S~ONOH II V~8391V M3I"3~ WVX3 lvnld

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Damian Ferdinand Wright
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2 Honors Algebra 2 Review for Final Exam Name _ Date _ 1. Simplify: (_3a3)2 (2ab)4 9 Iolla 6 \ L{ O;.\\) by X 10 -I".L--i) t 1.. (3 X + 4 ) 3. Simplify: 3X 4. Factor the polynomial ab + 2a + 5b + 10 completely. Qlbr) +- LIo' Y) ( Ct.'t- S- )C lo t-- a- ) " Factor the polynomial a 2 b 2 + ab" + a + b 2 completely. L CL I' b J t- \ (0-- b '"a- ) o...b d- 1- \ ') (..,-10 ;> ') 6. Which of the following is the factorization of b b + 36? a) (b + 2)(b + 18) b) (b + 3)(b + 12) c) (b - 2)(b - 13)Gb + 4)(b + 9) <:, <0..+ U)" b +- " --t- ).(, ' - \ a- 'f' tc\ )Lbt-Li ) e) (b + 6)(b + 6)

3 Page 2 7. Factor t + t 2 completely. -e.> i-l1:" t- T- b ( (b 1- Y) +- \ ) 8. Factor 25 + lon 4 + n 8 completely. l(\ +-)(J') UnL\ t- < ) 9. Find the complete factorization of 27u w :::s., L S LA... - lo4.> J( Of u.- J Du. V-> +- too w ) 'o -:::. 1 \) W 10. Give the excluded value(s) for the variable in the expression r ,_ \ r.o u- lor +r ('-(lot-') C' -(0) SVM t cuhe r-- Ck' 1- b -::... fc:-- ( Q+-"0 ) (a q. - ta- 11. When x IS completely factored, one of the factors is:,>'f.. a) x 2 + 8x + 64 b) x 2 + 8x - 64 c) x 2-8x + 64 d) x 2-16x + 64 e) x What factor do the following trinomials have in common? x 2 + lox + 24 and x 2-3x - 28 L "X-T )l't Jy ) ( v:t-l\ )l'>l --=1) et!r) 6.) iv\ (V'-<.X"' c9--c- ift'\ \"or t: X r-:1-)l.- ')

4 Page 3 C.'j.A":)U.- '> 14. Simplify: (X::) (X2 :22X) d- / y... (:./- r? - _ g(y--t'\) (;)-)L--r Express in simplest form: r 2 - r :..r 2 + llr+ 30 r 2 +7r+10' r 2-4r Express in simplest form: ;e :-e 2-4e + 3 e +7e+12 e 2 +Se+4 LLo -::.Co (O-t.}) 18. Solve: 3d _d Sd d+2 3d+6-6d+12 3( -t-)s') K d...) LC,O loll:. - ) 19. Solve the equation St - 2 _ 6t - 1 _ 2-7t t - 2 2t - 4-3t - 6' lt::-.).) s(t-a--) _ <.. r-to )(,+, ({/T ))(r1: ')" (r -<:,) C\-r)(rt"<.:.) 3Le.t-)(e-)?(e-C\) - L e'--\ S e. t-3>.-t Xl-+- ). ( +- ) to 1-0..;. a. ':;:. C R; \-\d"--r 0- =5' \ -l)d "Y (\"-b':l-r) Lr,\-'))(rT'- ') <- e+-\ ')( e +- <\. ) ( - \)(e.-'l) :s(e-t \) e...- \ ('5"l::.- J.)c - "5 (c,t-i).)-l;}-*)?>at -t o--lt:- r --:.c...t -( 4:- o-bt:=-\3 08

5 do- ()- 21. The solution set of the equatio -Jy - 2}<2- y s a) {2, 3} b {2} \6-2>- -=- (). -\.{ r o.::.'-j'd-- - <;""'l.d +-.<0 (J --=- c. 'j1j: ) 22. Simplify: 2rn- 5 ij375 d. '6 - -) "l-i s'" -Y3 - d') c) {3} d) 0 \""3vr 'S. C 1'3-;- ': ::,).-3 Yl*.hve- I -\ Page Simplify: 4JI8 + 3J75 + 2J45-2J50.r '3 "3 r " d- "T-q t- 1" -o-s" I0 1- \ IT t-- b -R" -[0-(' or- l '5n 1-6 is-/ 24. Simplify completely: 2J3"(3)6-3J3") biw" - '" l«) -1\ 25. The expression 7 is equivalent to 3 - J2 b) 3 - J2 \ t- -:::.. q -0-» c) 3 + J2 7 \ t- -:=t Q -:::r d) 21 + J What is the value of (x + l)-t if x = 7?, :;)... ( -=t t-\ ) -" \, d, d- 27. SOlve=(.J2x + - 1') d- )( t' d- :::'0)<. d- - X +\ o -::q)<.. a- - '"'6)( - I o -==- (q)(. + \ ) lx - <} x::- Y or 'X. '::- fy\ GL\(,L ( 1/ "./

6 Page 5 t 28. Solve:.-(5-n+-7-) ) 1 ) ;).'1-d-'1 (('r1- -= T ("'ntt)-1- r: < r.> do C-< - 5'c"-:'t J.1 '-J -f):: t- 29. When simplified, i 99 is equivalent to qq-. -t >.), 1) ;;- (,-::'0. c.r--=- -I L-:::'\ (. :..-\ The sum of 3H and 4J-50 is E 3L t ttl. SL do L.:(-r b(,1ry- 6L._ ) 31. The sum of J-27 and J-12 is a) -5J3 b) '3 C. "?> r ;}-C. d) 3iJ5 32. The product of (3-2i) and (7 + 6i) is a) 21-12i b 33 +4i c) 9+4i L-S-d-l. ') l-:t6l'). d\ -t-/ L -J'-IL-{"d-Ld--» I 1- et (, r ().. ;5r L/ C d)21+16i 33. The expression (3 - i)2 is equivalent to L'S--L Y-3-L) q 7J- 34. Expressed in a + bi form, -35. is equivalent to +1 c:- ]-L IS- - \---c: T\..-. -L fi'l 1-' ll d- ()-

7 Page What is the solution of the equation x = O? 'xlr:._-4 -::. 4: The roots of the equation x 2 X ceu0 + 3x - 1 = 0 are -:.$ ±- i 0\ - qli X -{J - - if(l) Find P(J2) if P(x) = x 4 - x f"3- J 38. What is the equation of the given parabola? \J (&\ -\) y (2, -1) '6 -= 0-- CX- : 1- k- '.S ::: 0 (y; - d-.) - \ 3 --=- (. 'j - \ L\.-=--'-lo- 39. What are the coordinates of the vertex of the parabola y - 2 = - l(x + 5)2? y ==- J+&-- X:c(- 10-) 40. C Which expression represents the number written in scientific notation? b) 1.7 X 10 4 c) 1.7 x 10-3 d) 1.7 X 10 3 o.oo()\t-

8 Page The roots of the equation x 2 + 2x + 4 = 0 are a) real, rational, and unequal c) rational and equal b imaginary and unequal d) rational and unequal ( Itu 0- dcc (L 42. If the discriminant of an equation, is 10, hen the roots are A a) real, rational, and unequal \..3real, irrational, and unequal c) real, rational, and equal d) imaginary 43. If the sum of the roots of the equation 2x 2-5x - 3 = 0 is added to the product of the roots, the result is»: SJN b) -! c) -1 d) l )") 44. What is the sum of the roots of the equation 2x 2-3x + 9 = O? -( ) =0 d- I) \ r,"" \C In If y = - tx2-2x + is put in the form y = a(x - h)2 + k, then what is the value of a? _ '3>. X &- <O><. ) (:3'<) - 3tj )d- _ I Gj > -r'.-'- 'Id- <0 + ) 'd :::. 'r SJ + -}" T- t\ ( /,-.J -. /(; - -1 " (})..Ll The graph of the parabola y = 2x 2-1 is symmetric abou rne.-wbatis the equation of that line?

9 os -v. S:u { sre: t6l lr-o-- (\'\\ \ 47. The parabola y = 5x 2-20x + 14 will have Page 8 a maximum at (2, -6) a minimum at (2, -6) b) a maximum at (-2,6) e) a minimum at (2,10) c) a minimum at (l O,-86) \J _ -(()) d d- C d-i- \ Xc - dc-;-) I rn$\\ y Ql.<J a, 5 Cd- Jd -dg() -+ l'f -c, -<P_ 48. In a 120-volt circuit having a resistance of 12 ohms, the \power W J in watts when a current 1 is flowing through is given by W = What is the maximum power, in watts, that can be delivered in this circuit? 1.- \J e- k)<." ( c...v v..j c:;...,lh.) l0 -= \tr0 -l- - l...l T::: _ -ld-o...,co LA; -=- -La 1...;). 1-\ D:s=. /- '\ 0\: -t'!j ) LU -:: I L!o) +- \.} L'O LN -:: "5 0,,.::.-;So lu'..-d> 49. A piece of land is to be fenced and then divided by an inner fence as shown in the diagram. A building forms one side of the total fenced area. If the total length of fencing available for both the outer fencing and the partition down the middle is 36 m, what is the maximum area that can be enclosed by the fencing? r----- : to : Y-.. S,---_. Q. I _. I :;l --- ()Q H- TIT :::-1{:\ '\ A - LY--)( '3 ) -xt-i 1$1 -.-)<. -:=l> -)l.. >I c. - (-r) t f;.'j.."":. - ( (,).r 50. The accompanying diagram shows a sketch of a quadratic function, f(x). What is the nature of the roots of the quadratic equation f(x) = O? f(x) (L' J.;) (\C( 0- nd] b CG. e., c cj lo.- ry l

10 Page 9 P,/ /' 51. cording to th ational Root Theorem, what are the possible rational roots of the equation 7x 3 + 3x 2 + 2x - 4 = O? 52. Which quadratic equation has roots of ( and (1-307 \. a) x 2 + 2x - 10 = 0 M -=- 0- _ \-C1 L d-:::,. b x 2-2x + 10 = 0 c) x 2 + 2x - 8 = 0 d) x 2-2x - 8 = 0 _C-- - -a- G { -- C= t c» 53. Consider solving n 2 +, -9n - 4 = 0 by completing the square. ::.9. \.&- -::5- \. n2 + -9n + _(-S< ( d-'..j What is the numb r that goes in the blanks? (-5 ""V- =- II ) LI J 54. One root of x 3-5x 2-4x + 20 = 0 is x = -2. Find the other roots, A j \,- -L{ 4"'_7, --=-C Ii' -69 (-'5""" )l X- ) -;=-CJ \ -l- lob.x-=oryd- 55. Two roots of 2x 4 - llx 3 + 5x x - 21 = 0 are 3 ± J2. Find the other two roots. (. X - (3 t-rk -( 's ):::. X <C)d:/ 'j. X - '5""C" _ d--'i d. +-x -.3 C d><" )( )C.) - \ X -b.x.. +-"1-.-J Lt -I Lx r '> "j.. '1J )f.. -d \ X::: - ) \ Solve: 8 3x = 4 2x - G ) 5 'lx _ 0- jj v ') Jq -;:. 4.;><.. -lu q )( 4-1( - X -(0 ID 57. If 8 x - 1 = 16 3 \ then what is the value of x? '?x-)-=-\\--)( -3:::- qx =o-l:o td

11 If):.. Page Solve: (3x)'l!=; What is the logarithmic form of 6 x = Write the equation 9 5m = 8 in logarithmic form. 61. Simplify: log, 81 E A <:r d-x - d-

12 Page Which of the following statements is/are true? I. 109(Z7 B = ) log4 / II. 109(Zf)=lOg28-10g7/' III. log(zf) = 1:g278 \ IV. 109(Z7 B = ) pog28 X a) I only d) I, II, and III only b) and II only e) II, III, and IV only c) II and ill only 65. Express the sum log, 8 + log, 16 in the form log, y. 66. Solve for x:? log x + log 3 = log(2 + x) 0::;> lc X;>'d3 I ('X); l X tu'0" & 1 )() 67. Solve for x: log(x - 3) + log(x + 4) -log x = log 5 loge. )(r-x.-i) -=- lu?-r l0(jx L.u( X t--x -r) -=- I us G rx ) 68. Write as a single logarithm: 310gB gB6 l D "b 3 f- IGCj b -! =t\() 5X d- -::- d -t X SIX ').-.--A - - 0<-+ - J "::?&<j if6=---_ x ).-+- X -\ if ::; )( 1\ ;r-x --(,) t::o a.h-)cl--b ) v V>6- vr-e 69 W log hm. nte log 3 as a smg e ogant. "'lr.\ v'\l-.b 'o k r-e--j-.. 1o<A- \ usc 10 (., _, 0'D I 3

13 Page Solve for x: log 81 = 4log x t oed- 'is l = lljccr x. <j 0\ -:: X Y "3 U -c; X Y

14 Honors Algebra 2 Review for Final Exam 71) How much water must be evaporated r from a 300 L tank of a 2% salt solution to obtain a 5% solution? I L f) u;f X:::'./L V-...J c::l-, 0\\6\ (,<.)o-)() S:cilt o... -ev- k- (.00 )( ><. "),.. G - 0 ls- -, OS-X -, -::..-(J) X X:::- I Q[,.Q l...us- ) ( '300 -X) t 72) The river boat Delta Duchess paddled upstream at 12 km/h, stopped for 2 h of sightseeing, and paddled back at 18 km/h. How far upstream did the bo t travel if the total time for the trip, including the stop, was 7 h? = r\::..-b::: \" - \-C c..c... c-g. <r \'()"" \ do- '-"" "------<- +Uh.S-1-' CJ d- ;- -:::.-=r --n ("UL- J s)«"" <:; '(:)t-..-\-,y{.1t.- 1''N-o-- G""L cl t-j.-+ J ca - l- I.x. -=. \\1-6 +-, cj.--1 '6D '- 1b \c:::-(y\ Lc.o -:::..S 73) The intake pipe can fill a certain tank in 6 h when the outlet pipe is closed, but with the outlet pipe open it takes 9h. How long would it take the outlet pipe to empty a full tank? \...t.;k- X. -:::. ** -{j v,- Uv UI rt-v --t ( -LX J. 'I-. q j -J LeO =-I 'Sx. - -d--x --- l -... {'(; ko-a Q\o- o., \L

15 74) Graph the following quadratic. Make sure that you use at least 5 points and that you show the work or explain how you found each point. You may not use the trace or table feature on your calculator. o :;)(..I'S J, Y=_(X+3)2 vuk:x clu<.,u() C-S{O) \ - ( - \t s '}-=-... o -9 to y, _L..,.. ;... -'--fr k, '-,---! l _jj i '- r",,, = - :"'=,..- L I. j I T I - i' I ' '!Th, ' I ""J I,., t, 1 r I =I. 'r.r.\ " r, I r 7 t I f I f if -.-. i'.... J!. I.. '-'" I- -I'-- '-. \ e- I I i l- ',v,_..l 1 _L j x 75) The height h, in feet of a stone thrown with an upward speed of 40 ft/s is given by the formula h = 40t -16t 2, where t is the time, in seconds, since the stone was thrown. How long does it take the stone to reach the highest point of its path of motion? h(t::) -lbtd-t-ljot -e 1t-t (t;\ ( N.t 1$ ) 'V \ - \:> -=- YO) ;;: - ::: [, ( c,,,-c v.r.-d\ -::. er''- -:. d ( -II...1- ld c.jv,j. -=- - I L\ r-s-) r- <..{ OL \\ ) d- Pr+ \,oc C ii--r.- s, fo NL is d) + lr l Cl-,I 76) Write the equation ofthe parabola in vertex form that passes through the points (-3, 2), (-2,8) and (1, 2). Hint: use the quadratic regression feature on your calculator. )

Using the Rational Root Theorem to Find Real and Imaginary Roots Real roots can be one of two types: ra...-\; 0 or - l (- - ONLl --

$Using the Rational Root Theorem to Find Real and Imaginary Roots Real roots can be one of two types: ra...-\; 0 or - l (- - ONLl --$ Using the Rational Root Theorem to Find Real and Imaginary Roots Real roots can be one of two types: ra...-\; 0 or - l (- - ONLl -- Consider the function h(x) =IJ\ 4-8x 3-12x 2 + 24x {?\whose graph is