AP CALCULUS AB 2003 SCORING GUIDELINES (Form B)

Size: px
Start display at page:

Download "AP CALCULUS AB 2003 SCORING GUIDELINES (Form B)"

Transcription

1 SCORING GUIDELINES (Form B) Quesion A ank conains 15 gallons of heaing oil a ime =. During he ime inerval 1 hours, heaing oil is pumped ino he ank a he rae 1 H ( ) = + ( 1 + ln( + 1) ) gallons per hour. During he same ime inerval, heaing oil is removed from he ank a he rae R( ) = 1 sin gallons per hour. 47 (a) How many gallons of heaing oil are pumped ino he ank during he ime inerval 1 hours? (b) Is he level of heaing oil in he ank rising or falling a ime = 6 hours? Give a reason for your answer. (c) How many gallons of heaing oil are in he ank a ime = 1 hours? (d) A wha ime, for 1, is he volume of heaing oil in he ank he leas? Show he analysis ha leads o your conclusion. (a) 1 Hd () = 7.57 or : 1 : inegral (b) H(6)(6) R =.94, so he level of heaing oil is falling a = 6. wih reason 1 (c) 15 + ( H ( )( R) d = 1.5 or 1.6 : 1 : limis 1 : inegrand (d) The absolue minimum occurs a a criical poin or an endpoin. H ()() R = when = 4.79 and = The volume increases unil = 4.79, hen decreases unil = 11.18, hen increases, so he absolue minimum will be a = or a 1 : ses H ( )( R) = 1 : volume is leas a : = : analysis for absolue minimum = ( H ()() R) d = 1.78 Since he volume is 15 a =, he volume is leas a = Copyrigh by College Enrance Examinaion Board. All righs reserved. Available a apcenral.collegeboard.com.

2 4 SCORING GUIDELINES (Form B) Quesion For 1, he rae of change of he number of mosquioes on Tropical Island a ime days is R = 5 cos mosquioes per day. There are 1 mosquioes on Tropical Island a 5 modeled by () ( ) ime =. (a) Show ha he number of mosquioes is increasing a ime = 6. (b) A ime = 6, is he number of mosquioes increasing a an increasing rae, or is he number of mosquioes increasing a a decreasing rae? Give a reason for your answer. (c) According o he model, how many mosquioes will be on he island a ime = 1? Round your answer o he neares whole number. (d) To he neares whole number, wha is he maximum number of mosquioes for 1? Show he analysis ha leads o your conclusion. (a) Since R ( 6) = 4.48 >, he number of mosquioes is increasing a = 6. 1 : shows ha R ( 6) > (b) R ( 6) = 1.91 Since R ( 6) <, he number of mosquioes is increasing a a decreasing rae a = 6. : 1 : considers R ( 6) wih reason 1 (c) 1 + R () d= To he neares whole number, here are 964 mosquioes. 1 : inegral : (d) R () = when =, =.5π, or = 7.5π R () > on < <.5π R () < on.5π < < 7.5π R () > on 7.5π < < 1 The absolue maximum number of mosquioes occurs a =.5π or a = 1..5π 1 + R () d= 19.57, There are 964 mosquioes a = 1, so he maximum number of mosquioes is 19, o he neares whole number. 4 : : absolue maximum value 1 : inegral : analysis 1 : compues inerior criical poins 1 : complees analysis Copyrigh 4 by College Enrance Examinaion Board. All righs reserved. Visi apcenral.collegeboard.com (for AP professionals) and (for AP sudens and parens).

3 5 SCORING GUIDELINES (Form B) Quesion A waer ank a Camp Newon holds 1 gallons of waer a ime =. During he ime inerval 18 hours, waer is pumped ino he ank a he rae () 95 sin ( ) W = gallons per hour. 6 During he same ime inerval, waer is removed from he ank a he rae () 75sin ( ) R = gallons per hour. (a) Is he amoun of waer in he ank increasing a ime = 15? Why or why no? (b) To he neares whole number, how many gallons of waer are in he ank a ime = 18? (c) A wha ime, for 18, is he amoun of waer in he ank a an absolue minimum? Show he work ha leads o your conclusion. (d) For > 18, no waer is pumped ino he ank, bu waer coninues o be removed a he rae R() unil he ank becomes empy. Le k be he ime a which he ank becomes empy. Wrie, bu do no solve, an equaion involving an inegral expression ha can be used o find he value of k. (a) No; he amoun of waer is no increasing a = 15 since W( 15) R( 15) = 11.9 <. wih reason 18 (b) 1 + ( W() R() ) d = gallons : 1 : limis 1 : inegrand (c) W() R() = =, , (hours) gallons of waer : inerior criical poins 1 : amoun of waer is leas a : = or : analysis for absolue minimum The values a he endpoins and he criical poins show ha he absolue minimum occurs when = or k (d) R () d= : limis : 1 : equaion Copyrigh 5 by College Board. All righs reserved. Visi apcenral.collegeboard.com (for AP professionals) and (for AP sudens and parens).

4 7 SCORING GUIDELINES (Form B) Quesion The wind chill is he emperaure, in degrees Fahrenhei ( F, ) a human feels based on he air emperaure, in degrees Fahrenhei, and he wind velociy v, in miles per hour ( mph ). If he air emperaure is F, hen he.16 wind chill is given by W( v) = v and is valid for 5 v 6. (a) Find W ( ). Using correc unis, explain he meaning of W ( ) in erms of he wind chill. (b) Find he average rae of change of W over he inerval 5 v 6. Find he value of v a which he insananeous rae of change of W is equal o he average rae of change of W over he inerval 5 v 6. (c) Over he ime inerval 4 hours, he air emperaure is a consan F. A ime =, he wind velociy is v = mph. If he wind velociy increases a a consan rae of 5 mph per hour, wha is he rae of change of he wind chill wih respec o ime a = hours? Indicae unis of measure. (a).84 W ( ) =.1.16 =.85 or.86 When v = mph, he wind chill is decreasing a.86 F mph. : { 1 : value 1 : explanaion (b) The average rae of change of W over he inerval W( 6) W( 5) 5 v 6 is =.5 or W( 6) W( 5) W ( v) = when v = : average rae of change : 1 : W ( v) = average rae of change 1 : value of v dw dw dv = = 5 5 =.89 F hr d dv d (c) ( ) W ( ) = = OR W = ( + 5).16 dw =.89 F hr d = dv 1 : = 5 d 1 : uses v( ) = 5, : or uses v () = + 5 Unis of F mph in (a) and F hr in (c) 1 : unis in (a) and (c) 7 The College Board. All righs reserved. Visi apcenral.collegeboard.com (for AP professionals) and (for sudens and parens).

5 For ime AP CALCULUS AB 8 SCORING GUIDELINES (Form B) 1 hours, le r () 1( 1 e ) Quesion = represen he speed, in kilomeers per hour, a which a car ravels along a sraigh road. The number of liers of gasoline used by he car o ravel x kilomeers is g x =.5x 1 e x. modeled by ( ) ( ) (a) How many kilomeers does he car ravel during he firs hours? (b) Find he rae of change wih respec o ime of he number of liers of gasoline used by he car when = hours. Indicae unis of measure. (c) How many liers of gasoline have been used by he car when i reaches a speed of 8 kilomeers per hour? kilomeers : { 1 : inegral (a) r() d = 6.7 dg dg dx dx (b) = ; = r () d dx d d dg dg r( ) d = dx = x= 6.7 = (.5)( 1) = 6 liers hour : uses chain rule : { wih unis (c) Le T be he ime a which he car s speed reaches 8 kilomeers per hour. Then, rt ( ) = 8 or T =.145 hours. 4 : 1 : equaion r () = 8 : disance inegral A ime T, he car has gone T xt ( ) = r( ) d= kilomeers and has consumed g( x( T )) =.57 liers of gasoline. 8 The College Board. All righs reserved. Visi he College Board on he Web:

6 9 SCORING GUIDELINES (Form B) Quesion 1 A a cerain heigh, a ree runk has a circular cross secion. The radius R() of ha cross secion grows a a rae modeled by he funcion dr = 1 ( + sin ( )) cenimeers per year d 16 for, where ime is measured in years. A ime =, he radius is 6 cenimeers. The area of he cross secion a ime is denoed by A (). (a) Wrie an expression, involving an inegral, for he radius R() for. Use your expression o find R (. ) (b) Find he rae a which he cross-secional area A() is increasing a ime = years. Indicae unis of measure. (c) Evaluae A () d. Using appropriae unis, inerpre he meaning of ha inegral in erms of crosssecional area. 1 (a) () = 6 + ( + sin( )) R 16 x dx R ( ) = 6.61 or : inegral : 1 : expression for R() 1 : R( ) (b) A () = π ( R ()) A () = π R() R () A ( ) = cm year 1 : expression for A () : 1 : expression for A () wih unis (c) A () d = A ( ) A ( ) = 4. or 4.1 From ime = o = years, he crosssecional area grows by 4.1 square cenimeers. 1 : uses Fundamenal Theorem of Calculus 1 : value of A () d : 1 : meaning of A () d 9 The College Board. All righs reserved. Visi he College Board on he Web:

7 11 SCORING GUIDELINES (Form B) Quesion 1 A cylindrical can of radius 1 millimeers is used o measure rainfall in Sormville. The can is iniially empy, and rain eners he can during a 6-day period. The heigh of waer in he can is modeled by he funcion S, where S () is measured in millimeers and is measured in days for 6. The rae a which he heigh of he waer is rising in he can is given by S ( ) = sin(.) (a) According o he model, wha is he heigh of he waer in he can a he end of he 6-day period? (b) According o he model, wha is he average rae of change in he heigh of waer in he can over he 6-day period? Show he compuaions ha lead o your answer. Indicae unis of measure. (c) Assuming no evaporaion occurs, a wha rae is he volume of waer in he can changing a ime = 7? Indicae unis of measure. (d) During he same 6-day period, rain on Monsoon Mounain accumulaes in a can idenical o he one in Sormville. The heigh of he waer in he can on Monsoon Mounain is modeled by he funcion M, where 1 M () = ( + ). The heigh M ( ) is measured in millimeers, and is measured in days 4 for 6. Le D ( ) = M ( ) S ( ). Apply he Inermediae Value Theorem o he funcion D on he inerval 6 o jusify ha here exiss a ime, < < 6, a which he heighs of waer in he wo cans are changing a he same rae. 6 (a) S( 6) = S ( ) d = mm : 1 : limis 1 : inegrand (b) S( 6) S( ) 6 =.86 or.864 mm day (c) V() = 1π S() V ( 7) = 1π S ( 7) = 6.18 The volume of waer in he can is increasing a a rae of 6.18 mm day. 1 : relaionship beween V and S : { (d) D ( ) =.675 < and D ( 6) = > Because D is coninuous, he Inermediae Value Theorem implies ha here is a ime, < < 6, a which D ( ) =. A his ime, he heighs of waer in he wo cans are changing a he same rae. 1 : considers D( ) and D( 6) : 1 : jusificaion 1 : unis in (b) or (c) 11 The College Board. Visi he College Board on he Web:

AP CALCULUS AB 2003 SCORING GUIDELINES (Form B)

AP CALCULUS AB 2003 SCORING GUIDELINES (Form B) SCING GUIDELINES (Form B) Quesion 4 A paricle moves along he x-axis wih velociy a ime given by v( ) = 1 + e1. (a) Find he acceleraion of he paricle a ime =. (b) Is he speed of he paricle increasing a ime

More information

AP CALCULUS AB/CALCULUS BC 2015 SCORING GUIDELINES. Question 1

AP CALCULUS AB/CALCULUS BC 2015 SCORING GUIDELINES. Question 1 AP CALCULUS AB/CALCULUS BC 15 SCORING GUIDELINES Quesion 1 The rae a which rainwaer flows ino a drainpipe is modeled by he funcion R, where R ( ) = sin 5 cubic fee per hour, is measured in hours, and 8.

More information

AP CALCULUS AB 2003 SCORING GUIDELINES (Form B)

AP CALCULUS AB 2003 SCORING GUIDELINES (Form B) SCORING GUIDELINES (Form B) Quesion A blood vessel is 6 millimeers (mm) long Disance wih circular cross secions of varying diameer. x (mm) 6 8 4 6 Diameer The able above gives he measuremens of he B(x)

More information

AP CALCULUS AB/CALCULUS BC 2016 SCORING GUIDELINES. Question 1. 1 : estimate = = 120 liters/hr

AP CALCULUS AB/CALCULUS BC 2016 SCORING GUIDELINES. Question 1. 1 : estimate = = 120 liters/hr AP CALCULUS AB/CALCULUS BC 16 SCORING GUIDELINES Quesion 1 (hours) R ( ) (liers / hour) 1 3 6 8 134 119 95 74 7 Waer is pumped ino a ank a a rae modeled by W( ) = e liers per hour for 8, where is measured

More information

AP CALCULUS AB 2017 SCORING GUIDELINES

AP CALCULUS AB 2017 SCORING GUIDELINES AP CALCULUS AB 17 SCORING GUIDELINES /CALCULUS BC 16 SCORING GUIDELINES Quesion 1 (hours) R ( ) (liers / hour) 1 6 8 14 119 95 74 7 Waer is pumped ino a ank a a rae modeled by W( ) = e liers per hour for

More information

AP CALCULUS AB 2017 SCORING GUIDELINES

AP CALCULUS AB 2017 SCORING GUIDELINES AP CALCULUS AB 17 SCORING GUIDELINES 16 SCORING GUIDELINES Quesion For, a paricle moves along he x-axis. The velociy of he paricle a ime is given by v ( ) = 1 + sin. The paricle is a posiion x = a ime.

More information

1998 Calculus AB Scoring Guidelines

1998 Calculus AB Scoring Guidelines AB{ / BC{ 1999. The rae a which waer ows ou of a pipe, in gallons per hour, is given by a diereniable funcion R of ime. The able above shows he rae as measured every hours for a {hour period. (a) Use a

More information

AP CALCULUS AB/CALCULUS BC 2016 SCORING GUIDELINES. Question 1

AP CALCULUS AB/CALCULUS BC 2016 SCORING GUIDELINES. Question 1 AP CALCULUS AB/CALCULUS BC 6 SCORING GUIDELINES Quesion (hours) R ( ) (liers / hour) 6 4 9 95 74 7 Waer is pumped ino a ank a a rae modeled by W( ) = e liers per hour for, where is measured in hours. Waer

More information

AP CALCULUS AB 2017 SCORING GUIDELINES

AP CALCULUS AB 2017 SCORING GUIDELINES AP CALCULUS AB 17 SCORING GUIDELINES /CALCULUS BC 15 SCORING GUIDELINES Quesion (minues) v ( ) (meers per minue) 1 4 4 4 15 Johanna jogs along a sraigh pah. For 4, Johanna s velociy is given by a differeniable

More information

AP CALCULUS BC 2016 SCORING GUIDELINES

AP CALCULUS BC 2016 SCORING GUIDELINES 6 SCORING GUIDELINES Quesion A ime, he posiion of a paricle moving in he xy-plane is given by he parameric funcions ( x ( ), y ( )), where = + sin ( ). The graph of y, consising of hree line segmens, is

More information

AP CALCULUS AB 2004 SCORING GUIDELINES (Form B)

AP CALCULUS AB 2004 SCORING GUIDELINES (Form B) 4 SCORING GUIDELINES (Form B) Quesion A es plane flies in a sraigh line wih (min) 5 1 15 5 5 4 posiive velociy v (), in miles per v ()(mpm) 7. 9. 9.5 7. 4.5.4.4 4. 7. minue a ime minues, where v is a differeniable

More information

2017 AP CALCULUS AB FREE-RESPONSE QUESTIONS

2017 AP CALCULUS AB FREE-RESPONSE QUESTIONS 17 FREE-RESPONSE QUESTIONS 5. Two paricles move along he x-axis. For 8, he posiion of paricle P a ime is given by xp () ln ( 1 ), while he velociy of paricle Q a ime is given by vq () 8 15. Paricle Q is

More information

ACCUMULATION. Section 7.5 Calculus AP/Dual, Revised /26/2018 7:27 PM 7.5A: Accumulation 1

ACCUMULATION. Section 7.5 Calculus AP/Dual, Revised /26/2018 7:27 PM 7.5A: Accumulation 1 ACCUMULATION Secion 7.5 Calculus AP/Dual, Revised 2019 vie.dang@humbleisd.ne 12/26/2018 7:27 PM 7.5A: Accumulaion 1 APPLICATION PROBLEMS A. Undersand he quesion. I is ofen no necessary o as much compuaion

More information

AP Calculus BC Chapter 10 Part 1 AP Exam Problems

AP Calculus BC Chapter 10 Part 1 AP Exam Problems AP Calculus BC Chaper Par AP Eam Problems All problems are NO CALCULATOR unless oherwise indicaed Parameric Curves and Derivaives In he y plane, he graph of he parameric equaions = 5 + and y= for, is a

More information

PROBLEMS FOR MATH 162 If a problem is starred, all subproblems are due. If only subproblems are starred, only those are due. SLOPES OF TANGENT LINES

PROBLEMS FOR MATH 162 If a problem is starred, all subproblems are due. If only subproblems are starred, only those are due. SLOPES OF TANGENT LINES PROBLEMS FOR MATH 6 If a problem is sarred, all subproblems are due. If onl subproblems are sarred, onl hose are due. 00. Shor answer quesions. SLOPES OF TANGENT LINES (a) A ball is hrown ino he air. Is

More information

AP Calculus BC - Parametric equations and vectors Chapter 9- AP Exam Problems solutions

AP Calculus BC - Parametric equations and vectors Chapter 9- AP Exam Problems solutions AP Calculus BC - Parameric equaions and vecors Chaper 9- AP Exam Problems soluions. A 5 and 5. B A, 4 + 8. C A, 4 + 4 8 ; he poin a is (,). y + ( x ) x + 4 4. e + e D A, slope.5 6 e e e 5. A d hus d d

More information

AP Calculus BC 2004 Free-Response Questions Form B

AP Calculus BC 2004 Free-Response Questions Form B AP Calculus BC 200 Free-Response Quesions Form B The maerials included in hese files are inended for noncommercial use by AP eachers for course and exam preparaion; permission for any oher use mus be sough

More information

Math 115 Final Exam December 14, 2017

Math 115 Final Exam December 14, 2017 On my honor, as a suden, I have neiher given nor received unauhorized aid on his academic work. Your Iniials Only: Iniials: Do no wrie in his area Mah 5 Final Exam December, 07 Your U-M ID # (no uniqname):

More information

Parametrics and Vectors (BC Only)

Parametrics and Vectors (BC Only) Paramerics and Vecors (BC Only) The following relaionships should be learned and memorized. The paricle s posiion vecor is r() x(), y(). The velociy vecor is v(),. The speed is he magniude of he velociy

More information

CALCULUS EXPLORATION OF THE SECOND FUNDAMENTAL THEOREM OF CALCULUS. Second Fundamental Theorem of Calculus (Chain Rule Version):

CALCULUS EXPLORATION OF THE SECOND FUNDAMENTAL THEOREM OF CALCULUS. Second Fundamental Theorem of Calculus (Chain Rule Version): CALCULUS EXPLORATION OF THE SECOND FUNDAMENTAL THEOREM OF CALCULUS 6 cos Secon Funamenal Theorem of Calculus: f a 4 a f 6 cos Secon Funamenal Theorem of Calculus (Chain Rule Version): g f a E. Use he Secon

More information

!!"#"$%&#'()!"#&'(*%)+,&',-)./0)1-*23)

!!#$%&#'()!#&'(*%)+,&',-)./0)1-*23) "#"$%&#'()"#&'(*%)+,&',-)./)1-*) #$%&'()*+,&',-.%,/)*+,-&1*#$)()5*6$+$%*,7&*-'-&1*(,-&*6&,7.$%$+*&%'(*8$&',-,%'-&1*(,-&*6&,79*(&,%: ;..,*&1$&$.$%&'()*1$$.,'&',-9*(&,%)?%*,('&5

More information

Math 111 Midterm I, Lecture A, version 1 -- Solutions January 30 th, 2007

Math 111 Midterm I, Lecture A, version 1 -- Solutions January 30 th, 2007 NAME: Suden ID #: QUIZ SECTION: Mah 111 Miderm I, Lecure A, version 1 -- Soluions January 30 h, 2007 Problem 1 4 Problem 2 6 Problem 3 20 Problem 4 20 Toal: 50 You are allowed o use a calculaor, a ruler,

More information

Multiple Choice Solutions 1. E (2003 AB25) () xt t t t 2. A (2008 AB21/BC21) 3. B (2008 AB7) Using Fundamental Theorem of Calculus: 1

Multiple Choice Solutions 1. E (2003 AB25) () xt t t t 2. A (2008 AB21/BC21) 3. B (2008 AB7) Using Fundamental Theorem of Calculus: 1 Paricle Moion Soluions We have inenionally included more maerial han can be covered in mos Suden Sudy Sessions o accoun for groups ha are able o answer he quesions a a faser rae. Use your own judgmen,

More information

Ground Rules. PC1221 Fundamentals of Physics I. Kinematics. Position. Lectures 3 and 4 Motion in One Dimension. A/Prof Tay Seng Chuan

Ground Rules. PC1221 Fundamentals of Physics I. Kinematics. Position. Lectures 3 and 4 Motion in One Dimension. A/Prof Tay Seng Chuan Ground Rules PC11 Fundamenals of Physics I Lecures 3 and 4 Moion in One Dimension A/Prof Tay Seng Chuan 1 Swich off your handphone and pager Swich off your lapop compuer and keep i No alking while lecure

More information

UCLA: Math 3B Problem set 3 (solutions) Fall, 2018

UCLA: Math 3B Problem set 3 (solutions) Fall, 2018 UCLA: Mah 3B Problem se 3 (soluions) Fall, 28 This problem se concenraes on pracice wih aniderivaives. You will ge los of pracice finding simple aniderivaives as well as finding aniderivaives graphically

More information

3.6 Derivatives as Rates of Change

3.6 Derivatives as Rates of Change 3.6 Derivaives as Raes of Change Problem 1 John is walking along a sraigh pah. His posiion a he ime >0 is given by s = f(). He sars a =0from his house (f(0) = 0) and he graph of f is given below. (a) Describe

More information

4.6 One Dimensional Kinematics and Integration

4.6 One Dimensional Kinematics and Integration 4.6 One Dimensional Kinemaics and Inegraion When he acceleraion a( of an objec is a non-consan funcion of ime, we would like o deermine he ime dependence of he posiion funcion x( and he x -componen of

More information

2.1: What is physics? Ch02: Motion along a straight line. 2.2: Motion. 2.3: Position, Displacement, Distance

2.1: What is physics? Ch02: Motion along a straight line. 2.2: Motion. 2.3: Position, Displacement, Distance Ch: Moion along a sraigh line Moion Posiion and Displacemen Average Velociy and Average Speed Insananeous Velociy and Speed Acceleraion Consan Acceleraion: A Special Case Anoher Look a Consan Acceleraion

More information

KINEMATICS IN ONE DIMENSION

KINEMATICS IN ONE DIMENSION KINEMATICS IN ONE DIMENSION PREVIEW Kinemaics is he sudy of how hings move how far (disance and displacemen), how fas (speed and velociy), and how fas ha how fas changes (acceleraion). We say ha an objec

More information

Math 105 Second Midterm March 16, 2017

Math 105 Second Midterm March 16, 2017 Mah 105 Second Miderm March 16, 2017 UMID: Insrucor: Iniials: Secion: 1. Do no open his exam unil you are old o do so. 2. Do no wrie your name anywhere on his exam. 3. This exam has 9 pages including his

More information

Math 1b. Calculus, Series, and Differential Equations. Final Exam Solutions

Math 1b. Calculus, Series, and Differential Equations. Final Exam Solutions Mah b. Calculus, Series, and Differenial Equaions. Final Exam Soluions Spring 6. (9 poins) Evaluae he following inegrals. 5x + 7 (a) (x + )(x + ) dx. (b) (c) x arcan x dx x(ln x) dx Soluion. (a) Using

More information

AP CALCULUS AB/CALCULUS BC 2014 SCORING GUIDELINES

AP CALCULUS AB/CALCULUS BC 2014 SCORING GUIDELINES AP CALCULUS AB/CALCULUS BC 14 SCORING GUIDELINES Question 1 Grass clippings are placed in a bin, where they decompose. For t 3, the amount of grass clippings remaining in the bin is modeled by At ( ) =

More information

Suggested Practice Problems (set #2) for the Physics Placement Test

Suggested Practice Problems (set #2) for the Physics Placement Test Deparmen of Physics College of Ars and Sciences American Universiy of Sharjah (AUS) Fall 014 Suggesed Pracice Problems (se #) for he Physics Placemen Tes This documen conains 5 suggesed problems ha are

More information

Answers to 1 Homework

Answers to 1 Homework Answers o Homework. x + and y x 5 y To eliminae he parameer, solve for x. Subsiue ino y s equaion o ge y x.. x and y, x y x To eliminae he parameer, solve for. Subsiue ino y s equaion o ge x y, x. (Noe:

More information

Math 333 Problem Set #2 Solution 14 February 2003

Math 333 Problem Set #2 Solution 14 February 2003 Mah 333 Problem Se #2 Soluion 14 February 2003 A1. Solve he iniial value problem dy dx = x2 + e 3x ; 2y 4 y(0) = 1. Soluion: This is separable; we wrie 2y 4 dy = x 2 + e x dx and inegrae o ge The iniial

More information

AP CALCULUS BC 2007 SCORING GUIDELINES (Form B)

AP CALCULUS BC 2007 SCORING GUIDELINES (Form B) AP CALCULUS BC 2007 SCORING GUIDELINES (Form B) Question 3 The wind chill is the temperature, in degrees Fahrenheit ( F, ) a human feels based on the air temperature, in degrees Fahrenheit, and the wind

More information

Topics covered in tutorial 01: 1. Review of definite integrals 2. Physical Application 3. Area between curves. 1. Review of definite integrals

Topics covered in tutorial 01: 1. Review of definite integrals 2. Physical Application 3. Area between curves. 1. Review of definite integrals MATH4 Calculus II (8 Spring) MATH 4 Tuorial Noes Tuorial Noes (Phyllis LIANG) IA: Phyllis LIANG Email: masliang@us.hk Homepage: hps://masliang.people.us.hk Office: Room 3 (Lif/Lif 3) Phone number: 3587453

More information

(π 3)k. f(t) = 1 π 3 sin(t)

(π 3)k. f(t) = 1 π 3 sin(t) Mah 6 Fall 6 Dr. Lil Yen Tes Show all our work Name: Score: /6 No Calculaor permied in his par. Read he quesions carefull. Show all our work and clearl indicae our final answer. Use proper noaion. Problem

More information

IB Physics Kinematics Worksheet

IB Physics Kinematics Worksheet IB Physics Kinemaics Workshee Wrie full soluions and noes for muliple choice answers. Do no use a calculaor for muliple choice answers. 1. Which of he following is a correc definiion of average acceleraion?

More information

1.6. Slopes of Tangents and Instantaneous Rate of Change

1.6. Slopes of Tangents and Instantaneous Rate of Change 1.6 Slopes of Tangens and Insananeous Rae of Change When you hi or kick a ball, he heigh, h, in meres, of he ball can be modelled by he equaion h() 4.9 2 v c. In his equaion, is he ime, in seconds; c represens

More information

72 Calculus and Structures

72 Calculus and Structures 72 Calculus and Srucures CHAPTER 5 DISTANCE AND ACCUMULATED CHANGE Calculus and Srucures 73 Copyrigh Chaper 5 DISTANCE AND ACCUMULATED CHANGE 5. DISTANCE a. Consan velociy Le s ake anoher look a Mary s

More information

Math 2214 Solution Test 1A Spring 2016

Math 2214 Solution Test 1A Spring 2016 Mah 14 Soluion Tes 1A Spring 016 sec Problem 1: Wha is he larges -inerval for which ( 4) = has a guaraneed + unique soluion for iniial value (-1) = 3 according o he Exisence Uniqueness Theorem? Soluion

More information

15. Vector Valued Functions

15. Vector Valued Functions 1. Vecor Valued Funcions Up o his poin, we have presened vecors wih consan componens, for example, 1, and,,4. However, we can allow he componens of a vecor o be funcions of a common variable. For example,

More information

The Fundamental Theorem of Calculus Solutions

The Fundamental Theorem of Calculus Solutions The Fundamenal Theorem of Calculus Soluions We have inenionally included more maerial han can be covered in mos Suden Sudy Sessions o accoun for groups ha are able o answer he quesions a a faser rae. Use

More information

Solutions to Assignment 1

Solutions to Assignment 1 MA 2326 Differenial Equaions Insrucor: Peronela Radu Friday, February 8, 203 Soluions o Assignmen. Find he general soluions of he following ODEs: (a) 2 x = an x Soluion: I is a separable equaion as we

More information

Motion along a Straight Line

Motion along a Straight Line chaper 2 Moion along a Sraigh Line verage speed and average velociy (Secion 2.2) 1. Velociy versus speed Cone in he ebook: fer Eample 2. Insananeous velociy and insananeous acceleraion (Secions 2.3, 2.4)

More information

MATH 4330/5330, Fourier Analysis Section 6, Proof of Fourier s Theorem for Pointwise Convergence

MATH 4330/5330, Fourier Analysis Section 6, Proof of Fourier s Theorem for Pointwise Convergence MATH 433/533, Fourier Analysis Secion 6, Proof of Fourier s Theorem for Poinwise Convergence Firs, some commens abou inegraing periodic funcions. If g is a periodic funcion, g(x + ) g(x) for all real x,

More information

KEY. Math 334 Midterm I Fall 2008 sections 001 and 003 Instructor: Scott Glasgow

KEY. Math 334 Midterm I Fall 2008 sections 001 and 003 Instructor: Scott Glasgow 1 KEY Mah 4 Miderm I Fall 8 secions 1 and Insrucor: Sco Glasgow Please do NOT wrie on his eam. No credi will be given for such work. Raher wrie in a blue book, or on our own paper, preferabl engineering

More information

Math 116 Practice for Exam 2

Math 116 Practice for Exam 2 Mah 6 Pracice for Exam Generaed Ocober 3, 7 Name: SOLUTIONS Insrucor: Secion Number:. This exam has 5 quesions. Noe ha he problems are no of equal difficuly, so you may wan o skip over and reurn o a problem

More information

Logistic growth rate. Fencing a pen. Notes. Notes. Notes. Optimization: finding the biggest/smallest/highest/lowest, etc.

Logistic growth rate. Fencing a pen. Notes. Notes. Notes. Optimization: finding the biggest/smallest/highest/lowest, etc. Opimizaion: finding he bigges/smalles/highes/lowes, ec. Los of non-sandard problems! Logisic growh rae 7.1 Simple biological opimizaion problems Small populaions AND large populaions grow slowly N: densiy

More information

Math 116 Second Midterm March 21, 2016

Math 116 Second Midterm March 21, 2016 Mah 6 Second Miderm March, 06 UMID: EXAM SOLUTIONS Iniials: Insrucor: Secion:. Do no open his exam unil you are old o do so.. Do no wrie your name anywhere on his exam. 3. This exam has pages including

More information

Physics 101 Fall 2006: Exam #1- PROBLEM #1

Physics 101 Fall 2006: Exam #1- PROBLEM #1 Physics 101 Fall 2006: Exam #1- PROBLEM #1 1. Problem 1. (+20 ps) (a) (+10 ps) i. +5 ps graph for x of he rain vs. ime. The graph needs o be parabolic and concave upward. ii. +3 ps graph for x of he person

More information

The average rate of change between two points on a function is d t

The average rate of change between two points on a function is d t SM Dae: Secion: Objecive: The average rae of change beween wo poins on a funcion is d. For example, if he funcion ( ) represens he disance in miles ha a car has raveled afer hours, hen finding he slope

More information

PHYS 1401 General Physics I Test 3 Review Questions

PHYS 1401 General Physics I Test 3 Review Questions PHYS 1401 General Physics I Tes 3 Review Quesions Ch. 7 1. A 6500 kg railroad car moving a 4.0 m/s couples wih a second 7500 kg car iniially a res. a) Skech before and afer picures of he siuaion. b) Wha

More information

MEI STRUCTURED MATHEMATICS 4758

MEI STRUCTURED MATHEMATICS 4758 OXFORD CAMBRIDGE AND RSA EXAMINATIONS Advanced Subsidiary General Cerificae of Educaion Advanced General Cerificae of Educaion MEI STRUCTURED MATHEMATICS 4758 Differenial Equaions Thursday 5 JUNE 006 Afernoon

More information

Math 10C: Relations and Functions PRACTICE EXAM

Math 10C: Relations and Functions PRACTICE EXAM Mah C: Relaions and Funcions PRACTICE EXAM. Cailin rides her bike o school every day. The able of values shows her disance from home as ime passes. An equaion ha describes he daa is: ime (minues) disance

More information

PHYSICS 220 Lecture 02 Motion, Forces, and Newton s Laws Textbook Sections

PHYSICS 220 Lecture 02 Motion, Forces, and Newton s Laws Textbook Sections PHYSICS 220 Lecure 02 Moion, Forces, and Newon s Laws Texbook Secions 2.2-2.4 Lecure 2 Purdue Universiy, Physics 220 1 Overview Las Lecure Unis Scienific Noaion Significan Figures Moion Displacemen: Δx

More information

Challenge Problems. DIS 203 and 210. March 6, (e 2) k. k(k + 2). k=1. f(x) = k(k + 2) = 1 x k

Challenge Problems. DIS 203 and 210. March 6, (e 2) k. k(k + 2). k=1. f(x) = k(k + 2) = 1 x k Challenge Problems DIS 03 and 0 March 6, 05 Choose one of he following problems, and work on i in your group. Your goal is o convince me ha your answer is correc. Even if your answer isn compleely correc,

More information

HOMEWORK # 2: MATH 211, SPRING Note: This is the last solution set where I will describe the MATLAB I used to make my pictures.

HOMEWORK # 2: MATH 211, SPRING Note: This is the last solution set where I will describe the MATLAB I used to make my pictures. HOMEWORK # 2: MATH 2, SPRING 25 TJ HITCHMAN Noe: This is he las soluion se where I will describe he MATLAB I used o make my picures.. Exercises from he ex.. Chaper 2.. Problem 6. We are o show ha y() =

More information

Kinematics Motion in 1 Dimension and Graphs

Kinematics Motion in 1 Dimension and Graphs Kinemaics Moion in 1 Dimension and Graphs Lana Sheridan De Anza College Sep 27, 2017 Las ime moion in 1-dimension some kinemaic quaniies graphs Overview velociy and speed acceleraion more graphs Kinemaics

More information

Exam 1 Solutions. 1 Question 1. February 10, Part (A) 1.2 Part (B) To find equilibrium solutions, set P (t) = C = dp

Exam 1 Solutions. 1 Question 1. February 10, Part (A) 1.2 Part (B) To find equilibrium solutions, set P (t) = C = dp Exam Soluions Februar 0, 05 Quesion. Par (A) To find equilibrium soluions, se P () = C = = 0. This implies: = P ( P ) P = P P P = P P = P ( + P ) = 0 The equilibrium soluion are hus P () = 0 and P () =..

More information

1. VELOCITY AND ACCELERATION

1. VELOCITY AND ACCELERATION 1. VELOCITY AND ACCELERATION 1.1 Kinemaics Equaions s = u + 1 a and s = v 1 a s = 1 (u + v) v = u + as 1. Displacemen-Time Graph Gradien = speed 1.3 Velociy-Time Graph Gradien = acceleraion Area under

More information

Practicing Problem Solving and Graphing

Practicing Problem Solving and Graphing Pracicing Problem Solving and Graphing Tes 1: Jan 30, 7pm, Ming Hsieh G20 The Bes Ways To Pracice for Tes Bes If need more, ry suggesed problems from each new opic: Suden Response Examples A pas opic ha

More information

F.LE.A.4: Exponential Growth

F.LE.A.4: Exponential Growth Regens Exam Quesions F.LE.A.4: Exponenial Growh www.jmap.org Name: F.LE.A.4: Exponenial Growh 1 A populaion of rabbis doubles every days according o he formula P = 10(2), where P is he populaion of rabbis

More information

4.5 Constant Acceleration

4.5 Constant Acceleration 4.5 Consan Acceleraion v() v() = v 0 + a a() a a() = a v 0 Area = a (a) (b) Figure 4.8 Consan acceleraion: (a) velociy, (b) acceleraion When he x -componen of he velociy is a linear funcion (Figure 4.8(a)),

More information

EQUATIONS REVIEW I Lesson Notes. Example 1. Example 2. Equations Review. 5 2 x = 1 6. Simple Equations

EQUATIONS REVIEW I Lesson Notes. Example 1. Example 2.  Equations Review. 5 2 x = 1 6. Simple Equations Equaions Review x + 3 = 6 EQUATIONS REVIEW I Example Simple Equaions a) a - 7 = b) m - 9 = -7 c) 6r = 4 d) 7 = -9x Example Simple Equaions a) 6p + = 4 b) 4 = 3k + 6 c) 9 + k = + 3k d) 8-3n = -8n + 3 EQUATIONS

More information

Instructor: Barry McQuarrie Page 1 of 5

Instructor: Barry McQuarrie Page 1 of 5 Procedure for Solving radical equaions 1. Algebraically isolae one radical by iself on one side of equal sign. 2. Raise each side of he equaion o an appropriae power o remove he radical. 3. Simplify. 4.

More information

Math Week 14 April 16-20: sections first order systems of linear differential equations; 7.4 mass-spring systems.

Math Week 14 April 16-20: sections first order systems of linear differential equations; 7.4 mass-spring systems. Mah 2250-004 Week 4 April 6-20 secions 7.-7.3 firs order sysems of linear differenial equaions; 7.4 mass-spring sysems. Mon Apr 6 7.-7.2 Sysems of differenial equaions (7.), and he vecor Calculus we need

More information

Math Final Exam Solutions

Math Final Exam Solutions Mah 246 - Final Exam Soluions Friday, July h, 204 () Find explici soluions and give he inerval of definiion o he following iniial value problems (a) ( + 2 )y + 2y = e, y(0) = 0 Soluion: In normal form,

More information

2. Nonlinear Conservation Law Equations

2. Nonlinear Conservation Law Equations . Nonlinear Conservaion Law Equaions One of he clear lessons learned over recen years in sudying nonlinear parial differenial equaions is ha i is generally no wise o ry o aack a general class of nonlinear

More information

Welcome Back to Physics 215!

Welcome Back to Physics 215! Welcome Back o Physics 215! (General Physics I) Thurs. Jan 19 h, 2017 Lecure01-2 1 Las ime: Syllabus Unis and dimensional analysis Today: Displacemen, velociy, acceleraion graphs Nex ime: More acceleraion

More information

Physics for Scientists and Engineers. Chapter 2 Kinematics in One Dimension

Physics for Scientists and Engineers. Chapter 2 Kinematics in One Dimension Physics for Scieniss and Engineers Chaper Kinemaics in One Dimension Spring, 8 Ho Jung Paik Kinemaics Describes moion while ignoring he agens (forces) ha caused he moion For now, will consider moion in

More information

2. What is the displacement of the bug between t = 0.00 s and t = 20.0 s? A) cm B) 39.9 cm C) cm D) 16.1 cm E) +16.

2. What is the displacement of the bug between t = 0.00 s and t = 20.0 s? A) cm B) 39.9 cm C) cm D) 16.1 cm E) +16. 1. For which one of he following siuaions will he pah lengh equal he magniude of he displacemen? A) A jogger is running around a circular pah. B) A ball is rolling down an inclined plane. C) A rain ravels

More information

WELCOME TO 1103 PERIOD 3. Homework Exercise #2 is due at the beginning of class. Please put it on the stool in the front of the classroom.

WELCOME TO 1103 PERIOD 3. Homework Exercise #2 is due at the beginning of class. Please put it on the stool in the front of the classroom. WELCOME TO 1103 PERIOD 3 Homework Exercise #2 is due a he beginning of class. Please pu i on he sool in he fron of he classroom. Ring of Truh: Change 1) Give examples of some energy ransformaions in he

More information

Final Spring 2007

Final Spring 2007 .615 Final Spring 7 Overview The purpose of he final exam is o calculae he MHD β limi in a high-bea oroidal okamak agains he dangerous n = 1 exernal ballooning-kink mode. Effecively, his corresponds o

More information

MEI Mechanics 1 General motion. Section 1: Using calculus

MEI Mechanics 1 General motion. Section 1: Using calculus Soluions o Exercise MEI Mechanics General moion Secion : Using calculus. s 4 v a 6 4 4 When =, v 4 a 6 4 6. (i) When = 0, s = -, so he iniial displacemen = - m. s v 4 When = 0, v = so he iniial velociy

More information

Course II. Lesson 7 Applications to Physics. 7A Velocity and Acceleration of a Particle

Course II. Lesson 7 Applications to Physics. 7A Velocity and Acceleration of a Particle Course II Lesson 7 Applicaions o Physics 7A Velociy and Acceleraion of a Paricle Moion in a Sraigh Line : Velociy O Aerage elociy Moion in he -ais + Δ + Δ 0 0 Δ Δ Insananeous elociy d d Δ Δ Δ 0 lim [ m/s

More information

Phys 221 Fall Chapter 2. Motion in One Dimension. 2014, 2005 A. Dzyubenko Brooks/Cole

Phys 221 Fall Chapter 2. Motion in One Dimension. 2014, 2005 A. Dzyubenko Brooks/Cole Phys 221 Fall 2014 Chaper 2 Moion in One Dimension 2014, 2005 A. Dzyubenko 2004 Brooks/Cole 1 Kinemaics Kinemaics, a par of classical mechanics: Describes moion in erms of space and ime Ignores he agen

More information

Lecture 2-1 Kinematics in One Dimension Displacement, Velocity and Acceleration Everything in the world is moving. Nothing stays still.

Lecture 2-1 Kinematics in One Dimension Displacement, Velocity and Acceleration Everything in the world is moving. Nothing stays still. Lecure - Kinemaics in One Dimension Displacemen, Velociy and Acceleraion Everyhing in he world is moving. Nohing says sill. Moion occurs a all scales of he universe, saring from he moion of elecrons in

More information

PHYSICS 149: Lecture 9

PHYSICS 149: Lecture 9 PHYSICS 149: Lecure 9 Chaper 3 3.2 Velociy and Acceleraion 3.3 Newon s Second Law of Moion 3.4 Applying Newon s Second Law 3.5 Relaive Velociy Lecure 9 Purdue Universiy, Physics 149 1 Velociy (m/s) The

More information

Week #13 - Integration by Parts & Numerical Integration Section 7.2

Week #13 - Integration by Parts & Numerical Integration Section 7.2 Week #3 - Inegraion by Pars & Numerical Inegraion Secion 7. From Calculus, Single Variable by Hughes-Halle, Gleason, McCallum e. al. Copyrigh 5 by John Wiley & Sons, Inc. This maerial is used by permission

More information

MA Study Guide #1

MA Study Guide #1 MA 66 Su Guide #1 (1) Special Tpes of Firs Order Equaions I. Firs Order Linear Equaion (FOL): + p() = g() Soluion : = 1 µ() [ ] µ()g() + C, where µ() = e p() II. Separable Equaion (SEP): dx = h(x) g()

More information

Section 4.4 Logarithmic Properties

Section 4.4 Logarithmic Properties Secion. Logarihmic Properies 59 Secion. Logarihmic Properies In he previous secion, we derived wo imporan properies of arihms, which allowed us o solve some asic eponenial and arihmic equaions. Properies

More information

SMT 2014 Calculus Test Solutions February 15, 2014 = 3 5 = 15.

SMT 2014 Calculus Test Solutions February 15, 2014 = 3 5 = 15. SMT Calculus Tes Soluions February 5,. Le f() = and le g() =. Compue f ()g (). Answer: 5 Soluion: We noe ha f () = and g () = 6. Then f ()g () =. Plugging in = we ge f ()g () = 6 = 3 5 = 5.. There is a

More information

APPM 2360 Homework Solutions, Due June 10

APPM 2360 Homework Solutions, Due June 10 2.2.2: Find general soluions for he equaion APPM 2360 Homework Soluions, Due June 10 Soluion: Finding he inegraing facor, dy + 2y = 3e µ) = e 2) = e 2 Muliplying he differenial equaion by he inegraing

More information

Name: Teacher: DO NOT OPEN THE EXAMINATION PAPER UNTIL YOU ARE TOLD BY THE SUPERVISOR TO BEGIN PHYSICS FINAL EXAMINATION June 2010.

Name: Teacher: DO NOT OPEN THE EXAMINATION PAPER UNTIL YOU ARE TOLD BY THE SUPERVISOR TO BEGIN PHYSICS FINAL EXAMINATION June 2010. Name: Teacher: DO NOT OPEN THE EXAMINATION PAPER UNTIL YOU ARE TOLD BY THE SUPERVISOR TO BEGIN PHYSICS 224 FINAL EXAMINATION June 21 Value: 1% General Insrucions This examinaion consiss of wo pars. Boh

More information

Kinematics Vocabulary. Kinematics and One Dimensional Motion. Position. Coordinate System in One Dimension. Kinema means movement 8.

Kinematics Vocabulary. Kinematics and One Dimensional Motion. Position. Coordinate System in One Dimension. Kinema means movement 8. Kinemaics Vocabulary Kinemaics and One Dimensional Moion 8.1 WD1 Kinema means movemen Mahemaical descripion of moion Posiion Time Inerval Displacemen Velociy; absolue value: speed Acceleraion Averages

More information

INDEX. Transient analysis 1 Initial Conditions 1

INDEX. Transient analysis 1 Initial Conditions 1 INDEX Secion Page Transien analysis 1 Iniial Condiions 1 Please inform me of your opinion of he relaive emphasis of he review maerial by simply making commens on his page and sending i o me a: Frank Mera

More information

u(x) = e x 2 y + 2 ) Integrate and solve for x (1 + x)y + y = cos x Answer: Divide both sides by 1 + x and solve for y. y = x y + cos x

u(x) = e x 2 y + 2 ) Integrate and solve for x (1 + x)y + y = cos x Answer: Divide both sides by 1 + x and solve for y. y = x y + cos x . 1 Mah 211 Homework #3 February 2, 2001 2.4.3. y + (2/x)y = (cos x)/x 2 Answer: Compare y + (2/x) y = (cos x)/x 2 wih y = a(x)x + f(x)and noe ha a(x) = 2/x. Consequenly, an inegraing facor is found wih

More information

Solutions from Chapter 9.1 and 9.2

Solutions from Chapter 9.1 and 9.2 Soluions from Chaper 9 and 92 Secion 9 Problem # This basically boils down o an exercise in he chain rule from calculus We are looking for soluions of he form: u( x) = f( k x c) where k x R 3 and k is

More information

Physics Notes - Ch. 2 Motion in One Dimension

Physics Notes - Ch. 2 Motion in One Dimension Physics Noes - Ch. Moion in One Dimension I. The naure o physical quaniies: scalars and ecors A. Scalar quaniy ha describes only magniude (how much), NOT including direcion; e. mass, emperaure, ime, olume,

More information

on the interval (x + 1) 0! x < ", where x represents feet from the first fence post. How many square feet of fence had to be painted?

on the interval (x + 1) 0! x < , where x represents feet from the first fence post. How many square feet of fence had to be painted? Calculus II MAT 46 Improper Inegrals A mahemaician asked a fence painer o complee he unique ask of paining one side of a fence whose face could be described by he funcion y f (x on he inerval (x + x

More information

a 10.0 (m/s 2 ) 5.0 Name: Date: 1. The graph below describes the motion of a fly that starts out going right V(m/s)

a 10.0 (m/s 2 ) 5.0 Name: Date: 1. The graph below describes the motion of a fly that starts out going right V(m/s) Name: Dae: Kinemaics Review (Honors. Physics) Complee he following on a separae shee of paper o be urned in on he day of he es. ALL WORK MUST BE SHOWN TO RECEIVE CREDIT. 1. The graph below describes he

More information

dy dx = xey (a) y(0) = 2 (b) y(1) = 2.5 SOLUTION: See next page

dy dx = xey (a) y(0) = 2 (b) y(1) = 2.5 SOLUTION: See next page Assignmen 1 MATH 2270 SOLUTION Please wrie ou complee soluions for each of he following 6 problems (one more will sill be added). You may, of course, consul wih your classmaes, he exbook or oher resources,

More information

Vehicle Arrival Models : Headway

Vehicle Arrival Models : Headway Chaper 12 Vehicle Arrival Models : Headway 12.1 Inroducion Modelling arrival of vehicle a secion of road is an imporan sep in raffic flow modelling. I has imporan applicaion in raffic flow simulaion where

More information

Math 334 Test 1 KEY Spring 2010 Section: 001. Instructor: Scott Glasgow Dates: May 10 and 11.

Math 334 Test 1 KEY Spring 2010 Section: 001. Instructor: Scott Glasgow Dates: May 10 and 11. 1 Mah 334 Tes 1 KEY Spring 21 Secion: 1 Insrucor: Sco Glasgow Daes: Ma 1 and 11. Do NOT wrie on his problem saemen bookle, excep for our indicaion of following he honor code jus below. No credi will be

More information

In this chapter the model of free motion under gravity is extended to objects projected at an angle. When you have completed it, you should

In this chapter the model of free motion under gravity is extended to objects projected at an angle. When you have completed it, you should Cambridge Universiy Press 978--36-60033-7 Cambridge Inernaional AS and A Level Mahemaics: Mechanics Coursebook Excerp More Informaion Chaper The moion of projeciles In his chaper he model of free moion

More information

Midterm Exam Review Questions Free Response Non Calculator

Midterm Exam Review Questions Free Response Non Calculator Name: Dae: Block: Miderm Eam Review Quesions Free Response Non Calculaor Direcions: Solve each of he following problems. Choose he BEST answer choice from hose given. A calculaor may no be used. Do no

More information

Physics 180A Fall 2008 Test points. Provide the best answer to the following questions and problems. Watch your sig figs.

Physics 180A Fall 2008 Test points. Provide the best answer to the following questions and problems. Watch your sig figs. Physics 180A Fall 2008 Tes 1-120 poins Name Provide he bes answer o he following quesions and problems. Wach your sig figs. 1) The number of meaningful digis in a number is called he number of. When numbers

More information