final exam review 11 2013

6. Solveforfollowingtriangle.

7. Solvethefollowingtrian Solvethefollowingtriangle.(Care gle.(Careful:ambiguous ful:ambiguouscase!!) case!!) a)

A = 60 ,a= ,a=18 18c cm, m,b= b=2 20c 0cm m      b b) ) °

A=1 A=110 10 ,a=8cm,b=10cm °

Chapter4:AbsoluteValu Chapter4:AbsoluteValueandReciprocal eandReciprocalFunction Functions s

1. Sketchagraphofeach Sketchagraphofeachabsolutevalue absolutevaluefunction. function. a)



=

b)



=

3 + 1 

−

+1

!

+2

2. Writeeachabsolutevalue Writeeachabsolutevaluefunctionin functioninpiecewisenot piecewisenotation. ation. a)



=

b)



=

−2 − 4 −  ! + 4

3. Solve − !

+ 3

−6

=

9bygraphing.

4. Usealgebratosolveea Usealgebratosolveeachequation. chequation. a)

2 2

b)

!



−1 9− − 7 + 6 4 =

=

5. Graphthefollowingreci Graphthefollowingreciprocalfunct procalfunction. ion. a) b) c)

!

!! !! ! !

!

!!!!! !

(!!!)!

Chapter5:AnalyzingQuadraticFunction

1. Sketcheachparabola: a)



=

b)



=

−



+3

!

!

−5

!



!

−1

2. Withoutsketchingeachp Withoutsketchingeachparabola,stat arabola,state: e: i)

Thedirectionoftheopening

ii)

Iftheparabolaisnarrow Iftheparabolaisnarroworwide(or orwide(orneither) neither)

iii)

Thecoordinatesofthevertex

iv)

Theequationoftheax Theequationoftheaxisofthesym isofthesymmetry metry

v)

Thedomainandrange

vi)

Themaximumorminimumvalue a)



=

b)



=

c)



=

− 1)! + 3 −2( − 3)! ! − 4 − 12 

0.2(

3. Writeanequationthat Writeanequationthatdefineeach defineeachparabola: parabola: !

a) Congruentto 

=



b) Congruentto 

=

5

c)

;opensdown;vertex(5,-2) !

;minimumvalue2;axisofsymmetryx=-1

Vertex(0,4);passingthrough(2,-1)

3. Findthesumoftheindicatedtermsofeacharithmeticseries. a ) 31 + 35 + 39 + … + 107

b) -13 – 10 – 7 - … + 62

4. Foreachgeometricsequence,findtheindicatedvalue. a)4,8,16,…determine !

b) 42, 21, 10.5, … determine !"

5. Inageometricsequence, !

=

3

and!" =9375,determine aand!

6. Foreachgeometricseries,determinehowmanytermsithasthencalculateitssum. a)

!

!"

!

+

+

!

+

⋯

!

!

b ) 4 – 16 + 64 – … – 6553 6

+ 729

7. Determinewhethereach Determinewhethereachinfiniteg infinitegeometricse eometricserieshasafi rieshasafinitesum.How nitesum.Howdoyouknow? doyouknow? !

a)1 −

+

!

!

−

!

b) 2 − 4 + 8 −

⋯

⋯

8. Eachinfinitegeometricseriesconverges.Determineeachsum. a)8+4+2+… !"

b)4 −

!

+

!"#

!"

!"

−

!"#

+

⋯

 ______________________________________________________________  t n

(

t n

)

a + n − 1 d 

=

S n

( n −1)

S n

a r 

=

⋅

=

(

n a + t n 2

(

a 1− r =

)

n



)

1− r

S n

=

S n

=

n⎡ ⎣ 2 a + ( n − 1) d ⎤⎦ 2

a − rt n 1− r

a

S 

∞

=

1− r

 ______________________________________________________________ 



=

! ! !!!"

!! ±



!!

=

 

−ℎ

!

+

 ______________________________________________________________  cos

!



=

!





=

!"# !

=

!

!

=



!

!

+

!

cos  

!

tan 

!"# ! =

!



! !! =

! =

+ !

!"# !

!



sin 

!

!

− 2 cos  

!! !

!!"

! =

!