Everything Maths Grade 12

199 Pages·2012·5.5 MB·English

Everything Maths
Grade 12 Mathematics
Version 0.9 – NCS
by Siyavulaand volunteers
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Authors List
ThisbookisbasedupontheoriginalFreeHighSchoolScienceTextwhichwasentirelywritten
by volunteer academics, educators and industry professionals. Their vision was to see a cur-
riculum aligned set of mathematics and physical science textbooks which are freely available
to anybody and exist under an open copyrightlicense.
Siyavulacore team
NeelsvanderWesthuizen;AlisonJenkin;MarinavanZyl;HelenRobertson;CarlScheffler;NicoladuToit;LeonardGumani
Mudau;
OriginalFree High School ScienceTexts core team
MarkHorner;SamuelHalliday;SarahBlyth;RoryAdams;SpencerWheaton
OriginalFree High School ScienceTexts editors
JayniePadayachee;JoanneBoulle;DianaMulcahy;AnnetteNell;RenToerien;DonovanWhitfield
Siyavulaand Free High SchoolScienceTexts contributors
SarahAbel;Dr. RoryAdams;AndreaAfrica;MatthewAmundsen;BenAnhalt;PrashantArora;AmosBaloyi;BonganiBaloyi;
RaymondBarbour;Caro-JoyBarendse;RichardBaxter;TaraBeckerling;Dr.SarahBlyth;SebastianBodenstein;MartinBongers;
GarethBoxall;StephanBrandt;HannesBreytenbach;AlexBriell;WilburBritz;GraemeBroster;CraigBrown;RichardBurge;
BiancaBhmer; GeorgeCalder-Potts; EleanorCameron; RichardCase; SithembileCele; AliceChang; RichardCheng; Fanny
Cherblanc;Dr. ChristineChung;BrettCocks;StefaanConradie;RoccoCoppejans;TimCraib;AndrewCraig;TimCrombie;
DanCrytser;Dr. AnneDabrowski;LauraDaniels;GarethDavies;JenniferdeBeyer;JenniferdeBeyer;DeannedeBude;Mia
deVos; SeanDobbs; BuhleDonga; WilliamDonkin; EsmiDreyer; NicoladuToit; MatthewDuddy; FernandoDurrell; Dr.
DanDwyer;AlexEllis;TomEllis;AndrewFisher;GiovanniFranzoni;NinaGitauMuchunu;LindsayGlesener;KevinGodby;
Dr.VanessaGodfrey;TerenceGoldberg;Dr.JohanGonzalez;SaalighaGool;HemantGopal;Dr.StephanieGould;Umeshree
Govender;HeatherGray;LynnGreeff;CarineGrobbelaar;Dr.TomGutierrez;BrookeHaag;KateHadley;AlexHall;Dr.Sam
Halliday;AsheenaHanuman;Dr. NicholasHarrison;NeilHart;NicholasHatcher;JasonHayden;LauraHayward;ChoHee
Shrader;Dr. FrithaHennessy;ShaunHewitson;MillieHilgart;GrantHillebrand;NickHobbs;ChrisHoldsworth;Dr. Benne
Holwerda; Dr. MarkHorner; RobertHovden; MfandaidzaHove; JenniferHsieh; LauraHuss; Dr. MatinaJ.Rassias; Rowan
Jelley;GrantJelley;ClareJohnson;LukeJordan;TanaJoseph;Dr. FabianJutz; BrianKamanzi; Dr. LutzKampmann;Simon
Katende; Natalia Kavalenia; Nothando Khumalo; Paul Kim; Dr. Jennifer Klay; Lara Kruger; Sihle Kubheka; Andrew Kubik;
Dr. Jannie Leach; Nkoana Lebaka; Dr. Tom Leinster; Henry Liu; Christopher Loetscher; Mike Loseby; Amandla Mabona;
Malothe Mabutho; Stuart Macdonald; Dr. Anton Machacek; Tshepo Madisha; Batsirai Magunje; Dr. Komal Maheshwari;
Michael Malahe; Masoabi Malunga; Masilo Mapaila; Bryony Martin; Nicole Masureik; John Mathew; Dr. Will Matthews;
ChiedzaMatuso;JoEllenMcBride;DrMelanieDymondHarper;NikolaiMeures;RianaMeyer;FilippoMiatto;JennyMiller;
AbdulMirza;MapholoModise;CarlaMoerdyk;TshwareloMohlala;RelebohileMolaoa;MarasiMonyau;AsoganMoodaly;
JothiMoodley;RobertMoon;CalvinMoore;BhavaniMorarjee;KholofeloMoyaba;KateMurphy;EmmanuelMusonza;Tom
Mutabazi; David Myburgh; Kamie Naidu; Nolene Naidu; Gokul Nair; Vafa Naraghi; Bridget Nash; Tyrone Negus; Huw
Newton-Hill; BuntuNgcebetsha; Dr. MarkusOldenburg; ThomasODonnell; Dr. WilliamP.Heal; Dr. JayniePadayachee;
Poveshen Padayachee; Masimba Paradza; Dave Pawson; Justin Pead; Nicolette Pekeur; Sirika Pillay; Jacques Plaut; Barry
Povey;BarryPovey;AndreaPrinsloo;JosephRaimondo;SanyaRajani;AlastairRamlakan;Dr.JocelynRead;JonathanReader;
JaneReddick;Dr.MatthewReece;RazvanRemsing;LauraRichter;MaxRichter;SeanRiddle;Dr.DavidRoberts;Christopher
Roberts; Helen Robertson; Evan Robinson; Raoul Rontsch; Dr. Andrew Rose; Katie Ross; Jeanne-Mari Roux; Mark Roux;
BiancaRuddy;NitinRughoonauth;KatieRussell;StevenSam;Dr. CarlScheffler;NathanielSchwartz;DuncanScott;Helen
Seals;RelebohileSefako;Prof. SergeyRakityansky;SandraSerumaga-Zake;PaulShangase;CameronSharp;IanSherratt;Dr.
JamesShort;RogerSieloff;BrandonSim;BongaSkozana;ClareSlotow;BradleySmith;GregSolomon;NicholasSpaull;Dr.
AndrewStacey; Dr. JimStasheff; MikeStay; MikeStringer; MasixoleSwartbooi; TshenoloTau; TimTeatro; BenTho.epson;
ShenTian;XolaniTimbile;RobertTorregrosa;JimmyTseng;TimvanBeek;NeelsvanderWesthuizen;FransvanEeden;Pierre
vanHeerden;Dr. MarcovanLeeuwen;MarinavanZyl;PieterVergeer;RizmariVersfeld;MfundoVezi;MpilonhleVilakazi;
IngridvonGlehn;TamaravonGlehn;KosmavonMaltitz;HelenWaugh;LeandraWebb;Dr. DawnWebber;MichelleWen;
Dr. AlexanderWetzler;Dr. SpencerWheaton;VivianWhite;Dr. GeraldWigger;HarryWiggins;HeatherWilliams;Wendy
Williams;JulieWilson;TimothyWilson;AndrewWood;EmmaWormauld;Dr.SahalYacoob;JeanYoussef;EwaldZietsman
Everything Maths
Mathematics is commonly thought of as being about numbers but mathematics is actually a language!
Mathematicsisthelanguagethatnaturespeaks tousin. Aswelearntounderstandandspeakthislan-
guage,wecandiscovermanyofnature’ssecrets. Justasunderstandingsomeone’slanguageisnecessary
to learn more about them, mathematics is required to learn about all aspects of the world – whether it
isphysicalsciences,lifesciencesorevenfinanceandeconomics.
Thegreatwritersandpoetsoftheworldhavetheabilitytodrawonwordsandputthemtogetherinways
thatcantellbeautifulorinspiringstories. Inasimilarway,onecandrawonmathematicstoexplainand
createnewthings. Manyofthemoderntechnologiesthathaveenrichedourlivesaregreatlydependent
on mathematics. DVDs, Google searches, bank cards with PIN numbers are just some examples. And
justaswordswerenotcreatedspecificallytotellastorybuttheirexistenceenabledstoriestobetold,so
themathematicsusedtocreatethesetechnologieswasnotdevelopedforitsownsake,butwasavailable
tobedrawnonwhenthetimeforitsapplicationwasright.
There is in fact not an area of life that is not affected by mathematics. Many of the most sought after
careers depend on the use of mathematics. Civil engineers use mathematics to determine how to best
designnewstructures;economistsusemathematicstodescribeandpredicthowtheeconomywillreact
to certain changes; investors use mathematics to price certain types of shares or calculate how risky
particular investments are; software developers use mathematics for many of the algorithms (such as
Googlesearchesanddatasecurity)thatmakeprogrammesuseful.
But, even in our daily lives mathematics is everywhere – in our use of distance, time and money.
Mathematicsisevenpresentinart, designandmusicasitinformsproportionsandmusicaltones. The
greaterourabilitytounderstandmathematics,thegreaterourabilitytoappreciatebeautyandeverything
in nature. Far from being just a cold and abstract discipline, mathematics embodies logic, symmetry,
harmony and technological progress. More than any other language, mathematics is everywhere and
universalinitsapplication.
SeeintroductoryvideobyDr. MarkHorner: VMiwdatwww.everythingmaths.co.za
More than a regular textbook
Everything Maths is not just a Mathematics textbook. It has everything you expect from your regular
printed school textbook, but comes with a whole lot more. For a start, you can download or read it
on-lineonyourmobilephone,computeroriPad,whichmeansyouhavetheconvenienceofaccessing
itwhereveryouare.
We know that some things are hard to explain in words. That is why every chapter comes with video
lessons and explanations which help bring the ideas and concepts to life. Summary presentations at
theendofeverychapterofferanoverviewofthecontentcovered,withkeypointshighlightedforeasy
revision.
Alltheexercisesinsidethebooklinktoaservicewhereyoucangetmorepractice,seethefullsolution
ortestyourskillslevelonmobileandPC.
We are interested in what you think, wonder about or struggle with as you read through the book and
attempt the exercises. That is why we made it possible for you to use your mobile phone or computer
todigitallypinyourquestiontoapageandseewhatquestionsandanswersotherreaderspinnedup.
Everything Maths on your mobile or PC
Youcanhavethistextbookathandwhereveryouare–whetherathome,onthethetrainoratschool.
Just browse to the on-line version of Everything Maths on your mobile phone, tablet or computer. To
readitoff-lineyoucandownloadaPDFore-bookversion.
Toreadordownloadit,gotowww.everythingmaths.co.zaonyourphoneorcomputer.
Using the icons and short-codes
Inside the book you will find these icons to help you spot where videos, presentations, practice tools
and more help exist. The short-codes next to the icons allow you to navigate directly to the resources
on-linewithouthavingtosearchforthem.
(A123) Godirectlytoasection
(V123) Video,simulationorpresentation
(P123) Practiceandtestyourskills
(Q123) Askforhelporfindananswer
Towatchthevideoson-line,practiseyourskillsorpostaquestion,gototheEverythingMathswebsite
atwww.everythingmaths.co.zaonyourmobileorPCandentertheshort-codeinthenavigationbox.
Video lessons
Look out for the video icons inside the book. These will take you to video lessons that help bring the
ideas and concepts on the page to life. Get extra insight, detailed explanations and worked examples.
See the concepts in action and hear real people talk about how they use maths and science in their
work.
Seevideoexplanation (Video: V123)
Video exercises
Whereverthereareexercisesinthebookyouwillseeiconsandshort-codesforvideosolutions,practice
andhelp. Theseshort-codeswilltakeyoutovideosolutionsofselectexercisestoshowyoustep-by-step
howtosolvesuchproblems.
Seevideoexercise (Video: V123)
Youcangetthesevideosby:
viewingthemon-lineonyourmobileorcomputer
•
downloadingthevideosforoff-lineviewingonyourphoneorcomputer
•
orderingaDVDtoplayonyourTVorcomputer
•
downloadingthemoff-lineoverBluetoothorWi-Fifromselectoutlets
•
To view, download, or for more information, visit the Everything Maths website on your phone or
computeratwww.everythingmaths.co.za
Practice and test your skills
One of the best ways to prepare for your tests and exams is to practice answering the same kind of
questions you will be tested on. At every set of exercises you will see a practice icon and short-code.
This on-line practice for mobile and PC will keep track of your performance and progress, give you
feedbackonareaswhichrequiremoreattentionandsuggestwhichsectionsorvideostolookat.
Seemorepractice (QM123)
Topracticeandtestyourskills:
Gotowww.everythingmaths.co.zaonyourmobilephoneorPCandentertheshort-code.
Answers to your questions
Have you ever had a question about a specific fact, formula or exercise in your textbook and wished
you could just ask someone? Surely someone else in the country must have had the same question at
thesameplaceinthetextbook.
Database of questions and answers
We invite you to browse our database of questions and answer for every sections and exercises in the
book. Find the short-code for the section or exercise where you have a question and enter it into the
short-codesearchboxonthewebormobi-siteatwww.everythingmaths.co.zaor
www.everythingscience.co.za. Youwillbedirectedtoallthequestionspreviouslyaskedandanswered
forthatsectionorexercise.
(A123) Visitthissectiontopostorviewquestions
(Q123) Questionsorhelpwithaspecificquestion
Ask an expert
Can’t find your question or the answer to it in the questions database? Then we invite you to try our
service where you can send your question directly to an expert who will reply with an answer. Again,
usetheshort-codeforthesectionorexerciseinthebooktoidentifyyourproblemarea.