Algebra Final Review Sheet

AlglA/Geometry Algebra Final Review Sheet

Name:

All work must be completed on (t sep(rratesheet. l.

Draw a sketchofa graph showing a systemofequations that has (you should have 3 separategraphs) a.) one solution b.) no solutions c.) infinitelymany solutions

l, <-!,*z 2

2. Giventhesystem:l-

l z y <x +4

a.) graphthe solution b.) determinewhich of the following points are solutionsto the system i v. (l ' 4) i i i . (-2 ,1) i i . (1 ,1 ) i. ( 0, 0)

Solve the linear systemusing the method of your choice.

^ 3'

7x*3Y =-9

9x+y-5 4x+3Y=-l$

zv=i*ts

.

5, = 4x*15 l2x+l}Y = -J

Simplifocompletely.No negativeexponents! s. (3 x 3 y z ) a . x y z

8. (-3x)z

7. -52

-6m3na l6m2 l o. (x2 + y')'

4n

I

6mn

9. 275

1.,

4xi y

"' --.--:gxsy4

So l v e:

t3. 3xz- 75=0

14. 5x2*1=0

15. l2x2-IM=O

Simplifl: t;; n j ' t .' ' 112

mtR .,"'lzs

t;1. -t s " iii J lz

(2xys1-3

,'y-'

t. 1 6 . : t " -4 = 0 4

21. Graphthe followingi y = xz - 3x+2 a.) find the vertex b.) find the equationof the axis of symmetry c.) by looking at the graph,determinehow many solutionsthere are' If there are solutions,circle them. 22. Graphthe followingi ! =-x2 * 4x*4 a.) find the vertex b.) find the equationof the axis of symmetry If there are solutions,circle them. c . ) by look inga tth e g ra p h ,d e te rmi n e h o w manysol uti onsthereare. 23. Solve using the quadraticformula: a .l 4x z = x *7

b .) x ' -4 x= -l

q L x z-2 x + 9 = 0

24. Find the x-interceptsof the graphof J =-3xz +4x+5 25. Determinethe numberof solutionsto

a) 2xz - 4x +3= 0

b . ) 3 x z= 6 x -3

Name:

AlglA/Geometry Algebra Final Review Sheet- Page2 FactorCompletely. 26. x2 -9x -22

27. l2x 2+ 3 2 x + 5

2g. 24x3y2 +30rys -l2x6ya

29. 8lx4 -16y4

30. 5x2-I3x+6

31. x' -l}xy +I6yz

Solvethe followingquadraticequationsby any method' =O

3 2 . x 2 - I 4x

3 5 . * '- * = 3x+1 2

3 3 . x 2 - 8x - 8 = 0

34. x2 -IS x+ M

=0

36. 9x3+6x2 * x= 0

37. 4x2-I6x-

4=0

Simpli$ the following expressions.

39.

Jy

x+ g

4 t +x':+

47

3- x -+

-r+l

40.Zlxs 8vu ETfr

x' -l6 y ' 4x + l6 y

9m + ZIy _-._..__

2x

x2+9x +g

42' ; - T- iT

x z+ 9 x + 2 0

x--x

2x- 5

AA ra'

x-2

x -2

x+5

,' -16

2x +8

solutions' Solvetheequations.Checkfor extraneous 1--

I

254xx-2x+5A1

x +|

3x + 6

a6'la4

46

= = ffi

+''

113

;= fr = t

Graph the function and identifli the domain and range'

4 8. y -f f i

4 e .v- 6 - t

Solvethe equation.

5 0.x = .Ex- 18

51. ff ia ) = g

52.x=,|ffi,

Solvethe equationby completingthe square' ' 5 3 . x z - 4x - I = 7

54.xz- 3x=5

5 5 . 2 x -6 2 x -1 6 = 0