ࡱ> #%"c ,bjbjZWZW 828=`\8=`\  TTTTThhhhTh*.k. 9*;*;*;*;*;*;*$ ,.^_*9Tkk_*TT*,TT9*9*rI'TI(Dx)ΊL'%**0*' /1 /I( /TI(_*_*ON* / > : Arholiadau Ysgoloriaeth Ionawr 2018 Scholarship Examinations January 2018 Amser a ganiateir : 2 awr MATHEMATEG Time allowed: 2 hours MATHEMATICS Gellwch roi cynnig ar unrhyw rai or cwestiynau. Rhoddir credyd am atebion cyflawn. [Cymerwch fod g = 10 m.s-2] 1. Swm y 3 term cyntaf mewn cyfres rifyddeg yw 45 a swm y 5 term cyntaf yw 105. Darganfyddwch swm y 6 term cyntaf. 2. Darganfyddwch holl ddatrysiadaur hafaliad  EMBED Equation.3  3. Cyfrifwch yr integryn pendant  EMBED Equation.3  4. Darganfyddwch hafaliad y tangiad ir cylch  EMBED Equation.3  ar y pwynt (3, 8), ar normal ir cylch or pwynt (10, 1). 5. Mynegwch  EMBED Equation.3  mewn ffracsiynau rhannol. 6. Ehangwch  EMBED Equation.3  mewn pwerau esgynnol o x hyd at y term yn x3. Am ba werthoedd o x maer broses o ehangu yn ddilys? Darganfyddwch frasamcan o ail isradd 1.05 trwy ddefnyddior ddau derm cyntaf. Pa mor gywir yw eich brasamcan? 7. Aildrefnwch y mynegiad  EMBED Equation.3  i roi mynegiad am x. Trwy hyn datryswch  EMBED Equation.3  8. Mae gan fertigau A, B, C triongl fectorau safle a, b, c. Maer pwynt X yn gorwedd ar y llinell AB fel bod AX : XB = 1 : 2. Ysgrifennwch fector safle X yn nhermau a, b, c. Darganfyddwch yn nhermau a, b, c fector safle pwynt P syn gwahanu XC yn y gymhareb XP : PC = l : 1 - l 9. Mae corff gyda ms o 12 kg yn hongian o gortyn ysgafn. Mae r cortyn wedi ei basio dros bwli di-ffrithiant gyda phen arall y cortyn wedi ei rwymo i fs arall o 10 kg ar bln goleddol ar oledd o 60 gradd i r llorweddol. Os yw r ddau fs yn ddisymud i ddechrau, i ba gyfeiriad fydd y ddau fs yn dechrau symud? Ymhen faint o amser fydd y ms 10 kg wedi symud 2 cm? 10. Datryswch yr hafaliad differol  EMBED Equation.3  gydar gwerthoedd cychwynnol  EMBED Equation.3 . 11. Mae gan yr hapnewidyn di-dor X ffwythiant dwysedd tebygolrwydd f a ddiffinnir gan  EMBED Equation.3  Darganfyddwch y paramedr !"#GHIJKdeo       ̴̿~sk`Uh|vphrmHRsHRh|vphhmHRsHRh|vpmHRsHRh|vph'mHRsHRh|vphM"mHRsHRh|vphq"mHRsHRhMh|vpH*mHRsHRhMh|vpH*mHRsHRhWmHRsHRhMh|vpmHRsHRhMh|vpCJmHRsHRhMh|vp6mHRsHR h$hW5 h$hhIh h$hq"h$hq"mHRsHR!$JKp  w x ' ? { | gd gdK" $a$gd$a$gdhgd|vpgdhgdq"$a$gd|vp$a$gd@gdq"gd   2 3 5 6 > ? 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Tynnwch fraslun o r ffwythiant dwysedd tebygolrwydd, gan farcio ar eich braslun y cymedr a r gwyriad safonol. 12. Mae 3 pl yn cael eu dewis ar hap o flwch sy n cynnwys 5 pl goch, a 6 pl las. Cyfrifwch y tebygolrwydd a) y bydd dwy bl goch ac un bl las yn cael eu dewis (mewn rhyw drefn) b) y bydd y tair pl o r un lliw 13. Mae ms cacennau Nadolig o ffatri cacennau yn dilyn dosraniad normal gyda chymedr o 1.1kg a gwyriad safonol o 0.02kg. Cyfrifwch y tebygolrwydd y bydd ms cacen a gymerwyd ar hap o r ffatri rhwng 1.08kg a 1.14kg. >(((()*)))))))))***:*<*@*F************2+++++++++++++++++,Z,\,f,h,ͲŪઢh|vph$?mHRsHRh|vphNmHRsHRhWmHRsHRh'hmHRsHRh|vphmHRsHRhT-mHRsHRhf4mHRsHRh|vph:hmHRsHRh `mHRsHRh@mHRsHRhMh@mHRsHRhMh@6mHRsHR5h,l,n,p,,,,,,,h|vph$?OJQJmHRsHRh|vph$?mHRsHRh@mHRsHRhT-mHRsHRhIhWmHRsHRhIh'hmHRsHR 6P&P . 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