Copyright © McDougal Litteil/Houghton Mifflin Company.

♦

9

3k;?..-i'"';.

Name

m Quiz for Lessons 3.1 -3o2

Evaluate the expression without using a calculator.

1. Zm 2. 8P3/2

4/33. -125

3/54. (-32)

Solve the equation. Round the result to two decimal placeswhen appropriate.

5. x5 = 25 6. x3 = -21

7. x4 + 11 =29 8. (x + 4)3 = -33

Simplify the expression. Assume all variables are positive.

9. yn-m io. (V6.^)6

n. (xV)i/i0 +3(xi/y/10)4 i2. *®^T®13 eV?vg 14 yif^ _7^ryi

Date

• 15. Find a radicalexpression for the perimeterof the shaded triangle.Simplify the expression.

Answers

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

13.

14.

15.


NameDate

Performance Task for Lessons 3*1 -3,2

GeorgiaSv Performance

Standard(s)

MM3A2a,MM3A2b

The table below shows the prices of several items or services in 1990and in 2005. Ifthe average price of an item or service increases from/?to p2 over a period of«years, the annual rate ofinflation r (expressed asa decimal) is given by

a. Rewrite the expression for r using radical notation.

b. Find the rate of inflation for each item or service in the table.Write eachanswer as a percent rounded to thenearest tenth.

•WvK' tfV:.•• ,'• >'• ttftfigt- aft

Unleaded regular gasoline (gal) $1.16 $2.30

Ice cream (half gal) $2.54 $3.69

One month of basic cable TV $16.78 $39.63

One year of private collegetuition/fees $8147 $18,374

c. Ifthe value ofan item decreases from px to p2 over aperiod ofnyears, the annual depreciation rate r (expressed as adecimal) isgiven by

p2\Unr = 1 - -

Ifthe original price ofa computer in 2003 was $1400 and thevalue ofthe computer in 2007 is determined to be $200, what isthe depreciation rate? Write your answer as apercent rounded tothe nearest tenth.

24 Georgia Assessment Book, Mathematics 3 Copyright © McOougal Uttell/Houghton Mifflin Company.

navimaM

#

•

WW

Name Date

Performance Task for Lessons 3,1 -3.2

GeorgiaPerformance

Standard(s)

MM3A2a,MM3A2bT

MM3A3d

The area A of an equilateral triangle with sidelength s is given by the formula

A =

a.

b.

c.

hl/24"'3

Write the formula in simplest form.

The area of an equilateral triangle is 64square meters. What is theside length of the triangle to the nearest tenth of a meter?

The area of an equilateral triangle is 105 square inches. What isthe side length of the triangle to thenearest tenth of an inch?

TheareaA of an equilateral triangle with height h is given bythe formula

-i-l-i 1/2

A = -—-—A h-2 •

d. Write the formula in simplest form.

e. Thearea of anequilateral triangle is 20square feet. What is theheight of the triangle to the nearest tenth of a foot?

f. The area of an equilateral triangle is 324 square centimeters. Whatis the height of the triangle to the nearest tenth of a centimeter?

The figure at the rightshows an isosceles triangle.

g. Showthat the heightof an isosceles triangle

is given by h -^?-h. Use the figure and the formula from part (g) to

write a formula for the area of an isosceles triangle.

i. Find the areaof an isosceles triangle when a = 6 centimeters andb = 9 centimeters. Round youranswer to the nearest tenth.

Copyright® McDougal Uttell/Houghton Mifflin Company Georgia Assessment Book, Mathematics 3 25

Name


Graph the function. Then state the domain and range.

1. y = ^x 2. y= Vx +5y I

i

!

X

....

— -- — — — —

3. v = Vjc-4 + 6

y

-2

••— I i • . —2 ' x

5. y = ^jc + 8

y

2

•m— —-— —J — _*i2 x

—

_

—

y

— -— -1

X

4. y=-frx

y

—

—

_

—•

I

6. v = ^jc + 6 - 7

-2

2_x

Solve the equation. Check for extraneous solutions.

7. V3;c +12=6

9. V8x + 9 + 3 = 6

11. \Ilx-l = V3x - 2

8. i(2x +1)3/2 =f10. x - 4 = V8jc - 48

12. ^5*-11 =#T=~4

Date

13. The period T(in seconds) ofa pendulum can be modeled byT= 1.1 lVJ where I is the pendulum's length (in feet). How longis a pendulum witha period of 5 seconds?

Answers

1. See left.

2. See left.

3. See left.

4. See left.

5. See left.

•-•

6. See left.

7.

8.

9.

10.

11.

12.

13.

26 Georgia Assessment Book, Mathematics 3 Copyright© McDougal Uttell/Houghton Mifflin Company.

♦

•

•

•

'•AX

rM

Name Date

Performance Task for Lessons 3*3-3*4

^ Georgiaf0;y Performance"'"'' Standard(s)

MM3A2b,

MM3A3d

The velocity v(in feet persecond) ofanobject that has been droppedcan be modeled by the equation

v = V6Ad

where d is the distance the object falls (in feet) before hittingthe ground.

a. Write the equation in simplest form.

b. Makea tableof values for the equation from part (a).

c. Use your table to graph the equation.

d. You drop a rock offof a cliff. When it hits the ground it istraveling at a velocity of 40 feet persecond. Find the distancethe rock falls.

e. A construction worker is standing on scaffolding outside ofa building, He drops a hammer. When it hits the ground it istraveling at a velocity of 80 feet persecond. Find the distancethe hammer falls.

f. If you double the distance anobject falls, is the velocity of theobject doubled? Explain your reasoning.


im[H".Jai>l^'W)ll!»UIUBUI,MUIgl.!aJM^^

Name Date


*&vWk Perforrr'ance

Standard(s)

MM3A2b,MM3A3d

Georgia The figure shows a rectangular prism withlength 1, width w, height h, and diagonal d.The length of the diagonal ofa rectangularprism is given by the formula

d = Vi2 + w2 + h2.

Consider a rectangular prism with length3 inches and width 2 inches.

a. Write a function for the diagonal ofthe rectangular prism in termsof the height.

b. What is the domain of the function from part (a)? Explain yourreasoning.

c. Make a table ofvalues for the function from part (a).d. Use your table to graph the function.

e. Solve the equation from part(a) for h.

f. What is the height, to the nearest tenth ofan inch, oftherectangular prism when the length of the diagonal is 18 inches?

g. What is the height, to the nearest tenth ofan inch, of therectangular prism when the length of the diagonal is 10 inches?

h. Ifyou double the length, width, and height ofarectangular prism,does the length ofthe diagonal double? Explain your reasoning.

I. Find and simplify aformula for the length ofthe diagonal dofacube with side lengths.

j. Rewrite the formula from part (i) using rational exponents.k. Find the side length, to the nearest tenth ofa centimeter, ofa cube

when the length of thediagonal is 27centimeters.

28 Georgia Assessment Book, Mathematics 3 Copyright ©McDougal Uttell/Houghton Mifflin Company.

•

0

•-IP'*

#

•

<»

Name Date

unit Test for Algebra; Rational Exponentsand Square Root Functions

1. Find the indicated real nth root(s) of a.

n = 5, a = -32

Evaluate the expression without using a calculator.

2. V729 3. V343

4/34. -27

3/25. 25

6. Evaluate "^-748 using a calculator. Round the result to twodecimal places if appropriate.

7. In physics, transitional kinetic energy E (in Joules) is given by theequation E = xmv2 where mrepresents the mass (in kilograms),and vrepresents the velocity (in meters per second). Find thevelocity ofa thrown baseball at the time ofrelease with a mass of0.148 kilogram, and a transitional kinetic energy of 90.65 Joules.

Solve the equation. Round the result to two decimal placeswhen appropriate.

8. x3 = 512 • 9. /+100 = 725

10. (x-8)s =96 H. /-22 =45

Simplify the expression. Assume all variables are positive.

12.27 -1/3

27-4/3

14. ^-125x3

13. V80-V245

y-715. ,1.35

Perform the indicated operation. Assume all variables are positive.

16. 2V7 + 8V7 17. -^16-4^2

18. 5^-3^ 19. Wy +\xi-y

Answers

1.

2.

3. .

4. .

5.

6.

7.

8.

9.

10.

11.

12.

13.

14.

15.

16.

17.

18.

19.


SMMgWMM^WI»W^»U.''9BBl

Name Date

unit Test for Algebra: Rational Exponentsand Square Root Functions continuedGraph the function. Then state the domain and range.

20. j> =fv* — — 3^

l y; |

~\~ —

-

i

j X

1•

21. v= -4^

\ y

.........

—•I'

X

|1

•

i

22. y = jVx+ A- I 1,3/23. v=-^V*-2+2

y—

,—._

—

X

1

I y•—

-1

l X

i

Solve the equation. Check for extraneous solutions.

24. $Ax - 8 = 2

25. 60 - ^(x +75)3/2 =1026. x + 1 = Vl9-x

27. 4Vx - 2 = VJ^

28.

29.

The orbital period ofaplanet is the time that it takes the planet totravel around the sun. The orbital period ofaplanet P (in Earthyears) is given by the formula P=fd where dis the averagedistance (inastronomical units) of the planet from the sun.Saturn's average distance from the sun is 9.5astronomical units.What is Saturn'sorbital period?

You are standing 50 feet from a building. The distance d(in feet)between you and the top ofabillboard on top ofthe building isgiven by d= V2500 + h2 where his the height (in feet) of the topof the billboard above the ground. To the nearest foot, what is theheight ofthe top ofthe billboard if the distance between you andthe top of the billboard is 230 feet?

Answers

20.

21.

22.

23.

24.

25.

26.

27.

28.

29.


t

*

Name Date

Benchmark Test for Algebra: RationalExponents and Square Root Functions1. What is the value of(-243)3/5? MM3A2b

(S> -27 <D -3 <§) 3

2. What is the solution of 3x5 + 350 = -379? MM3A3d

729Cg) -

mCD -3 CD 3

Cg) 27

®i3. A soccer ball has a volume of about 5575 cubic centimeters. What is the

radius of the soccer ball? Use the formula for the volume of a sphere

V=|irr3. MM3A3dCg) 11cm CD 13 cm Cg) 16 cm CD 36 cm

4. Which expression is the simplest form of4V32 - V32? MM3A2bCg) 3^4 CD 6^ ©6 CD 16^2-4

5. Which expression is thesimplest form of the length of the triangle'shypotenuse? MM3A2b

3x1/2

2x3/2

1/2Cg) vV'2 + 3x J/2CD 2xm + 3x

CD V4x3 + 9x CD 4x3 + 9x26. Assuming allvariables are positive, which expression is the simplest form

of-z2V/1623 + 3V36/? MM3A2b<g) -z3V~z CD Mz3\£ CD Hz4VI CD 92z3V^

7. The four corners are cut from a 4 foot by 8 foot sheet of plywood,asshown in the figure. Which expression is the simplest form of theperimeter of the remaining sheet ofplywood? MM3A2b

2ft 2ft

Cg) 4 + 4V2 CD 16 CD 8 + 8V2 (D 24

Answers

1.

2.

3.

4.

5.

6.

7.


i'i

Name Date

Benchmartc Test for Algebra: RationalExponents and Square Root Functions continued8. Which function's ^-intercepts are the solutions of Vx - 3 = 4? MM3A3d

Cg) y Vx - 3 - 4

CD y - Vx + 3 + 4

9. Use the graph to find the solution of the

equation 4Vx -3 = 5? MM3A3d

Cg) 4

CD 2

CD 0

CD -3

10. What is the solution of V2x + 4 = x - 2? MM3A3d

Cg) -6 CD -2 CD 2 CD 611. What is the solution of (x + 3)3/4 -2 = 6? MM3A3d

Cg) -3 CD 7 CD 9 CD 1312. What is the extraneous solutionof x - A= Vic? MM3A3d

Cg) -4 CD 2 CD 4 CD 8

13. The period T(in seconds) ofa pendulum can be modeled by T= 1.11Viwhere i is the pendulum's length (in feet). How long is a pendulum with aperiod of 4 seconds? MM3A3d

Cg) 3.2 ft CD 3.6 ft CD 8.4 ft CD 13.0 ft14. The geometric mean ofthree positive numbers a,b, and c is given by

labc. Ifthe geometric mean ofthree positive numbers is 64,. and a = 2

CD y = Vx - 3 + 4

CD v = Vjc + 3 - 4

and 6 = 8, what is the value of cl MM3A3d

<S> 4 CD 8 CD 16

y

(4,5)

i X

(0, -3}

CD 16,384

Answers

8.

9.

10.

11.

13.

14.


mum

$

9

Name Date

Performance Task for Algebra: RationalExponents and Square Root Functions

Georgia a nursery operator wants to buildaPerformance greenhouse inthe shape ofa halfcylinder.Standard(s) The voiume 0fthe greenhouse is to beMM3A2a, approximately 35,350 cubic feet.

^?*?1!' a- The formula for the radius r (in feet)of a half cylinder is given by

\2V

MM3A3d

where Vis thevolume (incubic feet) and i is the length (in feet).Find the radius of the greenhouse. Round the result to the nearestwhole number.

b. Beams for holding a sprinkler system j a 1are to be placed across the top of thegreenhouse. The formula for theheight h at which the beams are tobe placed is given by

-FHf

.-'" Beam ^-i».

i

h

"I

\\

^,:'^h:;>;^:':. '•" '.'. • •-:',*##>

where a is the length ofa beam. Rewrite has a function ofonly a.

c. The length ofeach beam is 25 feet. Find the height hatwhich thebeams should be placed. Round the result to two decimal places.

d. Show that the equation from part (b) can be written as

a = 2Vr2 - h2.

e. Use the value of r from part (a) to graph theequation from part (d).

f. Use the graph from part (e) to determine an appropriate domainfor the equation.

g. At what height should the beams be placed if the length ofeachbeam is 20 feet? Round the result to two decimal places.

h. The costof building the greenhouse is estimated to be $35,000.Inorder topay for the greenhouse, the nursery operator investedmoney inan interest-bearing account 10 years ago that has anannual interest rate of 5%. The amount of money earned can befound using the formula

r=^j -1where r is the annual interest rate (expressed as a decimal), A isthe amount in the account after 10years, P is the initial deposit,and « is the number of years. Whatinitial deposit would havegenerated enough money tocover the building cost of$35,000?


Name


Graph the function. State the domain and range.

r-31. y = 3 • 2

_i yt ' I4--,-X-* i —r— I —--♦__, | x

•- y® + 3

1y

11

I

— -1

l X

Date

Answers

1. See left.

3. You deposit $4000 in anaccount that pays 5% annual interest compoundedmonthly. In about how many years will the balance double?

2. See left.

3.

4.

5.

6. See left.

7. • See left.

8.

9.

10. See left.

11. See left.

12.

13.

Simplify the expression.

4. {-Ae2xf 5.,6x9£

3eAx


6. y = 3ex 7. y = 2e~4xy

X

1

y

X

•

Evaluate the logarithm without using a calculator.

8. logs5 9. log|/327


10. y = log5 jc 11. y = In x + 3

y

• X

y

X

Use a graphing calculator to graph the function, (a) Approximatethe zeros of the function, if any. (b) Determine the Intervals forwhich the function is increasing and decreasing.

12. y = Ax+] 13. f(x) = \ogAx-l34 Georgia Assessment Book, Mathematics 3 Copyright © McDougal Uttell/Houghton Mifflin Company.

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Name Date

Performance Task for Lessons 4.1 -4.5

GeorgiaPerformance

Standard(s)

MM3A2e,

MM3A2f,MM3A2g

In 1995, the population ofLake City was 49,250 and the population ofits neighboring city, Springfield, was 65,000. During the next 10 years,the population ofLake City increased by about 4% each year, while thepopulation of Springfield decreased by about 1% each year.

a. Write models giving the population P (in thousands) ofeach city tyears after 1995.

b. Graph each model from part (a) for the years 1995 through 2005.State the domain and range of each.

c.

d.

Analyze each graph from part (b). Identify the zeros ofeachfunction, and determine the intervals for which each function isincreasing and decreasing. Explain the meaning ofeach inthecontext of the problem.

Using the graphs from part (b), estimate the year when thepopulation of each city was about 60,000.

e. If the trends continue, when will the population of Lake Citybe double what it was in 1995?


Name Date


GeorgiaPerformance

Standard(s)

MM3A2e,

MM3A2f,MM3A2g,MM3A3d

1. A local bank offers certificates of deposit (CD) accounts thatyou can use to save money and earn interest. You are consideringtwo different CDs: a three-year CD that requires a minimumbalance of $1500 and pays 2% annual interest, and a five-year CDthat requires a minimum balance of$2000 and pays 3% annualinterest. The interest in both accounts is compounded monthly.

a. Write a model giving the account balance A after t years foreach CD. Assume that you deposit the minimum amount ineach account.

b. Graph each model given the year constraints. State the domainand range.

c. Analyze each graph from part (b). Identify the zeros of eachfunction, and determine the intervals for which each function isincreasing and decreasing. Explain the meaning of each in thecontext of the problem.

d. If you deposit the minimum amount in each CD, how muchmoney is in each account at the end of its term?

e. For each CD, find the amount of interest paid over the entireterm of the CD. How much more interest does the five-yearCD pay?

f. Describe the benefits and drawbacks of each account.

2. The amount y of oil collected by a petroleum companydrilling on the U.S. continental shelf can be modeled byy— 10.5 In x - 35.75 where y is measured in billions ofbarrels and x is the number of wells drilled.

a. Graph the model.

b. Analyze the graph from part (a). Identify the zeros of thefunction, and determine the intervals for which the function isincreasing and decreasing. Explain the meaning of each in thecontext of the problem.

c. About how many barrels of oil would you expect to collect afterdrilling 500 wells?

d. About how many wells need to be drilled to collect 25 billionbarrels of oil?


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Expand the expression.

1. log3 4jtr

Condense the expression.

3. log5 24 - log5 6

2. In4^v5

4. log.6 + 2 log,3

Date

Use the change-of-base formula to evaluate the logarithm.

5. log412 6. log, 18

7. The sound ofabarking dog has an intensity of/ = 10~4 watts per/ 12square meter. Use the model L(I) = 10 log j where J, = 10Q

watts persquare meter, to find thebarking dog's loudness !(/).

Solve the equation. Check for extraneous solutions. Round theresult to three decimal places if necessary.

8. 3* + 1 =27* +3 9. ex = 5

10. 23* + 9 = 25 11. 4*+I~7=14

12. log6(5x+8) = log6(13;c) 13. In (Ax - 2) = ln(8x)

14. 91nx = 54 15. log3(x + 7) = 3

Solve the inequality using a table or a graph.

16. 30(i)*>6.-/ 17. 140(0.3)*< 1218. log4*<l 19. log,x-4>-3

Write an exponential function y = ab* whose graph passes throughthe given points.

20. (1,6), (2, 36) 21. (2, 16), (3,64)

Write a power function y = axb whose graph passes through thegiven points.

22. (2,2), (4, 16) 23. (3, 3),(6, 12)

24. A store begins selling a new type of baseball shoe. The tableshows the number y of pairs sold during week x. Find a powermodel for the data.

l

ili§iilll§gfmm 10 80

Answers

1.

2. .

3. .

4. .

5. .

6. .

7. .

8.

9.

10.

11.

12.

13.

14.

15.

16.

17.

18.

19.

20.

21.

22.

23.

24.


Name Date


GeorgiaPerformance

Standard(s)

MM3A2d,MM3A2g,MM3A3b,MM3A3c,MM3A3d

For a sound with intensity / (in watts persquare meter), the loudness Lof the sound (in decibels) is given bythe function

L= 10 log/- 10 log70

where /„ is the intensity ofa barely audible sound (about 10"12 watts persquare meter).

a. Condensethe expression for L.

b. By about how manydecibels does the loudness of a soundincrease when its intensity doubles?

c. The ring tone for a cellular phone has anintensity of/ = 10~3'5watts per square meter. Findthe loudness of the ring tone.

d. What is the intensity ofa noise that has a loudness of 80 decibels?

e. You whisper at a loudness of 15 decibels, while you talkin normalconversation at a loudness of60decibels. About how many timesgreater is the intensity ofa normal conversation than a whisper?

f. At whichintensity levels will the loudness of a noiseexceed100 decibels?


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$&Georgia

$-tv;- PerformanceStandard(s)

MM3A2g,MM3A3b,MM3A3c,

MM3A3d

Date

In 1995, a home builder builds the same model of house in two differentstates. The table shows the value of each house, v, and v2, t years after 1995.

2 4 6 8 10

(inthousands of dollars),' 260 275 279 285 287

tin:thousands of doHate) 210 250 300 361 420

a. Use a graphing calculator to draw two scatter plots, one showing(t, In v,) and the other showing (In t, In v,) in the same viewingwindow.

b. Use a graphing calculator to draw two scatter plots, one showing(f, In v2) and the other showing (In /, In v,) in the same viewingwindow.

c. Based onyour scatter plots from parts (a) and (b), does anexponential function ora power function better fiteach setof original data?

d. Describe how to verify your answers for part(c)using a graphingcalculator.

e. Find a model for the value of each house.

f. Estimate the value of each house in 2002. Round your answersto the nearest thousand.

g. Approximately how many years would it take for the value of ,.house v, to reach $300,000? Find the answer algebraically.

h. Write an inequality that gives the years when the value ofhouse v,was less than $295,000. Then find your answer.

i. Assuming the trend continues, write an inequality that gives theyears when the value ofhouse v2 will be at least $500,000. Thenfind your answer.

j. Determine the year when the values of the two houses wereequal. Describe how you can find the answer graphically andalgebraically. Explain why finding the answer algebraically wouldbe more difficult than finding theanswer in part(g) algebraically.

k. Describe how the value of each house changes over time.What factors may have affected the values of the two houses?


Name Date

unit Test for Algebra: Exponential andLogarithmic FunctionsGraph the function. State the domain and range.

2. v=-2.3*+1+21. y = tr2x

y

— —

__ __

X

'

y

— —

—

X


y

X

— — —

•

'

y

X

•

5. On your birthday, you receive a personal digital assistant (PDA)that is worth $300. The value of the PDA decreases by 20% eachyear. What will its value be 4 years from now?

Graph the function. State the domain and range.-2x

6. v = 0.4e

y

1

1 Xj 1

•

0.5x7. v = -3e

y

X

Find the inverse of the function.

8. 7 = log4(* + 3) 9. y = 2ex~2

Answers

1. See left.

2. See left.

3. See left.

4. See left.

5.

6. See left.

7. See left.

8.

9.


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NameDate

unit Test for Algebra: Exponential andLogarithmic FunctionsSimplify the expression.

10. I*'*'**12. log5625x

11. fUte12

13. Al0S2&c

continued

Graph the function. State the domain and range.14. ;y = log7* 15- >» = log, (x + 2) - 2

y

X

•

y

' • ••-»-»1 X

16. Analyze the graph inExercise 15. Identify the zeros of thefunction, if any. Determine the intervals for which the functionis increasing and decreasing.

Expand the expression.

17. \og]/2\fxy

Condense the expression.

19. In4*y2-2lnx2.y

18. In xy

20. log, tfTy' + log, tfx~?

Solve the equation or inequality.

21. 4Zr +4= 163jc~6 22. 4x = (0.5)jr~3

23. l0g2(;c2 + 2x) = 3 24. log3 x+ log3 (x - 6) = 325. 6t"1>2200 26. -log3^ + 4S5

27. You deposit $300 into a savings account that pays 5%annualinterest compounded daily. How long will it take for the accountto reach $3000? If necessary, round your answer to the nearesthundredth.

28. Write an exponential function^ = ab* whose graph passes throughthe points (2, 16) and (5, 128).

29. Write a power function y = axb whose graph passes through thepoints (2, 5) and (6, 9).

Answers

10

11.

12.

13.

14. See left.

•

15. See left.

16.

17.

18.

19.

20.

21.

22.

23.

24.

25.

26.

27.

28.

29.


rracuB

Name Date

Benchmark Test for Algebra: Exponentialand Logarithmic Functions

1. The graph of which function is shown? MM3A2f

CD J{x) = 3-2or- I

CD M = 3 • r+' - 5

Cg) /(*) = 3 • 2X - s - 1

(g) /(x) = 3 • 2X +s - 1

'

j1^

.._ y!/-

7)!

-2

i * •*

kni X

'

2. You deposit $300 in an account that pays 2.5% annual interest. In abouthow many years will the balance double? MM3A2g

Cg) 2 .CD 10 (g) 22 CD 28

3. What is the domain and range, respectively, for the function

y=2(|)X "2+5? MM3A2e<D :t>5,y>-2

CD*>2,y<5

CD All real numbers, y> 5

CD All real numbers, y < -5

4. The value of a snowmobile can be modeled by the equationy = 4500(0.93)' where / is thenumber of years since thecarwaspurchased. After how many years will the value of the snowmobilebe about $2500? MM3A2g

CD 7 years CD 8 years CD 9 years CD 10 years

5. You boughta guitar 6 years ago for $400. Its valuedecreases by about 13%per year. How much is your guitar worth now? MM3A2g

CD $173.45 CD $226.55 CD $322 CD $351.23

6. What are the domain and range of the function y = 2e_a5(l + 1J - 3?MM3A2e

CD Domain: x > -6, Range: y > -3

CD Domain: x > -0.5, Range: y < -3

CD Domain: all real numbers, Range: y > -3

CD Domain: all real numbers, Range: y > 0.5

Answers

1.

2.

3.

4.

5.

6.


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Benchmark Test for Algebra: Exponentialand Logarithmic Functions

7. What is the inverse of the function y = 2 In (x - 5)? MM3A2c

CD y = 2ex~5 (f£>y = e2x + S

(g) y = e0.Sx + 5 CD^ = TT^ + 5In 2

continued

8. What is the interval for which the function y = log4 (x - 1) + 2is increasing? MM3A2e

CD [<>,«>) CD [i,«0 <D (o,-) CD 0,«)

9. The graph of which function is shown? MM3A2f

(D /(*) = "3 log x

<D/W=-31og,xCD/to = 31og3*

CD fix) = 3 log x

>__

—

-1Yap>

4 X

— — —

(10, -3)

10. Which of the following is not equivalent to log} 8? MM3A2d

CD 21og54 CD 31ogj2 CD logs4 + log52CD —K&J In5

11. What is the condensed form of the expression

In (a + 1) + 2 In b - In c + 2 In Adl MM3A2d

CD In

CD In

\6abd + I6bd

I6ab2d2 + I6b2d2

CD \n(a + 2b-c + &d+ 1)

CD \n(a + b2-c+ \6d2 + l)

12. What is (are) the solution(s) of the equation log4 Ax + log4 (x + 3) = 2?MM3A3b, MM3A3d

CD -4,1 CD 4 CD 4,-1 CD 1

13. What is the solution of the inequality 31 ~4 - 10 > -7? MM3A3c

CD (5,») CD (~»,-5) CD (-5,oo) CD (-o»,5)

14. What is an exponential function whose graph passes through (1,5) and(2, 30)? MM3A2e

CD y 5 6

©y = mx

CD y = 0.536JC0-387

CD y = 0.536(0.387)*

Answers

7.

8.

9.

10.

11.

12.

13.

14.

Copyright© McDougal Littell/Houghton Mifflin Company Georgia Assessment Book, Mathematics 3 43

Name Date

Performance Task for Algebra: Exponentialand Logarithmic Functions

GeorgiaPerformance

Standard(s)

MM3A2e,

MM3A2f,

MM3A2g,MM3A3d,MM3A3D,

MM3A3C

In the spring, you decide to clean your room every week.The fustcleaning takes you 135 minutes. The time it takes you to clean yourroom decreases by 20% each week.

a. Copy and complete the table below showing the time it takes toclean each week. Round to the nearest minute.

3$&te 1 2 3 4

Minutes 135 ? ? ?

S^jtS^ 5 6 7 8,',r.,:i,;v,!.,..'.<t,Minuses ? ? ? ?

b. Draw a scatter plot of the data given in the table.Then connectthe points with a smooth curve.

c. Find an exponential function that models the data. Explain howyou found the function.

d. In about how many weeks will your cleaningtime be about half ofwhat it was the first week?

e. Analyze the graph from part (b). Identifythe zeros of the function,and determine the intervals for which the function is increasingand decreasing. Explain the meaning ofeach in the context ofthe problem.

f. How long will it take you to clean your room in the 20th week?

g. When will it take you less than 45 minutes to clean your room?

h. The model y = 10 + A5e~°-25x +' gives the number ofminutes yit takes your brother to clean his room in week x. Does the modelrepresentexponential growth or decay?Explain.

i. Graph the function from part (h).

j. Who takes less time to clean their room in week 2? in week 4?in week 6?

k. Using your answers to part (j), will this be true for every week?Explain.


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Write the standard form of the equation of the parabola withthe given focus and vertex at (0, 0).

1. (0,4) 2. (-5,0) 3. (0,-6)

Graph the equation. Identify the radius of the circle.

4. jc2+y2 = 50 5. 2x2 + 2y2 =72

y

3

«— — 1 1—*

3 x

i

y

2 <•

a I I •— I — —«•_J 2 x

•

Graph the equation. Identify the vertices, co-vertices, and fociof the ellipse.

„2 y2 •

_y

2

^• — i i »

2 x

3 =7. 64^ + 16y^ = 1024

_>y

4

»- I .^ •' I' • —I-*4 x

Graph the equation. Identify the vertices, foci, and asymptotesof the hyperbola.

y2 x28* 16 36 ~ ]

y

—. 2

^• — — — 1 — -»2 x

1

9. 9^-25y^ = 225

y

3

«— ,— — _•-

3 x

1

10. A cellular phone tower services a 12 mile radius. You get a flat tire5 miles east and 10 miles south of the tower. Are you in the tower'srange? Explain.

Answers

1.

2.

3.

4. See left.

5. See left.

6. See left.

7. See left.

8. See left.

9. See left.

10.

Copyright© McDougal Uttell/Houghton Mifflin Company Georgia Assessment Book, Mathematics 3 45

Name Date


ips^ Georgiafj^gf Performance

Standard(s)

MM3G2c

A latus rectum of a conic section is theline segment that is perpendicular to theaxis of symmetry, passes through the focus,and has endpoints that lie on the conicsection. The figure shows the latus rectumof a parabola.

For a parabola, the length of the latusrectum is 4 \p\.

y

v latus x2 =4pk .\ rectum \/

XT y.vertex (0,0) X

1 y=-p

For an ellipse and ahyperbola, the length of the latus rectum is =£-.a. Explain why ellipses and hyperbolas have two latera recta

(plural form of latus rectum).

b. For the parabola y2 + 6x = 0, what is the length ofthelatus rectum?

c. For the ellipse 4.t2 + y2 = 36, what is the length ofthelatus rectum?

d. For the hyperbola 49jc2 - 4y2 = 196, what is the length ofthe latus rectum?

e. What are the endpoints of the latus rectum ofa parabola withvertex at (0, 0) and focus at (-5, 0)?

f. What are the endpoints ofthe latera recta ofan ellipse with avertex at (0,4), a co-vertex at (-3,0), andcenter at (0,0)?

g. What are the endpoints of the latera recta of a hyperbola with fociat (-6, 0) and (6,0) and vertices at (-2, 0) and (2, 0)?

h. Make a conjecture about the length of the latus rectum of a circle.Explain your reasoning.


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GeorgiaPerformance

Standard(s)

MM3G2D,MM3G2C

Comets can have parabolic, elliptical, or hyperbolic orbits. Thecenterof the sun is a focus of each of these orbits, and each orbit has a vertexat thepoint where thecomet is closest to the sun. In the figure, p is thedistance between the vertex and focus (inastronomical units orAU).

a.

b.

c.

d.

e.

f.

g.

h.

i.

J.

k.

-#yp«AoUc'Orbife&

Vertex

•Q^:

kMi&£<

The comet 1997 Al hasa parabolic orbit wherep = 3.17 AU.The vertex of the orbitof the comet is (0,0). Write an equationthat models the orbit of the comet.

Graph the equation from part (a).

Use the equation from part (a) to find thevalues ofy when x = 18.

The comet SWAN has a hyperbolic orbit where p = 0.132 AU.One vertexof the orbitof the comet is (-498, 0) and thecenteris (0,0). Write an equation that models the orbit of the comet.

Graph the equation from part (d).

Use the equation from part (d) to find the values ofy when x = 500.

The cometEncke has an elliptical orbitwhere/? = 0.339 AU.The major axis of the orbit of the comet is horizontal with alength of 4.436 AU and the center is (0,0). Write an equationthat models the orbit of the comet.

Graph the equation from part (g).

Use the equation from part (g) to find thevalue ofy when x = 1.5.

The cometTurtle has an elliptical orbit where/? = 1.026 AU.The major axis of the orbit of the comet is horizontal with alength of 11.386 AUand thecenteris (0,0). Write an equationthat models the orbit of the comet.

Graph the equation from part (j).

Use the equation from part (j) to find the value ofy when x = 4.

Copyright® McDougal Uttell/Houghton Mifflin Company Georgia Assessment Book, Mathematics 3 47

Name Date

Qjyiz for Lessons 5.5-5.7

Write an equation of the conic section.

1. Ellipse with vertices at (4, -9) and (4, 7) and foci at (4, -6)and (4, 4)

2. Parabola with vertex at(-4, 3) and focus at(-4, -2)

Classify the conic section and write Its equation in standard form.Then graph the equation.

3. x2+y2-6x-8y =0 4. x2 - 4y2 - 4x - 8y = 36j y\

r-2

!__? £

Solve the system.

5. -6*2+y2-5y = 03*2 + y2 - 9x - 5y = 18

9. (2, l,0);r = 2

y

-3

\ X

'

6. y2-5x-3y-4 = 03y2 - 9y + x - 12 = 0

Find the distance between the points.

7. (0,2,0), (6, 5,1) 8. (-2,4, 2), (3, -8, -1)

Write an equation of the sphere in standard form with the givencenter and radius.

10. (-3, 5, 5); r = .5

11. In a lab experiment, you record images ofa steel ball rolling pasta magnet. The equation 25x2 - 9y2 - 100x4- 72y - 269 = 0models the ball's path. Write the equation for the path instandardform.

Answers

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

See left.

See left.


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Name Date


GeorgiaPerformance

Standard(s)

MM3G2a,MM3G2b,MM3G2c,MM3G3C

In the exercises below, you will discover the relationship between acircle in 2-spaceand a sphere in 3-space.

In parts (a)-(d), determine whether the equation represents acircleor a sphere. If it is a circle, graph the equation.

a. (jc + l)2 + (y - 2)2 = 4{x - 2)2 + (y - 4)2 + (z - 3)2 = 9

-2x + 4y-6r + 8 = 0

b.

c.

d.

e.

x2 + y2 + z2x2 + y2 - 2x + 4y + 5 = IUsing your results from parts (a)-(d), describe the similaritiesanddifferences in thestandard equations of circles and spheres.

f. Use the definition of a circle to write a definition of a sphere.

g. You are designing aspherical light fixture. You draw the fixtureas a circle on a piece ofgraph paper. You place the center ofthecircle at the origin. The fixture is to have a radius of6 inches.Write an equation ofthe circle. Then write an equation for thespherical light fixture.

h. You are designing a spherical vase. You draw the vase as acircle on a piece ofgraph paper. You place the center ofthecircle at the origin. The vase is to have a diameter of8 inches.Write an equation ofthe circle. Then write an equation ofthespherical vase.


Name Date


GeorgiaPerformance

Standard(s)

MM3Gld,MM3G2C

You anda group of friends are on a scavenger huntin a park. The mapshows where the cluesare located. In the diagram, x andy are measuredin feet.

Clue #3(-40, -80),

a. Write and classify an equation thatmodels thepicnic area.

b. Write and classify anequation that models the bike path.

c. Write and classify anequation that models thewalking trail.

d. At what point is clue #1 located?

e. At what point is clue #2 located? Round the coordinates to onedecimal place.

f. You found clue #3 and want to let your group know where you are.You are using two-way radios to communicate.The radios have arange of 300 feet. Write aninequality that represents the regioncovered by the radios.

g. Ifyour group is located at the point (100,120), will they be ableto hear you?

h. Your group is walking west. For how many more feet will they bein the range of your radio?

i. Your group is now at thepoint (60, -60) and are within 150 feetofthe final prize. Write an inequality that represents the region inwhich the final prize could be located.

J. Is itpossible for the final prize to be located at the point (-65,45)?k. Is it possible for the final prize tobelocated at the point (20, -25)?


«

(I

Name

unit Test for Geometry

Graph the equation. Identify the focus, directrix, and axis ofsymmetry of the parabola.

i. H*2y

l X

•

2 -v2 = -x*' 6y 3

y

—

X

Date

3. Write the standard form of the equation of the parabola with focusat (2, 0) and vertexat (0, 0). -

Graph the equation. Identify the radius of the circle.

4. x2+y2 = 4 5. x2=-y2 + 16

1 y

1

X

•

. y—

i X

—

__ — _

6. Write an equation of the line tangent to the circle x2 + y2 = 29 atthe point (-2, 5).

2 y27. Graph the equation x + -g = 4.

Identify the vertices, co-vertices,and foci of the ellipse.

"1 I I \yT~T"'t

I IE""CIj 2 i

JJ U—

8. Write an equation of the ellipse with center at (0, 0), a focus at(-3, 0), and a vertex at (-4,0).

Answers

1. See left.

2. See left.

3.

4. See left.

5. See left.

6.

7. See left.

8.

Copyright O McDougal Littell/Houghton Mifflin Company Georgia Assessment Book, Mathematics 3 St

Name

unit Test for Geometry

9. You are drawing an elliptical eye for an artproject. The eye should be3 centimeters longand 2 centimeters wide. Usingthe jc-axis asthemajor axis, write an equation of this ellipse.

continued

y2 x210. Graph the equation Tg ~ 4" = 1•

Identify the vertices, foci, andasymptotes of the hyperbola.

y 1

2

2 X

Date

11. Write an equation of the hyperbola with foci at (-3, 0) and (3, 0)and vertices at (-2, 0) and (2, 0).

12. Write an equation of theellipse with vertices at (-2, 4) and(-2, -2) and co-vertices at (-3, 1)and (-1,1).

13. Identify the line(s) of symmetry for the conic section4(x - 2)2 + 9(y + 3)2 = 36.

14. Use the discriminant to classify the conic section2x2 - xy - 2y2 + 3x - 1 = 0.

Solve the system.

15.

17.

x_

4-1=0 16. 25*2 + 4y2- 100 = 0

y = 2xx = 4y

The range of a cellphonetower is bounded by a circle given bythe equation x2 + y2 = 225 where x and y are measured in miles.A straighthighway that passes through the range of the cell phonetowercan be modeled by the equationx —ly = -75. Find thelengthof the highway, to the nearest tenthof a mile, that lieswithin the range of the cell phone tower.

Find the distance between the points.

18. (3, 0, 5), (0, 7, 0) 19. (1,-1,4), (-8, 9,2)

Write an equation of the sphere in standard form with the givencenter and radius r.

20. (0,0,0);r = 4 21. (3, -2, 6); r = 5

11.

12.

13.

14.

15.

16.

17.

18.

19.

20.

21.

See left.


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Name Date

a Benchmark Test for Geometry

1. What is the focus of the graphshown? MM3G2b

<5) (0,-3) CD (0,3)

<g) (-3,0) <g) (3,0)

.

h '

— — — f —- —

X

\\/

2. What is the standard form of the equation of the parabola with directrixjc = -2 and vertex at (0,0)? MM3G2c

Cg) y2 = -8x CD x2 = -2y Cg) jc2 = 2y (§) y2 = &c3. What is the equation of the line tangent to a circle centered at the origin at

the point (-3, -4)? MM3GIc

CD y=-fx+ 4

/7?\ _3 23

25 SB\ 3 25® y = -4x~i-^ _ 3 . 25

4. Thepizzeria in your town delivers anywhere within a 4 mile radius. If youconsider that the pizzeria is located at theorigin of a coordinate plane, atwhichof your friends' houses can pizzabe delivered? The coordinates aregiven in miles. MM3GIa

<S) House A: (0.82, 3.92) CD House B: (1,3.9)

Cg) House C: (1.5, 3.8) CD House D: (2,3.4)

5. What is the equationof an ellipsewith a vertex at (0, 3), a co-vertex at(-2,0), and center at (0,0)? MM3G2c

CS) —+ —= 14 9 l CD T + T=l

Cg) 4x2 + 9y2 = 36 Cg) 9jc2-4y2 = 36

6. Which equation of an ellipse is shownby the graph? MM3G2b

<S> T9+T3 = i

<E> —+ —= i4^7 *

1

Answers

1.

2.

3.

4.

5.

6.

Copyright © McDougal Uttell/Houghton Mifflin Company Georgia AssessmentBook, Mathematics 3 53

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Name Date

Benchmark Test for Geometry continued

7. What is the equation of ahyperbola with vertices at (0, -6) and (0, 6) andfoci at (0, -8) and (0, 8)? MM3G2c

..2

r2 y2 ,-RN y2 X2 1®f6-l8=1 ®36"28 =1 9.

8. What are the asymptotes ofthe hyperbola y2 - 16x - 256 = 0? 10_MM3G2b

•<E)y-±fe CD y=±%* (®y=±4x (§)y=±\6x9. What is the equation ofthe parabola with vertex at (1, -5) and directrix

y = -3? MM3G2c 13.CS) *-l =-8(y +5)2 . CD *+l =-8(y-5)2<§) (x-l)2=-8(y + 5) CD (x + I)2 = ~8(y - 5)

10. Which conic section is represented bytheequation4x2 _ 9y2 _ i8x + 3y - 12 = 0? MM3G2a

Cg) Circle CD Ellipse CD Hyperbola CD Parabola11. The path of asoftball is modeled by x2 - 12x + 12y - 48 = 0where x

andy are measured in feet. How far does the ball travel horizontally beforestriking the ground? MM3G2b

(S) 4ft CD 6ft CD 7ft <S> 15ft12. Which ordered pair is a solution ofthe system ofequations shown?

MM3Gld

x2 + y2 - 2x + 6y + 1 = 0

2x-y- 2 = 0

Cg) (-1,0) CD (0,-D CD 0,0) CD (0,1)13. The graph ofthe plane 4.x - 8y + 4z = 8intersects the x-axis at which

point? MM3G3c

Cg) (2,o,o) CD (0,-1,0) CD (0,0,2) CD (4,0,0)14. What is the equation ofthe sphere in standard form with center (0, 5, -4)

and radius 3? MM3G3c

Cg) (y-5)2 + (z + 4)2 = 9CD x2 + (y - 5)2 + (z + A)2 = 3CD x2 + (y- 5)2 + (z + 4)2 = 9CD x2 + (y - 5)2 + (z - 4)2 = 9

Answers

7.

11.

12.

14.

54 Georgia Assessment Book, Mathematics 3 copyright ©McOougai utteii/Houghton Mifflin company.

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Name Date

4| Performance Task for Geometry

^ Georgia||||- Performance

Standard(s)

MM361a,MM3Glb,MM3Gld,MM3G2b

Your aunt is a mail carrier for a post office that receives mail for alladdresses within a 5-mile radius. Her route covers the portionsof MainStreet, Carson Road, and Eagle Drive that pass through this region.

a. If the post office is located at the point (0, 0), "write and graph aninequality that represents the region where the mail is delivered.

b. Carson Road follows one branch of a hyperbolic path given byy2 - x2 - 4y - 23 = 0. Graph the portion ofCarson Road thatis on your aunt's route in the same coordinate plane as part (a).

c. If your aunt begins delivery on Carson Road at the point (—3, -4),where on Carson Road does she end delivery? How do you know?Support your answer algebraically.

d. After Carson Road, your aunt continues on Eagle Drive. EagleDrive follows a path given byy2 + \6x - 64 = 0. Graph theportion of Eagle Drive that is on your aunt's route in the samecoordinate plane as part (a).

e. Does Eagle Drive follow a. parabolic, elliptical, or hyperbolicpath? Justify your answer.

f. Where on Eagle Drive does your aunt end delivery? Support youranswer algebraically.

g. AfterEagle Drive, your aunt turns on Main Street. MainStreet is astraight road that cuts throughthe centerof the circular region pastthe postoffice. Findthe equation that represents Main Street. Thengraph the portion of Main Streetthat is on youraunt's route in thesame coordinate plane as part (a).

h. Estimate the length of your aunt's route using the sidesof thetriangle formed by the intersections of the roads on her route.Does your answeroverestimate or underestimate the lengthofher route? Explain.


S&xaa

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Abinomial experiment consists of ntrials with P">bab» **/*success on each trial. Draw ahistogram of the binomial distributionthat shows the probability of exactly k successes.

1. n = 3,p = 0.5

0.500

£ 0.375J3CO

8 0.125

°- 0

0.250

0 12 3

Number of successes

2. Describe the distribution as either symmetric or skewed.

Anormal distribution has amean of 37 and astandard deviationof 4. Find the probability that arandomly selected x-value is inthe given interval.

3. Between 29 and 49

4. At least 33

5. At most 25

In Exercises 6 and 7, use the fact that 70% ofAmericans opposeraising taxes to reduce the federal budget deficit. Consider arandom sample of 220 Americans.6. What is the probability that at least 147 Americans oppose raising

taxes to reduce the federal budget deficit?7. What is the probability that at most 168 Americans oppose raising

taxes to reduce the federal budget deficit?

Answers

L See left.

2.

3.

4.

5.

6.

7.

56 Georgia Assessment Book, Mathematics 3Copyright ©McDougal Uttell/Houghton Mifflin Company.

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Name Date


1|. Georgia^ PerformanceWf

Standard(s)

MM3D1,MM3D2D,MM3D3

According to a recent poll, 72% of children ages 7-11 watch professionalfootball on television. You are conducting a random survey of 20 childrenages 7-11.

a. Draw a histogram of the binomial distribution that shows theprobability of exactly k successes.

b. What is the least likelyoutcomeof the survey?

c. Describethe shape of the binomial distribution.

d. Explain whythe binomial distribution can be approximated bya normal distribution.

e. What is the mean and standard deviation of the distribution?

f. What is the probability that you will find at most 12 childrenwatch professional football on television?

g. You decide to expand your survey to include 150childrenages7-11. You find that 95 of them watch professional football ontelevision. Should you rejectthe poll's findings? Explain.

Copyright © McDougal Uttell/Houghton Mifflin Company Georgia Assessment Book,Mathematics 3 57

v^

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Name Date


> Georgiam Performance

Standard(s)

MM3D2a,

MM3D2b,MM3D2c,

MM3D3

Automobile manufacturer Areports its new manual transmissioncompact car gets an average of27 miles per gallon (mpg) in citydriving with a standard deviation of 1.6 miles pergallon. Assumethat gas mileage is normally distributed.

a. What is the probability that a randomly selected car will get morethan 31 rhpg?

b. What is the probability that a randomly selected carwill get lessthan 25 mpg?

c. What percent of cars get less than 30.2 mpg?

d. What percent of cars get between 28.6 and 31.8 mpg?

Automobile manufacturer B reports its new manual transmissioncompact car gets anaverage of30 miles per gallon (mpg) in citydriving with a standard deviation of 2.1 miles per gallon. Assumethatgas mileage is normally distributed.

e. What is the probability that a randomly selected carwill get morethan 33 mpg?

f. What is the probability that a randomly selected car will get lessthan 28 mpg?

g. What percent of cars get less than 30 mpg?

h. What percent of cars get between 25.8 and 32.1 mpg?

i. A car from manufacturer A was tested. It got an average of26 mpg in city driving. Find the z-score for the car's gas mileage.

j. Acarfrom manufacturer B was tested. It got anaverage of27 mpg in city driving. Find the z-score for the car's gas mileage.

k. Which car has the bettergas mileage? Explain.

An article claims that 80%of all compact carsget an average of25 mpg orbetter in city driving. Aresearcher decides to test thisfinding by testing 50compact cars and finds that 39of them getan average of 25 mpg or better incity driving.

I. State the hypothesis.

m. Should the researcher reject thearticle's findings? Explain.


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Quiz for Lessons 6.4-6.$

1. Alocal bank wants to know if its customers are satisfy with metypes of accounts the bank offers. Each branch surveys every tentncustomer during the day. Identify the type ofsample dfcScribed

Find the sample size required to achieve the given ma^g,n of errorRound your answer to the nearest whole number.

2. 5%

4. 0.9%i

6. Tell whether the study isan experimental study oran observationalstudy. Explain your reasoning.

Ateacher wants to study the effect that group review h^s ontest scores. The teacher divides amath class into two g*-oupsThe control group isstudents who do not review for a test asa group. The experimental group is students who do re\,iewfor the test as a group.

3. 2%

5. 1.4%

Answers

1.

2.

3.

4.

5.

6.

Copyright© McDougal Uttell/Houghton Mifflin Company Georgia Assessment Book, Mathematics 3 59

Name Date


GeorgiaPerformance

Standard(s)

MM3D3

A local college is conducting a survey tohelp determine whether thecollege should renovate the athletic center or expand the computer lab.

The college decides to survey every fifth student who enters thecomputer lab. Identify the type ofsample described. Then tell ifthe sample is biased. Explain your reasoning.

The college reports that 560 people, or56% ofthose surveyed,are in favor of expanding the computer lab. How many peoplewere surveyed?

What is the margin of error for the survey described inpart (b)?Round your answer to thenearest tenth of a percent.

Give an interval that is likely to contain theexact percent ofpeople that are in favor of renovating the athletic center.

The college hires an independent researcher to conduct thesurvey. The experimental group consists ofstudents enrolled ininformation technology programs. The control group consists ofstudents enrolled in a theater program. Identify any flaws in thissurvey, and describe how they canbecorrected.

a.

b.

c.

d.

e.


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MM3D3

The student council at a school is responsible for surveying the studentsto determine whether they would prefer the school to offer study hallsand limited electives or no study hallsand a broad range of electives.Because 1740 students attend the school, the council decides to surveya sample of the students.

a. A student council member suggests that the four representativesfrom each class (grades 9-12) be surveyed during the next studentcouncilmeeting. Identify the type of sampledescribed. Then tell ifthe sample is biased. Explainyour reasoning.

b. How many students would participate in the survey describedin part (a)? Calculate the margin of error for a survey with thissample size. Is it acceptable, why or why not?

c. The student council would like the survey to havea margin oferror of no more than ±2% and include no more than one quarterof the student body. Is this possible? If not, explain why andfind the least margin of error (to the nearest percent) that can beachieved by surveying one quarter of the student body?

d. The student council decides to conduct a survey by forming anexperimental group and a control group.The experimental groupconsists of students who have one or more study halls. The controlgroup consists of students who do not have any study halls.

The student council finds that the students in the experimentalgroup are more likely to prefer more study halls and limitedelectives than the students in the control group and concludes thatthe school should offer more study halls and limited electives.Identify any flaws in this survey, and describe how they canbe corrected.

e. Describe how the student council might achieve an unbiased,random sample of one quarter of the student body.

f. The studentcouncil administers the surveyas described in part (e).46% of the students want study halls and limited electives, and54% of the students want no study halls and a broad range ofelectives. From this survey, can the school determine whichoptionthe student body prefers? Explain.

Uttell/Houghton Mifflin Company Georgia Assessment Book, Mathematics 3 61

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mHmaaaam

NameDate

unit Test for Data Analysis and Probability |

Calculate the probability of randomly guessing the given number ofcorrect answers ona 25-question multiple choice driver's educationexam that has choices A, B, C, and D for each question.

1. 12 2. 20 3. 10

A survey states that 70% of U.S. adults use the Internet at home.You randomly select 8 U.S. adults.

4. Draw a histogram ofthe binomial distribution that shows theprobability of exactly ksuccesses.

5.

30

25

•=. 0.20

15

10

05

0123 45678

Number of adults who usethe Internet at home

Describe the distribution as either symmetric orskewed.

A normal distribution has a mean of 81 and a standard deviationof 9. Find the probability that a randomly selected x-value from thedistribution is in the given interval.

6. Between 90 and 100 7. At least70

8. Astudy found that the temperature ofaceramic furnace isnormally distributed with mean temperature of 1425 degreesFahrenheit and standard deviation of40degrees. What isthe probability that a randomly selected furnace will have atemperature less than 1505 degrees Fahrenheit?

Use the fact that 43% of Americans have played golf. Consider arandom sample of 200 Americans.

9. What is the probability that 79 or fewer people have played golf?10. What is the probability that between 72 and 93 people have

playedgolf?

Answers

1.

2.

3.

4. See left.

5.

6.

7.

8.

9.

10.


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unit Test for Data Analysis andProbability continued11. Identify the type ofsample described. Then tell if the sample

is biased.

A newspaper issponsoring a poll, and wants tofind out thepreferences of farmers across the state regarding the stategovernor's election. The newspaper surveys farmers in the localarea to gather their data.

Find the margin of error for a survey with the given sample size.Round your answer to the nearest tenth of a percent.

12. 2400 13. 180

Find the sample size required to achieve the given margin of error.Round your answer to the nearest whole number.

14. 10% 15. 1%

16. Ina survey of212 people at the local track and field championship,72% favored the home team winning. Find the margin of error forthe survey, andgive an interval that is likely to contain theexactpercent of all people who favor the home team winning.

17. A schooldistrict conducts an experiment to determine whethera new SAT prepcourse will increase SAT scores of students.The experimental group consists of 12th grade students who takethe course. The control group consists of students enrolled in 11thgrade who do not take the course.

The school district finds that the students in the experimentalgroup receive higher SAT scores than the students in the controlgroup and concludes thattheprep course is effective at increasingSAT scores. Identify any flaws in the experiment, anddescribehow they can be corrected.

18. Tell whether the study is an experimental study or an observationalstudy. Explain your reasoning.

A teacherwants to studythe effects of classroom participation ona student's final grade. The control group is students who do notparticipate in class. The experimental group isstudents who doparticipate in class.

Answers

11.

12.

13.

14.

15.

16.

17.

18.


;lj

Name Date

Benchmark Test for Data Analysis andProbability1. You perform a binomial experiment that consists of20 trials with a

probability of27% success on each trial. What is the probability ofexactly3 successful outcomes? MM3D1

(A) 0.00009 CD 0.10653 <£) 0.45629 Cg) 2.10553

2. The histogram shows a probabilitydistribution for a random variable X.What is the probability thatX isat most 4? MM3D1

CD 0.15Cg) 0.05

Cfi) 0.85 (g) 0.95

3. What is the percent of the area undera normal curve that is representedbythe shaded region? MM3D2a

(A) 18.5% CD 47.5%

Cg) 81.5% CD 95%

2 3 4

Value of X

4. An hourly wage is normally distributed with a mean of$6.75 and astandard deviation of $.55. What is theprobability thatan employee'shourly wage is not between $5.65 and $7.85? MM3D2b

CS) 0.025 CD 0.05 CD 0.34 Cg) 0.685. The monthly utility bills ina city are normally distributed, with a mean

of$100 and a standard deviation of$12. What isthe probability that arandomly selected utility bill is at most $80? MM3D2b

CA) 0.0446 CS) 0.1357 © 0.9554 Cg) 1.04466. What is the mean and standard deviation ofa normal distribution that

approximates the binomial distribution with 50 trials and probability ofsuccess on each trial of0.25? MM3D2b

CA) x= 12.5; o-= 3.1 CE) * = 12.5; a = 3.5Cg) x = 37.5; <r= 3.1 Cg) x = 37.5; a= 6.1

Answers

1.

2.

3.

4.

5.

6.


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Benchmark Test for Data Analysis andProbability continuedIn Exercises 7 and 8, use the fact that 63% of people choose pizza as theirfavorite take-out food. Consider a random sample of 400 people.

7. What is the probability that at most 272 people choose pizza as theirfavorite take-out food? MM3D2b

CS) 2.5% CD 13.5% Cg) 84% CD 97.5%

8. What is the probability that between 242 and 262 people choose pizza astheir favorite take-out food? MM3D2b

Cg) 32% (D 34% CD 68% CD 84%

9. A telemarketer decides to contact every third person in a city's phone book.Which type of sample does this represent? MM3D3

CS) Convenience CD Random

CD Self-selected CD Systematic

In Exercises 10-12, use the information below.

A survey reported that 1260 shoppers, or 84% of those surveyed, were planningto use a credit card to purchase items.

10. How many people were surveyed? MM3D3

CS) 1058 (D 1260 (D 1500 CD 1740

11. What is the margin of error for this survey? MM3D3

CS) ±0.2% (D ±2.6% CD ±2.8% CD ±10.9%

12. Which interval is likely to contain the exact percent of people that wereplanning to use a credit card to purchase items? MM3D3

CS) between 13.4% and 18.6% CD between 81.4% and 86.6%

CD between 81.2% and 86.8% CD between 73.1% and 94.9%

13. An election poll reveals that 54% of voters favor the incumbent, with amargin oferror of ±2.5%. How many voters were polled? MM3D3

CS) 250 CD 400 (D 1600 CD 2500

14. Which is an experimental study? MM3D3

CS) The control group is shoppers atstore A. The experimental group is shoppersat store B.

CD The control group isshoppers who use checkout lane 1. The experimentalgroup is shoppers who use checkout lane 2.

•CD The control group isshoppers who are not given coupons. The experimentalgroup is shoppers who are given coupons.

CD The control group isshoppers who do not use a cart. The experimental groupis shoppers who do use a cart.

Answers

7.

8.

9.

10.

11.

12.

13.

14.

Copyright © McOougal Uttell/Houghton Mifflin Company Georgia Assessment Book, Mathematics 3 65

Name Date

Performance Task for Data Analysis andProbability

GeorgiaPerformance

Standard(s)

MM3D2D,

MM3D3

According toa survey, 85% of Internet users check their personal e-maildaily. You wantto test the findings of this survey.

a. You first decide to conducta surveyusingtwogroups. Theexperimental groupconsists of college students at a computerlab. The control group consists of people standing at a bus stop.Identify any flaws in the survey, and describe how they canbe corrected.

b. You now decide topost a poll onyour website. Identify the type ofsample described. Then tell if the sample isbiased. Explain yourreasoning.

c. Suppose 500 people respond to your poll. What is the probabilitythat you will find at most 441 Internet users check their personale-mail daily?

d. After conducting your survey of 500 people, you find that 80%ofInternet users said they check their personal e-mail daily. Whatisthe margin oferror for the survey? Round your answer to thenearest tenth of a percent, if necessary.

e. Use your result from part (e) to determine an interval that is likelyto contain the exact percent of Internet users that check theirpersonal e-mail daily.

f. About how many people should be surveyed sothat the margin oferror is approximately ±2.5%?

g. About how many people should be surveyed so that the margin oferror is approximately ±1.5%?

h. State the hypothesis of the original survey.

i. How many Internet users from your survey said they check theirpersonal e-mail daily?

j. Should you reject the original survey's findings? Explain.


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a. P = lx + lOy

b. x > 0 c.

y>0

x + y £ 2700

<. 1^<2-x

x < 5.y + 900

d. (0, 0), (1800, 900), (2400, 300), (900,0)e. (0, 0): 0; (1800, 900): 21,600;

(2400, 300): 19,800; (900, 0): 6300

f. Case I: 1800 units; Case II: 900 units

g. Yes; the maximum value ofP occurs at(2400, 300) instead of (1800,900). So, thecompany should produce 2400 units of Case Iand 300 units of Case II to maximize its monthlyprofit.

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Performance Task for Lessons 1.1-1.6(Full Page)

a. Downloaded

«pngS;>^Cf-0 25 50

mminWaM$9.50 $29.50 $49.50

mmmm $4.90 $26.15 $47.40

Downloaded75 100 125

Your annual i$69.50 $89.50 $109.50

Mrjft|irftjs|?aniW6lJlllii $68.65 $89.90 $111.15

You: about 60 songs; Your friend: about 50 songs

b.y = 9.5 + 0.8x; 61 songs C.y = 4.9 + 0.85x;48 songs d. Yes; 61 rounded to the nearest ten is60 and 48 rounded to nearest ten is 50.

consistent and independent

f. (92, 83.1); You and your friend each pay atotal cost of S83.10 when 92 songs have beendownloaded, g. v = 3.5 + 0.95* where;;represents the total cost and x represents thenumber of songs downloaded.

h. >140

120

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j. Sampleanswer: Because the graphs in eachsystem are so similar, it may be difficult todetermine or even estimate where the equationsintersect. Solving the systems algebraically usingthe elimination method may have been easier.

Georgia Assessment Book Answers, Mathematics 3 A1

k. your club; If you graph theequations over alarger range of*, you will see that your music clubis always cheaper than the other two music clubs.


1.(9,0,-8) 2.(3,-2,-3)

[4,:]4. not possible; The dimensions are not

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14.(17,9)15. b + c + g = 24; 1.56 + 1.00c + 2g = 33b = 2(c+g);b= 16,c = 7,g= 116. Sample answer: Let Arepresent Akini,B represent Beli, C represent Caya, D representDali, and E representElise.

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Performance Task forLessons 1.7-1.12 (Half Page)

A B c D E

A "0 1 0 1 1

B 1 0 1 0 1

a.M=C 0 1 0 1 1

D 1 0 1 0 1

E 1 1 1 1 0

A2 Georgia Assessment Book Answers, Mathematics 3

A B C D E

A '3 1 3 1 2 "

B 1 3 1 3 2

b.M2 = C 3 1 3 1 2 c. 3 d.

D 1 3 1 3 2

E .2 2 2 2 4 .

A B C D E

A "4 8 A 8 8 '

B 8 4 8 4 8

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D 8 4 8 4 8

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Performance Task forLessons 1.7-1.12 (Full Page)

a. Total Number Shipped (M

300W' 800W 1000W

Warehouse 1 7170 15,200 14,710"Warehouse 2 .6170 16,360 14,610.

,*=[:;

matrix M by

-170 500 -270

-210 260 290

c. Multiply the sum of matrices A + B or~3585 7600 7355"

3085 8180 7305

d. Total Number Shipped

Warehouse 1 I" 10,759,129.20Warehouse 2 |_ 10,859,128.60e. Letx represent the number of 300-watt systemssold, lety represent thenumber of 800-wattsystems, and let z represent the number of1000-watt systems sold.

x + y + z = 77149.99.x + 249.99v + 399.99z = 22,549.23

y = 2x

Copyright © McDougal Uttell/Houghton Mifflin Company.

:}lie SU1

l-V-

290 units

I

•OBBSEevg

f.

g.

1

49.99

-2

1 1

249.99 399.99

1 o.

X

y

_ z.

=

77

22,549.23

0

"15"30 ; The store sold 15 300-watt systems,

.32.

30 800-watt systems, and 32 1000-watt systemsfor the month.

Unit Test for Algebra: Linear Systems,Matrices, and Vertex-Edge Graphs

1. 150 mi 2. 18.8 mi/h

3. ; (1,0); consistent andindependent

s y

\ /\ /

\ /? \ X

/ \--

7I \

4.(3,1) 5. (-1,1) 6.(15,-5) 7.(1,-3)

8.

10.

$3 %* ¥ *s^

^ n\ 9.-

y h\$ $ S:; Ji •*k $ 4

ngassgnasa 4M '$i $ m ©5 & M '•fi >Mtip. * ^ h, 3 ?®?S /5I& VM

J. mffJ'- m i

f 3*5 •m M

y 11. V > /... ^ ?.

*-s%.£ ^ .,2 --^ „-- \ ' /

*' -' * w'/£ _Z5iP_

^ Z S__ _ ._ T Z _ St....

12. 29; 69 13.(1,2,4)

14. not possible; dimensions not compatible

-2 4 6~6 0-8

is. r-2 4 6iL 6 0 -8j

17.

-10 2

3 0 -6

-4 0 8J

20i 12 21. ant: 4 mg; cargo: 72 mg22. airfare: $408; hotel: $204; car: $68

23.(3,1) 24.(3,2)

16.x = 3,v = 1

18.

-4

2

L-7J

19.0

Copyright® McDougal Uttell/Houghton Mifflin Company

•M!«*MW WJWM*JM

BCD

A "0 1 0 1 "

B 1 0 1 1

C 0 1 0 1

D .1 1 1 o.

A B C D

A '2 1 2 1 "

B 1 3 1 2

C 2 1 2 1 »

D .1 2 1 3.

M2 =

There are 2 two-route trips from portB to port D.

Benchmark Test for Algebra: LinearSystems, Matrices, and Vertex-EdgeGraphs

1. D 2. A- 3. A 4. D 5. B 6. C 7. A

8.D 9.B 10. C 11. D 12. C

Performance Task for Algebra: LinearSystems, Matrices, and Vertex-EdgeGraphs

a. s + p + c = 40

c-Ap

s = p —2

b. You spend 5 hours serving at a soup kitchen,7 hours pickingup trash, and 28 hours collectingtoys.

c. s + p + c = 40

p = 3c

s = p + c

d. Ken spends 20 hours servingat a soup kitchen,15 hours pickingup trash, and 5 hours collectingtoys.

e. 5 + p + c = 40

s = p + c —A

p = 2c + 1

f. Sara spends 18 hours serving at a soup kitchen,15 hours pickingup trash, and 7 hours collectingtoys.

g. s + p + c = 40

c = s — 5

p = c + 8


$-3 =P

c.

40

-5

8JT " u l -ULcJ L sJ L9J•T^nS,pends 14 hours serving at asoup kitchen,j. / nours poking up trash, and 9hours collectingtoys. 'toys

c = 2P - 2— 1

27C - 1

L" i^hlan spends 9hours servir,gat asoup kitchen'nours Picking up trash, and 20 hours collecting: oys.

=*uizffor Lessons 2,1-2.4i-im 2^—

3- The graph ofg is the graph of/translated to-m rignt 5 units. 4. The graph ofg is the graphzfTS translated UD 3... 5

UP 3 units.

" 3%\ 3X*2 +3* +9) 6. {3x2 +l)(x +2)' Ax ^2 + «)(* - 2)(jc +2) 8. 5(x - 5){x +1)" 6^n- by 4in- by 20 in. 10. (-1,0) and (4, •)- t 2» -1] and [1,2]

^rforniance TaaR fQf Lessons 2.l-2.4—filaait Rage)

degree 3 (cubic) b. -4; the company had*. oss of,$4000 in 1991. c. $15,120,000; no,-oughtje profit increased from 1991 to 2006, it-^^^ for the Profit to decrease in the future.

curi—...

4_. v .tm 4

r s ? *

-ooand/(x)^+»as

° 2 4" flirffi6 8 10 12 14 16

Yoors alnco 1990

3.^97-2006

Georgia Assessment Book Answers, Mathematics 3


a. Vx(x) =x3 b. V2(x) =(x- l)3c. VJ(x)= (x - 2)3 d. 405 in.3e. v

70

60

50

40

30

20

10

0I

f. Vis the graph ofVx translated to the right 1unit.g. V is the graph ofVx translated to the right 2units.h. Bottom layer: 3 in. by 3 in. by 3 in.; middlelayer: 2in. by 2in. by 2 in.; top layer: 1in. by1in. by 1in. I. x>6 j. Bottom layer: 3 in. by3 in. by 3 in.; middle layer: 2 in. by 2in. by 2in.;top layer: 1 in. by 1 in. by 1 in.

Quiz for Lessons 2.5-2.81.x2+ 7*-8 2.2x2-9x+ll 3.-1,1,3-

4.6 5.-1,1,2 6.-4,^,2,37.f(x) = x2 - 6X2 - x + 308.f(x) = x3 - 2x2 + x - 29.f(x) = xl + 3x2 - 2x - 6

10, I I I i irl I H 11-

- \ ~l

UpJ !

I7mH•111

0 1 2 3 t 5 t 7 x

--v-

y-

20

\j i

- ~

12. 6 in. by 6 in. by 12in.

Performance Task for Lessons 2.5-2.8(Half Page)a. Vt(x) = ir(x - \)\4x - 1);4x3 - 9x2 + 6x - 141 = 0

b.±,,44±3,4±i±47,4,^,±141, ±4*-, ±^; None of the rationalpossibilities are reasonable, c. about 4 cmd. V2(x). = 47rx3 - ir(x - l)2(4x - 1);V2(A) ~ 380 cm3

%

Copyright ©McDougal UHell/Houghton Mifflin Company.

§ e. 190 cm3; Sample answer: Because the plasticaccounts for half of the thickness of the outer layer,it fakes up half of the volume of the outer layer.


(Full Page)

a. y = 120 - Ax b. V(x) = 120*2 - 4jc3c. x « 29 in. d. 4x3 - 120*2 +116 = 0

e. 1,2,4,29, 58, 116 f. jc = 1 is an actualsolution; 1 in. by 1 in. by 116 in. g. x ~ 3 in.

h. x = 15,15 + 15V3" 15- 15VJ

; the value2 ' 2

x = r 's physically impossible because

x is negative.

I.

j. (20, 16,000); the maximum volume of thepackage is 16,000 cubic inches when x - 20inches, k. 0 < y < 16,000 I. The maximumvolume of the package is 11,664 cubic incheswhen x = 18 inches.The range of the function is0<y< 11,664

Unit Test for Algebra: PolynomialFunctions

1.-6 2.-2

3.

4.

y

1

f\ ? *^

4-1,xyy

--1 —

- JT

The graph ofg is the graph of/*translated to theleft 4 units and down 2 units; the domains andranges of both functions are all real numbers;/ has an intercept of 0 andg has an x-interceptof about -2.74 and a,y-intercept of62;/is oddand symmetric with respect to the origin andg isneither even nor odd and has no symmetry.Copyright © McDougal Uttell/Houghton Mifflin Company

5. \{x2 +A)(x - 2){x +2) 6. (y +6)( v2 - 3)7. 4 in. by 2 in. by 12 in.

8. (-oo,-6] and [-1,0]

9. (-oo, -1.73) and (1.73, oo) 10. x2 + Ax + 311. x2 + 9x + 18 12. -6 and -3

13. 1,000,000

14. ±^, ±1, ±|, ±2, ±3, ±6 15.x =-4, ±VJ16. jc4 + x3 + 3x2 + 9x-5A

17. positive zeros: 0, 2, or 4; negative zeros: 1;imaginary zeros: 0, 2, or 4

i8.'~T~-i~!>nr\i 19.y <

I 1 1L 1 J I

20. zeros: —3 (multiplicity 2), 5; turning points: 2

21. zeros: 0 (multiplicity 2), -1 (multiplicity 3);

turning points: 4. 22. x-intercepts: -1,1, ±VJ;minima at x = -1.732 and x » 1.732; maximum .atx = 0 23. 194 in.3

Benchmark Test for Algebra:Polynomial Functions

1.A 2.C 3.C 4.C 5. A 6. B 7. D .

8. A 9.C 10. B 11. A 12. A 13. B

14. B

Performance Task for Algebra:Polynomial Functions

a. CompanyA: degree 3, company B: degree 4

b. 1996,2000 c. 2001

d. Company A:

Company B:

p 0 2 4 6 8 10

f§ 4 2 4 22 68 154

If0 2 4 6 8 10

•wi^'

5 18 29 42 65 115

Georgia Assessment Book Answers,Mathematics 3 AS

e.

T"„ i'p: fl~ .'.']/.

i i 1 ii

4.

•Coni

i /I

1

nyA

i

ipany

i

J-T5" /f-i-Cotnpa

t I

s,

160

? 140(9

? 120

si ,0°U g 80

i 601 40~ 20

001 23 4S6789 10I

Vbare since 1996

f.The graph for company A has a turning pointat (2.7, 1.6). The minimum sales for the companyfrom 1996 to 2006 was $1.6 million whichoccurredin about 1999. The graph for company Bdoes not have any turning points, g. 1996-2004h. By evaluating each function when t = 14, youobtain $494 million in sales for companyA andabout $407 million in sales for companyB. So, in2010, company A will have the greater sales.I. 1,000,000 video games J. 2,000,000 video 'games


l1.4 2.^ 3. -625 4. -8 5. 1.90

6.-2.76 7.2.06 8.-7.21 9.12

10.65 = 7776 11.4jc4V5 12.1 13.

14. -5x4V 15. 16 + 4 + Vl62 + 42;20 + 4VT7

Performance Task for Lessons 3.1-3.2(Half Page)

a. r = ,"/— - 1 b. Unleaded regular gasoline:4.7%; ice cream: 2.5%; basic cable TV rate: 5.9%;private college tuition/fees: 5.6% c. 38.5%


a. A=^2 b. 12.2 mc. 15.6 in.d. A=̂ -h2 e. 5.9 ft f. 23.7 cm

2

27?


g. Use the Pythagorean theorem.

T + h1 = b24

a = h2 _ £

-^ih.A =̂ b2-j 1.25.5 cm


1. ; domain: all real numbers;range: all real numbers

—

y

- -j-^

1

__ _

»> •^ —

X

... ._.

2. ; domain: x £ 0;range^S 5

"*~ n i x

3.

4.

; domain: x > 4;range: v £ 6

y

-

—

— —

—

—

—

-2 ._

2 1 J

; domain: all real numbers;range: all realnumbers

i >\I i

1.

- -

^_ X

_..

._...._

5. ; domain: all realnumbers;range: all real numbers

y

- - -

Ilr

I l'


«

I

6. ; domain: all real numbers;range: all real numbers

i-2 >

1 I2 x

—

—

—

=

.—>

—

_ .....

7"

7. 8 8. 4 9. 0 10. 8 11. 7 12. -84

13. 20.29 ft


(Half Page)

a. v = sVdb.

m 0 2 4 6 8 10

0 11.3 16 19.6 22.6 25.3

C. _ «•g 25

*| 208 5 IS15 10

J 5~ 0

0 2 4 6 8 10 i

Distance (feet)

d. 25 ft e. 100 ft f. No; 2v = !6Vrf * 8V2rf


(Full Page)

a. d = Vl3 + h2 b. d>0; Because a rectangularprism can only have a positive diagonal length

c.

d.

MB 1 3 5 7 9 11

3.7 4.7 6.2 7.9 9.7 11.6

d

£ 10

-I 8i£ 6§• 4Q 2

n

0 2 4 6 8 1012 A

Height (inchas)

e. h = Vcf2-13 f. 17.6 in. g. 9.3 in.h.Yes; 2d = V(2i)2 + (2w)2 + {2hf= V4i2 + 4w2 + Ah2 = V4(i2 + w2 + h2)= 2Vi2 + w2 + h2 \.d = sV3 \.d=3msk. 15.6 cm


Unit Test for Algebra: RationalExponents and Square Root Functions

1. -2 2. 9 3. 7 4. -81 5. 125 6. -3.76

7. 35 m/s 8. 8 9. ±5 10. 10.49 11. ±2.02

12. 27 13. -3V5 14. -5x 15. 4v135

16. 10V7 17.-6^2 18. 2Vx 19. fx^20. IT"! I t'fTP; domain: x > 0; range: y > 0

21.

22.

23.

-f—H- -1

S ! 1

---1+ 1""'" ~f"

1

1

y_ _ ; domain: all real numbers;range: all real numbers

; domain: x > -4;range: y > -1

y .

y

—-1 :r= —

domain: all real numbers;range: all real numbers

24. 10 25. 25 26. 3 27. 1 28. 2.1 Earth

years 29.224 ft

Benchmark Test for Algebra: RationalExponents and Square Root Functions

1.A 2. B 3. A 4.B 5. C 6. B 7. C

8. A 9. A 10. D 11. D 12. B 13. D

14. D

Performance Task for Algebra: RationalExponents and Square Root Functions

a. 15 ft b. h=^225 - (|)2 c. 8.29 ft


f.7

at(

fro

0C(

dot

h.

ob

ab>

20

I.

ga

Q

i

1>

l

2«

P

(I

||d. -F1®h = Jr2 - =-

4

A2 = r2 - K-

J +t-S

a - 2 .2j = #•' - Az

a2 = 4(r2-A2)

e.30

£ 25f 20§ is

I »& 5

0 2 4 6 8 10 12 14 A

Height (feet)

f.A>0 g. 11.18ft h. $21,486.96


!• I I ' »y| i "J; domain: all real numbers;range: y > 0

a = V4(r2 - h2)a = 2Vr2 - A2r _

^^

_k_

-rt

y f

1 — ^ —

1 X

2. 1 y

1±zzz-

1

_J_ X

; domain: all real numbers;range: y > 3

3. 14yr 4.-64efa 5.3c2*6. ; domain: all real numbers;

range: y > 0>r ,

1 X

i "l [

7. ; domain: all real numbers;range: y > 0

^ y -r~

z—it—zX


8. 1 9. -3

10. L J_7TT1

~ ~ zfc ~'

J

J: i

domain: x > 0; range: allreal numbers

11. ; domain: x > 0; range: allreal numbers

T'Lr ^

- a. 23-i-.t i

L ^,.:t^ X

i

12. (a) none (b) increase: (-oo, oo)13. (a) x = A (b) increase: (0, <»)


a. Lake City: P = 49,250(1.04)';Springfield: P = 65,000(0.99)'b. e

72,000

| 68.000| 84,000" 60,000

60,000

52.000

48,000,o'

-X-

P> 49,250qo"4>'

01234567891Year* since 1995

domain: [0, 10]; range: [49,250, 72,902]

68,000

66.000

64.000

82.000

60.000

58.000

58.000

P = 65,000(0.99)'-

0123456789)

Years since 1995

domain: [0,10]; range: [65,000, 58,785]c. Lake City: no zeros, increase: [0, 10];Sample answer: The population ofLake Cityincreases from 1995 to 2005, and it is never 0.;Springfield: no zeros, decrease: [0, 10];.Sample answer: The population ofSpringfielddecreases from 1995 to 2005, and it is never 0.d. Lake City: 2000; Springfield: 2003 e. 2013

Copyright ©McDougal Uttell/Houghton Mifflin Company.


(Full Page)

/ 0 02\I2/La.A = 1500(1 +*-§*) ;

b. *•a 1600

« 1560

8 1540

5 1520

6 1500,0

A=200011 +̂ f)'2'• |

' \

_.

/\ \1i!

4t

15 10

I 1 L^.

1 2 3

Years

domain: [0, 3]; range: [1500,1592.7]

domain: [0, 5]; range: [2000,2323.2]

c. three-year CD: no zeros, increase: [0, 3];Sample answer: The CD increases each year,and it is never 0.; five-year CD: no zeros,increase: [0, 5]; Sample answer: The CD increaseseach year, and it is never 0. d. three-year CD:$1592.68; five-year CD: $2323.23 e. three-yearCD: $92.70; five-year CD: $323.20; $230.50

'f. Sample answer: A benefit of using a three-yearCD is that you can withdraw your money withoutpenalty in a shorter amount of time than youwould for the five-year CD, and a drawback wouldbe that you earn less interest. A benefit of usinga five-year CD is that you earn more interest, anda drawback is that you would have to wait longerto withdraw your money than you would for thethree-year CD.

2. a.—

y

-yo

10I

5 In > 35 75

—

10j

-

MOO

T__ ....... .... .... _

JC

b. x = 30; increase: (0, oo); Sampleanswer: Theoil company must drill at least 30 wells to collectoil, and the amount of oil collected increases asthe number of wells drilled increases.

c. 29.5 billion barrels d. about 326 wells



1. log3 4 + log3 x 2. In 4 + 2 In x + 5 In v

3. log5y 4. log86(32) 5.1.79 6.1.32

7. 80 db 8.-4 9.1.61 10. | 11.1.2012.1 13.-0.5 14.403.4 15.20

16. (-oo, 1.16] 17.(2.04,00) 18.(0,4]

19.(5,oo) 20..y = 6* 21. y = Ax

22.v =0.25*3 2Z.y =\x2 24.v=10.t3


a. log (jt° b.3db c. 85 dbd. 10-4 watt per square metere. about 31,623 times

f. 0.01 watt per square meter


(Full Page)

2. a.

c. v,(/): power function; v2(t): exponential functiond. Sampleanswer: You can use the linearregression feature of a graphing calculator to seewhich sets of data in parts (a) and (b) have a largercorrelation coefficient.

e. Sample answer: v,(0 = 250/006;v2(0 = 177(1.09)'f. Sample answer: v,(7) « $281,000;v2(7) « $324,000 g. 21 years

Georgia Assessment BookAnswers, Mathematics 3 A9

h. Sample answer: 250/006 < 295; Between years1995 and2011 i. Sample answer: 177(1.09)' > 500;year 2007 and beyond j. Sample answer: 2000;Youcan find the solution graphically by findingthe intersection of the graphs of v,(/) and v2(t) andalgebraically bysetting v,(f) equal to v2(r); Settingv,(f) and v2(t) equal results in an equation forwhich it is difficult to isolate t. The variable t is a

base on one side of the equation and an exponenton the other. In part (g), the equation is easilysolved by taking each side of the equation to thereciprocal power, k. Sample answer: The value ofthe first house increased less and less over time,while the value of the second house increased

more and more over time; The location of thehouses can greatly affect their values. Factors,such as population growth/decline, economicdevelopment, reassessment, and surroundingdevelopment, all contribute to a home's value.

Unit Test for Algebra: Exponential andLogarithmic Functions

1.1 I I I UI I A ', domain: all real numbers;range: y > 0

3.

4.

\ I ~x

y ; domain: all real numbers;range: y < 2

; domain: all real numbers;range: y > 0

~SSL,.5^-

X

]; domain: all real numbers;range: v > -2

y

-

... ...

-

...

- -

"

1

X

-*

...

5. $122.88

A10 Georgia AssessmentBook Answers, Mathematics 3

6.

7.

s—__J I JC

-i—i

B

; domain: all real numbers;range: v > 0

; domain: all real numbers;range: y < 0

8. ^ = 4*-3 9. v = In 0.5*+ 2 10.2

11.2e4^2 12. Ax 13.64a:214. || | | \y\ | | |; domain: x > 0;

range: all real numbersy

—.

(... X

15. ; domain: x > —2;range: all real numbers

X

•

16. x = 7; increase (-2, oo)

17. 0.51og1/2 x + 0.51og1/2 v 18. Injc + ln^

19. In 4 20.1og5*y2 21.4 22.1 23.-4,2

24.-3,9 25.(3.3,oo) 26. (j, oo)27. about 46 years 28. v = 4 • 2X29.y = 3.A5xi.0.54

Benchmark Test for Algebra:Exponential and Logarithmic Functions

1. B 2. D 3.C 4. B 5. A 6. C 7. C

8.D 9. A 10. B 11. C 12. A 13. A

14. C


I

I

^jj7

Performance Task for Algebra:Exponential and Logarithmic Functions

b.

1

135 108

55 44

y 11

j1

20

X

86 69

35 28

c.v= 135(0.8)*-1 d. 4 weekse. no zeros; decrease: [1, oo); Sample answer:The time it takes you to clean your room decreasesas the weeks go on, but never reaches zero.

f. about 2 minutes g. week 6 and beyond

h. decay; Sampleanswer: The graph of thefunction decreases from left to right, so itrepresents an exponential decay.

1. \ y

\,v ,

\

X

j. brother; brother; brother

k. No; Sampleanswer: After week 9, you willclean your room in less time than your brothercleans his room.


1. x2 = 16v 2. y2 = -20* 3. x2 = -24^4. i pi I n 5. y__

±H S|§§5V2


6. [ T J 111J "II]; vertices: (±6, 0),co-vertices: (0, ±3),

foci: (±3V3,0):e||

~~ 1,,1

7. TT'n» T~]J vertices: (0, ±8),co-vertices: (±4,0),

foci: (0, ±4V3)

1 y.r _

v ~v-t- *w ...

1

8.L I II \y\ I U; vertices: (0, ±4),foci: (0, ±2V/i3)l

asymptotes: v = ±tjc

y

f^"--* X

;^ f

_^i xkt X

1' -S_.

9. n 7TTvrTT~]; vertices: (±5,0),foci: (±V34, 0);

asymptotes: y = ±7*

-4--fFi

%s^N3i*^ *£


(Half Page)

a. Ellipses and hyperbolas have two foci, so theyhave two latera recta, b. 6 c. 3 . d. 49

e. (-5,10), (-5,-10)

f.(f,V7)and(-|,V7);(|,-V7)and(-|,-V7)g. (6, 16) and (6, -16); (-6, 16) and (-6, -16)

h. The length of the latus rectum of a circle is 2r,or the diameter, because the center represents thefocus of the circle and any line segment that passesthrough the center of a circle and has endpointsthat lie on the circle is a diameter.


(Full Page)

a.v2=12.68*

b.

~_<5 I 'x

Georgia Assessment Book Answers, Mathematics 3 All

I

I!c. ±15.1 d. 248,004 131.5

= 1

i e. V !

Ty\• "i -

1-

\ 4' 1

j '-

—

\i

"f230

i

._LL _^._ L\

»i;

f. ±1.03 g-4920 + 1.389

h.

= 1

—

y\

j2 —t—-12

s ""> \• \

s >•1

X

-l-

1; i

I. ±0.868 j. 32^jQ + 10>629 - !k. >

I. ±2.320

Quiz for Lessons 5.5-5.7(x - A)2 (y + l)2 _

1. 39 64

2. (x + 4)2 = -200> - 3)3. circle; (x - 3)2 + {y - A)2 = 25;

>—J

~tz S-— f 1

^-zztz-2 -3_i

4. hyperbola; —j^

~T~ ' y

4;-3 —*?*rn^iit 3sf: -J*

= 1

{x -2)2 (v + l)2= i;

5. (2, 8), (2,-3), (-1,6), (-1,-1)6. (0,4), (0,-1) 7.V46 8.VT78


9. (x - 2)2 + (v - l)2 + z2 = 410. (x + 3)2 + (v - 5)2 + (z - 5)2 = 25

11.{x - 2)2 (y - 4)2

25= 1


a. circle

_ l_„i„_

pfe+4i x

b. sphere c. sphere

d. circle

"y

-

—

-1

i X

- ) - -

e. The standard equation for a circle hastwovariables in x andy, whereas the standard equationfor a sphere has three variables in x, y, and z. Bothequations contain the radius rofthe figure.f. Asphere is the set ofall points (x, y, z) in3-space that are equidistant from a fixed point,called the center.

g.x2 + /=36;x2+.v2 + z2 = 36h.x2 + y2 = 16;;t2+y2 + z2 = 16


a. x2 + v2 = 1600; circleb. v2 = -320(jc + 20); parabolac.y= -|x +50;line d. (24, 32)e. (-23.3, 32.5)f. (x + 40)2 + (v + 80)2 <90,000 g. yesh. 363.6 ft I. (x - 60)2 + (v+ 60)2 <22,500j. no k. yes


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Unit Test for Geometry

;focus: [0, ^j,1.

I I 1 I I 1 i

directrix: y = -r,

axis of symmetry: x-axis

=M; focus:

directrix: x = -t

ps axis ofsymmetry: y-axis

3.y2 = 8x4. 5.I y

! " "

^"y=*. J *•^w-7 _,

r = 2

2

5'

c 2 , 296.y = ?x + y

y

-=2"gdy. 1; .,'

fc— I

r = A

7. ; vertices: (0, ±6),co-vertices: (±2, 0),

foci: (0, ±4V2)

"

""'"ZS1 2

4 <

i _j

XZ

x2 y2 4x2 i16

; vertices: (0, ±4),

foci: (0, ±2V?),asymptotes: y = ±2x

"•T-T=1 12' 1 • 913. x = 2, y = -3 14. hyperbola

4V3 _V|\ (4_V3 V|\3 ' 3 M 3 ' 315.

(x + 2)2 , C -1)2

ia LlO^H 20V4T\ (10V4T 20V4T\lb'l 41 ' 41 /'\ 41 ' 41 /

17. 21.2 mi 18.V83 19. Vl85

Copyright© McDougal Uttell/Houghton Mifflin Company

= 1

20.x' +y2 + z2= 1621. (x - 3)2 + (y + 2)2 + (z - 6)' = 25

Benchmark Test for Geometry

1. D 2. D 3. B 4. D 5. A 6. B 7. D

8.C 9.C 10. C 11. D 12. C 13. A

14. C

Performance Task for Geometry

a. x2 + y2 <, 25; See graph below, b. See graphbelow, c. (3, -4); This point represents thesecond intersection of the circle and the bottom

branch of the hyperbola, d. See graph below.

e. parabolic; B2 - AAC = 02 - 4(0)(1) = 0f. (3,4); This point represents the secondintersection of the circle and parabola.

4g. y = ^x;See graph below.

h. 24 mi,' underestimates; Sampleanswer:Thestraight-line distance from the intersection ofMain St and Carson Rd to the intersection of

Carson Rd and Eagle Dr is shorter than thecurved path traveled on Carson Rd. Similarly, thecurved path followed on Eagle Dr is longer thanthe straight-line distance from the intersectionof Carson Rd and Eagle Dr to the intersection ofEagle Dr and Main St.

usgsasss'A

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2 _

2. symmetric 3.97.35% 4.84% 5.0.15%

6.0.84 7.0.975


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b 0children watch professional football ontelevision, c. skewed d. Because up = 14.4which is >5and n(l - p) = 5.6 which is >5.e x= 14 4, o-« 2 f. 0.16 g. So, ifit is truethat 72% ofchildren ages 7-11 watch professionalfootball on television, then there is about a0.82 /o •probability of finding 95 or fewer children ages7_11 who watch professional football on televisionin arandom sample of 150 children ages 7-11.With aprobability this smallryou should rejectthe hypothesis.

Performance Task for Lessons 6.1-6.3(Full Page)a. 0.0062 b. 0.1056 c.97.5% d. 15.85%e. 0.0808 f. 0.1587 g. 50% h. 81.5%j _0 6 j. _1.4 k. The car from manufacturer A;In astandard normal distribution, the car frommanufacturer Ahas agreater gas mileage.I 80% of all compact cars get an average of 25 mpgor better in city driving, m. So, if it is true that80% of all compact cars get an average of 25 mpgor better in city driving, then there is about a34% probability of finding 39 or fewer compactcars that get an average of 25 mpg or better inarandom sample of 50 compact cars. With aprobability this large, you should not rejectthe hypothesis.

Quiz for Lessons 6.4-6.51.systematic sample 2,400 3.25004.12,346 5.5102 6. experimental study;

The teacher is assigning students to the controlgroup and the experimental group.

Performance Task for Lessons 6.4-6.5(Half Page)a. systematic sample; biased; Students enteringthe computer lab may be more likely to favor therenovation of the computer lab. b. 1000 peoplec. ±3.1% d. between 52.9% and 59.1%e. Sample answer: Because information technologystudents are more likely to use the computer lab,they may be more likely to favor renovating thecomputer lab. To correct the flaw, the researchershould redesign the survey so that there is nopotential bias in both groups.

Performance Task for Lessons 6.4-6.5(Full Page)a. Convenience sample; Sample answer: Thesample is biased because students on studentcouncil may be more motivated, higher-achievingstudents who would prefer abroader range ofelectives over extra study time. b. 16 students;±25%- Sample answer: No. Amargin of errorthat large will probably make it impossible todetermine amajority opinion, c.Sample answer:No Amargin of error of ±2% requires asamplesize of 2500, which is more students than attendthe school. One quarter of the student body is 435students. The least margin of error possible tor asurvey with that sample size is ±5%.d. Sample answer: The flaw is that students whohave astudy hall are the experimental group andstudents who have no study halls are the controlgroup. To correct the flaw, the student councishould redesign the survey so that the schedules ofthe students in both groups are similar.e. Sample answer: The student council could useacomputer to randomly generate 435 student IDnumbers to determine which students to survey,f Sample answer: No. Because the margin oferror is ±5%, the exact percent of the studentbody who wants study halls and limited electivesis likely between 41% and 51%. Similarly, theexact percent of the student body who wantsno study halls and abroad range of electives islikely between 49% and 59%. The overlap in theintervals makes it impossible to determine for surewhat the majority of the student body prefers.

A14 Georgia Assessment Book Answers, Mathematics 3• Copyright ©McDougal Uttell/Houghton Mifflin Company.

/

/

Unit Test for Data Analysis andprobability1.0.007 2.0.00000001. 3.0.042

4. 0.30

0.25

0.20

0.15

0.10

0.05

0

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Number of adults who usethe Internet at home

5. skewed 6.0.141 7. 0.889 8. 0.977

9.0.16 10.0.815 11. convenience; biased

12. ±2.0% 13. ±7.5% 14.100 15. 10,000

16. ±6.9%; between 65.1% and 78.9%

17. Sampleanswer: The flaw is that 12thgrade students are the experimental group and1lth grade students are the control group. Theexperimental and control groups should both be12th graders or 1lth graders.

18. observational study: The assignments of thestudents to the experimental group and the controlgroup'are outside of the teacher's control. Thestudents "sort themselves" into the two groupsbased on ther previously-made decisions aboutwhether to participate in class..

Benchmark Test for Data Analysis andprobability

1. B 2. D 3. C 4.B 5. A 6. A 7. D

8. C 9.D 10. C 11. B 12. B 13. C

14. C

performance Task for Data Analysisand Probability

a. Sample answer: Because students at acomputer lab are likely to have access to theire-mail accounts, they are more likely to checktheir personal e-mail daily. To correct the flaw,you should redesign the surveyso that eachgroup contains Internet users, b. self-selected;unbiased;The sample would be representative ofInternet users, c. 0.975 d. ±4.5%

e. between 75.5% and 84.5% f. 1600 g. 4445

h. 85% of Internet users check their e-mail daily.


i. 400 j. If it is true that 85% of Internet userscheck their e-mail daily, then there is about a 0.1%probabilityof finding 400 or fewer Internetuserswho check their personal e-mail daily in a randomsample of 500 Internetusers. With a probabilitythis small, you should reject the hypothesis.

Georgia Assessment Book Answers, Matiiematics 3 A15

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