A Resource for Freestanding Mathematics Qualifications


 Drusilla Dorsey
 2 years ago
 Views:
Transcription
1 A pie chrt shows how somethig is divided ito prts  it is good wy of showig the proportio (or frctio) of the dt tht is i ech ctegory. To drw pie chrt:. Fid the totl umer of items.. Fid how my degrees represet ech item y dividig 360º y the totl. Put this vlue ito your clcultor s memory so tht you c recll it whe eeded. 3. Clculte the gle for ech ctegory y multiplyig the umer of degrees per item y the umer of items i the ctegory. 4. Check the gles dd up to 360º. 5. Write title to sy wht iformtio the pie chrt gives. 6. Drw circle d divide it ito sectors usig the gles you hve foud. 7. Iclude key to show wht ech sector represets or lel ech sector of the pie chrt. Work through this exmple: A shop sells differet sizes of gloves. The tle shows the percetge of gloves sold i yer tht were ech size. Size Smll Medium Lrge % of gloves sold 4% 40% 35% Extr Lrge % As the vlues re percetges, the totl must e 00% (ut check to mke sure). Ech % will e represeted y: 360 = 3.6º 00 The tle shows how to fid the first gle. Use your clcultor to check this gle, the work out the others. Check tht the totl gle is 360º The pie chrt is show here check tht its gles gree with those you hve foud. Size % of gloves sold Agle (erest º) Smll 4% = 50 Medium 40% Lrge 35% Extr Lrge % Totl 00% Glove sizes sold i shop Note Sometimes roudig the gles leds to totl gle of more or less th 360º. If this hppes, djust the gle of the lrgest sector so tht the totl is correct eg if the totl comes to 36º, tke º wy from the lrgest gle. Smll Medium Lrge Extr Lrge The Nuffield Foudtio
2 Worksheet The tle shows the umer of studets i clss who chieved ech grde. Use this dt to drw pie chrt. Accordig to your chrt which grde hd i the lrgest proportio of studets ii the smllest proportio? Grde Numer of studets Distictio 5 Merit 8 Pss 9 Fil The tle shows the results of survey i which people who moved house were sked to give the mi reso. Use this dt to drw pie chrt. Descrie riefly wht your pie chrt shows. Reso % Needed differet size of house 9 Persol (eg mrrige, divorce) 34 To move to etter re 9 Jorelted reso Other 6 3 The tle gives the popultio of differet regios of the world i 00. Drw pie chrt. Descrie riefly wht your pie chrt shows. Regio Popultio (millios) Asi 37 Afric 83 Europe 76 Lti Americ 57 North Americ 37 Ocei 3 4 The tle elow gives the popultio d re of ech coutry i the UK i 00. c Coutry Are (000 km ) Popultio (millios) Egld Norther Ireld Scotld Wles Use the re dt to drw pie chrt. Use the popultio dt to drw pie chrt. Expli wht your chrts show. The Nuffield Foudtio
3 Whe you wish to drw pie chrts from differet qutities of dt, the size of the pie chrts should reflect the qutities of dt represeted. If the first pie chrt represets totl of items d the secod represets totl of items, the the res of the pies should e proportiol to these totls. This gives: π π r r = so r r so the rdius of the secod pie should e = d r = r times the rdius of the first pie. Work through this exmple: The tle gives the umer of mle d femle officers i differet rks of the police force i Egld d Wles i 00. Rk Numer of Officers Femle Mle Costle Serget Ispector & Higher Rks Totl If pie chrts re used to illustrte this dt, the rdius of the pie chrt for mle officers should e = =. 4 times tht for femle officers The gle for ech femle officer is = 0.058º (to 3sf) 785 Check this o your clcultor the multiply y the umer of femle officers i ech rk to check the gles give i the tle elow. Rk Numer of Officers Femle Mle Costle 38º Serget 3º Ispector & Higher Rks º Totl 360º Complete the tle to give gles for ech rk for mle officers. Drw pie chrts to illustrte the dt rememer tht the rdius of the circle represetig the mle officers should e.4 times tht for the femle officers. The Nuffield Foudtio 3
4 Worksheet The umer of households i Gret Briti icresed from 8.6 millio i 97 to 4.4 millio i 00. The tle elow shows how the percetge of households of differet sizes chged over this period. Household Size Percetge i 97 Percetge i 00 Oe perso 8 9 Two people 3 34 Three people 9 6 Four people 7 4 Five people 8 5 Six or more people 6 Drw pie chrts for 97 d 00 d descrie the similrities d differeces. The tle elow shows the proportio of the mle d femle popultio i the UK of differet mritl sttus i 97 d 000. The mle popultio icresed from 7. to 8.8 millio d the femle popultio from 8.8 to 30. millio over this period. Mritl Sttus Percetge i 97 Percetge i 000 M F M F Sigle Mrried Widowed Divorced 8 9 Drw pie chrts for the mles d femles for ech of 97 d 000. Descrie the similrities d differeces. 3 The tle elow gives estimtes of the ir pollutts from differet sources i the UK i 000. Source Cro Mooxide Sulphur Dioxide Nitroge Oxides Rod Trsport 69% % 4% Idustry & Power 4% 90% 36% Other 7% 9% % Totl (thousd toes) Drw pie chrts for ech pollutt. Write prgrph descriig wht your chrts show. The Nuffield Foudtio 4
5 Techer Notes Uits Foudtio Level, Mkig sese of dt Itermedite Level, Hdlig d iterpretig dt Advced Level, Usig d pplyig sttistics. Skills used i this ctivity: drwig pie chrts y hd (or i Excel) Preprtio Studets eed to kow how to use protrctor to drw gles. Notes Studets studyig Mkig sese of dt eed oly work through the first pges. Studets studyig Hdlig d iterpretig dt re likely to eed to work through ll of this ctivity. Studets studyig Usig d pplyig sttistics will proly lredy kow how to drw simple pie chrts. They my oly eed to work through pges 3 to 5. Agles for pie chrts Pge Pge Size Agle (erest º) Smll = 50 Medium = 44 Lrge = 6 Extr Lrge 3.6 = 40 Totl 360 i Pss Grde Agle ii Fil Distictio 75º Merit 0º Pss 35º Fil 30º Reso Agle Needed differet size of house 68º Persol (eg mrrige, divorce) 3º To move to etter re 3º Jorelted reso 43º Other 94º 3 Regio Agle Asi 7º Afric 48º Europe 43º Lti Americ 3º North Americ 9º Ocei º 4, Coutry Are gles Popultio gles Egld 93º 30º Norther Ireld 0º 0º Scotld 6º 3º Wles 3º 8º The Nuffield Foudtio 5
6 Pge 3 Rk Numer of Officers Femle Mle Costle 38º 74º Serget 3º 57º Ispector & Higher Rks º 9º Totl 360º 360º Rks of femle police officers i Egld d Wles i 00 Costle Serget Ispector & Higher Rks Rks of mle police officers i Egld d Wles i 00 Costle Serget Ispector & Higher Rks r =.4r The Nuffield Foudtio 6
7 Pge 4 Household Size Agles for 97 Agles for 00 Oe perso 65º 04º Two people 5º 3º Three people 68º 58º Four people 6º 50º Five people 9º 8º Six or more people º 7º Mritl Sttus Agles for 97 Agles for 000 M F M F Sigle 86º 68º º 94º Mrried 56º 34º 95º 87º Widowed 4º 54º 4º 47º Divorced 4º 4º 9º 3º r =.5r r =.03r r 3 =.03r r 4 =.05r (very little differece) 3 Source Cro Mooxide Sulphur Dioxide Nitroge Oxides Rod Trsport 49º 4º 5º Idustry & Power 50º 34º 30º Other 6º 3º 79º r = 0.58r, r 3 = 0.60r The Nuffield Foudtio 7
n Using the formula we get a confidence interval of 80±1.64
9.52 The professor of sttistics oticed tht the rks i his course re orlly distributed. He hs lso oticed tht his orig clss verge is 73% with stdrd devitio of 12% o their fil exs. His fteroo clsses verge
More informationArithmetic Sequences
Arithmetic equeces A simple wy to geerte sequece is to strt with umber, d dd to it fixed costt d, over d over gi. This type of sequece is clled rithmetic sequece. Defiitio: A rithmetic sequece is sequece
More informationSummation Notation The sum of the first n terms of a sequence is represented by the summation notation i the index of summation
Lesso 0.: Sequeces d Summtio Nottio Def. of Sequece A ifiite sequece is fuctio whose domi is the set of positive rel itegers (turl umers). The fuctio vlues or terms of the sequece re represeted y, 2, 3,...,....
More informationRepeated multiplication is represented using exponential notation, for example:
Appedix A: The Lws of Expoets Expoets re shorthd ottio used to represet my fctors multiplied together All of the rules for mipultig expoets my be deduced from the lws of multiplictio d divisio tht you
More informationThe Fundamental Theorems of Calculus
The Fudmetl Theorems of Clculus The Fudmetl Theorem of Clculus, Prt II Recll the Tkehome Messge we metioed erlier Exmple poits out tht eve though the defiite itegrl solves the re problem, we must still
More informationA black line master of Example 3 You Try is on provided on page 10 for duplication or use with a projection system.
Grde Level/Course: Algebr Lesso/Uit Pl Nme: Geometric Sequeces Rtiole/Lesso Abstrct: Wht mkes sequece geometric? This chrcteristic is ddressed i the defiitio of geometric sequece d will help derive the
More informationA function f whose domain is the set of positive integers is called a sequence. The values
EQUENCE: A fuctio f whose domi is the set of positive itegers is clled sequece The vlues f ( ), f (), f (),, f (), re clled the terms of the sequece; f() is the first term, f() is the secod term, f() is
More informationMore About Expected Value and Variance
More Aout Expected Vlue d Vrice Pge of 5 E[ X ] Expected vlue,, hs umer of iterestig properties These re t likely to e used i this course eyod this lesso, ut my come ito ply i lter sttistics course Properties
More informations = 1 2 at2 + v 0 t + s 0
Mth A UCB, Sprig A. Ogus Solutios for Problem Set 4.9 # 5 The grph of the velocity fuctio of prticle is show i the figure. Sketch the grph of the positio fuctio. Assume s) =. A sketch is give below. Note
More informationCHAPTER 7 EXPONENTS and RADICALS
Mth 40 Bittiger 8 th Chpter 7 Pge 1 of 0 CHAPTER 7 EXPONENTS d RADICALS 7.1 RADICAL EXPRESSIONS d FUNCTIONS b mes b Exmple: Simplify. (1) 8 sice () 8 () 16 () 4 56 (4) 5 4 16 (5) 4 81 (6) 0.064 (7) 6 (8)
More informationChapter 3 Section 3 Lesson Additional Rules for Exponents
Chpter Sectio Lesso Additiol Rules for Epoets Itroductio I this lesso we ll eie soe dditiol rules tht gover the behvior of epoets The rules should be eorized; they will be used ofte i the reiig chpters
More informationReleased Assessment Questions, 2015 QUESTIONS
Relesed Assessmet Questios, 15 QUESTIONS Grde 9 Assessmet of Mthemtis Ademi Red the istrutios elow. Alog with this ooklet, mke sure you hve the Aswer Booklet d the Formul Sheet. You my use y spe i this
More informationPrealgebra 7* In your group consider the following problems:
Prelger * Group Activit # Group Memers: In our group consider the following prolems: 1) If ever person in the room, including the techer, were to shke hnds with ever other person ectl one time, how mn
More informationGaussian Elimination Autar Kaw
Gussi Elimitio Autr Kw After redig this chpter, you should be ble to:. solve set of simulteous lier equtios usig Nïve Guss elimitio,. ler the pitflls of the Nïve Guss elimitio method,. uderstd the effect
More informationMATH 90 CHAPTER 5 Name:.
MATH 90 CHAPTER 5 Nme:. 5.1 Multiplictio of Expoets Need To Kow Recll expoets The ide of expoet properties Apply expoet properties Expoets Expoets me repeted multiplictio. 3 4 3 4 4 ( ) Expoet Properties
More informationGeometric Sequences. Definition: A geometric sequence is a sequence of the form
Geometic equeces Aothe simple wy of geetig sequece is to stt with umbe d epetedly multiply it by fixed ozeo costt. This type of sequece is clled geometic sequece. Defiitio: A geometic sequece is sequece
More informationApplication: Volume. 6.1 Overture. Cylinders
Applictio: Volume 61 Overture I this chpter we preset other pplictio of the defiite itegrl, this time to fid volumes of certi solids As importt s this prticulr pplictio is, more importt is to recogize
More informationChapter 04.05 System of Equations
hpter 04.05 System of Equtios After redig th chpter, you should be ble to:. setup simulteous lier equtios i mtrix form d vicevers,. uderstd the cocept of the iverse of mtrix, 3. kow the differece betwee
More informationm n Use technology to discover the rules for forms such as a a, various integer values of m and n and a fixed integer value a.
TIth.co Alger Expoet Rules ID: 988 Tie required 25 iutes Activity Overview This ctivity llows studets to work idepedetly to discover rules for workig with expoets, such s Multiplictio d Divisio of Like
More informationMATHEMATICS FOR ENGINEERING BASIC ALGEBRA
MATHEMATICS FOR ENGINEERING BASIC ALGEBRA TUTORIAL  INDICES, LOGARITHMS AND FUNCTION This is the oe of series of bsic tutorils i mthemtics imed t begiers or yoe wtig to refresh themselves o fudmetls.
More informationMath Bowl 2009 Written Test Solutions. 2 8i
Mth owl 009 Writte Test Solutios i? i i i i i ( i)( i ( i )( i ) ) 8i i i (i ) 9i 8 9i 9 i How my pirs of turl umers ( m, ) stisfy the equtio? m We hve to hve m d d, the m ; d, the 0 m m Tryig these umers,
More informationUNIT FIVE DETERMINANTS
UNIT FIVE DETERMINANTS. INTRODUTION I uit oe the determit of mtrix ws itroduced d used i the evlutio of cross product. I this chpter we exted the defiitio of determit to y size squre mtrix. The determit
More informationShowing Recursive Sequences Converge
Showig Recursive Sequeces Coverge Itroductio My studets hve sked me bout how to prove tht recursively defied sequece coverges. Hopefully, fter redig these otes, you will be ble to tckle y such problem.
More informationMaths Assessment Year 4: Number and Place Value
Nme: Mths Assessment Yer 4: Numer nd Plce Vlue 1. Count in multiples of 6, 7, 9, 25 nd 1 000; find 1 000 more or less thn given numer. 2. Find 1,000 more or less thn given numer. 3. Count ckwrds through
More informationSquare Roots Teacher Notes
Henri Picciotto Squre Roots Techer Notes This unit is intended to help students develop n understnding of squre roots from visul / geometric point of view, nd lso to develop their numer sense round this
More informationIntroduction to Hypothesis Testing
Itroductio to Hypothesis Testig I Cosumer Reports, April, 978, the results of tste test were reported. Cosumer Reports commeted, "we do't cosider this result to be sttisticlly sigifict." At the time, Miller
More informationBinary Representation of Numbers Autar Kaw
Binry Representtion of Numbers Autr Kw After reding this chpter, you should be ble to: 1. convert bse rel number to its binry representtion,. convert binry number to n equivlent bse number. In everydy
More information8.2 Simplifying Radicals
. Simplifig Rdicls I the lst sectio we sw tht sice. However, otice tht (). So hs two differet squre roots. Becuse of this we eed to defie wht we cll the pricipl squre root so tht we c distiguish which
More informationChapter 13 Volumetric analysis (acid base titrations)
Chpter 1 Volumetric lysis (cid se titrtios) Ope the tp d ru out some of the liquid util the tp coectio is full of cid d o ir remis (ir ules would led to iccurte result s they will proly dislodge durig
More informationBasic Arithmetic TERMINOLOGY
Bsic Arithmetic TERMINOLOGY Absolute vlue: The distce of umber from zero o the umber lie. Hece it is the mgitude or vlue of umber without the sig Directed umbers: The set of itegers or whole umbers f,,,
More informationParents Guide to helping your child with Higher Maths
Prets Guide to helpig your child with Higher Mths The essece of mthemtics is ot to mke simple thigs complicted, but to mke complicted thigs simple. S. Gudder Arithmetic is beig ble to cout up to twety
More informationWe will begin this chapter with a quick refresher of what an exponent is.
.1 Exoets We will egi this chter with quick refresher of wht exoet is. Recll: So, exoet is how we rereset reeted ultilictio. We wt to tke closer look t the exoet. We will egi with wht the roerties re for
More informationLet us recall some facts you have learnt in previous grades under the topic Area.
6 Are By studying this lesson you will be ble to find the res of sectors of circles, solve problems relted to the res of compound plne figures contining sectors of circles. Ares of plne figures Let us
More informationSTUDENT S COMPANIONS IN BASIC MATH: THE SECOND. Basic Identities in Algebra. Let us start with a basic identity in algebra:
STUDENT S COMPANIONS IN BASIC MATH: THE SECOND Bsic Idetities i Algebr Let us strt with bsic idetity i lgebr: 2 b 2 ( b( + b. (1 Ideed, multiplyig out the right hd side, we get 2 +b b b 2. Removig the
More informationBasic Math Review. Numbers. Important Properties. Absolute Value PROPERTIES OF ADDITION NATURAL NUMBERS {1, 2, 3, 4, 5, }
ƒ Bsic Mth Review Numers NATURAL NUMBERS {1,, 3, 4, 5, } WHOLE NUMBERS {0, 1,, 3, 4, } INTEGERS {, 3,, 1, 0, 1,, } The Numer Line 5 4 3 1 0 1 3 4 5 Negtive integers Positive integers RATIONAL NUMBERS All
More informationLecture 15  Curve Fitting Techniques
Lecture 15  Curve Fitting Techniques Topics curve fitting motivtion liner regression Curve fitting  motivtion For root finding, we used given function to identify where it crossed zero where does fx
More information2 If a branch is prime, no other factors
Chpter 2 Multiples, nd primes 59 Find the prime of 50 by drwing fctor tree. b Write 50 s product of its prime. 1 Find fctor pir of the given 50 number nd begin the fctor tree (50 = 5 10). 5 10 2 If brnch
More information11. PYTHAGORAS THEOREM
11. PYTHAGORAS THEOREM 111 Along the Nile 2 112 Proofs of Pythgors theorem 3 113 Finding sides nd ngles 5 114 Semiirles 7 115 Surds 8 116 Chlking hndll ourt 9 117 Pythgors prolems 10 118 Designing
More informationSecondary Math 2 Honors. Unit 2 Polynomials, Exponents, Radicals & Complex Numbers
Secodr Mth Hoors Uit Polomils, Epoets, Rdicls & Comple Numbers. Addig, Subtrctig, d Multiplig Polomils Notes Moomil: A epressio tht is umber, vrible, or umbers d vribles multiplied together. Moomils ol
More informationThe Math Learning Center PO Box 12929, Salem, Oregon 97309 0929 Math Learning Center
Resource Overview Quntile Mesure: Skill or Concept: 1010Q Determine perimeter using concrete models, nonstndrd units, nd stndrd units. (QT M 146) Use models to develop formuls for finding res of tringles,
More information4 Geometry: Shapes. 4.1 Circumference and area of a circle. FM Functional Maths AU (AO2) Assessing Understanding PS (AO3) Problem Solving HOMEWORK 4A
Geometry: Shpes. Circumference nd re of circle HOMEWORK D C 3 5 6 7 8 9 0 3 U Find the circumference of ech of the following circles, round off your nswers to dp. Dimeter 3 cm Rdius c Rdius 8 m d Dimeter
More informationSection 3.3: Geometric Sequences and Series
ectio 3.3: Geometic equeces d eies Geometic equeces Let s stt out with defiitio: geometic sequece: sequece i which the ext tem is foud by multiplyig the pevious tem by costt (the commo tio ) Hee e some
More informationPicture Match Words Planets Energy Space Matter Galaxies Universe Star Time Particles Atom
Picture Mtch Words Plnets Energy Spce Mtter Glxies Universe Str Time Prticles Atom Mterils copyrighted by the University of Louisville. Eductors re free to use these mterils with the proper cknowledgement
More information1.2 Accumulation Functions: The Definite Integral as a Function
mth 3 more o the fudmetl theorem of clculus 23 2 Accumultio Fuctios: The Defiite Itegrl s Fuctio Whe we compute defiite itegrl b f (x) we get umber which we my iterpret s the et re betwee f d the xxis
More informationPopulation Distribution
Why? Popultion Distriution How does popultion distriution ffect the environment? Alsk contins over 127 million cres of untouched forest lnd. It is the lrgest stte in the United Sttes, yet with popultion
More informationSuggested Exercises from M&M Chapter 4 [Homegrown exercises begin on next page] These pages were updated on September 16
Suggested Exercises from M&M Chpter 4 [Homegrown exercises egin on next pge] These pges were updted on Septemer 16 To strt with, do some of the oddnumered exercises. nswers to ll oddnumered exercises
More informationSTRAND I: Geometry and Trigonometry. UNIT I2 Trigonometric Problems: Text * * Contents. Section. I2.1 Mixed Problems Using Trigonometry
Mthemtics SKE: STRND I UNIT I Trigonometric Prolems: Text STRND I: Geometry nd Trigonometry I Trigonometric Prolems Text ontents Section * * * I. Mixed Prolems Using Trigonometry I. Sine nd osine Rules
More informationSirindhorn International Institute of Technology Thammasat University at Rangsit
Sirindhorn Interntionl Institute of Technology Thmmst University t Rngsit School of Informtion, Computer nd Communiction Technology COURSE : ECS 204 Bsic Electricl Engineering L INSTRUCTOR : Asst. Prof.
More informationA. Description: A simple queueing system is shown in Fig. 161. Customers arrive randomly at an average rate of
Queueig Theory INTRODUCTION Queueig theory dels with the study of queues (witig lies). Queues boud i rcticl situtios. The erliest use of queueig theory ws i the desig of telehoe system. Alictios of queueig
More informationEXPONENTS AND RADICALS
Expoets d Rdicls MODULE  EXPONENTS AND RADICALS We hve lert bout ultiplictio of two or ore rel ubers i the erlier lesso. You c very esily write the followig, d Thik of the situtio whe is to be ultiplied
More informationUnit 29: Inference for TwoWay Tables
Unit 29: Inference for TwoWy Tbles Prerequisites Unit 13, TwoWy Tbles is prerequisite for this unit. In ddition, students need some bckground in significnce tests, which ws introduced in Unit 25. Additionl
More informationName: Period GL SSS~ Dates, assignments, and quizzes subject to change without advance notice. Monday Tuesday Block Day Friday
Ne: Period GL UNIT 5: SIMILRITY I c defie, idetify d illustrte te followig ters: Siilr Cross products Scle Fctor Siilr Polygos Siilrity Rtio Idirect esureet Rtio Siilrity Stteet ~ Proportio Geoetric Me
More informationReasoning to Solve Equations and Inequalities
Lesson4 Resoning to Solve Equtions nd Inequlities In erlier work in this unit, you modeled situtions with severl vriles nd equtions. For exmple, suppose you were given usiness plns for concert showing
More informationSection 54 Trigonometric Functions
5 Trigonometric Functions Section 5 Trigonometric Functions Definition of the Trigonometric Functions Clcultor Evlution of Trigonometric Functions Definition of the Trigonometric Functions Alternte Form
More informationm, where m = m 1 + m m n.
Lecture 7 : Moments nd Centers of Mss If we hve msses m, m 2,..., m n t points x, x 2,..., x n long the xxis, the moment of the system round the origin is M 0 = m x + m 2 x 2 + + m n x n. The center of
More informationMATHEMATICS SYLLABUS SECONDARY 7th YEAR
Europe Schools Office of the SecretryGeerl Pedgogicl developmet Uit Ref.: 201101D41e2 Orig.: DE MATHEMATICS SYLLABUS SECONDARY 7th YEAR Stdrd level 5 period/week course Approved y the Joit Techig
More informationCHAPTER 7: Central Limit Theorem: CLT for Averages (Means)
CHAPTER 7: Cetral Limit Theorem: CLT for Averages (Meas) X = the umber obtaied whe rollig oe six sided die oce. If we roll a six sided die oce, the mea of the probability distributio is X P(X = x) Simulatio:
More informationLines and angles. Name. Use a ruler and pencil to draw: a 2 parallel lines. c 2 perpendicular lines. b 2 intersecting lines. Complete the following:
Lines nd s 1 Use ruler nd pencil to drw: 2 prllel lines 2 intersecting lines c 2 perpendiculr lines 2 Complete the following: drw in the digonls on this shpe mrk the interior s on this shpe c mrk equl
More informationPicture Match Words. Strobe pictures. Stopping distance. Following. Safety
Tuesdy: Picture Mtch + Spelling Pyrmid Homework [the hndout for it is two pges down] Mterils: 1 bord + 1 set of words per 2 students (totl: 12 of ech) Routine: () once the Pictionry is completed; pirs
More informationScalar Line Integrals
Mth 3B Discussion Session Week 5 Notes April 6 nd 8, 06 This week we re going to define new type of integrl. For the first time, we ll be integrting long something other thn Eucliden spce R n, nd we ll
More informationLecture 3 Gaussian Probability Distribution
Lecture 3 Gussin Probbility Distribution Introduction l Gussin probbility distribution is perhps the most used distribution in ll of science. u lso clled bell shped curve or norml distribution l Unlike
More informationUnit 8 Rational Functions
Uit 8 Ratioal Fuctios Algebraic Fractios: Simplifyig Algebraic Fractios: To simplify a algebraic fractio meas to reduce it to lowest terms. This is doe by dividig out the commo factors i the umerator ad
More informationTwo special Righttriangles 1. The
Mth Right Tringle Trigonometry Hndout B (length of )  c  (length of side ) (Length of side to ) Pythgoren s Theorem: for tringles with right ngle ( side + side = ) + = c Two specil Righttringles. The
More informationUnit 6 Solving Oblique Triangles  Classwork
Unit 6 Solving Oblique Tringles  Clsswork A. The Lw of Sines ASA nd AAS In geometry, we lerned to prove congruence of tringles tht is when two tringles re exctly the sme. We used severl rules to prove
More informationFourier Series (Lecture 13)
Fourier Series (Lecture 3) ody s Objectives: Studets will be ble to: ) Determie the Fourier Coefficiets for periodic sigl b) Fid the stedystte respose for system forced with geerl periodic forcig Rrely
More informationN Mean SD Mean SD Shelf # Shelf # Shelf #
NOV xercises smple of 0 different types of cerels ws tken from ech of three grocery store shelves (1,, nd, counting from the floor). summry of the sugr content (grms per serving) nd dietry fiber (grms
More informationTwo hours UNIVERSITY OF MANCHESTER SCHOOL OF COMPUTER SCIENCE. Date: Friday 16 th May 2008. Time: 14:00 16:00
COMP20212 Two hours UNIVERSITY OF MANCHESTER SCHOOL OF COMPUTER SCIENCE Digitl Design Techniques Dte: Fridy 16 th My 2008 Time: 14:00 16:00 Plese nswer ny THREE Questions from the FOUR questions provided
More informationA REA AND INTEGRALS. 1 Sigma Notation 2. 2 Area 7. 3 The Definite Integral 16
ALTERNATIVE TREATMENT: A REA AND INTEGRALS Sigm Nottio Are 7 The Defiite Itegrl Reprited with permissio from Clculus: Erl Trscedetls, Third Editio Jmes Stewrt 995 Brooks/Cole Pulishig Comp, A divisio of
More informationGENERAL APPLICATION FOR FARM CLASSIFICATION
SCHEDULE 1 (section 1) Plese return to: DEADLINE: Plese return this form to your locl BC Assessment office y Octoer 31. Assessment Roll Numer(s) GENERAL APPLICATION FOR FARM CLASSIFICATION Section 23 (1)
More information1+(dy/dx) 2 dx. We get dy dx = 3x1/2 = 3 x, = 9x. Hence 1 +
Mth.9 Em Solutions NAME: #.) / #.) / #.) /5 #.) / #5.) / #6.) /5 #7.) / Totl: / Instructions: There re 5 pges nd totl of points on the em. You must show ll necessr work to get credit. You m not use our
More informationAddition and subtraction of rational expressions
Lecture 5. Addition nd subtrction of rtionl expressions Two rtionl expressions in generl hve different denomintors, therefore if you wnt to dd or subtrct them you need to equte the denomintors first. The
More informationAQA STATISTICS 1 REVISION NOTES
AQA STATISTICS 1 REVISION NOTES AVERAGES AND MEASURES OF SPREAD www.mathsbox.org.uk Mode : the most commo or most popular data value the oly average that ca be used for qualitative data ot suitable if
More informationA Resource for Freestanding Mathematics Qualifications Working with %
Ca you aswer these questios? A savigs accout gives % iterest per aum.. If 000 is ivested i this accout, how much will be i the accout at the ed of years? A ew car costs 16 000 ad its value falls by 1%
More informationCypress Creek High School IB Physics SL/AP Physics B 2012 2013 MP2 Test 1 Newton s Laws. Name: SOLUTIONS Date: Period:
Nme: SOLUTIONS Dte: Period: Directions: Solve ny 5 problems. You my ttempt dditionl problems for extr credit. 1. Two blocks re sliding to the right cross horizontl surfce, s the drwing shows. In Cse A
More informationAssuming all values are initially zero, what are the values of A and B after executing this Verilog code inside an always block? C=1; A <= C; B = C;
B26 Appendix B The Bsics of Logic Design Check Yourself ALU n [Arthritic Logic Unit or (rre) Arithmetic Logic Unit] A rndomnumer genertor supplied s stndrd with ll computer systems Stn KellyBootle,
More informationRational Functions. Rational functions are the ratio of two polynomial functions. Qx bx b x bx b. x x x. ( x) ( ) ( ) ( ) and
Rtionl Functions Rtionl unctions re the rtio o two polynomil unctions. They cn be written in expnded orm s ( ( P x x + x + + x+ Qx bx b x bx b n n 1 n n 1 1 0 m m 1 m + m 1 + + m + 0 Exmples o rtionl unctions
More informationSmall Business Cloud Services
Smll Business Cloud Services Summry. We re thick in the midst of historic sechnge in computing. Like the emergence of personl computers, grphicl user interfces, nd mobile devices, the cloud is lredy profoundly
More informationWords Symbols Diagram. abcde. a + b + c + d + e
Logi Gtes nd Properties We will e using logil opertions to uild mhines tht n do rithmeti lultions. It s useful to think of these opertions s si omponents tht n e hooked together into omplex networks. To
More informationSINCLAIR COMMUNITY COLLEGE DAYTON, OHIO DEPARTMENT SYLLABUS FOR COURSE IN MAT 1355  INTERMEDIATE ALGEBRA I (3 CREDIT HOURS)
SINCLAIR COMMUNITY COLLEGE DAYTON OHIO DEPARTMENT SYLLABUS FOR COURSE IN MAT 1355  INTERMEDIATE ALGEBRA I (3 CREDIT HOURS) 1. COURSE DESCRIPTION: Ftorig; opertios with polyoils d rtiol expressios; solvig
More informationNQF Level: 2 US No: 7480
NQF Level: 2 US No: 7480 Assessment Guide Primry Agriculture Rtionl nd irrtionl numers nd numer systems Assessor:.......................................... Workplce / Compny:.................................
More information1. Find the zeros Find roots. Set function = 0, factor or use quadratic equation if quadratic, graph to find zeros on calculator
AP Clculus Finl Review Sheet When you see the words. This is wht you think of doing. Find the zeros Find roots. Set function =, fctor or use qudrtic eqution if qudrtic, grph to find zeros on clcultor.
More informationChapter 18 Superposition and Standing Waves
hpter 8 Superpositio d Stdig Wves 8. Superpositio d Iterereces y '(, y(, + y (, Overlppig wves lgericlly dd to produce resultt wve (or et wve). Overlppig wves do ot i y wy lter the trvel o ech other. Superpositio
More informationPREMIUMS CALCULATION FOR LIFE INSURANCE
ls of the Uiversity of etroşi, Ecoomics, 2(3), 202, 97204 97 REIUS CLCULTIO FOR LIFE ISURCE RE, RI GÎRBCI * BSTRCT: The pper presets the techiques d the formuls used o itertiol prctice for estblishig
More informationPresent and future value formulae for uneven cash flow Based on performance of a Business
Advces i Mgemet & Applied Ecoomics, vol., o., 20, 9309 ISSN: 7927544 (prit versio), 7927552 (olie) Itertiol Scietific Press, 20 Preset d future vlue formule for ueve csh flow Bsed o performce of Busiess
More informationLiveEngage Agent Guide. Version 1.0
Agent Guide Version 1.0 Tle of Contents Contents LOGGING IN... 3 NAVIGATING LIVEENGAGE... 4 Visitor List, Connection Are, Enggement Br & Going Online... 4 ENGAGEMENT OPTIONS... 5 Tking n Enggment... 5
More informationSect Simplifying Radical Expressions. We can use our properties of exponents to establish two properties of radicals:
70 Sect 11.  Simplifyig Rdicl Epressios Cocept #1 Multiplictio d Divisio Properties of Rdicls We c use our properties of epoets to estlish two properties of rdicls: () 1/ 1/ 1/ & ( ) 1/ 1/ 1/ Multiplictio
More informationDescriptive statistics deals with the description or simple analysis of population or sample data.
Descriptive statistics Some basic cocepts A populatio is a fiite or ifiite collectio of idividuals or objects. Ofte it is impossible or impractical to get data o all the members of the populatio ad a small
More informationTHE GEOMETRIC SERIES
Mthemtics Revisio Guides The Geometic eies Pge of M.K. HOME TUITION Mthemtics Revisio Guides Level: A / A Level AQA : C Edexcel: C OCR: C OCR MEI: C THE GEOMETRIC ERIE Vesio :. Dte: 8060 Exmples 7 d
More informationWarmup for Differential Calculus
Summer Assignment Wrmup for Differentil Clculus Who should complete this pcket? Students who hve completed Functions or Honors Functions nd will be tking Differentil Clculus in the fll of 015. Due Dte:
More informationSquare & Square Roots
Squre & Squre Roots Squre : If nuber is ultiplied by itself then the product is the squre of the nuber. Thus the squre of is x = eg. x x Squre root: The squre root of nuber is one of two equl fctors which
More informationfraction arithmetic. For example, consider this problem the 1995 TIMSS Trends in International Mathematics and Science Study:
In recent yers, mthemtics eductors hve begun to relize tht understnding frctions nd frctionl rithmetic is the gtewy to dvnced high school mthemtics. 1 Yet, US students continue to do poorly when rnked
More information4.5 The Converse of the
Pge 1 of. The onverse of the Pythgoren Theorem Gol Use the onverse of Pythgoren Theorem. Use side lengths to lssify tringles. Key Words onverse p. 13 grdener n use the onverse of the Pythgoren Theorem
More informationhp calculators HP 30S Base Conversions Numbers in Different Bases Practice Working with Numbers in Different Bases
Numbers i Differet Bases Practice Workig with Numbers i Differet Bases Numbers i differet bases Our umber system (called HiduArabic) is a decimal system (it s also sometimes referred to as deary system)
More informationP.3 Polynomials and Factoring. P.3 an 1. Polynomial STUDY TIP. Example 1 Writing Polynomials in Standard Form. What you should learn
33337_0P03.qp 2/27/06 24 9:3 AM Chpter P Pge 24 Prerequisites P.3 Polynomils nd Fctoring Wht you should lern Polynomils An lgeric epression is collection of vriles nd rel numers. The most common type of
More informationOr more simply put, when adding or subtracting quantities, their uncertainties add.
Propgtion of Uncertint through Mthemticl Opertions Since the untit of interest in n eperiment is rrel otined mesuring tht untit directl, we must understnd how error propgtes when mthemticl opertions re
More informationUnit 6: Exponents and Radicals
Eponents nd Rdicls : The Rel Numer Sstem Unit : Eponents nd Rdicls Pure Mth 0 Notes Nturl Numers (N):  counting numers. {,,,,, } Whole Numers (W):  counting numers with 0. {0,,,,,, } Integers (I): 
More informationNet Change and Displacement
mth 11, pplictions motion: velocity nd net chnge 1 Net Chnge nd Displcement We hve seen tht the definite integrl f (x) dx mesures the net re under the curve y f (x) on the intervl [, b] Any prt of the
More informationDetermining the sample size
Determiig the sample size Oe of the most commo questios ay statisticia gets asked is How large a sample size do I eed? Researchers are ofte surprised to fid out that the aswer depeds o a umber of factors
More informationTHE ARITHMETIC OF INTEGERS.  multiplication, exponentiation, division, addition, and subtraction
THE ARITHMETIC OF INTEGERS  multiplicatio, expoetiatio, divisio, additio, ad subtractio What to do ad what ot to do. THE INTEGERS Recall that a iteger is oe of the whole umbers, which may be either positive,
More informationContent Objectives: After completing the activity, students will gain experience of informally proving Pythagoras Theorem
Pythgors Theorem S Topic 1 Level: Key Stge 3 Dimension: Mesures, Shpe nd Spce Module: Lerning Geometry through Deductive Approch Unit: Pythgors Theorem Student ility: Averge Content Ojectives: After completing
More information