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UK GCSE 2010 : Mathematics Paper II (Irish Medium)

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General Certificate of Secondary Education 2010 P ip ar 2 Meicnic agus Statistic G0302 Matamaitic Bhreise [G0302] D C ADAOIN 19 BEALTAINE, MAIDIN AM 2 uair an chloig. TREOIR D IARRTH IR Scr obh d Uimhir L rionaid agus d Uimhir Iarrth ra ar an Leabhr n Freagra agus ar an Leabhr n Freagra Breise at ar f il. Freagair gach ceann den d cheist d ag. Ag deireadh an scr daithe seo ceangail an Leabhr n Freagra Breise den Leabhr n Freagra leis an scor n comhaid at ar f il. EOLAS D IARRTH IR Is 100 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 cead agat ireamh n a s id. T c ip den liosta foirml ar f il. Glac leis go bhfuil g = 10 m/s2 nuair a bh onn s de dh th. 5494.05 Freagair gach ceann den d cheist d ag. 1 (Tr d s os an cheist seo l ir onn i agus j aonadveicteoir comhthreomhar le sraith d aiseanna caighde nacha x y.) T pac iste dar mais 4 kg ar fos i gcothroma ocht ar phl na m n cothrom nach faoi ghn omh 3 fh rsa chothrom nacha (2i 3j) N (7i 5j) N agus (ai + bj) N an it ar tairisigh iad a agus b. (i) Faigh luach a agus luach b. [3] Baintear na 3 fh rsa ar shi l anois agus cuirtear f rsa amh in (8i 6j) N ina n- it agus tosa onn an pac iste ag bogadh feadh an phl na. (ii) Faigh luasgh ar an phac iste i bhfoirm veicteora. 2 [1] Thaifead na an m id breosla a d s id gach ceann de 38 carr ar an turas c anna. Shl naigh s gach taifead ceart go dt an l tear is c ngara . T achoimre ar na tortha in T bla 1. T bla 1 Breosla a s ideadh (l tir) An l on carranna 8 9 6 10 11 8 12 14 12 15 17 9 18 19 3 Ag s id F or 1 sa Leabhr n Freagra Breise, tarraing histeagram leis an eolas seo a l iri . Lip adaigh gach ais go soil ir. [5] 5494.05 2 [Turn over 3 Nuair a bh dalta i bp irc spraoi, thaifead siad an t-am, t n im ad, a bh orthu fanacht le rotha ocht a fh il ar an Roth M r. T achoimre ar na tortha in T bla 2. T bla 2 Am (t n im ad) An l on dalta 0 t<2 2 t<4 4 t<6 6 t<8 35 36 33 8 t < 12 12 t < 15 19 6 Faigh meastach n ar airmhe n na n-amanna. 4 2 [5] Chroch Se n bloc adhmaid dar mais M kg as s le il le dh shreang n adroma neamh-ins nte mar a thaispe nann F or 2. 42 54 35 N Mg F or 2 Bh an bloc ar crochadh i gcothroma ocht. Bh sreang n amh in claonta ar 42 leis an chothrom n agus ba 35 N an teannas sa sreang n seo. Bh an dara sreang n claonta ar 54 leis an chothrom n. Faigh, agus scr obh na freagra ceart go dt 2 ionad de dheach lacha, (i) an teannas sa dara sreang n, [3] (ii) mais an bhloic adhmaid. [3] 5494.05 3 [Tiontaigh an leathanach 5 (a) Rinne dalta staid ar ar na h iseanna ags la i mbaile m r. Ba 22.8 me n agus ba 4.3 diall caighde nach na sonra a bhailigh na dalta . (i) Cad athraitheas na sonra seo? [1] Le compar id a dh anamh le staid ar a rinneadh i mbaile m r eile inar bail odh sonra comhchos la, cheartaigh na dalta gach m r sonra tr 10 a shuimi l i agus a iolr faoi 2 ansin. (ii) Faigh an me n agus an diall caighde nach do na sonra i ndiaidh do na dalta iad a cheart . [3] (b) Is iad seo a leanas na c atad in a fuair Eibhl s sna trialacha ranga an t arma seo: 62, 72, 41, 89, 86, 72, 42, 50 C n me n (me n, m d n airmhe n) ba ch ir di a s id lena tuismitheoir a sh samh? Luaigh f th le do fhreagra agus taispe in na h irimh a dh anann t . 6 [3] Bh buachaill ina sheasamh ar bhalc in 8 m adar n os airde n talamh cothrom nach. Chaith s liathr id go ceartingearach in airde faoi luas 6 m/s. (i) Taispe in gurb 9.8 m an airde is m os cionn an talaimh a shroich an liathr id. [2] Glac leis n r bhuail an liathr id an bhalc in agus ag teacht anuas. Faigh (ii) luas na liathr ide, ina m/s, nuair a bhuail s an talamh, [2] (iii) an t-am a d imigh thart n mheandar a chaith an buachaill an liathr id gur bhuail s an talamh. [3] 7 T na doirse i gc ras sl nd la gcosaint le gl as eochaircheapa at bunaithe ar uimhir 3 dhigit. Leis na doirse a oscailt caithfear an uimhir 3 dhigit cheart a iontr il ar an eochaircheap. Beidh an uimhir seo sa raon 000 go 999 (i) Cad an d ch lacht go bhfaighfear an uimhir cheart ar an ch ad iarracht? [2] Athra tear an uimhir gach seachtain. N cuimhin liom uimhir na seachtaine seo ach t a fhios agam gur 3 dhigit dhifri la at inti. (ii) Cad an d ch lacht go bhfaighidh m uimhir na seachtaine seo ar an ch ad iarracht? [2] (iii) Uaidh sin, cad an d ch lacht nach bhfaighidh m ar an ch ad iarracht? [1] (iv) Cad an d ch lacht nach bhfaighidh m ar an ch ad iarracht ach go bhfaighidh m ar an dara hiarracht? [4] 5494.05 4 [Turn over 8 T planc aonfhoirmeach AB dar fad 5 mh adar ina lu ar dh on r idh cothrom nach de halla sp irt agus t 1.6 m den phlanc ag gobadh amach thar imeall an d n mar a thaispe ntar in F or 3. 5m X A B 0.5 m Halla sp irt 1.6 m F or 3 Si lann cail n dar mais 54 kg feadh an phlainc fhoirceann A. Nuair a shroicheann s pointe X ar an phlanc, 0.5 m B, t an planc ar t claonadh thart ar imeall an d n. (i) Luaigh an frithghn omh ag A nuair at an planc ar t claonadh. [1] (ii) Faigh mais an phlainc. [3] Cuirtear bosca dar mais M kg ag foirceann A an phlainc. Is f idir leis an chail n lean int uirthi de bheith ag si l feadh an phlainc i dtreo B. Nuair a shroicheann s B t an planc ar t claonadh ar s. (iii) Faigh luach M. Scr obh do fhreagra ceart go dt ionad amh in de dheach lacha. 5494.05 5 [5] [Tiontaigh an leathanach 9 Eagra onn Eoin turais rotha ochta ceithre l gach seachtain. In T bla 3 t achoimre ar l on na ndaoine a ghlac p irt sna turais seo in I il 2009. T bla 3 Seachtain 1 Seachtain 2 Seachtain 3 Seachtain 4 D ardaoin 240 212 172 157 Aoine 237 208 168 148 Satharn 270 221 202 179 Domhnach 297 263 241 T na sonra seo breactha ar F or 4 sa Leabhr n Freagra Breise. (i) Faigh me in ghluaisteacha fh irsteanacha leis na sonra a dh anamh r idh. [3] (ii) Breac na me in seo in F or 4 agus tarraing an treol ne. [3] (iii) Agus aon l amh a ghlactar thaispe int go soil ir, s id an treol ne le meastach n a dh anamh ar l on na ndaoine a chuaigh ar thuras rotha ochta ar an Domhnach i seachtain 4. [4] (iv) C n tsainghluaiseacht d amshraith lena mbaineann na sonra seo? [1] 5494.05 6 [Turn over 10 T bosca dar mais 6 kg ar fos ar dhromchla garbh at claonta ar 25 leis an chothrom n mar a thaispe ntar in F or 5. 25 F or 5 T an bosca d reach ar t sleamhn s os an pl na. (i) C ipe il F or 5 agus marc il go soil ir ar do l ar id na f rsa uilig at ag feidhmi ar an bhosca. [2] (ii) Faigh frithghn omh normalach an phl na ar an bhosca. [1] (iii) Taispe in gurb 0.47, ceart go dt 2 ionad de dheach lacha, an chomh ifeacht frithchuimilte idir an bosca agus an pl na. [2] Tarraing tear an bosca suas an pl na anois le sreang n adrom neamh-ins nte a choinn tear comhthreomhar le l ne is m f na an phl na. Feidhm onn s f rsa P ni tan ar an bhosca, mar a thaispe ntar in F or 6. Gluaiseann an bosca suas an pl na faoi threoluas tairiseach. P 25 F or 6 (iv) C ipe il F or 6 agus marc il go soil ir ar do l ar id na f rsa uilig at ag feidhmi ar an bhosca anois. [1] (v) Faigh luach P. [2] M ada tear ar mh id fh rsa P agus gluaiseann an bosca suas an pl na faoi luasgh ar 3.5 m/s2. (vi) Faigh luach nua P. 5494.05 [3] 7 [Tiontaigh an leathanach 11 Taispe nann T bla 4 na sc ir a bh ag ochtar galfair i gcom rtas 2 l . T bla 4 Babhta 1 Babhta 2 88 86 80 83 87 85 88 87 85 86 84 82 79 81 86 84 (i) Faigh na rang-oird do na sc ir sa d bhabhta. [2] (ii) Faigh comh ifeacht rang chomhghaol Spearman. [4] (iii) C n tsuntasacht, m t suntasacht ar bith ann, a bhaineann leis an luach a fuair t in (ii)? [1] T na sonra in T bla 4 breactha in F or 7 sa Leabhr n Freagra Breise. (iv) Tarraing l ne an oiri naithe is fearr. [3] (v) Faigh cothrom id l ne an oiri naithe is fearr at tarraingthe agat. [3] 5494.05 8 [Turn over 12 T rotha ag gluaiseacht feadh b thair chothrom naigh d righ faoi luas tairiseach de 12 m/s. D reach nuair at an rotha ag dul thar st isi n peitril S tosa onn veain ag imeacht as an st isi n sa treo c anna leis an rotha agus feadh an bh thair ch anna. Gluaiseann an veain fhos faoi luasgh ar tairiseach de 3 m/s2 go dt go sroicheann s uasluas de 18 m/s. Leanann s uirthi ag gluaiseacht faoin luas seo. (i) Faigh an t-am a ghlacann an veain lena huasluas a bhaint amach. [2] (ii) Faigh an fad a ghluaiseann an veain san am seo. [2] (iii) Taispe in nach dt ann an veain thar an rotha sula mbaineann s a huasluas amach. [2] T ann an veain thar an rotha d reach nuair at an d cheann acu ag dul thar bhosca teileaf in T. (iv) Agus F or 8 sa Leabhr n Freagra Breise in s id agat, sceitse il ar na haiseanna c anna an graf luais is ama don veain agus an graf luais is ama don rotha agus iad ag gluaiseacht S go T. [2] Glac leis gurb t soicind an t-am a ghlactar le taisteal S go T. (v) Scr obh i dt arma t slonn don fhad a thaistil (a) an veain, (b) an rotha [3] S go T (vi) Uaidh sin, n ar bhealach eile, faigh an fad ST. [2] SEO DEIREADH AN SCR DPH IP IR 5494.05 9 [Turn [Turn over [Tiontaigh an leathanach 5494.05 12

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