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GCE MAY 2006 : AS, C1: Core Mathematics 1(Irish Medium)

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ADVANCED SUBSIDIARY (AS) General Certificate of Education 2006 Matamaitic Aonad Meas naithe C1 ag meas n Mod l C1: Cro mhatamaitic 1 [AMC11] D LUAIN 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. N l s ceadmhach aon is a s id sa ph ip ar seo le h ireamh a dh anamh. 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. AAMC1S6 1565.03 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. N l s ceadmhach aon is a s id sa ph ip ar seo le h ireamh a dh anamh. 1 Faigh dy it a bhfuil dx y = 2x3 3x2 + 4x 6 2 [4] (a) Athscr obh an slonn th os agus ainmneoir c imheasta aige 2 + 3 3 1 [4] (b) Simpligh chomh fada agus is f idir (x2 16) x+3 2 (x + 6x + 9) x 4 [4] (i) Faigh an chothrom id at ag an l ne dh reach L a cheangla onn na point (1, 3) agus (2, 1). [4] (ii) Faigh cothrom id na l ne P, ingearach le L, a th ann tr d an phointe (6, 2). [3] (iii) Faigh na comhordan id at ag an phointe trasnaithe de na l nte L agus P. 3 [3] AAMC1S6 1565.03 2 [Turn over (i) Faigh amach c mh ad fr amh r adach at ag an chothrom id x2 + 5 = 4x. [3] (ii) Scr obh x2 4x + 5 san fhoirm (x a)2 + b [3] (iii) Uaidh sin scr obh osluach x2 4x + 5 agus an luach de x ag a dtarla onn s . [2] (iv) Uaidh sin d an sceitse den ghraf y = x2 4x + 5 4 [2] 5 Agus luas de x m le san uair faoi, t ann carr fad y m le ar 1 ghal n amh in de dhiosail, it a bhfuil y = x (100 x) 60 Agus calcalas in s id agat, faigh an luas is ceart a bheith faoin charr le go rachaidh s an t-uasfhad ar 1 ghal n amh in de dhiosail, agus uaidh sin faigh an t-uasfhad seo. [7] 6 T fortheach le t g il ag a mbeidh bonn dronuilleogach. Caithfidh fad an fhorth bheith n os m n an leithead de 10 m. B odh leithead an fhorth = x. (i) Scr obh slonn do achar an fhorth i dt arma x. [2] Caithfidh achar an fhorth bheith n os l n 375 m2 (ii) D an agothrom id in x agus r itigh lena fh il amach cad raon na luachanna a d fh adfadh a bheith ag leithead an fhorth . AAMC1S6 1565 3 [7] [Tiontaigh an leathanach 1 7 M t f(x) = 8x 2 x 1 (i) faigh f(9) [2] (ii) r itigh f(x) = 0 [4] (iii) faigh f ' (x), nuair is f ' (x) an d orthach de f(x) i leith x [2] (iv) faigh f ' (4) [2] 8 T facht ir (x 1) ag an slonn 2x3 + ax2 + bx + c Is 1 an fu lleach a bheidh ann nuair a roinnfear ar (x 2) . Is 14 an fu lleach a bheidh ann nuair a roinnfear ar (x 3) . (i) Faigh a, b agus c. [11] (ii) Uaidh sin r itigh an chothrom id 2x3 6x2 + 5x 1 = 0, agus f g do fhreagra i bhfoirm shurda. AAMC1S6 1565.04 4 [6] [Turn over

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Additional Info : Gce Mathematics May 2006 Assessment Unit C1 Module C1:Core Mathematics 1 (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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