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GCE MAY 2006 : A2, C3: Core Mathematics 3 (Irish Medium)

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ADVANCED General Certificate of Education 2006 Matamaitic Aonad Meas naithe C3 ag meas n Mod l C3: Cro mhatamaitic 3 [AMC31] D C ADAOIN 24 BEALTAINE, IARN IN AM 1 uair 30 n im ad. TREOIR D IARRTH IR Scr obh d Uimhir L rionaid agus d Uimhir Iarrth ra ar an Leabhr n Freagra at leis seo. Freagair gach ceann de na hocht gceist. Taispe in go soil ir forbairt ioml n do fhreagra . Ba cheart na freagra a thabhairt ceart go dt 3 fhigi r bhun sacha mura ndeirtear a mhalairt. T cead agat ireamh n grafach n eola och a s id sa ph ip ar seo. EOLAS D IARRTH IR Is 75 an marc ioml n don ph ip ar seo. L ir onn figi ir ar thaobh na l imhe deise de leathanaigh na marcanna at ag dul do gach ceist n do gach cuid de cheist. T c ip den leabhr n Foirml agus T bla Matamaitice leis seo. S os tr d an ph ip ar seo is ln z an nodaireacht logartamach a s idtear it a dtuigtear go bhfuil ln z log e z AMC3S6 782.04 Freagair gach ceann de na hocht gceist. Taispe in go soil ir forbairt ioml n do fhreagra . Ba cheart freagra a thabhairt ceart go dt 3 fhigi r bhun sacha mura ndeirtear a mhalairt. 1 Scr obh mar ph irtchod in 5x + 2 x2 4 2 [6] T p irc suite idir abhainn agus dh bh thar. Caithfear garmheastach n a fh il ar achar na p irce. F adtar samhail a dh anamh de ch rsa na habhann tr d an chuar y = 2 sin x idir x = 0 agus x = agus de na b ithre mar an d l ne dh reacha y = 0 agus x = mar a 2 2 thaispe ntar in F or 1 anseo th os. b thar y 2 0 inn a abh b thar 0 y=0 x =p 2 F or 1 Is i gcilim adair a thomhaistear na faid. Agus calcalas in s id agat, d an garmheastach n ar achar na p irce. AMC3S6 782.04 2 [6] [Turn over 3 (i) Ar an l ar id ch anna d an sceits de na graif and y = ex agus y = x2 [3] N l ach pointe trasnaithe amh in ag na graif agus f adtar x comhordan id an phointe a fh il tr d an chothrom id seo th os a r iteach ex x2 = 0 (ii) Cruthaigh go bhfuil an luach seo de x idir x = 1 agus x = 0 [3] (iii) Ag glacadh le x = 0.6 mar an ch ad gharmheastach n den luach seo de x, s id an modh Newton-Raphson dh uair le garmheastach n is fearr a fh il. [5] AMC3S6 782.04 3 [Tiontaigh an leathanach 4 (a) In F or 2 anseo th os t sceitse de ghraf na feidhme y = f(x). y 3 x 4 F or 2 Ar l ar id leithleacha d an sceits de na graif: (i) y = 1f(x + 1); 3 [2] (ii) y = f( 2x). [2] (b) In F or 3 anseo th os taispe ntar na graif de y = | 2x 1| agus y = 3 y = |2x 1| y y=3 x F or 3 Faigh comhordan id na bpoint trasnaithe acu. AMC3S6 782.04 4 [6] [Turn over 5 I dturgnamh bitheola ochta glactar leis go dtugtar l on, N, na miocrorg nach at i substaint ag am T uair an chloig leis an chothrom id N = abT an it ar tairisigh iad a agus b. (i) Ag glacadh leis go mbeidh N = 60 nuair a bheidh T = 0 agus go mbeidh N = 480 nuair a bheidh T = 3, faigh luach a agus luach b. [3] (ii) Faigh an luach a bheidh ag T nuair a bheidh N = 1040 6 [6] R itigh an chothrom id 5 sec x 4 = sec x an it a bhfuil Y x Y 7 [7] (a) Difre il i leith x x2 (i) 3+x [4] (ii) 2x ln x [3] (iii) sin3 4x [4] (b) Suime il i leith x 1 x2 + e3x + 2x AMC3S6 782.04 5 [5] [Tiontaigh an leathanach 8 x2 9 (a) Simpligh (x + 3) x2 5x + 6 [3] (b) Agus an teoirim dh th armach in s id agat forbair i gcumhachta m adaitheacha de x 1+x 1 2 (1 x)2 suas go dt an t arma in x2 agus an t arma sin san ireamh. [7] SEO DEIREADH AN SCR DPH IP IR AMC3S6 782.04 6AMC3S6 782 6[Turn over

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Additional Info : Gce Mathematics May 2006 Assessment Unit C3 Module C3 : Core Mathematics 3 (Irish Medium)
Tags : General Certificate of Education, A Level and AS Level, uk, council for the curriculum examinations and assessment, gce exam papers, gce a level and as level exam papers , gce past questions and answer, gce past question papers, ccea gce past papers, gce ccea past papers

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