. ~ ~~::::~m Review Sheet #1

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1 . ~ ~~::::~m Review Sheet #1 Math lla Which ofthe following represents a function(s)? (1) Y... v \ J 1\ \ V i e5 3. The solution set for = 0 is :---:---:- --:...:-._",,, :- --;- --:---;-..!,..;-,... _-;---:---;. --_.! (3) i"-:---:"-:-- -;-'-;-'. '--i---:---:--- ;- --;-- '...'...'...,...'_..'...'...'...'-- no (1) {3,-4} (2) {-3,-4} (3) {-3, 4} {3,4} ('t - 3) (~-4) ~ 0 J.. =- 3, )( >:.. 4. Sketch a quadratic function that has a negative discriminant. o.ho\ ~at :* o.t''1 -pw 0.. V ~ ( does Nftr c.ro~..s ~c X - ().,)(),s S l f 8 +J3 j~ 6 _ ' v r~ :. mp 1: r;; 4-,,3 'tt-f3 - H ~Ll(j - &t(j' - rr 35 ""' 2 13_ \ f a function is defined b the equation = , what is the inverse of this function? ~ =- '+'1 3 + :l ~ X - 2 _ X - 2 ~ t.j~j J '-t ~3 h~w- o. ~,, (~~ 119/2010 Page 1

2 Solve for : 16.<+1 = (,. ~ X+-t :. ~ ~ L~-4 Lf (+) ;: (, ( z. -ci) 4')(. +-'-t ; rz.", - zc.f 2'8 = ~)( (.. :., S l f 77 r:-l. 9. mp 1 : 1 := ~ -.::::J 77 -:- Lj = 1'1. zs 2S ~ l~+r...c,., :.. "'"..< = _ - 3 '1 -<- ::. -...L lo. For the polnomialf() graphed at the right a. State the real solutions. ~ -= -s, X =',,,'; 2 b. Write the equation off() in factored form. r Ci) ::: (+ S)(~-)(~-2) -'i , 11. Solve: = 4 ::< '( ~12 :: if>' 2)(+1'2 =-4)(,z. =- -ld" c.h! z X..., z., ' ::. 4)( ::::.fo \ -z.,+-"l...\:' 'l.'-i -2=X, 'Z.-"n ~ ~ z..&4 =.. z..'" vi Solvelor in simplest radical farm : + 7t 6 X + l~ - l; :. 0 X. -= 0..: \ \:)::.1,-= _.1/9/2010 Page 2

3 Name:_ Midterm Review #2 Math lla 1. The solution(s) ofthe equation = 0 are '0 2._ t.\ ~C (1) 1 real root 2 imaginar roots (2) 2 real roots (4) 1 imaginar root (-) 1._ 4(\)(') [ 3 } 2. What is the value of g(-3) for g() = 3-2X2 +? t ~ e",+n b~ jvh.s\-\~ i (\ ~O M(' ~tr(e.n,2nd +o..bk.. '3(-3) ~ (- '3Y~ _2(- 3)2 4-, ) q (-3) = - 4 Y 1 ~- tty 3. The graph ofj() is shown at the right. Sketch the graph which represents f( + 2) - 3? \cft- 2 ckwy'\ "3 1\ 'l..--' ' f\ '..,. V 4. Solve for the following: = 0 l..:; (1) { {-loi, loi} )(. =- ± V-OD (2) {-10, 10} (4) {10i} + 4 =- - 0, 5. Find the sum and the product of the roots ofthe e uation = 36. '6 ~1. ~)t..- '"3lg :. 0 -l SLU"t) - ~ =-4:. -..!.. ~\..Lm _~ ~ 0 2 f ~d 4 o -~. :. - alp - q 1'v\)\.J T:' - ~ 6. Factor completel: 3a 3-4a 2 + 9a - 12 <0(3CA--'\) -\- 313 ~-~) [(~ -\- 3) 3<>..-4} 1 1/9/2010 Page 3

4 7. A model rocket is launched from ground level. ts height, h meters above ground, is a, function of time, t seconds after launch, and is given b the equation h =-4.9t t.\ \.. a. How long till the rocket reaches the ground again? +0 +"'~ \~S-\- nu.n~cdt" b. What is the maimum height of the rocket? \-0 +h.. V'\e~~+ +e.n1-h Xv\ (\ ~ 0 o..}.dti S~. (1.0~ ) ll.j.s02) XrY'().,)( :. 1S ~ 'h-:. D X ~c..\ :::., '~.,.. li ~ ~~~ 'i ml r") ~ 0 i mo-... ~ 300 ~ 'Sc..\ :. 50 ~ :: - 4,'1 Xz.~ "80S,,, 8. For the function g() shown at the right, find Domain: ~l'~} -3 ~ X L Lt Range: 1~ -;? =. 3L L) 0... g(-l) -\ 0 '(" [ - 3}Y) [ - 2) 'Z.) 4\"V~ \a) t Ll ',.5 m~kr.s 1""" 1/ L/ Simplif: s.fi4.2m 1t> ~ Cc ' 2 ~ O ~Y Ljl. =- 'Ol'4VLf'~ ~ 1 4D{cfl.l 10. Simplif: (-3 + 8i) - (4-9i) - 4 +q ; [ ; 7 J ~ =J2. (X_ \)2 ::. - LJ ' )<. 2. _ LX +5 =D )( - :::: t: A 11. Solve b completing the square and epress our answer in simplest a + bi form. ' X '- - L 't. 4--L ::: -,5 +-L ' -:. l"t z: For the graph shown at the right, find Domain: ~ 'f... '- L.\J 0 (' [- 3, 4) ~ange: t~ ) -3 f ~ ~ 41 o-r [-~) 4J s this a function? 'j -e..'5 \JLT f o..scf)es f es, is it one-to-one? ntl \i-l.t d oes n~ rq.ss J, "\ f " V Findj(-) :4 ---'----- Findj(4) on :SO\~o\. 1/ Page 4

5 Name: '----- Midterm Review Sheet #3 Math lla 1. Find the number of points ofintersection ofthe following graphs: = X = 3+ 5 (1) (2) o (3) 3 3. A function is defined b the equation = S - S. Which equation defines the inverse of this function? =- 5' (1) =-- (3) =-- ~+-~ = ' S-S S-S (2) Y = S + =SY - S 4. Solve and graph: ~ 2 1 ~ -\ "i" ;) ~'ft" s '" c.hl' ex. X - 1- " X 2 ~'Z-~ - \ ~ -2.. _ 2 - \ ~ A ol'z Z -5 '1) Z. 5 z. 2 ~ -. - D- J! Z \ () _ \ ~ Z2. \ 10-1\ ~! 3 \9\Zl. \-) 2 L,~ l, 1!; ) "\J 0< ~ -i ~Z, \ \ "2. '2.,... F T' S. The graph below shows the function f(). lhich graph represents the function fe + 2)? \~~\- ~ Y,. 3) 1) (i)) 4) Y,,

6 6. Simplif: (2+3i)+(4+2i) _ JiP i-st} Lj+ ( \ Solve for : X < 0 < e ()( -~)LX +') "D D ~=-v,':...-\ ~ S +- ".5""- p f /) '\ DC '" (., 0 F F Solve: 2X2 = 144 (> X = ±: ~71.. ' X 7.::1~ J -=. t{5bf2 t< ; "tldril Simplif: 4J8 3J2 sj3 (PO ~ ~ ~ r 2Qo f31 {PO m; (3 lpo(ltf3) : ~'---- For the equation = ( - 4i - 3 a. State the shift from the parent graph f() = 2 \\~,,\- L.\ dow,", 3.. b. dentif the verte. ('"\ 1-3) c., J, W Jl 1-\f' 12. a. Describe the n~e ofthe roots. (1 ) 1 real 2 real (3) 1 imaginar (4) 2 imaginar '!?_ ~~Cr :...,1.._ ~ ()(~) ; 33. b. Solve for in simplest form~. X= b:!. ~ 'o1-4a..c.. =\- l ± "; 33 2D \ 2.. 1/9/2010 Page ~

7 Name: Math lla j Midterm Review Sheet #4 1. A rocket is launched from the ground and follows a parabolic path represented b the equation = lo. At the same time, a flare is launched from a height of 10 feet and follows a straight path represented b the equation = - + 1O. Find the number of points of intersection. (1) (2) o (3) Find the inverse of the equation: = ~ -= -7 ~ - L, OX \-l. -: - -, :1,,+-!e =- ui Y'\\l - 1 J 4. Solve for : 14-91::; 7 q.~ -q ~ 1 ~-q! ;3 Y ~ 110 4'1.! 2. D-ql~ 7 Z-q/t:7 J4D - CJ ~! 3=7 3' ~ 7 )(~'-f )(21 q~i 2.. T F" F t + ~~ 'X ~ ~) 5. For the graph shown at the right, which graph fi)"\.,. represents g( - 4) - 3 down 3 T'5h\- t..\ \ '\., (1) (3) '\. '\. "" ['\. '\,.!'. 119/2010 Page

8 6. Simplif: (3 ~ 2i) - (8-17i) J- 5" + S,07 - ~+17i - 7. Solve: :0,( ()( +- ~)(X ~Lf)? () tot \) )\:.-3 X-=-4 :<S+s-1"'2. "!.U 0-0-1"2.-!.D 100-'0-",!. D S' 2 D - rz.. ::? 0 7~2. D T t= t ~- 3 V X ~~} T 8. For the following quadratic equation, g() = ( - 9)( + 2) Roots: 'i'l - 2. AOS: X = -; Verte: ( 3.S) - 30."Z..S) J '/.. 9. Solve for in simplest radicalfarm: 2X2-16 = 24 2 ~7..: L\ C ~ -t J7frs X 2-; 2.0 ~ -:. t 'l (5] X::. ~ VZ-b 10. Simplif: 25M ~J20 5' {~ r-:- 5S\Ofi,) =l5ori] 5 1\00 \ 2. =- l 11. For the equation = a. State the shift from the parent graph f() = l,&\- 2, do"""t1, X " - 5 L b. dentif the verte. - '-\ \ (-2 -) o c. Graph the new equation. - z.. - \ - t) b L 12. For the equation, = 5 6 ' 'Z-_ 5" ~ ~ :. 0. ~Z._ 4o.L (-s)' - '-\t~)(:~) ::. - \) a. Descnbe the nature of the roots. (1) 1 real (2) 2 real 2 imaginar (4) 1 imaginar b. Solve for in simplest form. X :.. - 'n 'L ~ b 'Z._~ ClC. %.0...,> / \' V' \ ~ ~ 1.,/ /,,/ ~ \ f' L 119/2010 Page 8

9 Name: Math lla Midterm Review Sheet #5 Z 1. The solution(s) of the equation = 0 are b - 4QC (- 5)1. -L\ ll)(-z.) (1 ) 1 real root (3) 2 imaginar 2 real roots ( 4) 1 imaginar root 2. What is the value ofg(-2) for g() = 2X ? [;(-1.) ~- 3l ~(- "L) ~ 2( ~ l) Z.~5(- ")-l c". co.j c.. ~. ~ -.3 ~~d +~l<.. 3. The graph ofj() is shown at the right. Sketch the graph which represents fi + 4) - 5? \ 'Co ~+- '" doli'ln S ~ 1. ~ J, V / / 4. Solve for the following: 3 2 = 108 X 2-_ '3lP (1) { } (3) {-6i, 6i} X :::. -::. 6} (4) {6} 5. Find the sum and the product of the roots of the equation 2X = -8. ~.. ~ =- - L~) _ -~ L.J 2 '" S =. "0 \.J\AJ W a ,,1'"OOl ':.. :. :...! : r ~" Factor completel: X1.(",-3) - \(,..(~-:,) ( '2._\L,) ~ - 3) ;.'".-'" "'. Page 9

10 7. A ball is thrown straight up. The height h ofthe ball, in feet, t seconds after it is thrown is given b the fonnula h(t) =-8t t a. How man seconds after the ball is thrown will it return to the ground? Round to nearest hundredth. b. What is the maimum height reached b the ball? Round to nearest hundredth. 'h =- - 8 ~ z...., 5)<. ~ "Z.. -=-{) ~ N\ i ~ ~ D a..) L q ~ seconds X~ :. 5 X ~d:. \ ' m iv) :: '0 'i VVl~= 1"0 sc..\ -=, b) p+~ 8. For the functionf() shown at the right, find. 9. Domain: 1)(' \~ ~ Range: ~ ~ \ 0 ~ j) FindfC5) = 2. [\ )00") ['0 lo<j) Simplif: (2J8)( -3.)5) -(pf4c) =-~~\\5 =f-\l.\\o] '--..._ _ v _ Simplif: (23 8i ~ ( i) 14 - \~\ 11. Solve b completing the square and-epress our answer in Sijplest radical fonn. 42, =JL X - 5 ::. -t q 'i-'- +- ~ )(1- _ \0)(.- "3 ::.1) L X '2t:'" - \t~t ~ C' )2- -:.< S 3+ LS -- = 5-2..l P 12. For the graph shown at the right, find 2 ::J c 110 1/9/2010 Domain: 1X10':' 'X ~ L.l3 [0, ~ F QJ Range: 1 ~\tpd =~ :: \D~ (be) ~ s this a function? f es, is it one-to-one? 'i ~ n t> 1: V FindfCl) 100 FindfC4) \ \ D J: =100 ~ 90 ~ 80.9., 7C 'i5 a: GO r:; f,... / r'\., / 23 4 Time (minutfjs) - -cr 10

11 Name:_- Midterm Review Sheet #6 Math 11A a. Which graph(s) represents a function? ~)b b. Which graph(s) is one-to-one? b ) 2 - c. Which graph(s) is onto? b A B 3. Solve: =0 5 'f.., L.-=. 45 X. 1..: Jacob is solving a quadratic equation. He eecutes a program on his graphing calculator and sees that the roots are real, rational, and unequal. This information indicates to Jacob that the parabola a) lies entirel above or below the - ais Simplif: L - 2. J2-2i rz -~ J2+i (i -~ A -.A.~ +-...L("i -.-4,'Z. ~?... = :. {[\ -..i ff - 2 ',~ b - 3'\ a :3 1/9/2010 Page 11 " -"

12 7. Find the inverse of = = ~ 3 ' X -17 =0-3! 8. Solve for : 4+3 =8 2 +! l),2.)"'1... ' =.. (2.. ~}1.1..+) 2(>e. +3) ::: 3? -+ ) 2.~+ (p =\O~ -\-3 9. Simplif: i ~ "O.iS 1O. For the polnomialf() graphed at the right a. State the real solutions. X=- -1 :.-3 X-= :: 1 ) i ) b. Write the equationf() in factored form Solve: 16-3kl = 21 Lo- 3.. =- 2. \ (g -3~ ~ -2 \ en. \ ~- ~",\::.2..\ - 3$.: \S -3.-:. -27 ~- S (\( :: [K ~ G ) \ 1..\'=2\ J \ ",,~q, '" 1- S) :: 'Z..,. \(;-'2.;\= 2.\ - 20\ \ ::. "2..\ 4; ) '%,.\ ::. Z. \ V -s 12. Using the given set, h() = {(3, 1), (2,4), (1, )} Find the domain: 13,1., $ range: ") write the inverse 1(1,3)(L4.2) ( t, 1)) is the original a function?---4~j-,,<-=5,---- is the original 1-1?_Y1~O,---- is it onto?_-=j'if-\-f...",s'-'. 1/9/2010 Page 12

QUEEN ELIZABETH REGIONAL HIGH SCHOOL MATHEMATICS 2201 MIDTERM EXAM JANUARY 2015 PART A: MULTIPLE CHOICE ANSWER SHEET

QUEEN ELIZABETH REGIONAL HIGH SCHOOL MATHEMATICS 01 MIDTERM EXAM JANUARY 01 PART A: MULTIPLE CHOICE NAME: ANSWER SHEET 1. 11. 1.. 1... 1... 1... 1... 1.. 7. 17. 7. 8. 18. 8. 9. 19. 9. 10. 0. 0. QUADRATIC