Special Topics Trig unit 13 A Nÿiile

Multiple ChoiceIdentify the choice that best completes the statement or answers the question,

/2ÿ 1. Use the graph below. Determine the period of this function,

b, 1,5 c. 6 d. -1,95

k 2. Find the measure of the angle below.

>x

110° b. 250° c. 900 d. 210°

Sketch the angle in standard position.

, 55°

a,'y

55°\

b, dJ

55o

÷x

,

'y C°

-150

, t

y

o-150

>x

>x

d,

'y

o-150

-9

5, Find the measure of an angle between 0° and 360° coteiaTtinal with an angle of-110° in standard position,(_a') 250° b, 20° c, 110° d, 70°

55_ , In which quadrant does the terminal side of a 118° angle lie?a. third quadxant c. first quach'ant

second quadrant d, fourth quadrant

.(D, Find the exact value of cos 300° and sin 300°,

a. 1 ,ÿ c. "ÿ 1

cos=--ÿ, sin- 2 cos = 2 sin 2

b@. 1 'ÿ d. "f3' sin - 1cos= ÿ, sin- 2 cos- 2 ' 2

Write the measm'e in radians. Express the answer in terms of or.

8.ÿ0°

16x b. 9_ffK c. 99 16 lÿyi

d, 169st

,

d,

45°

.) z b. 97e c. ÿr

4 20 6)'r

8

Write the measure in degrees.

10. -ÿ radians! -ÿ ÿ, -ÿ

a. 1O8ÿr° b, _ff__ÿ o (ÿ")108°300

d. 1.880

C_ 7ÿr11. --ÿ radians ÿ' ,

a. -315ÿ b. _7_.ÿo ÿdÿ)

720-3 ! 5° d. -5.5°

C 12. Find the exact vÿluos of coÿIÿ ÿoÿ)ÿnd ÿIÿ raÿsl

a. ,,ÿ ÿ b. 1 ,',f3 ÿ'ÿ ,xf2 qÿ"

2' 2 2'2 2'2

d, i2 '2

13,

14. Use the circle below. Find the length s to the nearest tenth.

a. 7.Oft b. 3,1ft @22,Oft d. 44,0 ft

Use the graph to find the value ofy = sin O for the value of Oo

15, 270°

0

a. -0.4 b, -0,8 c. -0.6 d, -1

1Lÿ 4sr radians

b .... i" ""1

yi i i i i g i n

iÿi : '2' :ii1!ii iiiiiiiii iiii i ! i ! ! i !

a, -0.7 ÿ 0.7 c. -0,9 d, 0,9

17, Find the period of the graph shown below,/

;- - ÿ-2 - 'ÿ, .................................. , , , , , , ,'' I I II

01 ill ii i ÿli iiI I

1,ÿ

i qJ iu.. i""

iu u

u

lallll

I

Iÿn II IIl0 )

i I ii Ikg._.d. _ÿ ...... L- t'i

i n

II IIJ[ÿ

i u i ÿ u u----2. , I

a, 2ÿr b, '2 c, '1

3x 2ÿvd, 4ÿr

---....

\_) 18, Find the am ÿlitude of the sine cmwe shown below,

''y

i'-ÿ.-ÿ- ",'--ÿ--! -,ÿ'-,ÿ"ÿ'"ÿ"ÿ" "!

! i iii!!i :ia. 2ÿ b. 8 c, 2

19. A particular sotmd wave can be graphed using the function y = -3 sin x. Find the amplitude and pelqod of

the function,@ amplitude = 3, period = 27r c. amplitude,= 2ÿr, period =.3b, 1 d. 1

amplitude = 2 a' period = -3 amplitude = -3, period = 2

iI

i!--a-

ii

"4-

'y

: , , : : .....

p

% 21. Write the equation for the sine function shown below.

i---r-, i

, i

I qI - - -b--2-,i ii--4--i ,i---ÿi t

'y

,i,,llÿlDI**III*illlÿllj*llllÿl

l*llllll

illllll

/! ÿ i/:x: I i-- i i -iIg

jl|MÿltllllPJ*l

#Jill

iI111

>0

\'0 ,.

k) ssP

a. y= smO c. y=-lsin60

) y = sin3e9 d. y =-lsin30

lh 22.3

Find the period, range, and amplitude of the cosine function y = -j cos -ÿ,

3< <3 3period = 4g,ÿ range:-ÿ_ y- -ÿ, amplitude --.5

3 3 3b. period = -12, range:-ÿ-< 2' -2' < - amplitude = --2

3 3 3c. period = 4ÿr, range:-ÿ -< y -< -ÿ, amplitude - 2

3 3d, period = 1, range: y -< ÿ, amplitude =

;g, :-

Write a cosine function for the graph.

23. ly"':'-'[-'F--,'''''"''",-''"'"'"'', ,,1:1 .... ,

--'-4+-->--ÿ .....iÿ1111

ii illlll)lllÿ

{:::i:{: 'iili .....ii Illlllljill

........ ÿ:,

C,a, ,ÿy = -2 cos 3

,ÿ..c_ %

0y = 2 cos 3

b, 2 cos 3 @ y = -2 cos 3#

a,

r...ÿ

i--6-

i ....

}--4-

i.-2-

!oii

iV....

!=4-} ....

t ....

24.

y= -2 cos ;ÿ+-- -2 y=-2cos ÿ-

y = 2cos x- -2 y=2cos x+ -2

->

0

-2

>__ 25. What is the value of h in the translation of the function g(x) =J(x - 6)? Describe the phase shift (use a phraselike 3 units 1o the left),a. h = 6; die phase shift is 6 units to the left,b. h = -6; the phase shift is -6 units to the right.._% h = 6; the phase shift is 6 units down.

@,5 h = 6; the phase shift is 6 units to the right.

Graph the function in the interval fl'om 0 to 2m

[.ÿy=,ÿ ÿ5= ÿ,+,ÿvq

--+i-+-

r- ÿ -I ....

i+.. , ....

F'-', ...., i,ÿ-.-ÿ+

[ ,,

r'--,--"

i ii ir- "% ....i i

: :0l +

i i

i i

!...ÿ+

b, d.

i ,

b---: ....

, ii ii ,

, ,,

t :

/

r---, ....i i, i!...i.++

t

F...: ....

k ;o i

i i

'y

ll,+l'iiii11

........ :>

i i ! ÿi i !2ÿi

!:: ,,,''...ÿ...ÿ...ÿ.. ,...,...,...,..-,--.'

iiii,

.....''''I"ÿ"-°ÿ''"ÿ''''111

"ÿ o'3 ÿ'--ÿ ÿ-' :ÿ/

:2

(:.E-ÿ 'ÿ'9

/.'ÿ-vv, ÿ") --"9

.2

3. 9-

' T--"

--6-i

}--4-

--2-LL ....

___L_9_

....

!ÿ4'-

Tÿ'"£IF--6-i

i ....

i--2-i

:.___90<-'----i ....

} ....

iL ....

Y'''*I ....| ÿ .... I .... t .... r .... , ...._

.... .... : ..... ', .... .I .... F ............... ! 1 :

......... -1 .... "I .... I' .... " .... l ..... ii l ÿ i u

i i i J i i i

i i i ÿ i i i-ÿÿ'i

............ i

i e .... , .... 9

,' - --4 .... I .... {. .... b .... : .... 4!

'. ......... , .... J .... J .... l .... t. .... ' .... J

.... , ..... , .... ;--,--4, .... : .... -,/

.... ; .... -: .... t .... ," .... ,t .... : .... .:

".T""

..... ; .... 4 .... '1 .... I .... I. .... : .... i

C,

d,

..6- 'i ..................... i ..... i

........... .: .; .... [ .... 1. .... ', ..... :, 4 I , -.ÿ---'ÿ ; : ,, ,,

....... ,ÿ " t .... ,ÿ , ,

b-2: .....

, Oÿ , , , .>

...... : ',

4 .... " .... 4--- -,

!=6- --! .... ! .... ÿ .... i ..... i

.....I : : ',,-.c,-.ÿ ........... ÿ .... ÿ .... , .... , ..... .

/-ÿ ........... ÿ .... I .... F .... , ..... ',

"2" , ÿ"ÿ, .... , ..... ,

0 ' * '

i2 ' '

i ÿ4 ......, ', .... 4.., , ' ,' ', ,' "" ",..... ', .... 4-- --I .... f .... ¢''" ÿ

!=6 ...... ', ..... i .... ! .... ÷ ..... ÿ ...... " ..... "........ ', .... ÿ .... a .... [ .... ÿ .... " ..... "

b_ 28. Write an equation for the translation 3 units down ofy = sin x,a, y= sin(x+3) c, y= smx+3b, y = sin (x- 3) (_B-) y sin z- 3

16, ANS: B PTS: 1 DIF: L2 REF:OBJ: 13-4.1 Interpreting Sine Functions TOP: 13-4 Example 2

I¢.£Y: sine function I graphing

13-4 The Sine Function

[

qLÿ

Name.

Sections 14ol to 14-3 TestPer,

Multiple ChoiceIdentify the choice that best completes the statement or answers the question.

) 1. Identify the expression that completes'the equation so that it is an identity.

sin ÿ 81 -cos2 6ÿ

l+secO 1'sinea, b, sin 9 c. ÿ-- 1

Sec (ÿ cos e

Simplify the trigonometric expression.

c, sece d, cosO

Use a unit circle and 30°-60°ÿ90° triangles to find the degree measures of the angle.

3. angles whose sine is ---ÿ,2

a, 30° and 330°

(_ÿ 60° and 120°c, 240°and 300°d. 150° and 210°

a,

b.

4, angles whose tangent is ÿ/rÿ,120° and 300° cÿ 60° and 240°150° and 330° d. 30° and 210°

5, angles whose cosine is2

a. 60° and 120° c,

b. 30 and 330° d.240° and 300°150° and 210°

Use a calculator and inverse functions to find the degree measures of the given angle,Round your answer to the nearest hundredth.

6. angles whose sine is 0.53

S2 ooi°

7. angles whose tangent is 0,59

.SO o,ÿ° ÿ 21ooÿ-ÿ

Solve the equation for 0° <L e < 360°.

8, 5tane =6 -tanO

135° and 315° ffb.ÿ 45° and 225°a. c. 90° and 270° d. 60° and 120°

9, cos 0 ÿ tan 0 cos e = 0

a. 0°, 45°, 180°, and 225°

b. 45°, 135°, 225°, and 315°

@45°, 90°, 225°, and 270°d. 90°, 210°, 270°, and 330°

cÿo"

,2-fOÿ

t,,r-ÿ 10, 3 o sin e = 5 sin o.

.' 30° and 150°

b. 30° and 210°c, 30° and 330°

d, 30° and 120°

In AXVZ,/Y is a right angle and sinX = 2025

Find cos X in frac1"ion form,

b, 25 15 d. 25

25 20 20 15

X

"ÿ 12. In AXYZ, ZY is a righf angle and sinX = 14

50a. 50 b, 50 c. 14

48 14 50

d. 0.5°

Find the angle ÿmeasure to ¢he nearest tenth of a degree.

) 13, sin-I 0,5166

a. 1° @ 31.1° c. 58,9°

25\S

Y 20

. Find sin Z in fracfion form,

" 48

5O

×5O

Y 14

__ 14, cos"1 0.0682

a. 0,1° (ÿ 86.1° c, 1.5° d. 3.9°

_ÿ 15. tanI 7,9321

e. 7,2° b. 82,8° c. 1,4° d. 01°

In AABC, ZC is a right angle. Find the remaining sides and angles. Round your answers 'tothe nearest tenth.

'ÿ 16, a = 3.4, c = 5,8

a, mZA = 30,4°, mZB = 59.6°, b = 4,7

b, m,ZA = 59.6°, mZB = 30,4°, b = 4.7

L2ÿ ÿ"3r

,f

Chapter 14.4-14.6 Test A Name

1. Use the Law of Sines. Find b to the nearest tenth,

C

4,,'\ Gÿ"jf

A

31

Use the LaW, of Sines, Find taLC to the nearest tenth,

C

69

67°

72

\

B A

Find the remaining sides and angles in the triangle, Round yore' answers to the nearest tenth.

t

fmAA =55°, mAN=44°, andb=68

I

4, a=ll, b=12, and¢=17

&

,' ,r

)

5. Use the Law of Cosines. Find b to the nearest tenth.

bÿ to5o

C

6O

48°B 85

6. Use the Law of Cosines. Find mZA to the nearest tenth of ad •

('O2ÿ

C

B 3 A

7, In AJKL,jÿ= 9 in., k = 5 in., and roll = 43°. Find re.d/&

\L--

8, In kABC, b = 7, c = 10, and mZA = 146°. Find a, Round your answer to the neai:est ÿcenth.

ca= \kooÿ 1ÿ

9. hi ANGH, g = 8 It, h : 13 ft, and mZF = 72°, Find mZG, Round your answer to the nearest tenth.

Verify the identity.

10,l

tanS+cotO=sm 8cos 8

,5ÿr, t..0%

\

5ÿ.v,,. ,5/) ") '5w,, ÿ-ÿ%

11,sec 8 sec 8--, = 2 csc 8

csc ÿ- cot ÿ - csc O+ cot 4?

Simplify the following. ..

12, sin 40°cos50° + cos40°sin50°f

At7ÿ © ÿ k

13, €os105°cos15° - sinlOS°sini5°

Co¼ I o')-©

Find the exact value, Use a sum or difference identity,

14. cos 15° 15, sin 15°

4 ½

Chapter 7 Test A Name: __

1. A polling company conducted a survey of voters to obtain data for a political campaign.They selected 3500 voters randomly from the 168,000 names on the voter registrationlists of the county and found that 1372 intended to vole for candidate Doe, The

(ÿ8,000 names represent:the population,B) the sample.

2. A marketing company conducted a survey of college students to obtain data for anadvertising campaign. They selected 1421 students randomly from campus directoriesof 132 colleges and universities, The 1421 students represent:

(ÿ) the population,the sample.

3. To determine the proportion of voters who favor a certain candidate for governor, thecampaign staff phones 2500 residents of the state chosen from the state property taxrolls. The 2500 residents represent:

the population.the sample,

4. A national poll asked 1581 adults whether they were satisfied with their jobs, and 54%said they were, Estimate a 95% confidence interval for the actual percentage among alladults,A) 53%to 55%

52% to 56%51.5% to 56.5%

D) 50% to 58%

5. To detelrnine the proportion of students at a university who favor the construction of aparking garage, a sample of people on the CulTent enrollment list is surveyed and it isfound that 45% favor the garage, The actual proportion of the student body who favorthe garage is 40%. This difference is most likely an example of sampling:

bias,variability,

Page l

6. A polling company surveys 200 people outside a county courthouse concerning tighterrestrictions on smoking in public buildings. Their results indicate that 34% of thosesurveyed favor tighter restrictions. The actual proportion of county residents who favortighter restrictions is 65%, The difference is most likely due to:

ariability in sampling.bias due to the use of a convenience sample. 'confounding variables in the survey,

D) the wording of the smwey,

7. In order to determine the proportion of voters in a small town who favor a candidate formayor, the campaign stafftakes out an ad in the paper asking voters to call in theirpreference for mayor. This type of sample is a:A) convenience sample.B) simple random sample.

multi-stage random sample,voluntary response sample,

,

provided by the county license office.

(ÿ) convenience sample.simple random sample,C) multi-stage random sample,D) volunta13, response sample.

To estimate the number of motorists likely to favor a tax increase for road repair, apolling company chooses 1000 names at random from a list of registered car owners

This type of sample is a:

9, A polling company conducted a smwey of voters to obtain data for a political campaign,They selected 3500 voters randomly fi'om the 16,800 names on the voter registrationlists of the county and found that 1365 intended to vote for candidate Doe, The sampleproportion is:A) 0,081

0,2080,390.1365

Page 2

Use the following to answer questions 10-11:

Use the following random digits to answer the question(s) below.

101 01033 08705 42934 79257 89138 21506 26797102 49105 00755 39242 50772 44036 54518' 56865103 61589 35486 59500 20060 89769 54870 75586104 08900 87788 73717 19287 69954 45917 80026105 75029 51052 25648 02523 84300 83093 39852106 91276 88988 12439 73741 30492 19280 41255107 74008 72750 70742 67769 72837 27098 07049108 98406 27011 76385 "15212 03806 85928 76385

10. Beginning with line 102 of the random digits table above, select three individuals fromthe list below to serve on a student affairs committee.

01 Crosby 06 Jones02 Hunter 07 Smith03 Cooper 08 Davis04 Grant 09 Ewing

Rciley 10 Doeooper, Doe, Smith

Doe, Ewing, Grant(2) Doe, Smith, SmithD) Crosby, Ewing, Grant

11 Turner 16 Bush12 Baker 17 Thompson13 Wilson 18 Goodman14 Adams 19 Stevens15 Hill 20 Williams

11. Usetherandomdigitstable above, staGing ÿ line 104, to chooser our people @om alistnumbered 001to 500to call fora poll.i

089,008,778,873089,008,192,445089,008,77,88

D) 089,192,459,256

12, Random selection of subjects for surveys is used to avoid:A) placebo effects.B) variability.

double-blindness.bias.

Page 3

13.

experiment with compounding variables.observational study.retrospective study.

A 10-year study of low-birth-weight babies is performed to determine if birth weightaffects IQ and performance in elementary school, Children are identified in hospitals atbirth and their performance is tracked until they are 10 years old. This type of study isa(n):A) comparative experiment.

14, A group of 100 students is randomly chosen and divided into two groups, One group istaught typing using a set of new materials and the other using ta'aditional methods,After instruction, typing speeds are compared to determine if the new materials improve

rning. This type of study is a(n):comparative experiment.observational study.

C) prospective study.D) retrospective study.

15, Consider the following situation: Doctors identify 500 women, ha!f of whom hadmothers with breast cancer and half of whom did not, The medical records of thewomen are followed for 20 years to determine if heredity plays a role in breast cancer,

s escribes a prospective study,True

B) False

16. tÿ experiment may be used to show cause and effect.Aÿ) TrueB) False

17. A dummy medication (such as a salt tablet) will often help a patient who trusts thedoctor who administers the medicine, This is called:A) confidentiality.B) double-blindness.

confounding variables.the placebo effect.

Page 4

18, A survey is sent to 100 employees at a community hospital asking if they support a lawrequiring motorcycle riders to wear helmets. The results indicate 88% support the law,If the actual proportion of the community's residents who support the law is 72%, the

erence is most likely a result of:sampling bias.sampling variability.

C) an insufficient sample size.D) a poorly worded questionnaire,

19, In a medical study that is double-blind, participants do not lcnow whether or not they aretaking the experimental drug. This is to avoid:

(Bÿ) selection bias.the placebo effect.C) having too small a sample.D) statistical significance,

20. In an experiment, an observed effect is called statistically significant if:A) the experiment will help a large number of people.B) the study was double-blind,

(ÿthe experiment was well designed.the effect is too large to attribute to chance.

Page 5

OO NOT- oChapter 7 Test B Name: ÿ3ÿ(_. Q.o N bÿ

1, A marketing company conducted a survey of College students to obtain data for anadvertising campaign. They selected 1421 students randomly from campus directoriesof 132 colleges and universities, The 1421 students represent:

the population,the sample.

2, A survey is sent to 100 employees at a community hospital asking if they support a lawrequiring motorcycle riders to wear helmets, The results indicate 88% support the law,If the actual proportion of the community's residents who support the law is 72%, thedifference is most likely a result of:

) ampling bias,sampling variability.C) an insufficient sample size,D) a poorly worded questionnaire,

3. In a medical study that is double-blind, participants do not know whether o1' not they aretalcing the experimental drug, This is to avoid:

) election bias,

the placebo effect,having too small a sample.

D) statistical significance,

4, Random selection of subjects for surveys is used to avoid:A) placebo effects.B) variability,

double-blindness.bias.

5, In order to determine the proportion of voters in a small town who favor a candidate formayor, the campaign staff takes out an ad in the paper asking voters to call in theirpreference for mayor, This typeof sample is a:A) convenience sample,B) simple random sample,

multi-stage random sample,voluntary response sample,

Page 1

6. To determine the propolÿion of voters who favor a certain candidate for governor, thecampaign staff phones 25.00 residents of the state chosen from the state property taxrolls. The 2500 residents represent:

(ÿ the population.the sample.

Use the following to answer questions 7-8:

Use the following random digits to answer the question(s) below.

101 01033 08705 42934 79257 89138 21506 26797102 49105 00755 39242 50772 44036 54518 56865103 61589 35486 59500 20060 89769 54870 75586104 08900 87788 73717 19287 69954 45917 80026105 75029 51052 25648 02523 84300 83093 39852106 91276 88988 12439 73741 30492 19280 41255107 74008 72750 70742 67769 72837 27098 07049108 98406 27011 76385 15212 03806 85928 76385

7. Usetherandom digitstable above, staGing a line 104, to choose fourpeople ÿom alistnumbered 001to 500to call fora poll.A) 089,008,778,873

) 89,008,192,445089,008,77,88D) 089,192,459,256

1 Beginning with line 102 of the random digits table above, select three individuals fi'omthe list below to serve on a student affairs committee.

01 (2rosby 06 Jones02 Hunter 07 Smith03 Cooper 08 Davis04 Grant 09 Ewing

Riley 10 DoeCooper, Doe, SmithDoe, Ewing, Grant

(2) Doe, Smith, SmithD) Crosby, Ewing, Grant

11 Turner 16 Bush12 Baker 17 Thompson13 Wilson 18 Goodman14 Adams 19 Stevens15 Hill 20 Williams

Page 2

9,,ÿn experiment may be used to show cause and effect,,!..ÿ .... True

B) False

10. A polling company surveys 200 people outside a county courthouse concerning tighterrestrictions on smoking in public buildings. Their results indicate that 34% of thosesurveyed favor fighter restrictions, The actual proportion of county residents who favortighter restrictions is 65%, The difference is most likely due to:Aÿ variability in sampling,

bias due to the use of a convenience sample.C) confounding variables in the survey,D) the wording of the survey,

11. Consider the following situation: Doctors identify 500 women, half of whom hadmothers with breast cancer and half of whom did not, The medical records of thewomen are followed for 20 years to determine if heredity plays a role in breast cancer,This describes an experiment,

@ÿ TrueFalse

12, A group of 100 students is randomly chosen and divided into two groups, One group istaught typing using a set of new materials and the other using traditional methods,After instruction, typing speeds are compared to determine if the new materials improvelearning, This type of study is a(n):

, omparative experiment,observational study,

C) prospective study.D) retrospective study,

13.!

A polling company conducted a survey of voters to obtain data for a political campaign,They selected 3500 voters randomly from the 168,000 names on the voter registrationlists of the county and found that 1372 intended to vote for candidate Doe, The168,000 names represent:

the population,B) the sample,

Page 3

14, In an experiment, an obselwed effect is called statistically significant if:A) the experiment will help a large number of people,B) the study was double-blind,

the experiment was well designed,the effect is too large to attribute to chance, ,

15. A dummy medication (such as a salt tablet) will often help a patient who trusts thedoctor who administers the medicine, This is called:A) confidentiality.B) double-blindness,

,(ÿ confounding variables,the placebo effect.

16, A 10-year study of low-birth-weight babies is performed to determine if birth weightaffects IQ and performance in elementary school, Children are identified in hospitals atbirth and their performance is tracked until they are 10 years old, This type of study isa(n):A) comparative experiment,

Qÿ experiment with compounding variables,observational study.D) retrospective study,

17. A national poll asked 1581 adults whether they were satisfied with their jobs, and 854said they were. Estimate a 95% confidence interval for the actual percentage among alladults.A) 53% to 55%!ÿ 52% to 56%

51.5% to 56,5%D) 50% to 58%

18. A polling company conducted a survey of voters to obtain data for a political campaign,They selected 3500 voters randomly fi'om the 16,800 names on the voter registrationlists of the county and found that 1365 intended to vote for candidate Doe, The sampleproportion is:A) 0.081

{ÿt 0,2080.39D) 0.1365

Page 4

19. To estimate the number of motorists likely to favor a tax increase for road repair, apolling company chooses 1000 names at random from a list of registered car ownersprovided by the county license once. This type of sample is a:A) convenience sample.

(ÿ simple random sample.C) multi-stage random sample,D) voluntary response sample,

20. To determine the proportion of students at a university who favor the construction of aparking garage, a sample of people on the cmTent enrollment list is surveyed and it isfound that 45% favor the garage, The actual proportion of the student body who favorthe garage is 40%. This difference is most likely an example of sampling:

.ÿ bias.

variability,

Page 5

CH 8 TEST Name: Q L)

Ii A spinner numbered 1 through 10 is spun and one die is tossed simultaneously, Thenumber spun and the number rolled are recorded, How many outcomes are in thesample space?

6016

C) lOD) 6

, Tba'ee dice are rolled and the number rolled on each die is recorded,the sample space are all equally likely,

TrueB) False

The outcomes in

, A fair coin is tossed three times,A) 1/2B) 1/3C) 2/3

) 3/8

Find the probability of getting exactly 2 heads,

, We need to create serial numbers that start with one of the letters a, b, c, d, or f followedby three non-repeating digits. How many serial numbers can be created?A) 5000B) 2520C) 725@ 36oo

, Either Terry, Chris, or Kim will attend a party, The probability Terry attends is 0,31and the probability Chris attends is 0,5, What is the probability that Kim attends?A) 0,33B) 0,5c) o,81(ÿ 0,19

Page l

1 If there is a 0,8 probability of rain today, what is the probability it will not rain?A) 0.8B) 0,5

1) 0,2D) 0,1

, A sample space has three outcomes, A, B, and C, The probability of outcome A is 0,39and the probability of outcome B is 0.25, What is the probability of outcome C?@) 0,36B) 0,33c) 0,5D) 0,64

1 A raffle ticket costs $5, First and second prize winners will be drawn at random, Theprobability of winning the $100 first prize is 1/40 and the probability of winning the $25second prize is 1/20, What is the mean winnings for one play, taking into account the$5 cost of the ticket?

) -1,25B) -0,875c) 3,375D) 3,75

. At a certain discount store, the number of people in checkout lines varies,probability model for the number of people in a randomly chosen line is;

The

Number in line 0 1 2 3 4 5Probability 0,08 0,15 0.20 0.22 0,15 0.20

What is the mean number of people in a line?A) 2,5B) 15.92

) 2,81D) 2,89

Page 2

10, The scores of students on a standardized test are normally distributed with a mean of300 and a standard deviation of 40, Between what two values do 99,7% of the testscores lie?A) 260 to 340B) 220 to 380C) 297 to 303

{ÿ1 180 to 420

11, A game consists of rolling a regular dieÿ, You pay $5 to play the game, and the $5 is notreturned, If you roll a 1 or 2, you win $6, If you 1'oll a 3, 4, 5, or 6, you win nothing,What is the mean value for this game, taking into account the $5 cost of the game?A) -$5@ -$3c) $1D) $3

12, The mean weight of a collection of potatoes in a shipment to a fruit market is 1,3 lbs,with a Standard deviation of 0,35 lbs, The distribution of weights is approximatelynormal, What fraction of the potatoes in the shipment will weigh between 0.25 and2,35 lbs?

q@oq13, In the manufacturing process for ball bearings, the mean diameter is 5 mm with a

standard deviation of 0,002 mm, Between what two measurements will 95% of alldiameters of ball bearings be found?

t ,qqtQ + So009

14, A game consists of tossing tba'ee coins, Find the probability model tbr the number ofcoins showing heads.

q¢o%,

Page 3

15. A pizza can be made with any of the following toppings: cheese, pepperoni, sausage,mushrooms, anchovies, green peppers, or olives. You only have enough money for 3toppings. Doubling of any topping is not allowed. How many different combinationsare there?

16. We must create a license plate code that consists of two letters followed by three digits,The letters cannot repeat, but the digits may. How many such license plate codes canbe formed?

17, Below is a probability model for the number of automobiles owned by a randomlychosen family in a large town. What is the mean number of automobiles owned?

Number of automobiles 0 1 2 3

Probability 0,15 0,20 0,55 0,10

Page 4

'a

Name: Class: Date: ID: B

Test Radicals

Multiple ChoiceIdentify the choice that best completes the statement or answers the question,

Multiply and simplify if possible.

Sÿ3 2, ÿ,'47a, 3 b, 34ÿ-3 C,. --3 d. not possible

Simplify.

>_ 3. -4ÿ - 34g + 6ÿa. -5.q/ÿ- 18 o. 5ÿ4f-5- 3ÿ,/ÿ

b, 5ÿ4/5 - 18 d. none of these

:.. .ÿ-, ,'.

a. 16 '" " 'ÿ: " b,

I .t I

5. 207 . 20ÿ

512//

(° d, 4,096

a. ÿ b.

I

e, 204 d, 20

ii

,6, 33 ' 93

a, b, 9 c, ,ÿ d, 3

Subtract if possible.

a, 84ÿa

b, -204ÿa

e. -4 4,,ÿa

d. not possible to simplify

Name: ID: B

Multiply.

. (7a, 54- ÿ o, 58 + s6ÿ

b, 54 + 564ÿ d. 13 + 15ÿ

a. -13 +5,ÿ e. 28 + 10,ÿ/ÿ

b. 25- 10,ÿ/-3 d. 28- 10,,]3

'_ÿ 10, /8-,,,ÿ/(9+,,f5/

a. 72+8,,ÿ-9,,ÿ-,,fÿ e. 72-ÿ1-0

b. 72-2,,fÿ d. 72-,,ÿ-,ÿ

..... ,, (:

a. 17 b. -3,ÿ O, --3

[ÿ\ 12, Simplify,ÿ8a'?b6 .Assume that all variables are positive.

,, a. 4",b2ÿ o. 2a, b2ÿdÿ

b. 4a4 b 3qÿ: d, none of these

Solve. Cheek for extraneous solutions.

6x= 427+ lzÿ2

a. I b. --3 O, ÿ12

d. 1 and --3

Simplify the radical expression. Use absolute value symbols if needed.

81x2Oy8

a, 3x']y21 b. 9x251y'[ °, 3Ix'l: d,

15.

b. 694 °. 36g4 d.

91x2s ly4

361931

2

l-D: B

Add if possible.

a. 16ÿf-ÿ

b. 84ÿx

e. 84ÿ ,

d. not possible to simplify

3

17. Write the exponential oxpresmon 3ÿ

o. 3 47;: b,

in radical tOrm.

• Solve the equation.

4

4(3-x) 3 _5 = 59a, 5 b. -5, 11 c. 11 d,

b, -6

,,/x+ 10 -7 = -5

a, -8 c. 4 dÿ

-11

14

O20. Find all the real square roots of-l-ÿ.

; i,,;oiÿ : ....... ÿ ,ÿ

. . . :..81

b, 256

3

3 3d, --ÿ and "ÿ

21,8

Write the radical expression ÿ in exponential form.4Xl5

7 ÿ' 15 7 15

a. 8x 1ÿ b. 8x 7 e, 8xl5 d, 8x7

22.

Rationalize the denominator of the expression. Assume that all variables are positive.

46xay9

x3y2a, 5

b.5x2y4

.c. 5x3y2 3ÿ

d. none of these

Name: ID: B

23.

a. 9 - 2,,fi-ff O,

d)

-3 - 2,,]ÿ

9-1 - 2ÿ,l-ff

3

24.

a, 11b. 3ÿ o. 113",ÿ

11d. none ofthese

A rope is ÿÿ units long, The rope is out into two pieees, so that the lengths of the pieces are in tile ratio 2: 3. What is the length of the longer pieee expressed in simplest radical form?

a, 6,,f5 units e. 6,,f2 units

b. 2,x/6 units d. 3,,/6 units

A garden has width ÿfÿ and length 7,x!ÿ. What is the perimeter of' the garden in simplest radieal form?

a. 8ÿ units e. 14,x/ÿ units

b. 16,ÿ'units ..... d. 91 units

Divide and simplify. Assume that all variables are positive.

a. 3 l'x/ÿX'9 . b, 3X6ÿ e. 3X63"xÿ d. 2x3 3ÿX6

Test Rationals Name

Multiple ChoiceIdentify the choice that best completes the statement o1' answers the question,

Simplify the rational expression, State ally restrictions on the variable.

'ÿ 1, P2-4p-32

p+4

a. -p+8;p ÿ-4 c, -p-8;p ÿ 4

b. p-8;pÿ-4 d, p+8;pÿ4

q2 + l lq + 24• 2, qÿ- 5q-24

a. q+8 c, q+8

8; q ÿ -3,q ÿ -8 8; q ÿ -3,q ÿ 8q- q-

b, -(q+8) d. -(q+8)---',q ÿ 8 --;q ÿ -3,q ,# 8q-8 q-8

Multiply or divide. State any restrictions on the variables.

4a5 2b2' 2a-ÿ

a,

b,

4(t97b6,aÿO,bÿO

4c!7bÿ, a ÿ O, b ÿ 0

e, 7b2,aÿO,bÿO

4ad, 4 9.6 '

-ÿao,aÿO,bÿO

zÿ z2 + 3z + 2

z+l z2+ÿ

a. z2 +2z,zÿ-l,-3

. z.+ '3 ....,ÿi."b. z4-2

., zÿ-l, O, -3z+3

0,

dl

z+2--,zÿ-l,-3z+3

zÿ+2z, zÿ-l, O, -3

z+3

_ÿ c+l c-25, +c-5 c2-7c+ 10

a (c+0(c-2)(c- 5) :ÿ(c-2)' c ÿ 5,2,2

b. (c + 1)(c - 2),cÿ5,2

C-2

Ct

dl

(c + 1)(e - 2),cÿ2,2

c-2

(c + I)(c - 2)(c- 5)2(c- 2)' c ÿ 5,2

U x2 - 16 x2 + 5x + 4+6. xÿ+ 5x+ 6 xÿ-2x-8

a. (x - 4)2(ÿ + 3)(ÿ ÷ i);x ÿ - 3, - 1

b. (ÿ+4)ÿ(x, 1)(x+ 2)ÿ(x+ 3)'x ÿ - 3, - 2, 4

o. (x - 4)ÿ

(x+3)(x+ 1);xÿ-4'-3'-2'- 1, 4d, 1

(x+ 3)(x+ 1)'x ÿ -4, - 3, - 2, - 1, 4

\

7. IfR is the total resistance for a parallel circuit with two resistors of resistances r1 and rÿ, then

i 1, 1-- = -- + Find the resistanoe r1 if the total resistance R is 20 ohms and r2 is 75 ohms. Round your

• /ÿ ÿ;iÿ "rÿ ....

,:[' .... .answer to .the nearest ohm if necessary,

a. 16ohms b. 1405ohms e. 27 ohms d. 102ohms

Add or subtract. Simplify if possible.

7 78, +

a+ 8 aÿ - 64

a, 7a - 49 o, 14

(a - 8)(a + 8) (a - 8)(a + 8)b. 14 d. 7a + 63

aÿ + a - sÿ (ÿ - 8)(a + 8)

bÿ - 2b- 8 6

9. b2+b_2 b-1

a, b-lO

b, d°

b-4

b-tb-lO

b-1

Simplify the complex fraction.

3 2

4y y10, 1 3

y 2),

a, 20

3b. 1

2O, ÿ2 d, 3

20

4

/'/ 11. x + 31-+3X

bt

12x+ 4

xÿ + 3x4x

3x+ 9

c, 4X

3xÿ + lOx + 3d, not here

Solve the equation. Check the solution.

fÿ a 2 112. a2 36 +- a-6 a+6

a, -9 b. -6 e, -9 and -6 d, 6

(.ÿ/ 5 113. -- + -- = -4

a, 3 b. 11 e, I1 d, 3114 6 24 24

1ÿ4i: ' Alieia ÿan row 6 miles downstream in the same time it takes her to row 4 miles upstream, She rowsdownstreain 3 miles/houi' faster than she rows upstream, Find Alieia's rowing l'ate eaeh way. Round youranswers to the nearest tenth, if necessary,a. 4 mi/h downstream, 2.7 mi/h upstreamb. 20 mi/h downstream, 13,3 mi/h upstream,,, 2.7 mi/h downstream, 4 mi/h upstream

/ÿd,) 9 mi/h downstream, 6 mi/h upstream