Algebra 2 Mid-Year TestStudy Guide - Dec.2019
Simplify each expression.
Name: M KS l A ‘
Date:
Block:
1. 24302
2. 3V72 —2V8 + 2/20 3. /2(V2 - 6V10) 4.2
2-42+4V6 2.- 120 ie aie |: [5 ofi2 = IDB .nar yis ||[212i mz aE
5 J2-2V3 J/® 6 zie aie"ve @ 5-13 SS
e284 _ 4No| \-Je W3+3 _— 8 ~ 8 Tn] 25-2
*Recall: i= JF} | —
Simplify each expression.
7. -81 8. 2-14. /8 9. isi” 10.Oe,5) 2
L ioi —
C) | ;[Ouve2°U = |O [
11. (4-71) -(5+2i) ~
|
12, (9+2i)(4-i) | 13. (6-23) |, ~ y ,y)1 z - ta ' 2.
36 ~ 4 Ur @ Un PU 3o—aftit u L
N)
\
po ~ ape
i <A ( f (F
fi 3-31) Tt
16. —— :7-i Tte
LI + e-2-307aae
24-18. _|12—4¢50 AS
18. /-36 — [oil |
Lend Q compley- Complexanf! fF o ~ - f
WO| iMag indsscageernh cl
21) 245) | ~ YY|2+5i 22. vi5 23. 45 —
Complex Read irrational:
j x Lec»Q COPte
ComplyWataa ln
_
.- 5 = 70)
enWnOf €,
eoef |Natt Woe (
Namethe property that justifies each statement.
25. /5(8— /3) = 8v5 - V3 -V5
Disinbuhive, Propert26. 2m +(-2m’*) =0
Add hve Inverse,
(ty27, -9.(2+3i) =(2+3i)--9
Commutatve (mutt.) 1me
Multipitcate Inverse
Identify the special factoring patterns.
DIFFERENCE OF SQUARES
SUM OF CUBES
@+b =
DIFFERENCE OF CUBES
Factor the expressions below completely.
29. 36x* -64y"
4 (9xIby*)
(4¢(Sx+4y)(3x “4y)\
30. m> +64 _.
[(n+4) m0? 4rn +16)
31. 81k* — 3k
ak271)[ak (3K-1)(9K74 3K +1) |
32. 2xy° +250xy"
Dry? Cy? + |[25)
sc(ytd*4 +25)
33. p’-10p* +25p
plp?—lOpt 2S)
[p(p-5)(p-5)
34. x* —11x7 +28
35. 4x° +18x* — 10x
2x(2x7+9% -5)Ix(X°+9%= 10).2x (%+10)(x cL)
x(x+5)(2x-1)
36. 9x° —-63x* —x+7
Gx*(x-#) | (x-3.
9x"-1\(x-#)
(By. E1\(3x1(x=)
__ Topic5:AbsoluteValueEquations&Inequalities_ Solve each equation. Checkall solutions.
37. |4m+5|=9
ri..,0 qfont whA i. ~ ~—_A
re
OY,to ufpt
| Wy
encenT
38. -5|7-x1+6 =-14.
—5}-x| =-20
|7-x|=4
7x=4 T-—%=-4
x= ||
Solve each inequality and graph your solution. Write the solution in interval notation.
39. |x -2| <3
X-LED X-22.-5 pureeTOTES
Interval Notation:
[xe5 Aud x>
C-1,
21
o——8
5|
40. —2|2x —1| < -14
\2x-1] > +
2x-17 F 2x-| -F4
1x78 2x 4.76
pert eebad
4 -4
-8
Interval Notation: (-@,-2) (4,a
2 0 2 4 6
Discriminant Formula:
e lf d<0, there are 2 imaginary roots.
e lf d=0,thereis 1 rational root
e |lfd>0Oand a perfect square, there are 2 rational roots
e |fd>0and not a perfect square, there are 2 irrational roots.
Find the discriminant of each equation. Then, determine the numberand typeof roots.
41. x? -7x+15=0 42, 2x? -72 =0 43. -x° + 9x +23 =0
(-4)*-4 (I)U5) ) (9-423)H4- 00 (Ble92
| —|| | 2 imaginal[| 13| [2 iCrotpona’
Solve using the most appropriate method. Simplify all irrational and complex solutions.
44, 2x -18 = 78
I= Alo
x= 48x= +48
x =t4i3
x = 16x + 73 = 0
gg_
Xx -Ilox = -/>
45.
46. 9x? —18x =11
9x18 -I( =O
K=-C18)+"Ve(0)
“iq \ |
16
BE 432 fe
- 1ai o_a
T Bx?Ws |x= Oe
3
47. 2x? -10x-26=x-5
48. Theroots of a quadratic equation are -7 and 1.
STD. FoRMLf <ee 2 ° P —)
F(x) —_ x + ioxX% _ + function. Give your answerin standard form and factored formWrite an equation that could represent this
'FACTORED FORM
Fx) = (xt F)(K-1)
ee:(eae
Solveeachequation. Simplify allirrational| andcomplex solutions. }
49, x°-27=0
(X-3)(x~3x +) = 0an
x=3) x= -)t cay49)
50. 2x° —5x? +18x—45 =0{= a
x*(2x-5 )t 4(Z2x-5) =O
(x74 4) (2x-
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
CrosstS
—2/3 crosseS
1| 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.
Yr (xt “| \? (x-3)
fl rr . f Yh , an %
= (x YX ilo JX “2 )
‘ 4 C Pe ss j { V/ _ 2.44uy i} i
=A T 4 ye bOK ZI = ] %
- ‘Topic8: Parent Functions,Transformations,and Graphing —
Identify eachiA parent function, then sketch the graph.
Linear Absolute ValueK 1
a Ww
Cubic”.9
—
— =<
Cé<
wa|
For each equation:(1) identify the function family, and (2) describe the transformations.
71, f@)=5(+7) -2
i i _ 21) quodrone : y=Xrx
Zz) vethcal ssheINES Left
Graph each function and identify its key characteristics. nd tt
53. f(x) =(x-5)°-3 yw Domain: Keo. Sx| | Range: U i=4
a f A Vertex: C5 a 3)
2160 \ j . End Behavior: As x0, f(x) > CO_
5|-2 Nha As x0, f(x)9
| 6 Inc. Intervals: C5, oo)
Dec.Intervals: (- , 5 5
B4. f(x) = 2h +31- t Domain: Leol S$
Range: y— |
Vertex: (— 2, ~ | )
, End Behavior: As x00, f(x) os ae)
ih¥ As x—>-00, fe)§CO
f Inc.Intervals: aa, ~ 3)
4 fK Dec.Intervals: ( “ _c)
¥ \
55. f(x) =x° —9x° +24x-16Domain: (WC
Range:
\
Rel. Maximum(s): ( 2 !
Rel. Minimum(s): C4, 0)
End Behavior: As x0, f(x)—> G
As x0, f(x) > °C
Inc. Intervals: (- eo 2) (4,0)
(2 “uy,
Dec.Intervals: V )
Topic 9: Graphing Absolute' equalitiesGraph each inequality.
56. f(x) <|x-4]-1 57. fjz-2ld 45
2
_Topic10:Applicationsé Regression
58. This mast aura,Tack worked for 3 hours mowing the lawn and doin¢chores|in‘the Rouse, aMowing 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=hs. mowing lau 557K + | by =570
Y=he doing Chores X+ YaYY
st esty — a
52% +130(3-= 540 x= 6IShr or 45 rnin |ZSZXK +408 -130X% = 540 atsoA be ff
Z1b6X = Io 2 ee
59. Thepilot in a helicopter tossed life float down to a swimmerin the water. The height, 4, of the
float after time ¢ seconds is represented by the equation A(t) = -16/? — 3¢ + 55. Find the timeittakes the float to reach the swimmer.
lot3t +65=0
-2
= | (16 second
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 teachersfor aschool with 1,500 students.
115 140 76 168 110 92
Ss 1,122 1,390 788 1,564 1,081 924
y = B, Bx +120,36 1500 = 8.08x+130: 3¢|x ~ |teachers \
61. The table below showsthe population, p, of a city during certain years, ¢. Write a cubic equation
to model the data, then predict the population of the city in 2020.
1993 1996 2000 2005 2009 2014
s 2,850 3,257 4,234 6,475 10,158 27,385
~~£ -¥
— C ‘ 3 > Z. N71g sant?) As g
Y = 6.B0x— 4//10.9 Fy~¢ BZIFI5IOP“,, BYx
___Topic11:Fun
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.
FH= T74D-14 = HW K+ (= -22
70-2 =| [x=-24]
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