Algebra II Midterm Exam Review Solve: R view of Algebra 1 4. 215x + 31 = 16 /5xt3 1:: & 3 :: 2.1 3" ::. -J5 /,:::-=r\ or L":: -j) 2. II-2xl = 15 / j - ;).'1 -:.115 00( 1-).)(":.-15 - X-: 1"1 by:-t3-8 5 --... 1 \ j( :: -II/il {fevylemr.eor k, ("p J -4" e S ' e, :; ij or J iv I 0"'& a. 11 qa. v0 Solve and Graph each inequality. 6. 14 + 2xl 12 (qred. or') v LfJx >/1.1 orz Lf f d.. X ---/;L o L{ l(- oo)-j u 7. - 3 S 2x + ) < 7 - Lj ;?,X <. b \ -J r" 8. 13x - 61 < 9 less +h. --4<: 3i-( 9-3 (.3)(.LS [-I <. )( L6\ 'II I I I 1 1.4 /hf.' 1 I I 1-7 -6-5 -4-3 -2 -I 0 1 2 4 5 6 7 'II 1 1 I 1 1 I CDf:!1'iVA/J.,A,,,,, vu.rd I I -7-6 -5-4 -3-2 -I 0 1 2 3 4 5 6 7 9. 12x + 11 5 J. ;I -t \ )'/ 5 0-2 -I 0 1 2 3 4 5 6 7
Write the inequality from the given graph. 10. I I I I I I I I I I I [;L.. -j_x_ -: 3. -I )( O I_... /531 4 5 6 7 11. OIl I I 1 1 1 I 1 EI3 I I 1 I. I -7-6 -5-4 -3-2 1 0 2 3 4 5 6 7 I -5X < 3J Solve for the indicated variable: 12. A =7rr2 for r A -r TT 1 ftr } 13. A = P + P r t for t A-P =Prt A-P t Pr 14. Graph the system of inequalities. 15. Graph the system of inequalities. 1 y -x -2 y 2x +l 3 y < -x- l x <4 )( -......... c. Algebra II Midtenn Review ( 1I /l91j3) Page 2 of"
16. Graph the system of inequalities. 1............ '''1 r.. &\...\.., y>-x -2 3 '-J y'::; -2x-l \ :!,.. I"" l1li'" 1\ 'W' 1.,..l..oI!. ;. L.,_..........(,..........J " / 17. According to the table, what is the domain and range of the data? input o utput 19 26 20 27 21 28 22 29 23 30 18. What is the domain and range of the relation {(3, 2), (5, -:- 1),(-1, 0), (9, - 2), (- 7,5)}? borrlullo f-1 ) - 3)3 /l.s ROJA.t 0,,, )5' 1 o [-,) ) - \ ) 19. What is the domain and range of the graphs below. a. b. c. 10 ' 0 y ( '., I '0! \..,." / 10 I i I \ :.0 X \)OfYttUJl\. t-x.. \ - 4(.)( <.,} 'J '-al.'\1 () D" (YI ().J./I,AU e 1' \ lf5 D.OJY\ (-)\) Do O (-cd ov ') Rtl» f} C-cJ)) yj Alg'bt R"':: ('l?ij3 ) Page 3 of ))
1 :l... t; '1 <0 0 {jl 0-2 (fp1-20. Sketch the graph of the equation: 2..L Which ordered pair is a solution of the inequality -3x+ 8y 11? V.e.v- hz.x (4) A.) y= -lx-41+2 I L 1. Q (2, 2) - 3r;l..)tr.()-:= [D II '1e. B) (-1, 2) - 3(-/) t () 111 Il h:u.:se. C) (6, 7) -3("\rV(T -3f II FaJsQ.. D) (-8, -1) - 3C-:l?)i- (-I}= 1'- = \ a..(vy1)ttlo\ 22. What is the vertex of the following absolute value equations? v yte (-:> c..) a. y =Ix -41-8 [SV te-t (4 2 FJ li. It IX-31+;t..) 24. Write the equation ofthe following absolute value equations. 25. Is (-9, 2) a solution of: 26. Solve the system. -X+2Y =5 J- 12x + 4y =8 ==J -1;tl(4-'fra { 2x-4y = 8 - V- 3x +y= 4) -=1 1J.1-L(o:.-)b 11iQJ o - Fo..\Se. ----,,I, So \u hoy1 \
27. Determine the number of solutions: == - 3 2 3Y -7 9y + 3x 2 7 => d-"' - K-I-3 { x= 4y + 13.so...Me \ \ Y'\ e J. ( \3 '!.:3 -= - 1- X { 28. Solve the system. + 3Y = 9 2)."\TiI,' OJ2" I + 3 "1 = -:j, 0 -t Alp :. - =t e.... I.lM 50\ hwl) ' O lid Chapter 5 - Quadratic Equations and Parabolas 29. Solve!x 2 3 :1-'4(-3)1-13 J{:= -/;t f 1"3= I (,.) -3') - 't - 'b = 27. X=-g \ x-=!n; - '/.. :.:t '1 Axis of Symm etry \Jf)( is 'ryiv-)( W 'vir\ 0.. <. n \J(II-+e)l. b. I.: \ 2(L \.t.)'., 'J\ 'f'(\."" 'I =- - - -.2 i -2- Max or m in '---'-'---l'yi i \") c... 7'0 = x 2 +4x -1 y Q.-::: \ ) ;: -,5 33b. Vertex ( - ),. ) 51 4, c:.. -:. -/ (j = 1 (j. Axis of Symmetry 'l. '" -1)-\ i' - \ X' :: Q Max or min (- -n VY\ I Yl ' fj Vertex X =- ). 1;) - 1 Axis of Symmetry A = Y- Max or min V\ Y'(\ Page 5 of II
- 34. What is the discriminant of the equation? 5x 2-12x+ 10 = 0 0... -== 5.> b = -Id-. 10 h 1 - '-ItA c. = I '1-4( )(I Q) =ILjY -).00 :E.s-toJ - jjq =illj = [-i r,s] 43. - {2if - (J. L )(Ji) _-0 = - L{ t" - Lt{-/) -t!:ij 44. 3i 2 =- (-I) = /-3/ 46. (_5i)2 : (-ShY-s-).J) - S /w J = ds(-t) :/-) s'l... 47. _i 2 =_j,, ;: _ (-I) -:I-I ] Solve the equation. 48. x 2 =-9 X im 0::!:3d Algebra II Midterm Review ( 11 /19/13) 49. x 2 =-7 - X =!: M &::!ijr] Page 6 of II
_ 50. 4x 2 + 17 = 5 il-3x 2-8 =4 '-I'f.. 2.= -, - 3r: 2 ""-' )<..2.=-3 _ X:J = -4 [! '" =':El E: 1). Perform the indicated operation. l=oll 52. (9 + 3i + (7 - i) (5+4i )(2+i) 1 1G-+2. L 10 t51 2t... +4L2 ":- r OtI3-LJ (1-6i) - (8 + i).:: i3 &\ I - L - - }..- Efill 54. 4i(l +i) +3i(6-7i) 't.i..2 «/L - l\n').. 4i. -4 t-18i. +-1.-1 \ \1- +-12 \ Solve the equations over the set of complex numbers. 58. x2+ 2x +7=0 X ::- - 2 : Ji - t ;'... - j, J'4-1 fs I,)., j... ::: -:( fi'i." - J :U- _=20-J b- d. Sketch the graph of each equation. Identify the vert.ex. 59. x 2 + 2x + 2 = 0 _. l. + J y - 4 (, ij)..,. -:2 : J -g -:2. -.: -cj G -:: 'v l' x z.. 0 - I - 2 61. y=-x 2 +3 62. Y = 2X2-8x + 5 r T....................T......) 1/ o!: 'L I, -/ 3!? -3 1... - \ AIgebra II Midti-+-f-+-+-fIt\I ' -+-I-+-+"'wlrl-+-+-f--+---!.L _, I. ( r -- -- - - ---- - -- a 3) '('(1Q.)f ('t>\'l\ lif'yb 1-31 '\ i " 1 \ 3 -/ Ij 5" I i \ \!\ \ J L............... _ 1._._..................J
Scottie tossed a stone up and into a pond. The function that describes the position of the stone at any time it is in the air is h(t) = 2t - -'!'t 2, where t is the time in seconds and h is the height in 4 feet. The graph ofthis function is shown below. Height (feet) / v...... / \ / f\ 1/ \ I \ Time (seconds) a) Use the graph to explain how to fi nd the maximum height of the stone. e '1Y\(I.I.'...1vM ne45 r-ecat-'('(,j ' 'h> Q.. IS 't COOVGlI'r1t(t(.. 0-+ -thlt \/ "'+-e.x ' tv\..:, he.11l- :. 4.(){-. b) How many seconds will it take for the stone to reach maximum height. Explain. c) How many seconds will it take for the stone to hi t the pond? Explain L t- \1.) ' \\ -\n.. -c..e.? Se c:.o V\J s. 1h..t s {') e. +i ()\-f...(::br- helj It! 1- +0 o (.+. 63. What are the x-intercepts ofgraph also known as? -e )(1 V\-\.e v rer a I{ p a. 5 0 \.v1 OU)V1 Q 5. +t1 e.. - -t'h 4" Cl- 2:eY"os or roan. 0.\= #>e. O'j"lOVVuuJ. ("" ("ey\ CJ... Algebra II Midterm Review (11/19/13) Page 8 of II
64. Which of the following is not a polynomial? Chapter 6 - Pol ynomials I 3 A) - x- J - C) 4x +l D) (X_ 2)2 3 4 3 &1 v,'j")1. u /(1 1 0 L 65. Simplify. (3x 2 +4x - 9)+(2x2 -x-7) 1s)\ 2..1.3 X -lfo \ Perfonu the foll owing operations. 66. (6x 2-18x + 1) - (14x? - l2x + 9 ) 69. (x - 7)(x+ 8) f 91< 2 X - <6 '\ '/..2. +&"i - r'f..- -=-[;( 'L t X - 70. (2x + 3)2 -- Ciy+) (2,)< 3 ) Lf'i 2-- t G {g '-t -!- G l{?-+-\_-1-'f..-t"--j--' 68. (4x + 7)( 4x - 7) 71. ()")l c xc} -;/.1<.'-1- xtsx'=-io)(i-5... >f--1)c,1 =-K'< -9 L_ Factor. 72. x 2 - [ 6 75. 2X2-5x - 12 llrt- ')( -w) ] ( (1'H-3 1.1- - 4) \ ;;. X 3 1-3 X2.-'1 +s-1. 76. 27x 3-125 (use SO 9 J J (3](. - 5 Xq/' + lsj(, --+ s ) 1 Algebra II Midtenn Review (1 1119/13) Page 9 of II
Solve for x by factoring. 78. 2X2-50 =0 80. x 2-8x = 0 1. (t. 2 -.l5j: 0-1-( X -) :: 0 ;IC"t- +-5) ("/.--5):: 0 or t -y =rj l-f-5"=0 a/.. 'l - 5' () /7-: -!) X. =7 79. 6x 2-22x - 40 = 0 ( 3 'l;' - 1/ t -).6) :: () (3 y t-'/ X"t- - ;-):- 0 81. 31-:: -'I 5J 82. Use synthetic division to divide the following: (7X2 +4x + 3) +( x+ 2) 1-3 -/'I 26 '1 -/IJ )3 83. Use the Remainder Theorem to evaluate the function: J(x) =5x 4 + 2x 3-20x + 6 at x =2 84. Find the missing factors: l + 2/ - 5y - 6 = (y + 3)(?)(?) ::.31 I -f -t y'--y -2. I -I -,2 [(1-:»(;r' 85. Is (x - 3) a factor of(x 4 - IOx 3 + 2x + 3)? How do you know? JJ I - If} (} j.. 3 3-11"113 -Ig.3 Algebra II Midterm Review ( 11119/13) Page 10 of II
Probability and Statistics </0 For numbers PJ, use the following set of numbers. {34, 35, 40,31,34, 31,38,29,35, 35,32,37,33,34,37,37,35,34,32} n19 la, 3/.3IJ3LI32. 33 3'1 3'J3t/...iV)J5, 3S;35)3Y;37)37-)3J'3i}"I)J 86. Fi nd the mean, median, and mode of the data. r!)h' r'1 3 '/. j yyi po /lui -::; 3'f---tyJ-o-p-e-,s-=-3-'1-"1'-..;-5'"-_--" 9} tu n' For numbers.ljlf and, use the fact that a bag of balloons contains 2 yellow balloons, 2 blue balloons, 2 white balloons, and 1 red balloon. Vi::= 7 87. You randomly choose a balloon, what is the probability that you choose a red one? [rcrd ) 1: 88. You randomly choose a balloon, what is the probability that you choose a yellow one? t-\ 89. Find the probabil ity of a successful event given the number of successes and the number of possibilities. Number of successes: "*: 50 Number of possibilities: 350 J P(SUCWS) t j 90. There are 13 blue marbles, 14 white marbles 15 green marbles. and 10 blue-white marbles. If you select one marble from a bag, what is the probability that you select a marble that has blue or white on it? Explain how you got your answer. I':. 5 13 +-14 +-10 3 = = S.;l, 5.:L Algebra II Midtenn Reyiew (11 / 19/13) Page II of I I