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GCE JUN 2006 : A2, C4: Core Mathematics 4 (Irish Medium)

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ADVANCED General Certificate of Education 2006 Matamaitic Aonad Meas naithe C4 ag meas n Mod l C4: Cro mhatamaitic 4 [AMC41] D ARDAOIN 8 MEITHEAMH, 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 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 log e z AMC4S6 1558.04 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 2 Is iad 2i j + 3k, 2i + j k agus i + 5j 2k na su omh-veicteoir at ag na reanna faoi seach den triant n ABC. Cruthaigh go bhfuil dronuillinn ag B sa triant n. [7] Faigh cothrom id an normal don chuar x2 4xy + y2 = 13 ag an phointe (2, 1). [9] 3 D an sceitse den chuar y = sec x an it a bhfuil Y x Y , agus taispe in na luachanna t bhachtacha ar na haiseanna. [4] 4 Faigh 4xe 2x dx 5 [5] (i) Ag tos le foirmle na n-uillinneacha comhshuite do cos(A + B), taispe in go bhfuil 2 cos2 1 + cos 2 [3] (ii) s id an ionada ocht x = 2 sin , n bealach ar bith eile, lena thaispe int go bhfuil 1 2 x 2 dx = 0 AMC4S6 1558.04 2 2+ 4 [12] [Turn over 6 R itigh an chothrom id dhifre lach 1 dy x y = 2 dx x 1 ag glacadh leis go mbeidh y = 4 nuair at x = 2 7 [9] Agus babhla dhearadh, s idtear achar a rothla tear tr 2 raidian thart ar an x-ais mar bhonn don dearadh. An t-achar a s idtear, t s idir an cuar y = 4 x + 2, an x-ais, agus na l nte x = 0 agus x = a, mar a thaispe ntar in F or 1 anseo th os. y (cm) y = 4 x + 2 0 a x (cm) F or 1 (i) Faigh slonn i dt arma a do thoilleadh an bhabhla. [7] Caithfidh toilleadh an bhabhla bheith cothrom le 1000 cm3 (ii) Faigh luach a ceart go dt ionad amh in de dheach lacha. AMC4S6 1558.04 3 [7] [Tiontaigh an leathanach 8 (i) Ag glacadh leis go bhfuil 2 sin x + 2 3 cos x = r sin x + 3 faigh r. [2] Sainmh n tear an fheidhm f mar f : x 2 sin x + 2 3 cos x 0 Y x Y 2 (ii) Luaigh raon f. [1] (iii) Agus sceitse de f in s id agat, n ar bhealach ar bith eile, m nigh cad chuige nach bhfuil inbh arta ag f. [2] Sainmh n tear an fheidhm g mar g : x 2 sin x + 2 3 cos x aYxYb nuair at 0 Y a I b Y 2 T an raon do g mar an gc anna leis an raon do f agus t an fheidhm inbh artach g 1 ann. (iv) Scr obh luach a agus luach b. [2] (v) Faigh an fheidhm inbh artach g 1 [5]

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Additional Info : Gce Mathematics June 2006 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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