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

Size: px
Start display at page:

Transcription

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

### QUEEN ELIZABETH REGIONAL HIGH SCHOOL MATHEMATICS 2201 MIDTERM EXAM

QUEEN ELIZABETH REGIONAL HIGH SCHOOL MATHEMATICS 0 MIDTERM EXAM JANUARY 0 NAME: TIME: HOURS 0 MINUTES ( INCLUDES EXTRA TIME ) PART A: MULTIPLE CHOICE ( Value: 0 % ) Shade the letter of the correct response

### Final Exam Review Part 2 #1 Page 1 / 21

Final Eam Review Part #1 Intermediate Algebra / MAT 135 Spring 017 Master ( Master Templates) Student Name/ID: v 1. Solve for, where is a real number. v v + 1 + =. Solve for, where is a real number. +

### SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

Spring 0 Math 08 Eam Preparation Ch Dressler Name SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Solve the quadratic equation b the square root propert.

### Final Exam Review Part 2 #4

Final Eam Review Part # Intermediate Algebra / MAT 135 Fall 01 Master (Prof. Fleischner) Student Name/ID: 1. Solve for, where is a real number. + = 8. Solve for, where is a real number. 9 1 = 3. Solve

### Final Exam Review Part 2 #4

Final Eam Review Part # Intermediate Algebra / MAT 135 Fall 01 Master (Prof. Fleischner) Student Name/ID: 1. Solve for, where is a real number. + =. Solve for, where is a real number. 9 1 = 3. Solve for,

### Chapter 9 Notes Alg. 1H 9-A1 (Lesson 9-3) Solving Quadratic Equations by Finding the Square Root and Completing the Square

Chapter Notes Alg. H -A (Lesson -) Solving Quadratic Equations b Finding the Square Root and Completing the Square p. *Calculator Find the Square Root: take the square root of. E: Solve b finding square

### MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Math 2 Stud Guide-Chapters 8 and 9 Name Date: Time: MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find all square roots of the number. ) 600 9,

### Self- assessment 1010 (Intermediate Algebra)

Self- assessment (Intermediate Algebra) If ou can work these problems using a scientific calculator, ou should have sufficient knowledge to demonstrate master of Intermediate Algebra and to succeed in

### REVIEW KEY VOCABULARY REVIEW EXAMPLES AND EXERCISES

Etra Eample. Graph.. 6. 7. (, ) (, ) REVIEW KEY VOCABULARY quadratic function, p. 6 standard form of a quadratic function, p. 6 parabola, p. 6 verte, p. 6 ais of smmetr, p. 6 minimum, maimum value, p.

### Algebra I Practice Questions ? 1. Which is equivalent to (A) (B) (C) (D) 2. Which is equivalent to 6 8? (A) 4 3

1. Which is equivalent to 64 100? 10 50 8 10 8 100. Which is equivalent to 6 8? 4 8 1 4. Which is equivalent to 7 6? 4 4 4. Which is equivalent to 4? 8 6 Page 1 of 0 11 Practice Questions 6 1 5. Which

4-1 Graphing Quadratic Functions Quadratic Function in standard form: f() a b c The graph of a quadratic function is a. y intercept Ais of symmetry -coordinate of verte coordinate of verte 1) f ( ) 4 a=

### Integrated II: Unit 2 Study Guide 2. Find the value of s. (s - 2) 2 = 200. ~ :-!:[Uost. ~-~::~~n. '!JJori. s: ~ &:Ll()J~

Name: 1. Find the value of r., (r + 4) 2 = 48 4_ {1 1:. r l f 11i),_ == :r (t~ : t %J3 (t:; KL\J5 ~ ~ v~~f3] ntegrated : Unit 2 Study Guide 2. Find the value of s. (s 2) 2 = 200 ~ :!:[Uost ~~::~~n '!JJori

ALGEBRA II-GRAPHING QUADRATICS THE GRAPH OF A QUADRATIC FUNCTION The Quadratic Equation is written as: ; this equation has a degree of. Where a, b and c are integer coefficients (where a 0) The graph of

### 2 nd Semester Final Exam Review Block Date

Algebra 1B Name nd Semester Final Eam Review Block Date Calculator NOT Allowed Graph each function. 1 (10-1) 1. (10-1). (10-1) 3. (10-1) 4. 3 Graph each function. Identif the verte, ais of smmetr, and

### MAT 1033C -- Martin-Gay Intermediate Algebra Chapter 8 (8.1, 8.2, 8.5, 8.6) Practice for the Exam

MAT 33C -- Martin-Ga Intermediate Algebra Chapter 8 (8.1 8. 8. 8.6) Practice for the Eam Name Date Da/Time: SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

### Chapters 8 & 9 Review for Final

Math 203 - Intermediate Algebra Professor Valdez Chapters 8 & 9 Review for Final SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Solve the formula for

### 2 If ax + bx + c = 0, then x = b) What are the x-intercepts of the graph or the real roots of f(x)? Round to 4 decimal places.

Quadratic Formula - Key Background: So far in this course we have solved quadratic equations by the square root method and the factoring method. Each of these methods has its strengths and limitations.

### 2 nd Semester Final Exam Review Block Date

Algebra 1B Name nd Semester Final Eam Review Block Date Calculator NOT Allowed Graph each function. Identif the verte and ais of smmetr. 1 (10-1) 1. (10-1). 3 (10-) 3. 4 7 (10-) 4. 3 6 4 (10-1) 5. Predict

### Mathematics 2201 Midterm Exam Review

Mathematics 0 Midterm Eam Review Chapter : Radicals Chapter : Quadratic Functions Chapter 7: Quadratic Equations. Evaluate: 8 (A) (B) (C) (D). Epress as an entire radical. (A) (B) (C) (D). What is the

### A L A BA M A L A W R E V IE W

A L A BA M A L A W R E V IE W Volume 52 Fall 2000 Number 1 B E F O R E D I S A B I L I T Y C I V I L R I G HT S : C I V I L W A R P E N S I O N S A N D TH E P O L I T I C S O F D I S A B I L I T Y I N

### MATH College Algebra Review for Test 2

MATH 4 - College Algebra Review for Test Sections. and.. For f (x) = x + 4x + 5, give (a) the x-intercept(s), (b) the -intercept, (c) both coordinates of the vertex, and (d) the equation of the axis of

### Mathematics 2201 Midterm Exam Review

Mathematics 0 Midterm Eam Review Chapter : Radicals Chapter 6: Quadratic Functions Chapter 7: Quadratic Equations. Evaluate: 6 8 (A) (B) (C) (D). Epress as an entire radical. (A) (B) (C) (D). What is the

### l(- oo)-~j [-I <. )( L6\ \ -J ~ ~ ~~~ ~~L{ ,~:::-=r\ or L":: -j) {fevylemr.eor k, ("p J~ -4" e S ' e,~ :; ij or J iv I 0"'& ~~ a. 11 qa.

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

### 121D Practice Test #

D Practice Test # College Algebra / Math D GARAGE (Prof. Vasan) Student Name/ID:. Write the epression as a single logarithm. 5log 8 w + 5 log 8 3log 8 z. Solve for. log + 3 = log + 6 ALEKS D Practice Test

### UNITS ALGEBRA II WORK PACKET ON QUADRATICS

UNITS ALGEBRA II WORK PACKET ON QUADRATICS Factoring Practice #1 Algebra II For #1-20, factor each expression completely. Name Date Per 10*3 + i6x2-15* - 24 5* * 3) x2-36 4) x2 + loj: + 24 5) x3-6x2 +

### A2 HW Imaginary Numbers

Name: A2 HW Imaginary Numbers Rewrite the following in terms of i and in simplest form: 1) 100 2) 289 3) 15 4) 4 81 5) 5 12 6) -8 72 Rewrite the following as a radical: 7) 12i 8) 20i Solve for x in simplest

### Test # 2 Review Sections (2.4,2.5,2.6, & ch. 3) Math 1314 Name

Test # Review Sections (.,.,., & ch. 3) Math 131 Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Write the equation of the line. 1) -intercept,

### Algebra I Quadratics Practice Questions

1. Which is equivalent to 64 100? 10 50 8 10 8 100. Which is equivalent to 6 8? 4 8 1 4. Which is equivalent to 7 6? 4 4 4. Which is equivalent to 4? 8 6 From CCSD CSE S Page 1 of 6 1 5. Which is equivalent

### Honors Algebra 2 ~ Spring 2014 Name 1 Unit 3: Quadratic Functions and Equations

Honors Algebra ~ Spring Name Unit : Quadratic Functions and Equations NC Objectives Covered:. Define and compute with comple numbers. Operate with algebraic epressions (polnomial, rational, comple fractions)

### T h e C S E T I P r o j e c t

T h e P r o j e c t T H E P R O J E C T T A B L E O F C O N T E N T S A r t i c l e P a g e C o m p r e h e n s i v e A s s es s m e n t o f t h e U F O / E T I P h e n o m e n o n M a y 1 9 9 1 1 E T

### College Algebra ~ Review for Test 2 Sections

College Algebra ~ Review for Test Sections. -. Use the given graphs of = a + b to solve the inequalit. Write the solution set in interval notation. ) - + 9 8 7 6 (, ) - - - - 6 7 8 - Solve the inequalit

### Baruch College MTH 1030 Sample Final B Form 0809 PAGE 1

Baruch College MTH 00 Sample Final B Form 0809 PAGE MTH 00 SAMPLE FINAL B BARUCH COLLEGE DEPARTMENT OF MATHEMATICS SPRING 00 PART I (NO PARTIAL CREDIT, NO CALCULATORS ALLOWED). ON THE FINAL EXAM, THERE

### For questions 5-8, solve each inequality and graph the solution set. You must show work for full credit. (2 pts each)

Alg Midterm Review Practice Level 1 C 1. Find the opposite and the reciprocal of 0. a. 0, 1 b. 0, 1 0 0 c. 0, 1 0 d. 0, 1 0 For questions -, insert , or = to make the sentence true. (1pt each) A. 5

### Lesson 7.1 Polynomial Degree and Finite Differences

Lesson 7.1 Polnomial Degree and Finite Differences 1. Identif the degree of each polnomial. a. 1 b. 0. 1. 3. 3 c. 0 16 0. Determine which of the epressions are polnomials. For each polnomial, state its

### Unit 2: Functions and Graphs

AMHS Precalculus - Unit 16 Unit : Functions and Graphs Functions A function is a rule that assigns each element in the domain to eactly one element in the range. The domain is the set of all possible inputs

### Quadratics Test 2 Study Guide

Algebra Name V Qj0H[` IKzuptGap ssconfxtlwabrqec [LfLJCf.N X ga^lalw UrViQg]hVtAsz Or\ejsZeErvdeYdn. Quadratics Test Stud Guide Solve each equation b taking square roots. ) m + = 0 ) - = Period Solve each

### In #8-11, Simplify the expression. Write your answer using only positive exponents. 11) 4

Semester Final Eam Review Packet Name Chapter 8: Eponents and Eponential Functions In #1-4 simplify the epression. Write your answer using eponents. 1) ( ) ( )( ) 5 ) ( 6 ) 5 4 ) 7 4 11 7 6 6 4) 8 6 1

### Pledged_----=-+ ---'l\...--m~\r----

, ~.rjf) )('\.. 1,,0-- Math III Pledged_----=-+ ---'l\...--m~\r---- 1. A square piece ofcardboard with each side 24 inches long has a square cut out at each corner. The sides are then turned up to form

Honors Algebra -3 Solving Quadratic Equations by Graphing and Factoring Learning Targets 1. I can solve quadratic equations by graphing. I can solve quadratic equations by factoring 3. I can write a quadratic

### MATH 60 Review Problems for Final Exam

MATH 60 Review Problems for Final Eam Scientific Calculators Onl - Graphing Calculators Not Allowed NO CLASS NOTES PERMITTED Evaluate the epression for the given values. m 1) m + 3 for m = 3 2) m 2 - n2

### First Semester Final Review NON-Graphing Calculator

Algebra First Semester Final Review NON-Graphing Calculator Name:. 1. Find the slope of the line passing through the points ( 5, ) and ( 3, 7).. Find the slope-intercept equation of the line passing through

### UNIT #9 ROOTS AND IRRATIONAL NUMBERS REVIEW QUESTIONS

Answer Key Name: Date: UNIT #9 ROOTS AND IRRATIONAL NUMBERS REVIEW QUESTIONS Part I Questions. Which of the following is the value of 6? () 6 () 4 () (4). The epression is equivalent to 6 6 6 6 () () 6

### Lesson 4.1 Exercises, pages

Lesson 4.1 Eercises, pages 57 61 When approimating answers, round to the nearest tenth. A 4. Identify the y-intercept of the graph of each quadratic function. a) y = - 1 + 5-1 b) y = 3-14 + 5 Use mental

QUADRATIC GRAPHS ALGEBRA 2 INU0114/514 (MATHS 1) Dr Adrian Jannetta MIMA CMath FRAS Quadratic Graphs 1/ 16 Adrian Jannetta Objectives Be able to sketch the graph of a quadratic function Recognise the shape

### Math 030 Review for Final Exam Revised Fall 2010 RH/ DM 1

Math 00 Review for Final Eam Revised Fall 010 RH/ DM 1 1. Solve the equations: (-1) (7) (-) (-1) () 1 1 1 1 f. 1 g. h. 1 11 i. 9. Solve the following equations for the given variable: 1 Solve for. D ab

### Math 150: Intermediate Algebra Spring 2012 Fall 2005 : Mock Exam 4 (z z

Math 150: Intermediate Algebra Spring 01 Fall 005 : Mock Eam 4 (z 9. - z NAME 10.6) TICKET # [ 13 problems: 10 points each ] Answer problems and epress your answers appropriately, that is ; simply state

### Quadratic Functions Objective: To be able to graph a quadratic function and identify the vertex and the roots.

Name: Quadratic Functions Objective: To be able to graph a quadratic function and identif the verte and the roots. Period: Quadratic Function Function of degree. Usuall in the form: We are now going to

### MPM 2D Final Exam Prep 2, June b) Y = 2(x + 1)2-18. ~..: 2. (xl- 1:'}")( t J') -' ( B. vi::: 2 ~ 1-'+ 4 1<. -t-:2 -( 6! '.

MPM 2D Final Exam Prep 2 June 2017 1. Express each equation in standard form and factored form: ~ ~ +et's 'leu t W (.. ".>tak( a) y = (x + 5)2 + 1 on ::t~'t.{1'" ~heeh v 1' K 1 C'. T.) '. (J. lr lov J

### Section 5.5 Complex Numbers

Name: Period: Section 5.5 Comple Numbers Objective(s): Perform operations with comple numbers. Essential Question: Tell whether the statement is true or false, and justify your answer. Every comple number

### Practice Problems for Test II

Math 117 Practice Problems for Test II 1. Let f() = 1/( + 1) 2, and let g() = 1 + 4 3. (a) Calculate (b) Calculate f ( h) f ( ) h g ( z k) g( z) k. Simplify your answer as much as possible. Simplify your

### i;\-'i frz q > R>? >tr E*+ [S I z> N g> F 'x sa :r> >,9 T F >= = = I Y E H H>tr iir- g-i I * s I!,i --' - = a trx - H tnz rqx o >.F g< s Ire tr () -s

5 C /? >9 T > ; '. ; J ' ' J. \ ;\' \.> ). L; c\ u ( (J ) \ 1 ) : C ) (... >\ > 9 e!) T C). '1!\ /_ \ '\ ' > 9 C > 9.' \( T Z > 9 > 5 P + 9 9 ) :> : + (. \ z : ) z cf C : u 9 ( :!z! Z c (! \$ f 1 :.1 f.

### Math 152 Chapter 8 Handout Helene Payne. Name:

Name: 1. Solve the equation by the square root property. If possible, simplify radicals or rationalize denominators. Epress imaginary solutions in the form a + bi. (a) 2 = 25 (b) 4 2 = 400 (c) 16 2 + 49

### MATH College Algebra Review for Test 2

MATH 34 - College Algebra Review for Test 2 Sections 3. and 3.2. For f (x) = x 2 + 4x + 5, give (a) the x-intercept(s), (b) the -intercept, (c) both coordinates of the vertex, and (d) the equation of the

### Lesson 7.1 Polynomial Degree and Finite Differences

Lesson 7.1 Polynomial Degree and Finite Differences 1. Identify the degree of each polynomial. a. 1 b. 0.2 1. 2 3.2 3 c. 20 16 2 20 2. Determine which of the epressions are polynomials. For each polynomial,

### Fair Game Review. Chapter 9. Find the square root(s) ± Find the side length of the square. 7. Simplify Simplify 63.

Name Date Chapter 9 Find the square root(s). Fair Game Review... 9. ±. Find the side length of the square.. s. s s Area = 9 ft s Area = 0. m 7. Simplif 0. 8. Simplif. 9. Simplif 08. 0. Simplif 88. Copright

### Name Date Class California Standards 17.0, Quadratic Equations and Functions. Step 2: Graph the points. Plot the ordered pairs from your table.

California Standards 17.0, 1.0 9-1 There are three steps to graphing a quadratic function. Graph y x 3. Quadratic Equations and Functions 6 y 6 y x y x 3 5 1 1 0 3 1 1 5 0 x 0 x Step 1: Make a table of

### Name Class Date. Quadratic Functions and Transformations. 4 6 x

- Quadratic Functions and Transformations For Eercises, choose the correct letter.. What is the verte of the function 53()? D (, ) (, ) (, ) (, ). Which is the graph of the function f ()5(3) 5? F 6 6 O

### 5. Determine the discriminant for each and describe the nature of the roots.

4. Quadratic Equations Notes Day 1 1. Solve by factoring: a. 3 16 1 b. 3 c. 8 0 d. 9 18 0. Quadratic Formula: The roots of a quadratic equation of the form A + B + C = 0 with a 0 are given by the following

### Lesson 9.1 Using the Distance Formula

Lesson. Using the Distance Formula. Find the eact distance between each pair of points. a. (0, 0) and (, ) b. (0, 0) and (7, ) c. (, 8) and (, ) d. (, ) and (, 7) e. (, 7) and (8, ) f. (8, ) and (, 0)

### 9-1. The Function with Equation y = ax 2. Vocabulary. Graphing y = x 2. Lesson

Chapter 9 Lesson 9-1 The Function with Equation = a BIG IDEA The graph of an quadratic function with equation = a, with a 0, is a parabola with verte at the origin. Vocabular parabola refl ection-smmetric

### Lesson 10.1 Solving Quadratic Equations

Lesson 10.1 Solving Quadratic Equations 1. Sketch the graph of a quadratic equation with each set of conditions. a. One -intercept and all nonnegative y-values b. The verte in the third quadrant and no

### Mth 95 Module 4 Chapter 8 Spring Review - Solving quadratic equations using the quadratic formula

Mth 95 Module 4 Chapter 8 Spring 04 Review - Solving quadratic equations using the quadratic formula Write the quadratic formula. The NUMBER of REAL and COMPLEX SOLUTIONS to a quadratic equation ( a b

### BARUCH COLLEGE MATH 1030 Practice Final Part 1, NO CALCULATORS. (E) All real numbers. (C) y = 1 2 x 5 2

BARUCH COLLEGE MATH 1030 Practice Final Part 1, NO CALCULATORS 1. Find the domain of f(x) = x + x x 4x. 1. (A) (, 0) (0, 4) (4, ) (B) (, 0) (4, ) (C) (, 4) (4, ) (D) (, ) (, 0) (0, ) (E) All real numbers.

### MATH 91 Final Study Package Name

MATH 91 Final Stud Package Name Solve the sstem b the substitution method. If there is no solution or an infinite number of solutions, so state. Use set notation to epress the solution set. 1) - = 1 1)

### Math 141 Review for Midterm

Math 141 Review for Midterm There will be two parts to this test. Part 1 will have graph sketching, and no calculator is allowed. Part will have everthing else, and a calculator and/or graphing calculator

### Precalculus Summer Packet

Precalculus Summer Packet These problems are to be completed to the best of your ability by the first day of school You will be given the opportunity to ask questions about problems you found difficult

### Unit 2 Notes Packet on Quadratic Functions and Factoring

Name: Period: Unit Notes Packet on Quadratic Functions and Factoring Notes #: Graphing quadratic equations in standard form, verte form, and intercept form. A. Intro to Graphs of Quadratic Equations: a

### ( ) f ( x 1 ) . x 2. To find the average rate of change, use the slope formula, m = f x 2

Common Core Regents Review Functions Quadratic Functions (Graphs) A quadratic function has the form y = ax 2 + bx + c. It is an equation with a degree of two because its highest exponent is 2. The graph

### math FALL developmental mathematics sullivan 1e

TSIpractice eam review 1 131 180 plus 34 TSI questions for elementar and intermediate algebra m0300004301 aaa Name www.alvarezmathhelp.com math0300004301 FALL 01 100 interactmath developmental mathematics

### APPH 4200 Physics of Fluids

APPH 42 Physics of Fluids Problem Solving and Vorticity (Ch. 5) 1.!! Quick Review 2.! Vorticity 3.! Kelvin s Theorem 4.! Examples 1 How to solve fluid problems? (Like those in textbook) Ç"Tt=l I \$T1P#(

### 1 k. cos tan? Higher Maths Non Calculator Practice Practice Paper A. 1. A sequence is defined by the recurrence relation u 2u 1, u 3.

Higher Maths Non Calculator Practice Practice Paper A. A sequence is defined b the recurrence relation u u, u. n n What is the value of u?. The line with equation k 9 is parallel to the line with gradient

### Algebra II Notes Unit Five: Quadratic Functions. Syllabus Objectives: 5.1 The student will graph quadratic functions with and without technology.

Sllabus Objectives:.1 The student will graph quadratic functions with and without technolog. Quadratic Function: a function that can be written in the form are real numbers Parabola: the U-shaped graph

### College Algebra ~ Review for Test 2 Sections

College Algebra ~ Review for Test Sections. -. Find a point-slope form for the equation of the line satisfing the conditions. ) a) Slope -, passing through (7, ) b) Passing through (-, -8) and (-, ) Write

### PRACTICE FINAL EXAM. 3. Solve: 3x 8 < 7. Write your answer using interval notation. Graph your solution on the number line.

MAC 1105 PRACTICE FINAL EXAM College Algebra *Note: this eam is provided as practice onl. It was based on a book previousl used for this course. You should not onl stud these problems in preparing for

### ALGEBRA II SEMESTER EXAMS PRACTICE MATERIALS SEMESTER (1.2-1) What is the inverse of f ( x) 2x 9? (A) (B) x x (C) (D) 2. (1.

04-05 SEMESTER EXAMS. (.-) What is the inverse of f ( ) 9? f f f f ( ) 9 ( ) 9 9 ( ) ( ) 9. (.-) If 4 f ( ) 8, what is f ( )? f( ) ( 8) 4 f ( ) 8 4 4 f( ) 6 4 f( ) ( 8). (.4-) Which statement must be true

### Algebra Notes Quadratic Functions and Equations Unit 08

Note: This Unit contains concepts that are separated for teacher use, but which must be integrated by the completion of the unit so students can make sense of choosing appropriate methods for solving quadratic

### Algebra II 5.3 Solving Quadratic Equations by Finding Square Roots

5.3 Solving Quadratic Equations by Finding Square Roots Today I am solving quadratic equations by finding square roots. I am successful today when solve quadratic functions using square roots. It is important

### Lesson #33 Solving Incomplete Quadratics

Lesson # Solving Incomplete Quadratics A.A.4 Know and apply the technique of completing the square ~ 1 ~ We can also set up any quadratic to solve it in this way by completing the square, the technique

### Mathematics Extension 1

BAULKHAM HILLS HIGH SCHOOL TRIAL 04 YEAR TASK 4 Mathematics Etension General Instructions Reading time 5 minutes Working time 0 minutes Write using black or blue pen Board-approved calculators may be used

### BRONX COMMUNITY COLLEGE of the City University of New York DEPARTMENT OF MATHEMATICS & COMPUTER SCIENCE. MTH 05 Review Sheet

BRONX COMMUNITY COLLEGE of the Cit Universit of New York DEPARTMENT OF MATHEMATICS & COMPUTER SCIENCE MTH 05 Review Sheet Go to http://www.cun.edu/testing for more information on the CUNY Elementar Algebra

### = x. Algebra II Notes Quadratic Functions Unit Graphing Quadratic Functions. Math Background

Algebra II Notes Quadratic Functions Unit 3.1 3. Graphing Quadratic Functions Math Background Previousl, ou Identified and graphed linear functions Applied transformations to parent functions Graphed quadratic

### G r a d e 1 1 P r e - C a l c u l u s M a t h e m a t i c s ( 3 0 S ) Midterm Practice Exam Answer Key

G r a d e 1 1 P r e - C a l c u l u s M a t h e m a t i c s ( 3 0 S ) Midterm Practice Eam Answer Key G r a d e 1 1 P r e - C a l c u l u s M a t h e m a t i c s Midterm Practice Eam Answer Key Name:

### Exam 2 Review F15 O Brien. Exam 2 Review:

Eam Review:.. Directions: Completely rework Eam and then work the following problems with your book notes and homework closed. You may have your graphing calculator and some blank paper. The idea is to

### ,y. ~ (Lo )-Y2 ') '---~ F( '...J ( '1, 4. \fer-\{:k. ('X -5)'1.-+ :tl\ ~\:,) ~::; fi(~ S:;')'"'--t L. X-lOX t ~5 = IJ~-~+~5.

Name. Date 18. Write the equation of this conic: No,y. ~ '---~ F( '...J ( '1, 4 2A. Write the equation of this conic: \fer-\{:k. (lo) -3~2 ') (Lo )-Y2 ') 28. Write the equation of this conic: - - - -...

Mth 0 - Quadratic functions and quadratic equations Name Find the product. 1) 8a3(2a3 + 2 + 12a) 2) ( + 4)( + 6) 3) (3p - 1)(9p2 + 3p + 1) 4) (32 + 4-4)(2-3 + 3) ) (4a - 7)2 Factor completel. 6) 92-4 7)

Unit 5: Quadratic Functions LESSON #2: THE PARABOLA APPLICATIONS AND WORD PROBLEMS INVERSE OF A QUADRATIC FUNCTION DO NOW: Review from Lesson #1 (a)using the graph shown to the right, determine the equation

### Math 155 Intermediate Algebra Practice Exam on Chapters 6 & 8 Name

Math 155 Intermediate Algebra Practice Eam on Chapters 6 & 8 Name Find the function value, provided it eists. 1) f() = 7-8 8 ; f(-3) Simplify by removing a factor equal to 1. ) 5 + 0 + 3) m - m - m Find

### 3) y = -3 x y ) n - 3 = -83

Algebra Honors d zy01e8_ RKRuItwao lsrosfrtawdaarbeg NLCLECK.i V KAflTlv orizgghjt^s YrYeesQedrev_emdK. Midterm Stud Guide Regression Name ID: 1 Date Period 1) a. You create a new website. The table below

### Math Departmental Exit Assessment Review (Student Version)

Math 03 - Departmental Eit Assessment Review (Student Version) Factor completel. (Factoring Review) ) 6-6 - 0 ) 3-343 3) 3 - + 8-40 4) - 36 ) + - 6 + 9 + 8 - + + Add or subtract as indicated. Simplif completel.

### Math 95 Practice Exam 2 Part 1: No Calculator

Show all our work so that: Math 9 Practice Eam Part 1: No Calculator someone who wanted to know how ou found our answer can clearl see how. if ou make a mistake, I can see where it happened and determine

Algebra Name _ B2g0gD6L jkwudtaaa msvopfwtowiarneq CLOLXCa.I K `Awljla `rtiugohhtfs_ QrIefsfeYrZvtetdf. 9.2 Quadratics Review ) What is the difference between the two mathematical statements below? Then

### Honors Pre-Calculus. Multiple Choice 1. An expression is given. Evaluate it at the given value

Honors Pre-Calculus Multiple Choice. An epression is given. Evaluate it at the given value, (A) (B) 9 (C) 9 (D) (E). Simplif the epression. (A) + (B) (C) (D) (E) 7. Simplif the epression. (A) (B) (C) (D)

### Math 1101 Chapter 3 Review. 1) f(x) = 2x2 + 2x - 4 A) Concave up B) Concave down. 2) f(x) = -2x2-2x + 2 A) Minimum B) Maximum. 3) f(x) = 0.

Math 11 Chapter 3 Review Determine if the graph of the function is concave up or concave down. 1) f() = + - Concave up B) Concave down Determine if the verte of the graph is a maimum point or a minimum

Test # 33 QUESTIONS MATH131 091700 COLLEGE ALGEBRA Name atfm131bli www.alvarezmathhelp.com website MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

### Study Guide and Intervention. The Quadratic Formula and the Discriminant. Quadratic Formula. Replace a with 1, b with -5, and c with -14.

Study Guide and Intervention Quadratic Formula The Quadratic Formula can be used to solve any quadratic equation once it is written in the form a 2 + b + c = 0. Quadratic Formula The solutions of a 2 +

### Math 103 Final Exam Review Problems Rockville Campus Fall 2006

Math Final Eam Review Problems Rockville Campus Fall. Define a. relation b. function. For each graph below, eplain why it is or is not a function. a. b. c. d.. Given + y = a. Find the -intercept. b. Find

### Absolute Value Equations(One Absolute Value) Objectives. Absolute Value Inequalities (> or ) Absolute Value Inequalities (< or )

Section 5 Absolute Value Equations and Inequalities Solve Absolute Value Equations Solve Absolute Value Inequalities Involving < or Solve Absolute Value Inequalities Involving > or Absolute Value Equations(One