SPECIALIST MATHEMATICS
|
|
- Janice O’Connor’
- 6 years ago
- Views:
Transcription
1 Victorin Certificte of Euction 00 SUPERVISOR TO ATTACH PROCESSING LABEL HERE STUDENT NUMBER Letter Figures Wors SPECIALIST MATHEMATICS Written exmintion Friy 9 October 00 Reing time: 9.00 m to 9.5 m (5 minutes) Writing time: 9.5 m to 0.5 m ( hour) QUESTION AND ANSWER BOOK Number of questions Structure of book Number of questions to be nswere Number of mrks Stuents re permitte to bring into the exmintion room: pens, pencils, highlighters, ersers, shrpeners, rulers. Stuents re not permitte to bring into the exmintion room: notes of ny kin, clcultor of ny type, blnk sheets of pper n/or white out liqui/tpe. Mterils supplie Question n nswer book of pges with etchble sheet of miscellneous formuls in the centrefol. Working spce is provie throughout the book. Instructions Detch the formul sheet from the centre of this book uring reing time. Write your stuent number in the spce provie bove on this pge. All written responses must be in English. Stuents re NOT permitte to bring mobile phones n/or ny other unuthorise electronic evices into the exmintion room. VICTORIAN CURRICULUM AND ASSESSMENT AUTHORITY 00
2 00 SPECMATH EXAM This pge is blnk
3 3 00 SPECMATH EXAM Instructions Answer ll questions in the spces provie. Unless otherwise specifie n exct nswer is require to question. In questions where more thn one mrk is vilble, pproprite working must be shown. Unless otherwise inicte, the igrms in this book re not rwn to scle. Tke the ccelertion ue to grvity to hve mgnitue g m/s, where g = 9.8. Question Consier f (z) = z 3 + 9z + 8z + 0, z C. Given tht f ( ) = 0, fctorise f (z) over C. 3 mrks TURN OVER
4 00 SPECMATH EXAM 4 Question A boy of mss kg is initilly t rest n is cte on by resultnt force of v 4 newtons where v is the velocity in m/s. The boy moves in stright line s result of the force.. Show tht the ccelertion of the boy is given by v t v 4. b. Solve the ifferentil eqution in prt. to fin v s function of t. mrk 4 mrks
5 5 00 SPECMATH EXAM Question 3 Reltive to n origin O, point A hs crtesin coorintes (,, ) n point B hs crtesin coorintes (, 3, 4).. Fin n expression for the vector AB in the form ibj ck. b. Show tht the cosine of the ngle between the vectors OA n AB is 4 9. mrk c. Hence fin the exct re of the tringle OAB. mrk 3 mrks TURN OVER
6 00 SPECMATH EXAM 6 Question 4 Given tht z = + i, plot n lbel points for ech of the following on the rgn igrm below. i. z ii. z iii. z 4 Im(z) O Re(z) mrks Question 5 Given tht f (x) = rctn(x), fin f. 3 mrks
7 7 00 SPECMATH EXAM Question 6 3π 4 Evlute cos (x)sin(x). π 3 mrks TURN OVER
8 00 SPECMATH EXAM 8 Question 7 Consier the ifferentil eqution y 4x, < x <, ( x ) for which y 3 when x = 0, n y = 4 when x = 0. Given tht 4x x ( x ), fin the solution of this ifferentil eqution. 3 mrks
9 9 00 SPECMATH EXAM Question 8 The pth of prticle is given by r( t) tsin( t) i tcos( t) j, t 0. The prticle leves the origin t t = 0 n then spirls outwrs. 3. Show tht the secon time the prticle crosses the x-xis fter leving the origin occurs when t =. 3 b. Fin the spee of the prticle when t =. mrk 3 mrks Let be the cute ngle t which the pth of the prticle crosses the x-xis. 3 c. Fin tn() when t =. mrk TURN OVER
10 00 SPECMATH EXAM 0 Question 9. On the xes below sketch the grph with eqution x xes n give the equtions of ny symptotes y ( y ). Stte ll intercepts with the coorinte 4 3 O 3 x 3 4 b. Fin the grient of the curve with eqution x ( y ) t the point where x = n y < mrks 3 mrks
11 00 SPECMATH EXAM Question 0 Prt of the grph with eqution y( x ) x is shown below. y O x Fin the re tht is boune by the curve n the x-xis. Give your nswer in the form b c where, b n c re integers. 4 mrks END OF QUESTION AND ANSWER BOOK
12 SPECIALIST MATHEMATICS Written exmintions n FORMULA SHEET Directions to stuents Detch this formul sheet uring reing time. This formul sheet is provie for your reference. VICTORIAN CURRICULUM AND ASSESSMENT AUTHORITY 00
13 SPECMATH Specilist Mthemtics Formuls Mensurtion re of trpezium: curve surfce re of cyliner: volume of cyliner: volume of cone: volume of pyrmi: volume of sphere: re of tringle: sine rule: cosine rule: bh π rh π r h π r h 3 3 Ah 4 3 π r 3 bcsin A b c sin A sin B sinc c = + b b cos C Coorinte geometry ellipse: x h y k b hyperbol: x h y k b Circulr (trigonometric) functions cos (x) + sin (x) = + tn (x) = sec (x) cot (x) + = cosec (x) sin(x + y) = sin(x) cos(y) + cos(x) sin(y) cos(x + y) = cos(x) cos(y) sin(x) sin(y) tn( x) tn( y) tn( x y) tn( x) tn( y) sin(x y) = sin(x) cos(y) cos(x) sin(y) cos(x y) = cos(x) cos(y) + sin(x) sin(y) tn( x) tn( y) tn( x y) tn( x) tn( y) cos(x) = cos (x) sin (x) = cos (x) = sin (x) tn( x) sin(x) = sin(x) cos(x) tn( x) tn ( x) function sin cos tn omin [, ] [, ] R rnge π π, [0, ] π, π
14 3 SPECMATH Algebr (complex numbers) z = x + yi = r(cos θ + i sin θ = r cis θ z x y r π < Arg z π z r z z = r r cis(θ + θ ) cis z r θθ z n = r n cis(nθ) (e Moivre s theorem) Clculus x n nx n n n x x c, n n e x e x x e e x c log e( x) x x log x c e sin( x) cos( x) sin( x) cos( x) c cos( x) sin( x) cos( x) sin( x) c tn( x) sec ( x) sin cos ( x) x ( x) x sec ( x) tn( x) c x x x sin c, 0 x cos c, 0 tn ( x) x x x tn c prouct rule: quotient rule: chin rule: Euler s metho: ccelertion: uvu v v u u v v y y u u If y v u u v f x, x 0 = n y 0 = b, then x n + = x n + h n y n + = y n + h f(x n ) x v v v v t t constnt (uniform) ccelertion: v = u + t s = ut + t v = u + s s = (u + v)t TURN OVER
15 SPECMATH 4 Vectors in two n three imensions r xi yj zk ~ ~ ~ ~ r ~ = x y z r ~ r. r ~ = r r cos θ = x x + y y + z z r ~ y z r i j k ~ t t ~ t ~ t ~ Mechnics momentum: p mv ~ ~ eqution of motion: R m ~ ~ friction: F μn END OF FORMULA SHEET
SPECIALIST MATHEMATICS
Victorin Certificte of Euction 009 SUPERVISOR TO ATTACH PROCESSING LABEL HERE STUDENT NUMBER Letter Figures Wors SPECIALIST MATHEMATICS Written exmintion Friy 30 October 009 Reing time: 3.00 pm to 3.5
More informationSPECIALIST MATHEMATICS
Victorin CertiÞcte of Euction 007 SUPERVISOR TO ATTACH PROCESSING LABEL HERE STUDENT NUMBER Letter Figures Wors SPECIALIST MATHEMATICS Written exmintion Mony 5 November 007 Reing time: 3.00 pm to 3.5 pm
More informationSPECIALIST MATHEMATICS
Victorin Certificte of Euction 04 SUPERVISOR TO ATTACH PROCESSING LABEL HERE Letter STUDENT NUMBER SPECIALIST MATHEMATICS Written exmintion Friy 7 November 04 Reing time: 9.00 m to 9.5 m (5 minutes) Writing
More informationSPECIALIST MATHEMATICS
Victorin Certificte of Euction 08 SUPERVISOR TO ATTACH PROCESSING LABEL HERE Letter STUDENT NUMBER SPECIALIST MATHEMATICS Written exmintion Friy 9 November 08 Reing time: 9.00 m to 9.5 m (5 minutes) Writing
More informationLetter STUDENT NUMBER SPECIALIST MATHEMATICS. Number of questions and mark allocations may vary from the information indicated. Written examination 1
Victorin Certificte of Euction 07 SUPERVISOR TO ATTACH PROCESSING LABEL HERE Letter STUDENT NUMBER SPECIALIST MATHEMATICS Written emintion Friy 0 November 07 Reing time: 9.00 m to 9.5 m (5 minutes) Writing
More informationSPECIALIST MATHEMATICS
Victorin Certificte of Euction 07 SUPERVISOR TO ATTACH PROCESSING LABEL HERE Letter STUDENT NUMBER SPECIALIST MATHEMATICS Written emintion Thursy 8 June 07 Reing time:.00 pm to.5 pm (5 minutes) Writing
More informationSPECIALIST MATHEMATICS
Victorin Certificte of Euction 08 SUPERVISOR TO ATTACH PROCESSING LABEL HERE Letter STUDENT NUMBER SPECIALIST MATHEMATICS Written exmintion Tuesy 5 June 08 Reing time:.00 pm to.5 pm (5 minutes) Writing
More informationSPECIALIST MATHEMATICS
Victorin Certificte of Euction 06 SUPERVISOR TO ATTACH PROCESSING LABEL HERE Letter STUDENT NUMBER SPECIALIST MATHEMATICS Written exmintion Friy 4 November 06 Reing time: 9.00 m to 9.5 m (5 minutes) Writing
More informationMATHEMATICAL METHODS (CAS) Written Examination 1
The Mthemticl Assocition of Victori Tril Exm 011 MATHEMATICAL METHODS (CAS) STUDENT NAME Written Exmintion 1 Reing time: 15 minutes Writing time: 1 hour QUESTION AND ANSWER BOOK Structure of book Number
More informationLetter STUDENT NUMBER SPECIALIST MATHEMATICS. Written examination 2. Number of questions and mark allocations may vary from the information indicated.
Victorin Certificte of uction SUPRVISOR TO ATTACH PROCSSING LABL HR Letter STUDNT NUMBR SPCIALIST MATHMATICS Section Written emintion Mony November Reing time:. pm to. pm ( minutes) Writing time:. pm to.
More informationSPECIALIST MATHEMATICS
Victorin Certificte of Eduction 006 SUPERVISOR TO ATTACH PROCESSING LABEL HERE STUDENT NUMBER Letter Figures Words SPECIALIST MATHEMATICS Written exmintion Mondy 30 October 006 Reding time: 3.00 pm to
More informationSPECIALIST MATHEMATICS
Victorian Certificate of Eucation 07 SUPERVISOR TO ATTACH PROCESSING LABEL HERE Letter STUDENT NUMBER SPECIALIST MATHEMATICS Written examination Friay 0 November 07 Reaing time: 9.00 am to 9.5 am (5 minutes)
More informationSPECIALIST MATHEMATICS
Victorian Certificate of Education 00 SUPERVISOR TO ATTACH PROCESSING LABEL HERE STUDENT NUMBER Letter Figures Words SPECIALIST MATHEMATICS Written eamination Monday November 00 Reading time:.00 pm to.5
More informationMATHEMATICAL METHODS (CAS) Written examination 1
Victorian Certificate of Eucation 2006 SUPERVISOR TO ATTACH PROCESSING LABEL HERE STUDENT NUMBER Letter Figures Wors MATHEMATICAL METHODS (CAS) Written examination 1 Friay 3 November 2006 Reaing time:
More informationMATHEMATICAL METHODS
Victorian Certificate of Eucation 207 SUPERVISOR TO ATTACH PROCESSING LABEL HERE Letter STUDENT NUMBER MATHEMATICAL METHODS Written examination Wenesay 8 November 207 Reaing time: 9.00 am to 9.5 am (5
More informationWritten examination 1 (Facts, skills and applications)
MATHEMATICAL METHDS (CAS) PILT STUDY Written emintion (Fcts, skills nd pplictions) Frid 5 November 004 Reding time: 9.00 m to 9.5 m (5 minutes) Writing time: 9.5 m to 0.45 m ( hour 0 minutes) PART I MULTIPLE-CHICE
More informationSPECIALIST MATHEMATICS
Victorian Certificate of Education 06 SUPERVISOR TO ATTACH PROCESSING LABEL HERE Letter STUDENT NUMBER SPECIALIST MATHEMATICS Section Written examination Monday 7 November 06 Reading time:.5 am to.00 noon
More informationSAINT IGNATIUS COLLEGE
SAINT IGNATIUS COLLEGE Directions to Students Tril Higher School Certificte 0 MATHEMATICS Reding Time : 5 minutes Totl Mrks 00 Working Time : hours Write using blue or blck pen. (sketches in pencil). This
More informationMathematics Extension Two
Student Number 04 HSC TRIAL EXAMINATION Mthemtics Etension Two Generl Instructions Reding time 5 minutes Working time - hours Write using blck or blue pen Bord-pproved clcultors my be used Write your Student
More informationYear 12 Mathematics Extension 2 HSC Trial Examination 2014
Yer Mthemtics Etension HSC Tril Emintion 04 Generl Instructions. Reding time 5 minutes Working time hours Write using blck or blue pen. Blck pen is preferred. Bord-pproved clcultors my be used A tble of
More informationMASTER CLASS PROGRAM UNIT 4 SPECIALIST MATHEMATICS WEEK 11 WRITTEN EXAMINATION 2 SOLUTIONS SECTION 1 MULTIPLE CHOICE QUESTIONS
MASTER CLASS PROGRAM UNIT 4 SPECIALIST MATHEMATICS WEEK WRITTEN EXAMINATION SOLUTIONS FOR ERRORS AND UPDATES, PLEASE VISIT WWW.TSFX.COM.AU/MC-UPDATES SECTION MULTIPLE CHOICE QUESTIONS QUESTION QUESTION
More informationSPECIALIST MATHEMATICS
Victorian Certificate of Education 08 SUPERVISOR TO ATTACH PROCESSING LABEL HERE Letter STUDENT NUMBER SPECIALIST MATHEMATICS Section Written examination Monday November 08 Reading time: 3.00 pm to 3.5
More informationSPECIALIST MATHEMATICS
Victorian Certificate of Education 08 SUPERVISOR TO ATTACH PROCESSING LABEL HERE Letter STUDENT NUMBER SPECIALIST MATHEMATICS Section Written examination Wednesday 6 June 08 Reading time: 0.00 am to 0.5
More informationSPECIALIST MATHEMATICS
Victorian Certificate of Education 07 SUPERVISOR TO ATTACH PROCESSING LABEL HERE Letter STUDENT NUMBER SPECIALIST MATHEMATICS Section Written examination Monday 3 November 07 Reading time: 3.00 pm to 3.5
More informationMATHEMATICAL METHODS
Victorian Certificate of Education 018 SUPERVISOR TO ATTACH PROCESSING LABEL HERE Letter STUDENT NUMBER MATHEMATICAL METHODS Written examination 1 Friday 1 June 018 Reading time:.00 pm to.15 pm (15 minutes)
More informationMathematics Extension 2
S Y D N E Y B O Y S H I G H S C H O O L M O O R E P A R K, S U R R Y H I L L S 005 HIGHER SCHOOL CERTIFICATE TRIAL PAPER Mthemtics Extension Generl Instructions Totl Mrks 0 Reding Time 5 Minutes Attempt
More informationMATHEMATICAL METHODS (CAS) Written examination 1
Victorian Certificate of Education 2010 SUPERVISOR TO ATTACH PROCESSING LABEL HERE STUDENT NUMBER Letter Figures Words MATHEMATICAL METHODS (CAS) Written examination 1 Friday 5 November 2010 Reading time:
More informationSummer Work Packet for MPH Math Classes
Summer Work Pcket for MPH Mth Clsses Students going into Pre-clculus AC Sept. 018 Nme: This pcket is designed to help students sty current with their mth skills. Ech mth clss expects certin level of number
More informationMathematics Extension 1
04 Bored of Studies Tril Emintions Mthemtics Etension Written by Crrotsticks & Trebl. Generl Instructions Totl Mrks 70 Reding time 5 minutes. Working time hours. Write using blck or blue pen. Blck pen
More informationMATHEMATICAL METHODS
Victorian Certificate of Education 2016 SUPERVISOR TO ATTACH PROCESSING LABEL HERE Letter STUDENT NUMBER MATHEMATICAL METHODS Written examination 1 Wednesday 2 November 2016 Reading time: 9.00 am to 9.15
More informationMathematics Extension 2
00 HIGHER SCHOOL CERTIFICATE EXAMINATION Mthemtics Etension Generl Instructions Reding time 5 minutes Working time hours Write using blck or blue pen Bord-pproved clcultors my be used A tble of stndrd
More informationMATHEMATICAL METHODS (CAS) Written examination 1
Victorian Certificate of Education 2008 SUPERVISOR TO ATTACH PROCESSING LABEL HERE STUDENT NUMBER Letter Figures Words MATHEMATICAL METHODS (CAS) Written examination 1 Friday 7 November 2008 Reading time:
More informationMATHEMATICAL METHODS (CAS)
Victorian Certificate of Education 2015 SUPERVISOR TO ATTACH PROCESSING LABEL HERE Letter STUDENT NUMBER MATHEMATICAL METHODS (CAS) Written examination 1 Wednesday 4 November 2015 Reading time: 9.00 am
More informationHigher Checklist (Unit 3) Higher Checklist (Unit 3) Vectors
Vectors Skill Achieved? Know tht sclr is quntity tht hs only size (no direction) Identify rel-life exmples of sclrs such s, temperture, mss, distnce, time, speed, energy nd electric chrge Know tht vector
More informationHIGHER SCHOOL CERTIFICATE EXAMINATION MATHEMATICS 3 UNIT (ADDITIONAL) AND 3/4 UNIT (COMMON) Time allowed Two hours (Plus 5 minutes reading time)
HIGHER SCHOOL CERTIFICATE EXAMINATION 998 MATHEMATICS 3 UNIT (ADDITIONAL) AND 3/4 UNIT (COMMON) Time llowed Two hours (Plus 5 minutes reding time) DIRECTIONS TO CANDIDATES Attempt ALL questions ALL questions
More informationActual Formula Test #1 Test #2 Formula. (x h) 2 + (y k) 2 = r 2 General equation of a circle
Actul Formul Test # Test # Formul ( + b)( b + b ) 3 + b 3 = ( b)( + b + b ) 3 b 3 = x = b ± b 4c f(x) = f( x) f( x) = f(x) Qurtic Formul Test for even functions Test for o functions (x h) + (y k) = r Generl
More informationLinear Inequalities: Each of the following carries five marks each: 1. Solve the system of equations graphically.
Liner Inequlities: Ech of the following crries five mrks ech:. Solve the system of equtions grphiclly. x + 2y 8, 2x + y 8, x 0, y 0 Solution: Considerx + 2y 8.. () Drw the grph for x + 2y = 8 by line.it
More informationFall 2017 Exam 1 MARK BOX HAND IN PART PIN: 17
Fll 7 Exm problem MARK BOX points HAND IN PART 3-5=x5 NAME: Solutions PIN: 7 % INSTRUCTIONS This exm comes in two prts. () HAND IN PART. Hnd in only this prt. () STATEMENT OF MULTIPLE CHOICE PROBLEMS.
More informationWarm-up for Honors Calculus
Summer Work Assignment Wrm-up for Honors Clculus Who should complete this pcket? Students who hve completed Functions or Honors Functions nd will be tking Honors Clculus in the fll of 018. Due Dte: The
More informationTime : 3 hours 03 - Mathematics - March 2007 Marks : 100 Pg - 1 S E CT I O N - A
Time : hours 0 - Mthemtics - Mrch 007 Mrks : 100 Pg - 1 Instructions : 1. Answer ll questions.. Write your nswers ccording to the instructions given below with the questions.. Begin ech section on new
More informationIntroduction and Review
Chpter 6A Notes Pge of Introuction n Review Derivtives y = f(x) y x = f (x) Evlute erivtive t x = : y = x x= f f(+h) f() () = lim h h Geometric Interprettion: see figure slope of the line tngent to f t
More information2008 Mathematical Methods (CAS) GA 3: Examination 2
Mthemticl Methods (CAS) GA : Exmintion GENERAL COMMENTS There were 406 students who st the Mthemticl Methods (CAS) exmintion in. Mrks rnged from to 79 out of possible score of 80. Student responses showed
More informationHIGHER SCHOOL CERTIFICATE EXAMINATION MATHEMATICS 4 UNIT (ADDITIONAL) Time allowed Three hours (Plus 5 minutes reading time)
HIGHER SCHOOL CERTIFICATE EXAMINATION 999 MATHEMATICS UNIT (ADDITIONAL) Time llowed Three hours (Plus 5 minutes reding time) DIRECTIONS TO CANDIDATES Attempt ALL questions ALL questions re of equl vlue
More informationSpring 2017 Exam 1 MARK BOX HAND IN PART PIN: 17
Spring 07 Exm problem MARK BOX points HAND IN PART 0 5-55=x5 0 NAME: Solutions 3 0 0 PIN: 7 % 00 INSTRUCTIONS This exm comes in two prts. () HAND IN PART. Hnd in only this prt. () STATEMENT OF MULTIPLE
More informationThomas Whitham Sixth Form
Thoms Whithm Sith Form Pure Mthemtics Unit C Alger Trigonometry Geometry Clculus Vectors Trigonometry Compound ngle formule sin sin cos cos Pge A B sin Acos B cos Asin B A B sin Acos B cos Asin B A B cos
More informationax bx c (2) x a x a x a 1! 2!! gives a useful way of approximating a function near to some specific point x a, giving a power-series expansion in x
Elementr mthemticl epressions Qurtic equtions b b b The solutions to the generl qurtic eqution re (1) b c () b b 4c (3) Tlor n Mclurin series (power-series epnsion) The Tlor series n n f f f n 1!! n! f
More informationMATHEMATICAL METHODS (CAS) PILOT STUDY
Victorian Certificate of Education 2004 SUPERVISOR TO ATTACH PROCESSING LABEL HERE MATHEMATICAL METHODS (CAS) PILOT STUDY Written examination 2 (Analysis task) Monday 8 November 2004 Reading time: 9.00
More informationMathematics Extension 2
00 HIGHER SCHOOL CERTIFICATE EXAMINATION Mthemtics Extension Generl Instructions Reding time 5 minutes Working time hours Write using blck or blue pen Bord-pproved clcultors m be used A tble of stndrd
More informationTO: Next Year s AP Calculus Students
TO: Net Yer s AP Clculus Students As you probbly know, the students who tke AP Clculus AB nd pss the Advnced Plcement Test will plce out of one semester of college Clculus; those who tke AP Clculus BC
More informationExploring parametric representation with the TI-84 Plus CE graphing calculator
Exploring prmetric representtion with the TI-84 Plus CE grphing clcultor Richrd Prr Executive Director Rice University School Mthemtics Project rprr@rice.edu Alice Fisher Director of Director of Technology
More information( x )( x) dx. Year 12 Extension 2 Term Question 1 (15 Marks) (a) Sketch the curve (x + 1)(y 2) = 1 2
Yer Etension Term 7 Question (5 Mrks) Mrks () Sketch the curve ( + )(y ) (b) Write the function in prt () in the form y f(). Hence, or otherwise, sketch the curve (i) y f( ) (ii) y f () (c) Evlute (i)
More informationMathematics for Physicists and Astronomers
PHY472 Dt Provided: Formul sheet nd physicl constnts Dt Provided: A formul sheet nd tble of physicl constnts is ttched to this pper. DEPARTMENT OF PHYSICS & Autumn Semester 2009-2010 ASTRONOMY DEPARTMENT
More informationIndividual Contest. English Version. Time limit: 90 minutes. Instructions:
Elementry Mthemtics Interntionl Contest Instructions: Individul Contest Time limit: 90 minutes Do not turn to the first pge until you re told to do so. Write down your nme, your contestnt numer nd your
More informationSULIT /2 3472/2 Matematik Tambahan Kertas 2 2 ½ jam 2009 SEKOLAH-SEKOLAH MENENGAH ZON A KUCHING
SULIT 1 347/ 347/ Mtemtik Tmbhn Kerts ½ jm 009 SEKOLAH-SEKOLAH MENENGAH ZON A KUCHING PEPERIKSAAN PERCUBAAN SIJIL PELAJARAN MALAYSIA 009 MATEMATIK TAMBAHAN Kerts Du jm tig puluh minit JANGAN BUKA KERTAS
More informationMath 190 Chapter 5 Lecture Notes. Professor Miguel Ornelas
Mth 19 Chpter 5 Lecture Notes Professor Miguel Ornels 1 M. Ornels Mth 19 Lecture Notes Section 5.1 Section 5.1 Ares nd Distnce Definition The re A of the region S tht lies under the grph of the continuous
More informationChapter 1 - Functions and Variables
Business Clculus 1 Chpter 1 - Functions nd Vribles This Acdemic Review is brought to you free of chrge by preptests4u.com. Any sle or trde of this review is strictly prohibited. Business Clculus 1 Ch 1:
More informationUNIVERSITY OF BOLTON SCHOOL OF ENGINEERING B.ENG (HONS) ELECTRICAL AND ELECTRONIC ENGINEERING EXAMINATION SEMESTER /2018
ENG005 B.ENG (HONS) ELECTRICAL AND ELECTRONIC ENGINEERING EXAMINATION SEMESTER 1-017/018 MODULE NO: EEE4001 Dte: 19Jnury 018 Time:.00 4.00 INSTRUCTIONS TO CANDIDATES: There re SIX questions. Answer ANY
More informationThe Fundamental Theorem of Calculus Part 2, The Evaluation Part
AP Clculus AB 6.4 Funmentl Theorem of Clculus The Funmentl Theorem of Clculus hs two prts. These two prts tie together the concept of integrtion n ifferentition n is regre by some to by the most importnt
More informationMATHEMATICAL METHODS (CAS) PILOT STUDY
Victorian CertiÞcate of Education 2005 SUPERVISOR TO ATTACH PROCESSING LABEL HERE STUDENT NUMBER Letter Figures Words MATHEMATICAL METHODS (CAS) PILOT STUDY Written examination 2 (Analysis task) Monday
More informationPhysicsAndMathsTutor.com
1. A uniform circulr disc hs mss m, centre O nd rdius. It is free to rotte bout fixed smooth horizontl xis L which lies in the sme plne s the disc nd which is tngentil to the disc t the point A. The disc
More informationAP * Calculus Review
AP * Clculus Review The Fundmentl Theorems of Clculus Techer Pcket AP* is trdemrk of the College Entrnce Emintion Bord. The College Entrnce Emintion Bord ws not involved in the production of this mteril.
More informationOverview of Calculus
Overview of Clculus June 6, 2016 1 Limits Clculus begins with the notion of limit. In symbols, lim f(x) = L x c In wors, however close you emn tht the function f evlute t x, f(x), to be to the limit L
More informationApplied. Grade 9 Assessment of Mathematics. Released assessment Questions
Applie Gre 9 Assessment of Mthemtics 21 Relese ssessment Questions Recor your nswers to the multiple-choice questions on the Stuent Answer Sheet (21, Applie). Plese note: The formt of this booklet is ifferent
More information( β ) touches the x-axis if = 1
Generl Certificte of Eduction (dv. Level) Emintion, ugust Comined Mthemtics I - Prt B Model nswers. () Let f k k, where k is rel constnt. i. Epress f in the form( ) Find the turning point of f without
More informationTABLE OF CONTENTS 3 CHAPTER 1
TABLE OF CONTENTS 3 CHAPTER 1 Set Lnguge & Nottion 3 CHAPTER 2 Functions 3 CHAPTER 3 Qudrtic Functions 4 CHAPTER 4 Indices & Surds 4 CHAPTER 5 Fctors of Polynomils 4 CHAPTER 6 Simultneous Equtions 4 CHAPTER
More informationA LEVEL TOPIC REVIEW. factor and remainder theorems
A LEVEL TOPIC REVIEW unit C fctor nd reminder theorems. Use the Fctor Theorem to show tht: ) ( ) is fctor of +. ( mrks) ( + ) is fctor of ( ) is fctor of + 7+. ( mrks) +. ( mrks). Use lgebric division
More informationMATHEMATICAL METHODS (CAS) Written examination 2
Victorian CertiÞcate of Education 2007 SUPERVISOR TO ATTACH PROCESSING LABEL HERE Figures Words STUDENT NUMBER Letter MATHEMATICAL METHODS (CAS) Written examination 2 Monday 12 November 2007 Reading time:
More informationLoudoun Valley High School Calculus Summertime Fun Packet
Loudoun Vlley High School Clculus Summertime Fun Pcket We HIGHLY recommend tht you go through this pcket nd mke sure tht you know how to do everything in it. Prctice the problems tht you do NOT remember!
More informationKeys to Success. 1. MC Calculator Usually only 5 out of 17 questions actually require calculators.
Keys to Success Aout the Test:. MC Clcultor Usully only 5 out of 7 questions ctully require clcultors.. Free-Response Tips. You get ooklets write ll work in the nswer ooklet (it is white on the insie)
More informationFirst Semester Review Calculus BC
First Semester Review lculus. Wht is the coordinte of the point of inflection on the grph of Multiple hoice: No lcultor y 3 3 5 4? 5 0 0 3 5 0. The grph of piecewise-liner function f, for 4, is shown below.
More informationCalculus AB Section I Part A A CALCULATOR MAY NOT BE USED ON THIS PART OF THE EXAMINATION
lculus Section I Prt LULTOR MY NOT US ON THIS PRT OF TH XMINTION In this test: Unless otherwise specified, the domin of function f is ssumed to e the set of ll rel numers for which f () is rel numer..
More informationEdexcel GCE Core Mathematics (C2) Required Knowledge Information Sheet. Daniel Hammocks
Edexcel GCE Core Mthemtics (C) Required Knowledge Informtion Sheet C Formule Given in Mthemticl Formule nd Sttisticl Tles Booklet Cosine Rule o = + c c cosine (A) Binomil Series o ( + ) n = n + n 1 n 1
More informationWhen e = 0 we obtain the case of a circle.
3.4 Conic sections Circles belong to specil clss of cures clle conic sections. Other such cures re the ellipse, prbol, n hyperbol. We will briefly escribe the stnr conics. These re chosen to he simple
More informationExam 1 September 21, 2012 Instructor: Timothy Martin
PHY 232 Exm 1 Sept 21, 212 Exm 1 September 21, 212 Instructor: Timothy Mrtin Stuent Informtion Nme n section: UK Stuent ID: Set #: Instructions Answer the questions in the spce provie. On the long form
More informationPREVIOUS EAMCET QUESTIONS
CENTRE OF MASS PREVIOUS EAMCET QUESTIONS ENGINEERING Two prticles A nd B initilly t rest, move towrds ech other, under mutul force of ttrction At n instnce when the speed of A is v nd speed of B is v,
More informationAP Calculus BC Review Applications of Integration (Chapter 6) noting that one common instance of a force is weight
AP Clculus BC Review Applictions of Integrtion (Chpter Things to Know n Be Able to Do Fin the re between two curves by integrting with respect to x or y Fin volumes by pproximtions with cross sections:
More informationPractice Final. Name: Problem 1. Show all of your work, label your answers clearly, and do not use a calculator.
Nme: MATH 2250 Clculus Eric Perkerson Dte: December 11, 2015 Prctice Finl Show ll of your work, lbel your nswers clerly, nd do not use clcultor. Problem 1 Compute the following limits, showing pproprite
More informationLesson 1: Quadratic Equations
Lesson 1: Qudrtic Equtions Qudrtic Eqution: The qudrtic eqution in form is. In this section, we will review 4 methods of qudrtic equtions, nd when it is most to use ech method. 1. 3.. 4. Method 1: Fctoring
More informationHomework Problem Set 1 Solutions
Chemistry 460 Dr. Jen M. Stnr Homework Problem Set 1 Solutions 1. Determine the outcomes of operting the following opertors on the functions liste. In these functions, is constnt..) opertor: / ; function:
More informationE S dition event Vector Mechanics for Engineers: Dynamics h Due, next Wednesday, 07/19/2006! 1-30
Vector Mechnics for Engineers: Dynmics nnouncement Reminders Wednesdy s clss will strt t 1:00PM. Summry of the chpter 11 ws posted on website nd ws sent you by emil. For the students, who needs hrdcopy,
More informationMathematics Higher Block 3 Practice Assessment A
Mthemtics Higher Block 3 Prctice Assessment A Red crefully 1. Clcultors my be used. 2. Full credit will be given only where the solution contins pproprite working. 3. Answers obtined from reding from scle
More informationx dx does exist, what does the answer look like? What does the answer to
Review Guie or MAT Finl Em Prt II. Mony Decemer th 8:.m. 9:5.m. (or the 8:3.m. clss) :.m. :5.m. (or the :3.m. clss) Prt is worth 5% o your Finl Em gre. NO CALCULATORS re llowe on this portion o the Finl
More informationFinal Exam - Review MATH Spring 2017
Finl Exm - Review MATH 5 - Spring 7 Chpter, 3, nd Sections 5.-5.5, 5.7 Finl Exm: Tuesdy 5/9, :3-7:pm The following is list of importnt concepts from the sections which were not covered by Midterm Exm or.
More informationPhysics 121 Sample Common Exam 1 NOTE: ANSWERS ARE ON PAGE 8. Instructions:
Physics 121 Smple Common Exm 1 NOTE: ANSWERS ARE ON PAGE 8 Nme (Print): 4 Digit ID: Section: Instructions: Answer ll questions. uestions 1 through 16 re multiple choice questions worth 5 points ech. You
More informationSPECIALIST MATHEMATICS UNIT 2 EXAMINATION. Paper 2: Multiple Choice and Extended Answer. November 2017
Mathexams 07 Student s Name. Teacher s Name. SPECILIST MTHEMTICS UNIT EXMINTION Paper : Multiple Choice and Extended nswer This exam consists of Section and Section November 07 Reading Time: 0 minutes
More informationMATHEMATICS (Part II) (Fresh / New Course)
Sig. of Supdt... MRD-XII-(A) MATHEMATICS Roll No... Time Allowed : Hrs. MATHEMATICS Totl Mrks: 00 NOTE : There re THREE sections in this pper i.e. Section A, B nd C. Time : 0 Mins. Section A Mrks: 0 NOTE
More informationReading Time: 15 minutes Writing Time: 1 hour. Structure of Booklet. Number of questions to be answered
Reading Time: 15 minutes Writing Time: 1 hour Student Name: Structure of Booklet Number of questions Number of questions to be answered Number of marks 10 10 40 Students are permitted to bring into the
More informationCorrect answer: 0 m/s 2. Explanation: 8 N
Version 001 HW#3 - orces rts (00223) 1 his print-out should hve 15 questions. Multiple-choice questions my continue on the next column or pge find ll choices before nswering. Angled orce on Block 01 001
More informationProblem Set 2 Solutions
Chemistry 362 Dr. Jen M. Stnr Problem Set 2 Solutions 1. Determine the outcomes of operting the following opertors on the functions liste. In these functions, is constnt.).) opertor: /x ; function: x e
More informationMath& 152 Section Integration by Parts
Mth& 5 Section 7. - Integrtion by Prts Integrtion by prts is rule tht trnsforms the integrl of the product of two functions into other (idelly simpler) integrls. Recll from Clculus I tht given two differentible
More informationf a L Most reasonable functions are continuous, as seen in the following theorem:
Limits Suppose f : R R. To sy lim f(x) = L x mens tht s x gets closer n closer to, then f(x) gets closer n closer to L. This suggests tht the grph of f looks like one of the following three pictures: f
More informationIndefinite Integral. Chapter Integration - reverse of differentiation
Chpter Indefinite Integrl Most of the mthemticl opertions hve inverse opertions. The inverse opertion of differentition is clled integrtion. For exmple, describing process t the given moment knowing the
More informationA sequence is a list of numbers in a specific order. A series is a sum of the terms of a sequence.
Core Module Revision Sheet The C exm is hour 30 minutes long nd is in two sections. Section A (36 mrks) 8 0 short questions worth no more thn 5 mrks ech. Section B (36 mrks) 3 questions worth mrks ech.
More informationMathematics of Motion II Projectiles
Chmp+ Fll 2001 Dn Stump 1 Mthemtics of Motion II Projectiles Tble of vribles t time v velocity, v 0 initil velocity ccelertion D distnce x position coordinte, x 0 initil position x horizontl coordinte
More informationSect 10.2 Trigonometric Ratios
86 Sect 0. Trigonometric Rtios Objective : Understnding djcent, Hypotenuse, nd Opposite sides of n cute ngle in right tringle. In right tringle, the otenuse is lwys the longest side; it is the side opposite
More informationAM1 Mathematical Analysis 1 Oct Feb Exercises Lecture 3. sin(x + h) sin x h cos(x + h) cos x h
AM Mthemticl Anlysis Oct. Feb. Dte: October Exercises Lecture Exercise.. If h, prove the following identities hold for ll x: sin(x + h) sin x h cos(x + h) cos x h = sin γ γ = sin γ γ cos(x + γ) (.) sin(x
More informationB Veitch. Calculus I Study Guide
Clculus I Stuy Guie This stuy guie is in no wy exhustive. As stte in clss, ny type of question from clss, quizzes, exms, n homeworks re fir gme. There s no informtion here bout the wor problems. 1. Some
More informationl 2 p2 n 4n 2, the total surface area of the
Week 6 Lectures Sections 7.5, 7.6 Section 7.5: Surfce re of Revolution Surfce re of Cone: Let C be circle of rdius r. Let P n be n n-sided regulr polygon of perimeter p n with vertices on C. Form cone
More informationAlg. Sheet (1) Department : Math Form : 3 rd prep. Sheet
Ciro Governorte Nozh Directorte of Eduction Nozh Lnguge Schools Ismili Rod Deprtment : Mth Form : rd prep. Sheet Alg. Sheet () [] Find the vlues of nd in ech of the following if : ) (, ) ( -5, 9 ) ) (,
More informationM 106 Integral Calculus and Applications
M 6 Integrl Clculus n Applictions Contents The Inefinite Integrls.................................................... Antierivtives n Inefinite Integrls.. Antierivtives.............................................................
More information