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GCE JAN 2011 : A2, C4: Core Mathematics 4 (Irish Medium)

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ADVANCED General Certificate of Education January 2011 Matamaitic ag meas n Mod l C4: Cro mhatamaitic 4 AMC41 Aonad Meas naithe C4 [AMC41] D HAOINE 28 EAN IR, MAIDIN 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 IRI 111531 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 loge z 6136.02 Freagair gach ceann de na hocht 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 (a) (i) Scr obh 1 ( x + 1)( x 1) ina ph irtchod in. [4] (ii) Uaidh sin, faigh 1 dx ( x + 1)( x 1) [4] (b) Agus suime il tr ph irteanna in s id, faigh x cos x dx 2 [5] Anseo th os t cothrom id veicteoireach na l ne PQ r = (2i + 3j) + (i j 2k). T treo-veicteoir (4i + 5j + k) ag an l ne PR. Faigh an uillinn idir l ne PQ agus l ne PR. 3 [7] R itigh an chothrom id cos x = 2 sin (x + 60 ) an it a bhfuil 180 < x < 180 6136.02 [7] 2 [Turn over 4 Tugtar cuar go paraim adrach mar x = cot y = cosec (i) Taispe in gurb y2 = 1 + x2 cothrom id Chairt iseach an chuair. [2] (ii) Uaidh sin, faigh f na beachta na dtadhlaithe go dt an cuar ag na point mar a bhfuil x = 1 5 [7] (i) Taispe in go bhfuil tan x sec4 x tan x sec2 x + tan3 x sec2 x [3] (ii) Uaidh sin, agus tr d an ionada ocht u = tan x a s id, n ar dh igh eile, faigh 4 tan x sec 4 x dx [7] 0 6 R itigh an chothrom id dhifre lach (1 + x 2 ) dy = x(1 + y ) dx le y a fh il i dt arma x, ag glacadh leis go mbeidh x = 0 nuair at y = 0 6136.02 3 [11] [Tiontaigh an leathanach 7 Is f idir samhail a dh anamh do bhabhla gloine tr d an chuar x 6 y =e a rothl idir x = 0 agus x = 9 cm, mar a thaispe ntar in F or 1 anseo th os, tr 2 raidian thart ar an x-ais. x y = e6 y 0 9 x F or 1 Faigh an uastoirt is f idir leis an ghloine a choinne il. 8 [7] Sainmh n tear an fheidhm f mar f : x sin x an it a bhfuil <x< 2 2 (i) Scr obh an fheidhm inbh artach f 1 agus luaigh an fearann agus an raon aici. [4] Sainmh n tear feidhm g mar g : x |x| an it a bhfuil x R (ii) Faigh an fheidhm chomhshuite gf agus luaigh an raon aici. [4] (iii) Uaidh sin, sceitse il an graf de y = gf(x) 6136.02 [3] [Turn over

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Additional Info : Gce Mathematics January 2011 Assessment Unit C4 Module C4 : Core Mathematics (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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