Algebra 2 Mid-Year Test vane:_MRS, A.Study Guide - Dec.2019 Date: stacks

2. 3V72 - 28 +220 3. J2(V2 - 6V10)

WR-4A+45 2-ef20

MD + WB 2-1255, ¥2-23 VB 6, 2453 pele"Ve WG 5-3 5S

Vio-2524 _ 4-'Nofig

|

roeN+3 _BT GB De 25-2

Topic2:ComplexNumbers

*Recall: i= | P= -|

Simplify each expression.

v-81 8. ne.ae 9.

0 a, rt:7

de “atee

| ai|Ia2))*u= J-[0¢

| 12. (9+2(4-1 143. (6-23

360- AtOU- L* Bo—-24¢+4 U

11. (4-71) -(5 +21)

ey ~ ap ¢@q| 7 aw } és

poe LT}|

16. 3-3i Jt

Gi LU7-i Tte

15 214-213.ee

Ya —-peL

Cl) 74/8 i

17.et a8. 18.36 ==188v3a20.|i -=A | IS|5 — Re Qeoe Z Reod “m ‘nAHe

Read compre Complex CoN WntegP4 Docume) WeImag inay Rothone| wnoale

21, 245i=) 22. [vis — VU a 1. fm

+H | 3 PeD LJComplex Read, irrational Lo 0 Woke

Comole Roald) COomPIeX Nene inte

mens’ __ neaer Natwad

Namethe property that justifies each statement.

25. /5(8- V3) = 8v5 -wl

Dismbunve. ProperTY

26. 2m+(-2m*) =0

Add:hive, InverseeC 27. -9- (243i) =(2+3i)--9

Comimutatwe (malt ) 1~OE

Multi pl CO+e Inverse.

> \C or

Identify the special factoring patterns.

DIFFERENCE OF SQUARES SUM OF CUBES DIFFERENCE OF CUBES

a —b’ = a+b = a—-b° =

O 2.)i

i

—ODT

Factor the expressions below completely.

29. 36x° -64y"

eommasiey30. m> +64

lak (2K —-1)(4K24 3K+1)|

4(9x>—Ioy*) [Entra4 tI) |

(40(2x+ 4y)(3x-4y)\B31. 81k* -3k 32. 2xy° +250xy*

3K (217-1) _ 2xy*ly? #125)

l2xy2(Cyt) Yy*-5y +25) 33. p?-10p’ +25p

34, x* -11x* +28

35. 4x° +18x" - 10x

2X(2x74+9% -5)Dx( XAK-10)2x (X*1OYOK aLt)

es (

Pema

|"

36. 9x? — 63x? —x+7

qy*( _° -| (x—4.

manx-| 0-F)|

Solve eeachequation Check all solutions.

-Topic.5:Absolute ValueEquations&Inequalities

37. [4m +5] = 38. -5|7-x|+6 =-14

dmt5 =4 Hint) =- Sh-x| =-29

ort TexTx=4

Solve each inequality and graph your solution. Write the solution in interval notation. 39, |x-2| <3

X-24%9 X-22-3

we AMD xz> -|\

hhle ee—eo—ouyyQyQyeeeueaeEeEeeeeeeeeeeeeee_eeeeeee

40, —2|2x —1| <-14

\2x-1| > +

2x—|17 F axe—| 2-7

E74 x --3|

hhhl eeeee aeSseaSar_—_—r————— Ts,

6

Discriminant Formula:

If d = 0, thereis

If d <0, there are 2 imaginary roots.

lf d>0 and a perfect square, there are 2 rational roots

lf d > 0 and not a perfect square, there are irrationalroots.

1 rational root

Find the discriminant of each equation. Then, determine the numberand type of roots.

41. x’? -7x+15=0 42. 2x -72=0 43. -x* +9x+23=0

(-H)*-¥ (I)U5) 12)

|

(DsA7123)44 ~0 —— Ble?

4ima nor a co opol (1712173

Solve using the mostSeemethod. Simplify all irrational and complex solutions.

44, 2x’ -18 = 78

af Yox=48

x= tl48

45. x? —16x +73 =03g

_

x —|x— —]>

xe lox #4 = ~1o4 64

(Xx : b ) =0

al

= Cc"

3

ime

46. 9x? —18x =11

Ix“18x. —I =0_ aaa Dy —Ihe

= -C1)+4618) (4)-11) }

— (x -14 (x +2 ) =OX= 18+t J720 4s fe -

47. 2x? -10x-26=x-5

met

(x-F)(Zx+3)=

ae (|

TO .24215fe

KS48. The roots of a quadratic equation are -7 and 1. Write an equation that could represent this

function. Give your answerin standard form and factored form.ACTORED FORM

STD. FoRM F ebFORIN\

f(x) = x*+lox- + F(x) = (xt#YK- 5)

_Topic7:PolynomialEquatiSolve each equation. Simplify all irrational and complex solutions,

49. x°-27=0

(X-2)(x43x +9) =0 x*(2x-5)t U2x-5) =Oaes

X=S X= “Ct2)rte3)409)

50. 2x? —5x? +18x-—45 =0

| _)

(x4 1) (2x-5) = 0K+q=0

51. A polynomial function is defined by theequation below. Identify the zeros,theirmultiplicity, and the effect on the graph

f(x) = -2x(3x +2)’(x-1/

Zero Multiplicity Effect

Crosse S

l| 2 } ’

bounces

52, The zeros of a polynomial equation are -4(multiplicity 2) and 3 (multiplicity 1). Writean equation in standard form that couldrepresent the function.

y= (xt “| ) (x-2 )

— Topic8:Parent Functions, Transformations, andGraphing —

Identify exch:‘parent function, then sketch the graph.

Linear |

Y=xK}

Absolute Value Kk

i, |y= | x |cw

Quadraticfd)f

p,m eermA

Cubic /x ZUfJ

\ ° ‘ ‘Square Root

Sau,ee

hy fo,=< Nm ae a—- ff neUJ é aK.

For each equation:(1) identify the function family, and (2)describe the transformations.

71. f(x) = te +7-2

e ‘2

1) quae ro : Y=x

v ¢ \ be {fhe J } Dp 1) )velM rt ms [pf 2 Dut2) vei pVTD

Graph each function and identify its key characteristics. ~~

53. f(x) =(x-5)°- y- “Ss Domain: KeaJ 2

Dal + Range: 7Z-“4

a ft H Vertex: -43)

2. fo \ End Behavior: As x0, f(x)> o982. x ~

D|~2 \k Asx0, f(xy PO

d 6 Inc. Intervals: ( 5 L oO )

Dec.Intervals: (- , 5 2

54. =—2|x+3|- nlcI) bs , fA Domain: CO. QS

1, La — |Range: 4=

~~ \

Vertex: (— 2, =| )

End Behavior: As x0, f(x)> DQx

¥ AS x —>-00, fO)>509

f Inc. Intervals: (~ OO,-~ 2 )

j ff crore ih g lif Dec. Intervals: |" =, cO)

\ é

55. f(x) = x° —9x° + 24x -16

. Do ol¢Domain: <2 ( a

i "OG 0 ¢Range: I Cbd Oo

Rel. Maximum(s): 2 4 |)

Rel. Minimum(s): ( A, 0)

End Behavior: As x0, f(x) > GQ_

As x>-0, f(x) > CO

“) \ fet ; .\

Inc. Intervals: [- oO, 2) L4,@)

f a ) , f \\

Dec.Intervals: V4, 7]

Topic9: GraphingAbsolute Value Inequalities

Graph each inequal

56. f(x) <|x-4|- 57. f(x) > ~$h +5

-Topic10:Applications;&Regression—

58.Thispast:Saturday, JJack swrarkcedd for 3 hours mowing the lawn and doingchores|inithe house,Mowing the lawn burns 352 calories per hour and doing chores burns 136 calories per hour. If heburned a total of 570 calories, how long did it take him to mow the lawn?

X=he. rrowing lawn SILK + ds_Y=hs, doing Cores xs JD

y =. ho

BELX + 1263-0)= 540 X= I5Shr or 45 min|352% +408 -130X = 540 _ ,

DIbX=2 ——"

59. Thepilot in a helicopter tossed a life float down to a swimmerin the water. The height, h, of the

float after time ¢ secondsis represented by the equation h(7) = -16f — 3t + 55. Find the timeittakes the float to reach the swimmer.

- o0-3t +55 =O

- Oo

‘| ilo secmdS.

\\

60, The table below shows the numberof teachers, t, and the numberof students, s, at 6 high schoolsin the city. Write a linear equation to model the data, then predict the numberof teachers for aschool with 1,500 students.

t 115 140 76 168 110 G2

Ss L,.22 1,390 788 1,564 1,081 924

y= B, 66x +130.260 [500 = §.08x +130, 26

[xX% 192B reacherS

61. The table below showsthe population,p, of a city during certain years, t. Write a cubic equation

to model the data, then predict the population of the city in 2020.

t 1993 1996 2000 2005 2009 2014

s 2,850 3,257 4,234 6,475 10,158 27,385

Y= 6.Bl0x~ 1116.9 77+ 82195108, Bt

Use f(x)=x?+5x-14, g(x)=x+1, and h(x) =15-2x’to answer questions 62 — 63.

62.Find [/(7)]-2 63. If g(x) = —23, find x.

f()=POT=W K+ /=-22

70-2 = [x=-24)