# MAC 1147 Final Exam Review

Size: px
Start display at page:

Transcription

1 MAC 1147 Final Exam Review nstructions: The final exam will consist of 15 questions plu::; a bonus problem. Some questions will have multiple parts and others will not. Some questions will be multiple choice and some will be free response. For the free response questions, be sure to show as much work as possible in order to demonstrate that you know what you are doing. The multiple choice questions will be graded partly on whether or not you circle the correct answer and partly on your work. So be sure to show your work for the multiple choice questions as well. The point value for y,ach question is listed after each question. There will be no bonus on this exam. A scientific calculator may be used but no graphing calculators or calculators on any device (cell phone, ipod, etc.) which can be used for any other purpose. The exam will be similar to this review, although the numbers and functions may be different so the steps and details (and hence the answers) may work out different. But the ideas and concepts will be the same. Additionally, you will be allowed to use the Trigonometric dentities and Unit Circle which have posted on my website, along with the formulas on the last page of this review. The formulas provided on the review will also be provided on the test but the Trigonometric dentities and Unit Circle will not. So if you wish to use either or both, you must bring them with you. The Trigonometric dentities and the Unit Circle may not be shared nor can they be used if they have any writing on them.

2 (1) Determine what transformations have been done to tbe function g(x) = Vi to get the function f(x) below. ndicate how you know. Then graph f(x). (8 points) f(x) = ij-x - 3 J -c.. d.ow~ ) CD rdi.tlo'" ~t 1-O.«.1~

3 (2) Determine what transformations have been done to the function g(x) = xl to get the function f(x) below. ndicate how you know. Then graph f(x). (8 points) 1 ~Q) ~ ;l. f(x) = ~ J X~ (4t1 \..31 rtfftui ~ ~ ~~S 10 \ \ 5-10 o

4 (3) (i) Find the vertical asymptotes, if any, of the rational function. (8 points - 4 points for the answer and 4 points for the steps) f(x) = x + 1 x -.,];2 (a) x = x=o, x= 1 (c).x=o, x=-l (d) x=o, x =-l, x=l (Ji) Give the equation of the horizontal asymptote, if any, of the function. (8 points - 4 points for the answer and 4 points for the steps). 3x 3 + 5x 2-7x - 4 f(x)= x2+4x+4 (a) y = 3 (b) y = -2 (c) y = 0 G None of (he above 1)t3r<.L n"..wwor:'" ~ o~~ ~ flo hlvi~ (")7""f4<ric V,m ~11\t>..ht'=:J.

5 (4) Graph thc function, (Hint: You will need the determine the domain, whether each point not in the domain of the function is a hole in the graph OT a vettical asymptote, intercepts, symmetry, horizontal or oblique aymptotes and locatwns where the function is positive or negative,) (8 points - 4 points for t he answer and 4 points for t he steps) (a) ; \; 0 10 ' - - 0,0 0 " 1 t''--. (c) (d) " 0 l 10 - ) if 0 - l ; v ; " ("" ~\,)l (.,. -1,)' :; 0 ~ t v - --\ tnj\t-"? ~ W",'W QS1 ",.. -, X-;.l, ~ \t:::' x-,~t', ~ J:;-O 0= ~~'" ("'-~ X.-:-0) ly\u \t -z-4 )<,-::'3, ~",\t~2 x:,.-'2. fw\u\t::. 2 ()on) Ujf"tl t'\~ -= ~ ~('t.t ~-..ahr ~ ~ ),.)~ ~-~.J ~~, ~-roj,t: yr:>o

6 (5) Solve the inequalit. (8., steps) y pomts each - 4 points for the answer and 4 points for the (i) x 5 + 4x 3 < 4.1:4 Q o,2) U (2, (0) (b) (-00, 0) U (2,00) (c) (0,2) (d) (2,00) XS- -~x~f~~~ LO K~( ~1. -~X +'~) 0 'i-~( X.-l}(~-1)LO x~:::o \$~ro X~D ~\t;1 };.-1-=O!1 +2 k-=-l. hu \t-=-f L(? 0 ~~ ~ r 0.,l1l W ~~ C~-1) ~O ~(O,~) U{l/ txj ) (ii) x3(x-5)(x-2) (x+l)2(x +2) < 0 (a) (-2,0] U (-2, -1) U (-1,0) U (2,5) (c) (-2,-1)U(-l,O]U[2,5] (d) (-oo,-2)u(0,2)u(5,00) x." ~ x.,-'f-=-o x-t~o.21.! ~~ ~ ')1. Ck~l-) ~ J& \f ::00 X.\.j=-'O - -l ~ -:...~l. ~. ;;.:<JO ~v\t ~ ~~ Mv\t'";;1 ~=-),""vlt::\ ).-:; z.. 'Nlt:; luou J ~ ~~;h' f ~ (-2-,-)V t"-'j o)v(2\$)

7 (6) For the given functions f and g, find the composite function (f 0 g)(x). (8 points - 4 points for the answer and 4 points for the steps) f(x) = x 2-3x + 2; g(x) = x 2-6 (a) X4-3x 2-16 (b) X4-3x (c) X4-6x x 2-12x - 2 ex'-15x (Jc,.)Y-J(jC>lJ ~ 1. - ~1oY -"3(/-0)+2 x~ - f2x\-3 b - 3 l t (8 t 1 X'4 -(~~ +-(10

8 (7) Find the inverse of j. State the domain and range of f and f-l. (8 points - 4 points for the answer and 4 points for the steps) f(x) = ~ x-4 (a) f(x) = ~ X~4 (c) [(x) ~ -,,,:, (d) f(x) = - x~4 "\,x ~ X-~ (~4\F tfj1r4 &jj ~ ~y 4~ X- \.f

9 (8) (i) Solve the equation. (8 points - 4 points for the answer and 4 points for the steps) 2 2x _ 3. 2x = 0 (a).1: = 2 (b).1: = = 2,3 (cl) No solution ( e ) None of the above ~1; ~J~ \.1. ~ ~ 2"t~ _ \1. 2.'t. f32'::0 z'x -::..~ u/\.{ 2 - ::.y '( 1\ ::-{,?, '1 \.A~~ ~~ lo,~~ L U _ \~~ -\-32 :::..0 X>3 (~_~\ (~-'i):;v ~~2. (ii) Solve the equation. (8 points - 4 points for the answer and 4 points for the steps) log3 (.1: + 10) = 2 - log3 (.1: + 2) (a) x~ -l1 Q X ~-1 (e) x~ -l1,-1 (cl) No solution 11l')~ (H.}) =0 ;Ho,} Cx J) \-"'i~ (V"') ~(f 3 ( t;l) [tij~ [X tf~ 1- ~J (ltt-))>j. \OjJ~1b)(U-~\ ~ J.,,~+-["l \ +-'1:;'0 (x.vll} (X H):::' 0 x+j-=o X-k'::: 0 J:1L r-- \ 'X.:: -H ~:~ 1 (X H\)) (~t J) ~ 3 k2u~~1=j

10 (9) St ate the amplit ude, period, and phase shift of t he function. Graph t he fu nction. Be sure to label t he intervals on the x- and y-axes and show at least two cycles. (8 points) y = - 2 cos ( 7r X + ~) ~rt~\t~~ oaoavt- ~-~\> ~ ( V 10.. "\, / ~ J \ J., r\ [\ L ~ \ V,, -:t..j 2 l\ ) l \.. \1\ 1f. JZ. '(1 3[1 " \ J k"l - \ V \ V ~ ~\i\ Vha.~ 5~,h-"-~. ~ 171r=l[;:, "f, t~t-l zt 1 - "') )f'.. '

11 (10 ) Establish the identity (8 pomts). 1 + sin.x 1 cos 2 x -1 =- esc x \+sk"x. { -~~\.'( -\ \ - (!-5\"~ \ - t\r\ X ~A-+S~X \-bl"-.)c -

12 (11) Find the exact value of sin( a - (3) under the given conditions. (8 points - 4 points for the answer and 4 points for the steps) tsj.,..,j E 10 31f. 10 ~ sec ex = 6 ' 2 < ex < 21f; S111 [3 = 26 ' "2 < [3 < 1f 61 (a) ~~ (b) -~~ ~ (d) -130 Q None of the l:1above.:::,.. i' S\f'rJ.. ': - To CoSrJ..~ 1D \Q \ ~L :;(b t 10 1 t-b 1 :; 7.L 2 2'{ o.'v V~~ ::. (00 a'l. :'--{g"1 ~ -=--~ ~i" (~-i):o slw..,l Ca; f - Co~.,("''''r tjo)(-~) -( ~oj({t) (Db -{,"L ::: ~"}<O bl':.~~ b;."t\{ ~_ l3 - JiL - ~o tho?,o l~l Lc,O t';d - c,s"

13 (12) Find the exact value of each expression. (8 points each - 4 points for the answer and 4 points for the steps).. _ " (1) cos (cot- 1 i~ - 8m 1 1~) (i) 2 (~b) 608 ( ~ ~ ~. 'tt e- ~ d..:- cot.- N ~f t~~ ~, l\{tti,tj.. ~t~ {~(,r l30~ :;' (1. ~S1>O=-t1. t~51> cj... -:::: ~v...,f E:,-.../'-- (ii) cos [2 sin -1 ( - 1~,) 1 _ ( -~\ f,, -d \ - - CPSltoi (~) COSL~"\ \:tl} C)\~lto () 608 (d) 87 ( ) C e ~ ~uff ~ ~~i'~- ' n. ~~r \~~ ~ S'L+-t > (1'2 j.~s" t'j,'j... ~:a~ bl-=-l..~ b-::::-g ) ~ f,.t-' ~ t ~ """""...!! (( Nfl one 0 above t 1e >"'.t.l' J J '- ~ [. r:;-\ C)(...'=- <;,\ ~ S1. t- \,").. ~\~ 1 1,,5' ~b ~ ::: \(0 ~ (a) 1 (b) ~~ \~ \? j, Of' - 11 J ~~ ()C (e) None of the above (),s LJ.L}-= cm2.. rj..- c,\,..l q.. :0 (!JjY- ~)' \U,-\ 1..1) ~ -- l~" \\~ -=-~ ((,'\ \ 'L ~ l'1 ~ ~ \1

14 (13) Solve the equation on the interval 0 :; B < 27f. (8 points each - 4 points for the answer and 4 points for the steps) (i) 1C 21C 1C 51C ( ) ( ) a 3' 3" c 6'6 S~ t'\&~~{ (ii) Solve the equation on the interval 0 :; B < 27f. (6 points - 3 points for the answer and 3 points for the st.eps) sin (4B) = 1 (a) ~ (b) ~ (\ (c) ~ 51C 91C 13". ~ 8' 8 ' 8' 8 (d) 31f 7". 1l7r 151f 8' 8' 8 '8 f..\.- ~ n-=--o ~ v - ~ \{s- -== ~\n-' (\) v\-:;.. : e ~ 1'r t - g + & - ~ 1r lc- Jt 1!L- Dr f'1. _.ll+ 11 -= lr+!!t: -= ~ 'T' n-;>-2 ~ v - '" "" ~ \ r lll ~ "t+ 12 rr ::::..rur- V\ -:;;. ~, '9:: g t"t. f \$ ~

15 (iii) Solve the equation on the interval 0 ::; x < 27r. (6 points - 3 points for the answer and 3 points for the steps) sin e + sin (2e) = 0 (b) 0 7r 7f 57f (c) ~ 37f 57f 77f, '3' 3 2'2'6'6 7r 37r 7r 57r ( d) of the above Co'> &:. - "i \ f7= ~ ~~ ~~S&::~ los e~ - \. (iv) Solve the equation. Give a general formula for all the solutions. (6 points 3 points for the answer and 3 points for the steps) (a) e = 2; + 2n7r, e= 4; + 2n7r (c) e= ~ + 2mr, e= i + 2nn sec (4e) = -2 Sic l'1.\1\~-2 c.o~ (~G)~ - ~ ~G- ~ Cbs' t- ~')

16 (14) Find the sum of the series. (8 points each - 4 points for the answer and 4 points for the steps) (i) L20 3 (k + 3k + 2) =- ttli,fod + <O~O H{Q:: \(41~u k=l "00 L 2 -:?.l1,())~l{o ~~ (ii ) (a) 400 (e) None of the above q l-r --

17 (15) Expand the expression using the Binomial Theorem. (8 points - 4 points for the answer and 4 points for the steps),,-.-v --., '",. (2x + 4)6 \f\t-\ -3J l \,,? l.~ \ 1. \ 64X x x , 240x , 360x , 288x ".,'} ~ \ ~ 3 1 (b) 2x x x , 240x , 360x , 288x + 4 t'~~ / '1 6 't, (c) 2x x x x x , 288x + 4 r\~~-...) \ ) to 10.s- (cl) 64x x x x x , 288x \-:.-c, -, C:; S- 20 rs- lo \ ~K-+ti) ::: \. (1)C)\. ~o + ~{1:~.)S_ ~ +(~{'l.x)~. ~1.+ ~O{"b)' ~3 +-1) (b.y V'1 +- ~ {Zk)' ttrt"{lk.)~y" -:: \ -(to~)c(,) t+ (.,62~5). ~ + ~(ll,~ ~).,~ +Jt,(~~}~~ tis"{'b:')ozslo «'{1.\) tol~ t-ol o ~o~b

### Jsee x dx = In Isec x + tanxl + C Jcsc x dx = - In I cscx + cotxl + C

MAC 2312 Final Exam Review Instructions: The Final Exam will consist of 15 questions plus a bonus problem. All questions will be multiple choice, which will be graded partly on whether or not you circle

### Math Exam 03 Review

Math 10350 Exam 03 Review 1. The statement: f(x) is increasing on a < x < b. is the same as: 1a. f (x) is on a < x < b. 2. The statement: f (x) is negative on a < x < b. is the same as: 2a. f(x) is on

### 11 /2 12 /2 13 /6 14 /14 15 /8 16 /8 17 /25 18 /2 19 /4 20 /8

MAC 1147 Exam #1a Answer Key Name: Answer Key ID# Summer 2012 HONOR CODE: On my honor, I have neither given nor received any aid on this examination. Signature: Instructions: Do all scratch work on the

### Total Possible Points = 150 Points. 1) David has 980 yards of fencing and wishes to enclose a rectangular area. (2.5 points) + '3 b. 7 + Ib+3, tf-.

MA180 Professor Fred Katiraie Test IT Form A (Fall 2007) Name: Total Possible Points = 150 Points 1) David has 980 yards of fencing and wishes to enclose a rectangular area. (2.5 points) a) Express the

### MIDTERM 2. Section: Signature:

MIDTERM 2 Math 3A 11/17/2010 Name: Section: Signature: Read all of the following information before starting the exam: Check your exam to make sure all pages are present. When you use a major theorem (like

### D. At the top right of your answer sheet, for "Test Form Code", encode B. A C D E

UFFLoRIfiA Department of Mathematics MAC2311 Exam 2B Spring 2015 A. Sign your bubble sheet on the back at the bottom in ink. B. In pencil, write and encode in the spaces indicated: 1) Name (last name,

### EXAM 2 MATH 161 BLAKE FARMAN. Lafayette College

EXAM 2 MATH 161 BLAKE FARMAN Lafayette College Answer the questions in the spaces provided on the question sheets and turn them in at the end of the exam period. It is advised, although not required, that

### or - CHAPTER 7 Applications of Integration Section 7.1 Area of a Region Between Two Curves 1. A= ~2[0- (x :2-6x)] dr=-~2(x 2-6x) dr

CHAPTER 7 Applications of Integration Section 7.1 Area of a Region Between Two Curves 1. A= ~[0- (x : 6x)] dr=-~(x 6x) dr 6~ 1356 or - 6. A: ~[(x- 1) 3 -(x-1)]dx 11. [~/3 ( - see x) dx 5- - 3 - I 1 3 5

### 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 +

### Calculus I Sample Exam #01

Calculus I Sample Exam #01 1. Sketch the graph of the function and define the domain and range. 1 a) f( x) 3 b) g( x) x 1 x c) hx ( ) x x 1 5x6 d) jx ( ) x x x 3 6 . Evaluate the following. a) 5 sin 6

### MTH 132 Solutions to Exam 2 November 21st, Without fully opening the exam, check that you have pages 1 through 11.

Name: Section: Recitation/Instructor: INSTRUCTIONS Fill in your name, etc. on this first page. Without fully opening the exam, check that you have pages through. Show all your work on the standard response

### y- 12X 7 7 Find the midpoint of the line segment joining the points Pj and?2. 2) PI = (b, 9); P2 = (0, 1) 2) _ A)(y,5) B)(b,10) C)(b,5) D)(-y,8)

Precalculus: Fall Final Review Questions MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the distance d(pj,?2) between the points PI and?2. 1)

### / =0. (c) Section P.3 Functions and Their Graphs. (c) g(-2) = 5-(-2) 2 = 5-4 = 1. (e) g(x) = 0 for x = -I, 1 and 2. 2.

Section P,3 Functions and Their Graphs 3 Section P.3 Functions and Their Graphs. (a) Domain off." -4 < x < 4 ~ [-4, 4] Range off:-3 < y < 5 ~ [-3, 5] Domain of g: -3 < x < 3 ~ [-3, 3] Range of g: -4

### MTH 132 Exam 2 November 21st, Without fully opening the exam, check that you have pages 1 through 11.

Name: Section: Recitation/Instructor: INSTRUCTIONS Fill in your name, etc. on this first page. Without fully opening the exam, check that you have pages 1 through 11. Show all your work on the standard

### ~t-,a~p.--e;;;;;i71- 0) x+ x2-sx+6. x x-38. PRECALCULUS Semester 1 Review

PRECALCULUS Semester 1 Review PART 1: CALCULATOR ALLOWED 1. If fix) = 1-x and [1 is the inverse off, how many solutions does the equation f(x) =[1 (x) have7 A) None B) One C) Three 0) Five Summer 015 6.

### SANDERSON HIGH SCHOOL AP CALCULUS AB/BC SUMMER REVIEW PACKET

SANDERSON HIGH SCHOOL AP CALCULUS AB/BC SUMMER REVIEW PACKET 017-018 Name: 1. This packet is to be handed in on Monday August 8, 017.. All work must be shown on separate paper attached to the packet. 3.

### 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

### MLC Practice Final Exam

Name: Section: Recitation/Instructor: INSTRUCTIONS Fill in your name, etc. on this first page. Without fully opening the exam, check that you have pages through. Show all your work on the standard response

### Math Final Exam - 12/12/2015

Math 121 - Final Exam - 12/12/2015 Name: Section: Section Class Times Day Instructor Section Class Times Day Instructor 1 09:00AM -09:50AM M T W F Sarah G Rody 12 11:00 AM - 11:50 AM M T W F Marci Ann

### 2. Determine the domain of the function. Verify your result with a graph. f(x) = 25 x 2

29 April PreCalculus Final Review 1. Find the slope and y-intercept (if possible) of the equation of the line. Sketch the line: y = 3x + 13 2. Determine the domain of the function. Verify your result with

### 1. Use the properties of exponents to simplify the following expression, writing your answer with only positive exponents.

Math120 - Precalculus. Final Review. Fall, 2011 Prepared by Dr. P. Babaali 1 Algebra 1. Use the properties of exponents to simplify the following expression, writing your answer with only positive exponents.

### Final Exam Review Exercise Set A, Math 1551, Fall 2017

Final Exam Review Exercise Set A, Math 1551, Fall 2017 This review set gives a list of topics that we explored throughout this course, as well as a few practice problems at the end of the document. A complete

### Tausend Und Eine Nacht

Connecticut College Digital Commons @ Connecticut College Historic Sheet Music Collection Greer Music Library 87 Tausend Und Eine Nacht Johann Strauss Follow this and additional works at: https:digitalcommonsconncolledusheetmusic

### Find the slope of the curve at the given point P and an equation of the tangent line at P. 1) y = x2 + 11x - 15, P(1, -3)

Final Exam Review AP Calculus AB Find the slope of the curve at the given point P and an equation of the tangent line at P. 1) y = x2 + 11x - 15, P(1, -3) Use the graph to evaluate the limit. 2) lim x

### Math 112 (Calculus I) Midterm Exam 3 KEY

Math 11 (Calculus I) Midterm Exam KEY Multiple Choice. Fill in the answer to each problem on your computer scored answer sheet. Make sure your name, section and instructor are on that sheet. 1. Which of

### 2. To receive credit on any problem, you must show work that explains how you obtained your answer or you must explain how you obtained your answer.

Math 50, Fall 2011 Test 3 PRINT your name on the back of the test. Directions 1. Time limit: 1 hour 50 minutes. 2. To receive credit on any problem, you must show work that explains how you obtained your

### Section Properties of Rational Expressions

88 Section. - Properties of Rational Expressions Recall that a rational number is any number that can be written as the ratio of two integers where the integer in the denominator cannot be. Rational Numbers:

### Math 121. Exam II. November 28 th, 2018

Math 121 Exam II November 28 th, 2018 Name: Section: The following rules apply: This is a closed-book exam. You may not use any books or notes on this exam. For free response questions, you must show all

### :i.( c -t.t) -?>x ( -\- ) - a.;-b 1 (o..- b )(a..+al,-+ b:r) x x x -3x 4-192x

-- -.. Factoring Cubic, Quartic, and Quintic Polynomials The number one rule of factoring is that before anything is done to the polynomial, the terms must be ordered from greatest to least dewee. Beyond

### THE USE OF A CALCULATOR, CELL PHONE, OR ANY OTHER ELEC- TRONIC DEVICE IS NOT PERMITTED DURING THIS EXAMINATION.

MATH 220 NAME So\,t\\OV\ '. FINAL EXAM 18, 2007\ FORMA STUDENT NUMBER INSTRUCTOR SECTION NUMBER This examination will be machine processed by the University Testing Service. Use only a number 2 pencil

### Part I: Multiple Choice Questions

Name: Part I: Multiple Choice Questions. What is the slope of the line y=3 A) 0 B) -3 ) C) 3 D) Undefined. What is the slope of the line perpendicular to the line x + 4y = 3 A) -/ B) / ) C) - D) 3. Find

### Math 12 Final Exam Review 1

Math 12 Final Exam Review 1 Part One Calculators are NOT PERMITTED for this part of the exam. 1. a) The sine of angle θ is 1 What are the 2 possible values of θ in the domain 0 θ 2π? 2 b) Draw these angles

### 3. Use absolute value notation to write an inequality that represents the statement: x is within 3 units of 2 on the real line.

PreCalculus Review Review Questions 1 The following transformations are applied in the given order) to the graph of y = x I Vertical Stretch by a factor of II Horizontal shift to the right by units III

### z E z *" I»! HI UJ LU Q t i G < Q UJ > UJ >- C/J o> o C/) X X UJ 5 UJ 0) te : < C/) < 2 H CD O O) </> UJ Ü QC < 4* P? K ll I I <% "fei 'Q f

I % 4*? ll I - ü z /) I J (5 /) 2 - / J z Q. J X X J 5 G Q J s J J /J z *" J - LL L Q t-i ' '," ; i-'i S": t : i ) Q "fi 'Q f I»! t i TIS NT IS BST QALITY AVAILABL. T Y FRNIS T TI NTAIN A SIGNIFIANT NBR

### 1. Use the properties of exponents to simplify the following expression, writing your answer with only positive exponents.

Math120 - Precalculus. Final Review Prepared by Dr. P. Babaali 1 Algebra 1. Use the properties of exponents to simplify the following expression, writing your answer with only positive exponents. (a) 5

### MTH 132 Solutions to Exam 2 Nov. 23rd 2015

Name: Section: Instructor: READ THE FOLLOWING INSTRUCTIONS. Do not open your exam until told to do so. No calculators, cell phones or any other electronic devices can be used on this exam. Clear your desk

### ~,. :'lr. H ~ j. l' ", ...,~l. 0 '" ~ bl '!; 1'1. :<! f'~.., I,," r: t,... r':l G. t r,. 1'1 [<, ."" f'" 1n. t.1 ~- n I'>' 1:1 , I. <1 ~'..

,, 'l t (.) :;,/.I I n ri' ' r l ' rt ( n :' (I : d! n t, :?rj I),.. fl.),. f!..,,., til, ID f-i... j I. 't' r' t II!:t () (l r El,, (fl lj J4 ([) f., () :. -,,.,.I :i l:'!, :I J.A.. t,.. p, - ' I I I

### MAC 1140 Spring 2014 Final Exam

MAC 1140 Spring 2014 Final Exam Section # _ Name _ UFID# _ Signature _ A. Sign your scantron on the back at the bottom in ink. B. In pencil, write and encode on your scantron in the spaces indicated: 1)

### r(j) -::::.- --X U.;,..;...-h_D_Vl_5_ :;;2.. Name: ~s'~o--=-i Class; Date: ID: A

Name: ~s'~o--=-i Class; Date: U.;,..;...-h_D_Vl_5 _ MAC 2233 Chapter 4 Review for the test Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Find the derivative

### Find the domain and range of each function. Use interval notation (parenthesis or square brackets).

Page of 10 I. Functions & Composition of Functions A function is a set of points (x, y) such that for every x, there is one and only one y. In short, in a function, the x-values cannot repeat while the

### 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

### (a) Write down the value of q and of r. (2) Write down the equation of the axis of symmetry. (1) (c) Find the value of p. (3) (Total 6 marks)

1. Let f(x) = p(x q)(x r). Part of the graph of f is shown below. The graph passes through the points ( 2, 0), (0, 4) and (4, 0). (a) Write down the value of q and of r. (b) Write down the equation of

### Calculus First Semester Review Name: Section: Evaluate the function: (g o f )( 2) f (x + h) f (x) h. m(x + h) m(x)

Evaluate the function: c. (g o f )(x + 2) d. ( f ( f (x)) 1. f x = 4x! 2 a. f( 2) b. f(x 1) c. f (x + h) f (x) h 4. g x = 3x! + 1 Find g!! (x) 5. p x = 4x! + 2 Find p!! (x) 2. m x = 3x! + 2x 1 m(x + h)

### Learning Target: I can sketch the graphs of rational functions without a calculator. a. Determine the equation(s) of the asymptotes.

Learning Target: I can sketch the graphs of rational functions without a calculator Consider the graph of y= f(x), where f(x) = 3x 3 (x+2) 2 a. Determine the equation(s) of the asymptotes. b. Find the

### 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

### PMI Rational Expressions & Equations Unit

PMI Rational Expressions & Equations Unit Variation Class Work 1. y varies inversely with x. If y = 1 when x =, find y when x = 6.. y varies inversely with x. If y = 8 when x =, find x wheny =.. y varies

### 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#(

### Lecture 7: Sections 2.3 and 2.4 Rational and Exponential Functions. Recall that a power function has the form f(x) = x r where r is a real number.

L7-1 Lecture 7: Sections 2.3 and 2.4 Rational and Exponential Functions Recall that a power function has the form f(x) = x r where r is a real number. f(x) = x 1/2 f(x) = x 1/3 ex. Sketch the graph of

### ,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: - - - -...

### Albertson AP Calculus AB AP CALCULUS AB SUMMER PACKET DUE DATE: The beginning of class on the last class day of the first week of school.

Albertson AP Calculus AB Name AP CALCULUS AB SUMMER PACKET 2015 DUE DATE: The beginning of class on the last class day of the first week of school. This assignment is to be done at you leisure during the

### ::::l<r/ L- 1-1>(=-ft\ii--r(~1J~:::: Fo. l. AG -=(0,.2,L}> M - &-c ==- < ) I) ~..-.::.1 ( \ I 0. /:rf!:,-t- f1c =- <I _,, -2...

Math 3298 Exam 1 NAME: SCORE: l. Given three points A(I, l, 1), B(l,;2, 3), C(2, - l, 2). (a) Find vectors AD, AC, nc. (b) Find AB+ DC, AB - AC, and 2AD. -->,,. /:rf!:,-t- f1c =-

### MLC Practice Final Exam. Recitation Instructor: Page Points Score Total: 200.

Name: PID: Section: Recitation Instructor: DO NOT WRITE BELOW THIS LINE. GO ON TO THE NEXT PAGE. Page Points Score 3 20 4 30 5 20 6 20 7 20 8 20 9 25 10 25 11 20 Total: 200 Page 1 of 11 Name: Section:

### Math 171 Spring 2017 Final Exam. Problem Worth

Math 171 Spring 2017 Final Exam Problem 1 2 3 4 5 6 7 8 9 10 11 Worth 9 6 6 5 9 8 5 8 8 8 10 12 13 14 15 16 17 18 19 20 21 22 Total 8 5 5 6 6 8 6 6 6 6 6 150 Last Name: First Name: Student ID: Section:

### AP Calculus BC Summer Assignment Mrs. Comeau

AP Calculus BC Summer Assignment 2015-2016 Mrs. Comeau Please complete this assignment DUE: the first day of class, SEPTEMBER 2nd. Email me if you have questions, or need help over the summer. I would

### 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

Th pr nt n f r n th f ft nth nt r b R b rt Pr t r. Pr t r, R b rt, b. 868. xf rd : Pr nt d f r th B bl r ph l t t th xf rd n v r t Pr, 00. http://hdl.handle.net/2027/nyp.33433006349173 P bl D n n th n

### L=/o U701 T. jcx3. 1L2,Z fr7. )vo. A (a) [20%) Find the steady-state temperature u(x). M,(Y 7( it) X(o) U ç (ock. Partial Differential Equations 3150

it) O 2h1 i / k ov A u(1,t) L=/o [1. (H3. Heat onduction in a Bar) 1 )vo nstructions: This exam is timed for 12 minutes. You will be given extra time to complete Exam Date: Thursday, May 2, 213 textbook.

### The above statement is the false product rule! The correct product rule gives g (x) = 3x 4 cos x+ 12x 3 sin x. for all angles θ.

Math 7A Practice Midterm III Solutions Ch. 6-8 (Ebersole,.7-.4 (Stewart DISCLAIMER. This collection of practice problems is not guaranteed to be identical, in length or content, to the actual exam. You

### Mathematic 108, Fall 2015: Solutions to assignment #7

Mathematic 08, Fall 05: Solutions to assignment #7 Problem # Suppose f is a function with f continuous on the open interval I and so that f has a local maximum at both x = a and x = b for a, b I with a

### Avon High School Name AP Calculus AB Summer Review Packet Score Period

Avon High School Name AP Calculus AB Summer Review Packet Score Period f 4, find:.) If a.) f 4 f 4 b.) Topic A: Functions f c.) f h f h 4 V r r a.) V 4.) If, find: b.) V r V r c.) V r V r.) If f and g

### a b c d e GOOD LUCK! 3. a b c d e 12. a b c d e 4. a b c d e 13. a b c d e 5. a b c d e 14. a b c d e 6. a b c d e 15. a b c d e

MA Elem. Calculus Fall 07 Exam 07-09- Name: Sec.: Do not remove this answer page you will turn in the entire exam. No books or notes may be used. You may use an ACT-approved calculator during the exam,

### AP Calculus Chapter 3 Testbank (Mr. Surowski)

AP Calculus Chapter 3 Testbank (Mr. Surowski) Part I. Multiple-Choice Questions (5 points each; please circle the correct answer.). If f(x) = 0x 4 3 + x, then f (8) = (A) (B) 4 3 (C) 83 3 (D) 2 3 (E) 2

Fry TAMU Spring 2017 Math 150 Notes Section 5.4 Page! 92 5.4 - Quadratic Functions Definition: A function is one that can be written in the form f (x) = where a, b, and c are real numbers and a 0. (What

### 1. The graph of a function f is given above. Answer the question: a. Find the value(s) of x where f is not differentiable. Ans: x = 4, x = 3, x = 2,

1. The graph of a function f is given above. Answer the question: a. Find the value(s) of x where f is not differentiable. x = 4, x = 3, x = 2, x = 1, x = 1, x = 2, x = 3, x = 4, x = 5 b. Find the value(s)

### 1 + x 2 d dx (sec 1 x) =

Page This exam has: 8 multiple choice questions worth 4 points each. hand graded questions worth 4 points each. Important: No graphing calculators! Any non-graphing, non-differentiating, non-integrating

### Mth Review Problems for Test 2 Stewart 8e Chapter 3. For Test #2 study these problems, the examples in your notes, and the homework.

For Test # study these problems, the examples in your notes, and the homework. Derivative Rules D [u n ] = nu n 1 du D [ln u] = du u D [log b u] = du u ln b D [e u ] = e u du D [a u ] = a u ln a du D [sin

### Use a graphing utility to approximate the real solutions, if any, of the equation rounded to two decimal places. 4) x3-6x + 3 = 0 (-5,5) 4)

Advanced College Prep Pre-Calculus Midyear Exam Review Name Date Per List the intercepts for the graph of the equation. 1) x2 + y - 81 = 0 1) Graph the equation by plotting points. 2) y = -x2 + 9 2) List

### Have a Safe and Happy Break

Math 121 Final EF: December 10, 2013 Name Directions: 1 /15 2 /15 3 /15 4 /15 5 /10 6 /10 7 /20 8 /15 9 /15 10 /10 11 /15 12 /20 13 /15 14 /10 Total /200 1. No book, notes, or ouiji boards. You may use

### F. KEEP YOUR BUBBLE SHEET COVERED AT ALL TIMES.

UF UNIVERSITY of Department of Mathematics FLORIDA MAC 2233 Exam 2A Spring 2017 A. Sign your bubble sheet on the back at the bottom in ink. B. In pencil, write and encode in the spaces indicated: 1) Name

### MATH 121: EXTRA PRACTICE FOR TEST 2. Disclaimer: Any material covered in class and/or assigned for homework is a fair game for the exam.

MATH 121: EXTRA PRACTICE FOR TEST 2 Disclaimer: Any material covered in class and/or assigned for homework is a fair game for the exam. 1 Linear Functions 1. Consider the functions f(x) = 3x + 5 and g(x)

### Properties of Graphs of Polynomial Functions Terminology Associated with Graphs of Polynomial Functions

Properties of Graphs of Polynomial Functions Terminology Associated with Graphs of Polynomial Functions Detennine what types of polynomial functions/, g, and hare graphed below Give a reason for your conclusions

### S O H C A H T O A i p y o d y a p d n p p s j p n p j

The Unit Circle Right Triangle Trigonometry Hypotenuse Opposite Side Adjacent Side S O H C A H T O A i p y o d y a p d n p p s j p n p j sin opposite side hypotenuse csc hypotenuse opposite side cos adjacent

### Core Mathematics Cl 2 Advanced Subsidiary

Write your name here c:rname Pearson Edexcel nternational Advanced Level Centre Number Core Mathematics Cl 2 Advanced Subsidiary Wednesday 25 May 216 Morning ime: 2 hours 3 minutes Paper Reference... WMAOl1

### Mission 1 Simplify and Multiply Rational Expressions

Algebra Honors Unit 6 Rational Functions Name Quest Review Questions Mission 1 Simplify and Multiply Rational Expressions 1) Compare the two functions represented below. Determine which of the following

### MTH30 Review Sheet. y = g(x) BRONX COMMUNITY COLLEGE of the City University of New York DEPARTMENT OF MATHEMATICS & COMPUTER SCIENCE

BRONX COMMUNITY COLLEGE of the City University of New York DEPARTMENT OF MATHEMATICS & COMPUTER SCIENCE MTH0 Review Sheet. Given the functions f and g described by the graphs below: y = f(x) y = g(x) (a)

### GOOD LUCK! 2. a b c d e 12. a b c d e. 3. a b c d e 13. a b c d e. 4. a b c d e 14. a b c d e. 5. a b c d e 15. a b c d e. 6. a b c d e 16.

MA109 College Algebra Fall 2018 Practice Final Exam 2018-12-12 Name: Sec.: Do not remove this answer page you will turn in the entire exam. You have two hours to do this exam. No books or notes may be

### Name: Instructor: 1. a b c d e. 15. a b c d e. 2. a b c d e a b c d e. 16. a b c d e a b c d e. 4. a b c d e... 5.

Name: Instructor: Math 155, Practice Final Exam, December The Honor Code is in effect for this examination. All work is to be your own. No calculators. The exam lasts for 2 hours. Be sure that your name

### No calculators, cell phones or any other electronic devices can be used on this exam. Clear your desk of everything excepts pens, pencils and erasers.

Name: Section: Recitation Instructor: READ THE FOLLOWING INSTRUCTIONS. Do not open your exam until told to do so. No calculators, cell phones or any other electronic devices can be used on this exam. Clear

### Midterm Review. Name: Class: Date: ID: A. Short Answer. 1. For each graph, write the equation of a radical function of the form y = a b(x h) + k.

Name: Class: Date: ID: A Midterm Review Short Answer 1. For each graph, write the equation of a radical function of the form y = a b(x h) + k. a) b) c) 2. Determine the domain and range of each function.

### Without fully opening the exam, check that you have pages 1 through 11.

Name: Section: Recitation Instructor: INSTRUCTIONS Fill in your name, etc. on this first page. Without fully opening the exam, check that you have pages through. Show all your work on the standard response

### MATH 121: EXTRA PRACTICE FOR TEST 2. Disclaimer: Any material covered in class and/or assigned for homework is a fair game for the exam.

MATH 121: EXTRA PRACTICE FOR TEST 2 Disclaimer: Any material covered in class and/or assigned for homework is a fair game for the exam. 1 Linear Functions 1. Consider the functions f(x) = 3x + 5 and g(x)

### Below is a list of topics covered in the packet with formulas and helpful websites:

Dear Student I Please find attached your summer review packet for Academic Calculus. The problems in this packet are taken from Precalculus and they should be familiar to you. However I if you need review

### I-1. rei. o & A ;l{ o v(l) o t. e 6rf, \o. afl. 6rt {'il l'i. S o S S. l"l. \o a S lrh S \ S s l'l {a ra \o r' tn \$ ra S \ S SG{ \$ao. \ S l"l. \ (?

>. 1! = * l >'r : ^, : - fr). ;1,!/!i ;(?= f: r*. fl J :!= J; J- >. Vf i - ) CJ ) ṯ,- ( r k : ( l i ( l 9 ) ( ;l fr i) rf,? l i =r, [l CB i.l.!.) -i l.l l.!. * (.1 (..i -.1.! r ).!,l l.r l ( i b i i '9,

### MA FINAL EXAM Green December 16, You must use a #2 pencil on the mark sense sheet (answer sheet).

MA 600 FINAL EXAM Green December 6, 205 NAME STUDENT ID # YOUR TA S NAME RECITATION TIME. You must use a #2 pencil on the mark sense sheet (answer sheet). 2. Be sure the paper you are looking at right

,,,,..,,., {. (, ),, {,.,.,..,,.,.,,....... {.. : N {, Z {, Q {, Q p { p{ {. 3, R {, C {. : ord p {. 8, (k) {.42,!() { {. 24, () { {. 24, () { {. 25,., () { {. 26,. 9, () { {. 27,. 23, '() { ( ) {. 28,

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

AB Fall Final Exam Review 200-20 Name Date Period MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Solve the problem. ) The position of a particle

### SOLUTIONS TO MIXED REVIEW

Math 16: SOLUTIONS TO MIXED REVIEW R1.. Your graphs should show: (a) downward parabola; simple roots at x = ±1; y-intercept (, 1). (b) downward parabola; simple roots at, 1; maximum at x = 1/, by symmetry.

### 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.

### Formulas that must be memorized:

Formulas that must be memorized: Position, Velocity, Acceleration Speed is increasing when v(t) and a(t) have the same signs. Speed is decreasing when v(t) and a(t) have different signs. Section I: Limits

### MATH 2053 Calculus I Review for the Final Exam

MATH 05 Calculus I Review for the Final Exam (x+ x) 9 x 9 1. Find the limit: lim x 0. x. Find the limit: lim x + x x (x ).. Find lim x (x 5) = L, find such that f(x) L < 0.01 whenever 0 < x

### S(x) Section 1.5 infinite Limits. lim f(x)=-m x --," -3 + Jkx) - x ~

8 Chapter Limits and Their Properties Section.5 infinite Limits -. f(x)- (x-) As x approaches from the left, x - is a small negative number. So, lim f(x) : -m As x approaches from the right, x - is a small

### rhtre PAID U.S. POSTAGE Can't attend? Pass this on to a friend. Cleveland, Ohio Permit No. 799 First Class

rhtr irt Cl.S. POSTAG PAD Cllnd, Ohi Prmit. 799 Cn't ttnd? P thi n t frind. \ ; n l *di: >.8 >,5 G *' >(n n c. if9\$9\$.jj V G. r.t 0 H: u ) ' r x * H > x > i M

### University of Connecticut Department of Mathematics

University of Connecticut Department of Mathematics Math 1131 Sample Exam 1 Fall 2013 Name: This sample exam is just a guide to prepare for the actual exam. Questions on the actual exam may or may not

### Calculus I Exam 1 Review Fall 2016

Problem 1: Decide whether the following statements are true or false: (a) If f, g are differentiable, then d d x (f g) = f g. (b) If a function is continuous, then it is differentiable. (c) If a function

### Solution: APPM 1350 Final Exam Spring 2014

APPM 135 Final Exam Spring 214 1. (a) (5 pts. each) Find the following derivatives, f (x), for the f given: (a) f(x) = x 2 sin 1 (x 2 ) (b) f(x) = 1 1 + x 2 (c) f(x) = x ln x (d) f(x) = x x d (b) (15 pts)

### Summer Review for Students Entering AP Calculus AB

Summer Review for Students Entering AP Calculus AB Class: Date: AP Calculus AB Summer Packet Please show all work in the spaces provided The answers are provided at the end of the packet Algebraic Manipulation

### wo(..lr.i L"'J b]. tr+ +&..) i'> 't\uow).,...,. (o.. J \,} --ti \(' m'\...\,,.q.)).

Applying Theorems in Calculus 11ter111ediate Value Theorem, Ettreme Value Theorem, Rolle 's Theorem, and l\ea11 Value Theorem Before we begin. let's remember what each of these theorems says about a function.

### Chapter 5B - Rational Functions

Fry Texas A&M University Math 150 Chapter 5B Fall 2015 143 Chapter 5B - Rational Functions Definition: A rational function is The domain of a rational function is all real numbers, except those values