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GCE MAY 2009 : A2, C2: Core Mathematics 2 (Irish Medium)

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ADVANCED SUBSIDIARY (AS) General Certificate of Education 2009 Matamaitic Aonad Meas naithe C2 ag meas n Mod l C2: AS Cro mhatamaitic 2 [AMC21] D HAOINE 22 BEALTAINE, 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 IR 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 4189.05 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) Simpligh x(3x2 + 2 + 4x 3) [1] (ii) Uaidh sin, suime il i leith x x(3x2 + 2 + 4x 3) [4] (b) Le riail an traip isiam le 6 ordan id, faigh garluach do 2 1 4 dx 0 (1 + x 2 ) [6] (i) Sainmh n tear seicheamh go hathch rsach ag un+1 = 2 un 3 an it a bhfuil u1 = 1 Faigh u2, u3 agus u4 [3] (ii) Luaigh c acu at an seiceamh seo coinbh irseach n dibh irseach. [1] D antar sraith iolra och tr th arma an tseichimh a shuime il le ch ile 1 + 2 + 4 + + .... 8 3 9 27 (iii) Faigh comhiolraitheoir an tseichimh iolra och seo. (iv) Faigh suim go h igr och an tseichimh iolra och seo. 3 [1] [2] San fhorbairt dh th armach de (1 + nx)10, t comh ifeacht x2 3 huaire chomh m r le comh ifeacht x. Faigh luach n, an it a bhfuil n 0 [6] 4189.05 2 [Turn over 4 (i) Ar an l ar id ch anna, sceitse il na cuair y = 2x agus y = 1 + 2x. Lip adaigh aon phointe suntasach ar na haiseanna. [4] T pointe P ar an chuar y = 1 + 2x , agus is 6 luach a chomhordan id y (ii) Tr d an chothrom id 1 + 2x = 6 a r iteach, faigh an chomhordan id x de P. [N ghlacfar le r iteach a fhaightear tr thriail agus fheabhs ] 5 [4] (a) Cruthaigh an t-ionannas tan + 1 1 ; tan sin cos [5] (b) R itigh an chothrom id sin2 x = 1 4 an it a bhfuil 90 , x < 90 [4] (c) R itigh an chothrom id cos 2x = 0.4 an it a bhfuil 0 , x < 4189.05 [4] 3 [Tiontaigh an leathanach 6 In F or 1 th os taispe ntar an cuar y = 4 + x2 y y = 4 + x2 4 x F or 1 (i) Faigh achar an r igi in idir an cuar y = 4 + x2, an x-ais, an y-ais agus an l ne x=1 [5] (ii) Uaidh sin, faigh achar an r igi in idir an cuar y = 4 + x2 agus an l ne y = 5 [4] 4189.05 4 [Turn over 7 An cl dach l onra at ag crann f in ph ca M, is f idir samhail a dh anamh de mar chiorcal, mar a thaispe ntar in F or 2 th os. B M A C F or 2 T na point A (2, 1), B(k, k + 5) agus C ( 1, 1) ar iml ne an chiorcail dar l rphointe M. Is AB trastomhas an chiorcail. (i) Faigh f na AC. [2] (ii) Uaidh sin, scr obh f na BC agus cruthaigh go bhfuil k = 3 [4] (iii) Faigh cothrom id an chiorcail san fhoirm (x a)2 + (y b)2 = r 2 4189.05 5 [5] [Tiontaigh an leathanach 8 Roinneann l ne AB bonn airgid ina dh chuid. T cruth ciorcail dar l rphointe O ar an bhonn mar a thaispe ntar in F or 3 th os. O x r A B F or 3 Is r ga an chiorcail agus is x raidian m id uillinn AOB. (i) Scr obh achar na mionteasc ige OAB. [1] (ii) Scr obh achar an triant in AOB. [1] Is sa ch imheas 5:1 at achar an d chuid den bhonn ar dh thaobh na l ne AB. (iii) Taispe in go bhfuil sin x = x 3 [8] SEO DEIREADH AN SCR DPH IP IR 4189.05 6 [Turn over

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Additional Info : Gce Mathematics May 2009 Assessment Unit C2 Module C2 : Core Mathematics 2 (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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