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GCE JAN 2011 : AS, C2 : Core Mathematics 2 (Irish Medium)

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ADVANCED SUBSIDIARY (AS) General Certificate of Education January 2011 Matamaitic ag meas n Mod l C2: AS Cro mhatamaitic 2 AMC21 Aonad Meas naithe C2 [AMC21] D LUAIN 24 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 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. 6080.02 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 Gabhann stua teasc g ciorcail uillinn 1.5 raidian ag a l rphointe mar a thaispe nann F or 1 anseo th os. 1.5 F or 1 Is 36 cm2 achar na teasc ige seo. (i) Faigh ga an chiorcail. [2] (ii) Faigh iml ne na teasc ige. [3] 6080.02 2 [Turn over 2 Taispe nann F or 2 anseo th os plean p irce ABCD. B C 35 120 150 m 200 m A 300 m D F or 2 (i) Faigh fad AC. [2] (ii) Faigh achar triant n ABC. [3] (iii) Faigh uillinn ADC. [3] (iv) Faigh achar na p irce. [2] 6080.02 3 [Tiontaigh an leathanach 3 Cothrom id ciorcail at anseo th os x2 2x + y2 + 4y = 4 (i) Faigh l rphointe agus ga an chiorcail. [4] Tarraing onn mac l inn tadhla chuig an chiorcal phointe A (5, 6). Tadhla onn an tadhla leis an chiorcal ag pointe B mar a thaispe ntar in F or 3 anseo th os. A B F or 3 (ii) Faigh fad AB. 4 [4] (a) (i) Sceitse il an graf de y = tan 2x it a bhfuil 180 < x < 180 [2] (ii) Luaigh peiriad an ghraif seo. [1] (iii) R itigh an chothrom id tan 2x = 3 it a bhfuil 180 < x < 180 [4] (b) Cruthaigh an t-ionannas 1 cos2 i tan i = sin i cos i 6080.02 4 [3] [Turn over 5 (a) Faigh [3] (b) T na graif y = x2 8x + 16 agus y = 4 + 6x x2 in F or 4 anseo th os. y 9 4 1 6 x F or 4 Is iad (1, 9) agus (6, 4) comhordan id na bpoint mar a dtrasna onn na cuair a ch ile. Faigh an t-achar idir an 2 chuar. 6080.02 [7] 5 [Tiontaigh an leathanach 6 (a) D antar seicheamh shainmh ni go hathch rsach ag it a bhfuil u1 5 5 (i) Faigh luach u2 agus luach u3 [2] (ii) T an seicheamh ag coinbh irsi i dtreo teorainn l. D an cothrom id agus r itigh le luach beacht l a fh il. [2] (b) N ghlacfar le r iteach a fhaightear tr thriail agus fheabhs . Fuair Liam airgead ar iasacht. Beidh ais oca ochta Liam i bhfoirm seichimh chomhbhreise. T s s sta 200 a ais oc i ndeireadh na ch ad mh osa, 195 i ndeireadh an dara m , 190 i ndeireadh an tr m agus mar sin de go mbeidh an t-airgead ais octha aige. (i) C mh ad a bheidh le hais oc aige i ndeireadh an 12 m ? (ii) C mh ad m a ghlacfaidh Liam leis an airgead go l ir a ais oc? [2] (iii) C mh ad airgid san ioml n a bheidh air a ais oc? 7 [2] [3] (a) (i) Athscr obh mar logartam singil log3 8 3 log3 x [3] (ii) Uaidh sin, r itigh an chothrom id log3 8 3 log3 x = 3 [4] (b) N ghlacfar le r iteach a fhaightear tr thriail agus fheabhs . Gach l tagann m ad 12% ar phaiste m sc in. Ba A0 achar an phaiste m sc in ar dt s. C mh ad l a bheidh i gceist le go mbeidh achar an phaiste m sc in 17 n-uaire chomh m r le A0? [4] 6080.02 6 [Turn over 8 M t (1 + ax)n = 1 4x + 7x2 + ... faigh luach a agus luach n. [10] SEO DEIREADH AN SCR DPH IP IR 6080.02 7 6080.02 [Turn over

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Additional Info : Gce Mathematics January 2011 Assessment Unit C2 Module C2 : Core Mathematics 2 (Irish Medium)
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