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GCE JAN 2011 : A2, C3: Core Mathematics 3 (Irish Medium)

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ADVANCED General Certificate of Education January 2011 Matamaitic ag meas n Mod l C3: AS Cro mhatamaitic 3 AMC31 Aonad Meas naithe C3 [AMC31] D HAOINE 14 EAN IR, 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 seacht 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 IRI 111025 Is 75 an marc ioml n don ph ip ar seo. L ir onn figi ir idir l ib n 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 Matamaitice agus T bla ar f il. 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 logez 6218.02 Freagair gach ceann de na seacht gceist. Taispe in go soil ir forbairt ioml n do fhreagra . Ba ch ir freagra a thabhairt ceart go dt 3 fhigi r bhun sacha mura ndeirtear a mhalairt. 1 Simpligh x2 + x 6 x2 9 2 x 2 4 [5] Sainmh n tear cuar de r ir na gcothrom id paraim adracha seo a leanas x = sin u + 1 y = 2 cos u 1 (i) Faigh cothrom id chairt iseach an chuair seo. [4] (ii) Faigh na point mar a dtrasna onn an cuar seo an x-ais. [4] 6218.02 2 [Turn over 3 Taispe nann F or 1 anseo th os an graf de y = ln x y = ln x y A x F or 1 (i) Sceitse il an graf de y = ln (x + 2) agus taispe in an asamt it cheartingearach. Scr obh comhordan id A , omh phointe A. [3] (ii) Sceitse il an graf de y = | ln (x + 2) | [2] (iii) Faigh luachanna beachta x d bhfuil | ln (x + 2) | = 2 4 [5] R itigh an chothrom id tan2 u = 1 sec u it a bhfuil 0 < u < 2 6218.02 [8] 3 [Tiontaigh an leathanach 5 Difre il i leith x x2 (i) ln x (ii) x sec x [3] (iii) cot3 (2x) 6 [4] [5] Is f idir samhail a dh anamh den trasghearradh tr leathph opa i bp irc sc t la leis an chuar ex 4 + y= x +1 5 idir x = 0 agus x = 3 mh adar mar a thaispe ntar in F or 2 anseo th os: y 5 0 1 2 3 x F or 2 (i) Agus Riail Simpson le 6 stiall in s id, faigh garluach don achar sc thaithe. [6] (ii) Faigh luach beacht an achair sc thaithe. 6218.02 4 [7] [Turn over 7 (i) Agus p irtchod in in s id, taispe in go bhfuil 2 x 1 1 = (1 + 2 x )(3 + x ) 1 + 2 x 3 + x [7] (ii) Uaidh sin, agus an teoirim dh th armach in s id, forbair, 2 x (1 + 2 x )(3 + x ) i gcumhachta ardaitheacha de x, suas go dt an t arma in x2 agus an t arma sin san ireamh. (iii) Faigh raon na luachanna de x d bhfuil an slonn bail . SEO DEIREADH AN SCR DPH IP IR 6218.02 5 [9] [3] 6218.02

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Additional Info : Gce Mathematics January 2011 Assessment Unit C3 Module C3 : Core Mathematics 3 (Irish Medium)
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