Name ________________________________________________________________________ Date ______________

HONORS ALGEBRA 2 FINAL REVIEW 2018-19 Chapters 6, 7, 8, and 10

Sections and Scoring

• Your final exam will test your knowledge of the topics we studied in the second half of the school year.

• There will be two sections – a calculator free section and a calculator active section.

• The exam consists of a variety of multiple choice and open-ended questions.

• There will be a formula sheet (see last page of this review packet).

• There will be a maximum possible score of 108 points. How do I prepare for the Final Exam?

• Answer as many problems as possible from this review packet and check your answers.

• You should only use a calculator when absolutely necessary.

• Do not wait until the last minute to begin reviewing for this exam.

• Review old tests and quizzes from the 3rd and 4th marking periods.

• Pay attention during class on the review days and ask questions.

• Get enough rest the night before. Wake up early and eat a healthy breakfast. What do I need with me on the day of the exam? What are your rules and expectations?

• TEXT BOOK.

• Bring at least two sharpened pencils with BIG erasers.

• You may only use a calculator that has been RESET BY ME.

• Bring things that will help you study for your other exams in case you finish early and have free time.

• If you do not like to study for your other exams, bring a book or school appropriate magazine to read. If you finish early, you must remain quiet until all exams have been collected!

• DO NOT bring hats, iPods, mp3 players, cellular telephones, or any other electronic devices. You are not permitted to use them at any point during the exam session (whether you are finished or not). In the past, students have been caught using these things to cheat. It is not wise to place yourself in that situation. Bring non-electronic forms of entertainment so that you do not get into trouble.

• NO ONE MAY LEAVE the room unless it is an absolute emergency. You are required to remain in the exam room the entire time. No one gets to leave early. Do not ask for passes to go hang out with other teachers. You will have a break between your exams to use the restroom.

Exam Schedule

Date Session 1 Session 2

9/10 7/8

8/9 6/7

5/6

4/5

12 11

2 1

Monday 6/17

Tuesday 6/18

Wednesday 6/19

Thusday 6/20

3

Domain

Range

x-int

y-int

INVERSES AND RADICAL FUNCTIONS AND RELATIONS (Chapter 6)

Let ( ) 451852 23 −−+= xxxxf , ( ) 3382 −+= xxxg , ( )2

53 −= xxc , ( ) 73 −= xxm , and ( ) 5−= xxp .

Find each of the following. State any restrictions in the domain, if necessary.

1) ( )( )xgf + 2) ( )( )xfg − 3) ( )( )xgm• 4) ( )xgm

5) ( )( )xg

f 6) ( )1+amg 7) ( ) 2−mg 8) ( )6.2pc

9) Find the inverse of ( )xm . Is the inverse a function?

10) Use 96)( 2 ++= xxxh to answer the following.

a) Is )(1 xh− a function? Why or why not?

b) Graph 96)( 2 ++= xxxh and its inverse on the

same coordinate plane without a calculator.

c) Find the equation of )(1 xh− . Show your steps.

11) If ( ) ( ) ( ) ( ) 3,8,6,6,3,5,9,0 −−−=f , find 1−f and state whether or not 1−f is a function.

12) Let 124)( += xxf and 3)(41 −= xxg .

a) Find ( )xgf .

b) Find ( )xfg .

c) Are )(xf and )(xg inverses?

13) Graph and provide the requested information for 14) Graph 372 −− xy

34 ++−= xy

15) Simplify: 22 2510 yxyx +− 16) Simplify: ( )( )4 13624 14 84 zyxxy

17) Subtract: 33 3752245 − 18) Rationalize the denominator: 35

3

9 p

q

19) Rationalize the denominator: 335

331

+

− 20) Evaluate:

31

23

8

125

−

+

21) Simplify: 535

6

32 −

•

xx 22) Solve: 3235 3

1

=+x

23) Solve: 15323 −+− x 24) Solve: 15 ++= xx

25) Simplify: 3 125 26) Simplify: 5 3xx •

27) Simplify: 1

2

21

21

−x

x 28) Rewrite 8

32

14

1

2 yx as a single radical.

CHAPTER 6 ANSWERS

1) 781062 23 −−+ xxx 2) 122642 23 ++−− xxx 3) 231155173 23 +−+ xxx

4) 106243 2 −+ xx 5) ( )( )11,3;

11

352−

+

++xx

x

xx 6) 499 2 −a

7) 32 8) 1− 9) ( )37

311 +=− xxm , yes

10a) )(1 xh− is not a function because )(xh fails the HLT. 10b)

10c) xxh −=− 3)(1

11) ( ) ( ) ( ) ( ) 8,3,6,6,5,3,0,9 −−− , Not a function

12) a) xxgf =)]([ b) xxfg =)]([ c) Yes

Domain

Range

x-int

y-int

)− ,4

( 3,−

5

1

13) 14)

15) yx 5− 16) 4 335 22 zxzy 17) 0

18) 2

3

3

3

p

pq 19) 3916 +− 20) 127

21) 5

1

x 22) 64− 23) )11,5.1−

24) 3:

8:

=

=

xrootExtraneous

xSolution 25) 5 26)

10xx

27) 1

22 21

−

+

x

xx 28) 8 344 yx

EXPONENTIAL AND LOGARITHMIC FUNCTIONS (Chapter 7) Graph each function. State the domain, range, and equation of any asymptotes.

1) 32 1 +−= −xy

2) ( )3log2 += xy

I’ve had a great time

appearing on your

math papers this year!

– The Deer

3) Determine whether ( ) xy

−= 75.05 represents exponential growth or exponential decay.

4) Simplify without using a calculator: 5

20

9

27

5) Describe how to transform the graph of xxf ln)( = into the graph of ( ) 1ln)(32 −−= xxg .

Solve each equation without using a calculator.

6) ( ) 14

2513 1255

2 ++− =• xxx 7) 7749 2 =+x

8) Write 636 2

1

= in logarithmic form.

9) Write 364log4 = in exponential form.

10) Write 6094.15ln in exponential form. Evaluate without using a calculator.

11) 49log7

1 12) ( )32loglog 25 13) 5loglog2 333+x 14) 27log48log 23

12 −

15) 7lne 16) eln 17) 1ln 18) 10log

Solve each equation or inequality without a calculator.

19) ( ) x=3log 9 20) ( )23

4 3log −x

21) 329log =x 22) ( ) ( )47log73log 88 +=+ xx

23) ( ) 2log32loglog 444 =−+ xx 24) 49log4loglog2 321

33 =−x

25) ( ) ( ) 212log3log 55 +−=+ xx 26) ( ) 4log2=x

27) Evaluate 2.1log5 in terms of common logarithms. Then approximate to four decimal places.

28) Rewrite as a single logarithm: CBA ln3lnln21 −+

29) Without using a calculator, determine which logarithm is greater in value: 17log2 or 80log3

30) Write the equation in xaby = form that passes through ( )61,1− and ( )

29,2 .

Solve each equation or inequality. Round to four decimal places.

31) 12532 +x 32) 7.325.4 22

=+x

33) 4ln2 =x 34) 3442 5 +− xe 35) Suppose Ms. Walsh finds an account that will allow her to invest her $300 at a 4.25% interest rate compounded quarterly. If there are no other deposits or withdrawals, what will Ms. Walsh’s account balance be after 20 years? Round to the nearest cent. 36) How long will it take an investment to double at 3.25% compounded continuously? 37) The Reidy family bought a new car for $26,500 in 2013. If the annual rate of depreciation is 12.5%

for that particular car, in what year would you expect the car to be worth $5000? Use tray )1( −= .

38) How old is a fossil that lost 75% of its Carbon-14? Use 00012.=k .

CHAPTER 7 ANSWERS 1) 2)

Domain: ( )− , Domain: ( )− ,3

Range: ( )3,− Range: ( )− ,

HA: 3=y VA: 3−=x

3) Growth 4) 543

5) Reflect over the y-axis, expand horizontally by a factor of 23 , translate one unit down

6) 7=x , 2−=x 7) 45−=x 8)

21

36 6log = 9) 6443 =

10) 6094.15 e 11) 2− 12) 1 13) 25x

14) 4 15) 7 16) 1 17) 0

18) 19) 41=x 20) 113 x 21) 27=x

22) 43=x 23) 2=x 24) 72=x 25)

74=x

26) 100=x or 100

1=x 27) 1133.05log

2.1log= 28) 3ln

C

BA 29) 80log17log 32

30) ( )xy 3

21= 31) 8856.0x 32) 5645.0x 33) 3891.7x

34) Ø 35) $698.75 36) about 21.3 years 37) the year 2025 38) about 11,552 years old Study Tip

Studying for 30-50 minutes at a time (with 10 minute breaks in

between) is the most effective way to retain information.

Undefined Value(s)

Equation of VA

Equation of HA

Domain

Range

RATIONAL EXPRESSIONS AND EQUATIONS (Chapter 8)

1) For what value(s) of “m” is mmm

mm

30212

12623

2

−+

−− undefined? Then, simplify the expression.

Simplify each expression.

2) 94

2782

3

−

+

x

x 3)

472

4

24183

162

3

23

2

−−

−•

++

−

xx

xx

xxx

x

4) 23

292

131

xx

x

−

− 5)

43

2

72

5

+−

+ xx 6)

42

22

3 6

3

2

yx

ba

abc

xy

−

7) 24

5

6

1

8

132

2

−+

+−

x

x

x

x 8)

16

2

82

522 −

−−+ xxx

State the excluded value(s). State the LCD. Solve each equation or inequality.

9) 3

2

62

7

9

112 +

=+

−− xxx

10) x

x

xx

x

−−

+=

−

+

2

5

2

2

4

252

11) 2

1

8

5

4

1+

xx

12) Last year, it took Miss Heidorn 2 hours and 30 minutes to stain her deck. This year, she asked Mr. Stramaglia for some assistance and together it took them 1 hour. How long would it have taken Mr. Stramaglia to stain the deck by himself?

The function below is a transformation of x

xf 1)( = . Complete the chart and sketch the graph.

13) 3)(2

2 +−=−x

xf

14) State the domain and range of 2

1)(x

xf = .

15) 2)(5

3 +=−x

xg is a transformation of x

xf 1)( = . Describe the transformations.

16) Is the graph of 52)( −= xxf the same as the graph of 3

15112 2

)(−

+−=x

xxxg ? Explain.

Undefined

Value(s)

VA Hole

HA OA

Zeros y-intercept

Undefined

Value(s)

VA Hole

HA OA

Zeros y-intercept

Undefined

Value(s)

VA Hole

HA OA

Zeros y-intercept

Undefined

Value(s)

VA Hole

HA OA

Zeros y-intercept

17) ( )xg is a transformation of 2

1)(x

xf = . Determine the equation of ( )xg if it has a vertical asymptote at

3−=x and a horizontal asymptote at 7−=y .

18) For the function 5216)(

−+=

xxxf , as __________)(, →→ xfx .

19) Write 2)(5

3 +=−x

xf in )(

)()(

xq

xpxf = form.

Complete the chart and then draw the graph.

20) 4

20132)(

2

−

+−=

x

xxxf

21) 34

124)(

2

2

+−

−=

xx

xxxf

Complete the chart for each given function. Do not draw the graph.

22) 4

3)(

2 −=

xxf 23)

1

74)(

2

−

−+=

x

xxxf

Undefined Value(s)

Equation of VA

Equation of HA

Domain

Range

2=x

2=x

3=y

( ) ( )− ,22,

( ) ( )− ,33,

CHAPTER 8 ANSWERS

1) The expression is undefined when 0,,35

23 orm −= . Simplified expression:

)53(2

43

+

+

mm

m

2) 32

964 2

−

+−

x

xx 3)

)12(3

2

+

−

x

x 4)

23x 5)

)43)(72(

611

++

+

xx

x

6) 2

2

8

3

y

bc 7)

2

2

24

348

x

xx −+ 8)

)2)(4)(4(

163

−−+

−

xxx

x

9) Excluded Values: 3,3 −== xx LCD: ( )( )332 −+ xx Solution: 5=x

10) Excluded Values: 2,2 −== xx LCD: ( )( )22 −+ xx Solution: 53=x

11) Excluded Values: 0=x LCD: x8 Solution: ( ) )− ,75.10,

12) 1 hour and 40 minutes

13) 3)(2

2 +−=−x

xf

14) Domain: ( ) ( )− ,00, Range: ( ),0

15) Reflection in the y-axis, expanded vertically by 3, translation of 5 units to the right and 2 units up

16) 3

15112 2

)(−

+−=x

xxxg is the same line as 52)( −= xxf , but it has a point discontinuity at ( )1,3 . Therefore, they

are not the same graph.

17) ( )

7)( 23

1 −=+x

xg 18) 3 19) 5

72)(

−

−=

x

xxf

20)

Undefined

Value(s)

VA Hole

HA OA

Zeros y-intercept

4=x

none ( )3,4

none none

25

5−

Undefined

Value(s)

VA Hole

HA OA

Zeros y-intercept

Undefined

Value(s)

VA Hole

HA OA

Zeros y-intercept

21)

22) 4

3)(

2 −=

xxf 23)

1

74)(

2

−

−+=

x

xxxf

SEQUENCES AND SERIES (Chapter 10)

1) a) List the first 6 terms in the sequence of perfect cubes.

b) Write a formula for the nth term and find 14a .

c) Is this sequence arithmetic, geometric, or neither? Explain.

2) Find 13a for the arithmetic sequence ...,7,12,17 −−−

3) In the arithmetic sequence ...,13,10,7,4 , which term has a value of 301?

4) Find the sum of the arithmetic series 2...323538 ++++ .

5) Find the sum of the arithmetic series: =

+10

4

12p

p

6) Find the next two terms in the geometric sequence: ...,8.1,5.1,25.1 −

7) Find the geometric means in the sequence: 162___,___,___,,32___,

8) Find the sum of the geometric series to 7 terms. ...120603015 −+−+−

9) Find the first term in the geometric series described: 48;;16532 =−== nn arS

10) Find the sum of the infinite geometric series, if it exists: ...469 +++

Undefined

Value(s)

VA Hole

HA OA

Zeros y-intercept

1=x 3=x

1=x ( )6,3

4=y none

0 0

2=x

2−=x2=x

2−=x

none

none0=y

none43−

1=x

1=x none

none 5+= xy

7112−

11) Contagious diseases can spread very quickly. Suppose five people are ill during the first week of an

epidemic and that each person who is ill spreads the disease to four people by the end of the next week.

By the end of the tenth week of the epidemic, how many people have been infected by the illness?

12) Find the value of x that makes ...,9,2,14 −++ xxx an arithmetic sequence. Then find the first 3 terms.

13) If 31 −=a and 2

1 naa nn +=+ , find the first five terms of the sequence.

14) Find the first three iterates of xxxf 3)( 2 −= for an initial value of 10 =x .

15) Mr. Geist loves geometry! He is planning on building a brick patio that approximates the shape of a

trapezoid. The shorter base of the trapezoid needs to start with a row of 5 bricks, and each row must

increase by two bricks on each end until there are 25 rows. How many bricks does Mr. Geist need

to buy?

16) Evaluate: 37 P 17) Evaluate: 37 C 18) Simplify: ( )( )!1

!3

−

−

n

n

19) Expand the binomial: ( )425 yx −

20) Find the 4th term in the expansion of ( )83

21 ix − , where i is the pure imaginary unit.

21) Factor using the Binomial Theorem: 1086243245 1040808032 yxyyxyxyxx −+−+−

CHAPTER 10 ANSWERS

1a) 1, 8, 27, 64, 125, 216 1b) 3nan = ; 274414 =a 1c) Neither, no common difference or ratio

2) 43 3) 100th term 4) 260 5) 105

6) 592.2,16.2− 7) 108,72,48,3

64 8) 645− 9) 243

10) 27 11) 1, 747, 625 12) 5,6,17;4 −=x 13) 27,11,2,2,3 −−

14) 70,10,2− 15) 1,325 bricks 16) 210 17) 35

18) 23

12 +− nn

19) 2234 161606001000625 yyxyyxyxx +−+− 20) 15

47 ix

21) ( )522 yx −

Study Tip

Break the study guide problems up in to sections, and do

a section each day. If you have any questions, come to

extra help and get them answered!

HONORS ALGEBRA 2 FINAL EXAM 2018-19

FORMULA SHEET

EXPONENTIAL GROWTH AND DECAY FORMULAS

( )tray += 1 Exponential growth, where r is the growth factor

( )tray −= 1 Exponential decay, where r is the decay factor

( )nt

n

rPA += 1 Interest, compounded n times a year rtPeA = Interest, compounded continuously

ktaey = Exponential growth, there k is the rate of continuous growth

ktaey −= Exponential decay, there k is the rate of continuous decay

SEQUENCE AND SERIES FORMULAS

( )dnaan 11 −+= ( )nn

n aaS += 12 ( ) dnaS n

n 12 12−+=

( ) 1

1

−=

n

n raa ( )

r

raS

n

n−

−=

1

11 r

raaS n

n−

−=

1

1 r

aS

−=

1

1

VARIATION FORMULAS

kxy = Direct variation

x

ky = Inverse variation

kxzy = Joint variation

PERMUTATION, COMBINATION, AND BINOMIAL THEOREM

( )!!

rn

nPrn

−=

( ) !!

!

rrn

nCrn

−= ( )

=

−•=+n

r

rrn

rn

nbaCba

0