P6 ISMC 2019 Questions W Answers

 

EBXATBJXE@BJL _EBKJY@TA MJXF_ O@MYAXEXE@B

EBXATBJXE@BJL _EBKJY@TA MJXF_ O@MYAXEXE@B 49:5 (Yremjry 7) : f`ur ?9 mebutas

Ebstruote`bs t` pjrteoepjbts :. H` b`t `pab tfa d` d``nlat `nlat ubtel y`u jra t`lh t` h` s` s`.. 4. Jttampt JLL 41 quaste`bs. ?. [reta y y`ur `ur jbsw jbswars ars ba bajtly jtly eb tfa Jbswar _faat pr`v pr`vehah. ehah. 8. Mjrns jra jwjrhah g`r o`rraot jbswars `bly. 1. Jll gekuras jra b`t hrjwb t` sojla. 7. _oeabtegeo ojlouljt`rs mjy da usah. Zuaste`bs eb _aote`b J ojrry 4 mjrns ajof, quaste`bs eb _aote`b D ojrry 8 mjrns ajof jbh quaste`bs eb _aote`b O ojrry datwaab 7 t` :9 mjrns ajof.

C`ebtly `rkjbesah dy

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EBXATBJXE@BJL _EBKJY@TA MJXF_ O@MYAXEXE@B _aote` _a ote` b J3

Ajof `g tfa quaste`bs : t` :9 ojrreas 4 mjrns. :.

[fab jsnah f`w `lh fa es, Mr Tjcu sjeh, “E well da B yajrs `lh eb tfa yajr B4.”  F`w `lh es Mr Tjcu eb 49:50 B = 81 jbh B4 = 4941 81 yajrs `lh eb 4941 majbs fa wjs d`rb eb :569. Xfjt mjnas fem ?5 yajrs `lh eb 49:5.

4.

Eg tfa heggaraboa heggarabo a `g 9.41 jbh 9.941 `g `g tfa jm`ubt `g wjtar eb j tjbn 4.41 letras, wfjt es tfa v`luma `g jll tfa wjtar eb tfa tjbn0 419 ‟ 41 ubets = 4.41 letras 441 ubets = 4.41 letras :999 ubets = :9 letras

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89% `g X`mmy―s waekft es aqujl t` 48% `g fes gjtfar―s waekft. Eg fes gjtfar―s waekft es :6 nk m`ra tfjb X`mmy, f`w muof h`as X`mmy waekf0 X`mmy ? ubets Gjtfar 1 ubets 1 ‟ ? = 4 ubets :6 nk ? ubets :6 û 4  ? = 4; nk ↔

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8.

Cjs`b fjs j sat `g ? aqueljtarjl trejbklas `g heggarabt sezas. Xfa labktfs ahkas `g trejbklas ajof `g tfasa trejbklas tfa rjte` : 3 4`g3 tfa 7. Xfa tfraa jra pljoah `bajra `bebt`p `g jb`tfar js sf`wb eb tfa gekura. [fjt es tfa rjte` `g tfa jraj `g tfa sfjhah pjrt t` tfa jraj `g b`b-sfjhah pjrts0 _emeljr trejbklas jraj rjte`  : 3 8 3 ?7 _fjhah 3 B`b _fjhah  (8 ‟ :) 3 (?7 ‟ 8 + :) = ? 3 ?? = : 3 :: ↔

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1.

J peaoa `g `g strebk es out ebt` tw` ubaqujl peaoas, ajof `g wfeof es usah g`r tfa parematar `g j squjra. Xfa sum `g tfa jrajs `g tfa tw` squjras es 494 om4. [fjt es tfa labktf `g tfa t fa strebk jt gerst0 494 = :4: + 6: O`mdebah parematar = ::  8 + 5  8 = 69 om

7.

J, D jbh O jra tfraa oeteas `b j mjp. J es b`rtf `g D jbh  JDO es 81¹. H es ajst `g D jbh s`utf `g O. j) Eb wfjt heraote`b es O gr`m D0 (: mjrn)  mjrn)  d) G`r O t` da js ol`sa t` J js D es t` J, wfjt wfjt es tfa heraote`b heraote`b `g O gr`m J0 J0 (: mjrn) mjrn)   j) B`rtf-Ajst d) Ajst

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E tfebn `g savab wf`la bumdars ‟ g`ur jra o`bsaouteva `hh bumdars jbh tfraa jra o`bsaouteva avab bumdars. Xfa jvarjka `g tfa tfraa avab bumdars es 4 lass tfjb tfa jvarjka `g tfa `hh bumdars. Eg jll tfa savab bumdars jra krajtar tfjb 9, wfjt es tfa t fa smjllast p`ssedla vjlua `g tfa ljrkast `hh bumdar0 Xfa `hh bumdars jra3 x-4, x, x+4, x+8  Jvarjka `g tfa `hh bumdars es3 (x-4 + x + x+4 x+4 + x+8) û 8 = x + :  Jvarjka `g tfa avab avab bumdars es3 x+: x+: ‟ 4 = x ‟ : Xfa avab bumdars jra3 x ‟?, x ‟:, x+: _eboa jll bumdars jra 2 9, x 2 ? jbh x must da jb `hh bumdar. _mjllast p`ssedla vjlua `g tfa ljrkast `hh bumdar3 1+8 = 5  5  4

 

EBXATBJXE@BJL _EBKJY@TA MJXF_ O@MYAXEXE@B

6.

J 4-nk hurejb eb j sf`p wjs s`lh jt $:; par nk. Jll tfa saahs `g tfjt hurejb mjna up 41% `g tfa hurejb dy waekft. F`w muof heh E pjy g`r tfa saahs jl`ba0 $6.19   4 x :; x 41% = $6.19

5.

_tuhy tfa pjttarb dal`w. F`w mjby oerolas jra tfara eb tfa :7tf gekura0

Gekura : Gekura 4 Gekura ?

Oerolas baahah g`r btf gekura = 8 + 6 (b ‟ :). _` g`r tfa :7tf gekura, et es 8 + 6  :1 = :48 oerolas :9.

_jbhy jrrjbkah 5 semeljr bjels t` g`rm tfa g`ll`webk sfjpa. Hrjw t` sf`w f`w fa ojb usa :1 semeljr bjels t` g`rm j sao`bh sfjpa tfjt es trepla tfa jraj `g tfa gerst Hrjwstjbh-jl`ba et eb y`ur Jbswar Xrepla jrajsfjpa. wetf semeljr sfjpa_faat. raqueras3 ? x 5 = 4; bjels O`bhete`b `g :1 raqueras sfjrebk `g 4;  ‟ :1 = :4 bjels. Xfa l`bkast seha `g tfa gekura es ? bjels. :4 bjels = sfjrebk/ram` sfjrebk/ram`vebk vebk 8 sehas. Y`ssedla o`bgekurjte`bs3

_aote` _a ote` b D  

Ajof `g tfa quaste`bs :: t` 49 ojrreas 8 mjrns. ::.

Ofjesaa es djnebk s`ma o``neas o``neas t` drebk drebk t` tfa ofelhrab ofelhrab jt j Ofelh Ofelh Ojra Oabtra. F`wavar, F`wavar, sfa ojbb`t ramamdar wfatfar tfa oabtra fjs 88 `r 86 ofelhrab. F`w mjby o``neas sf`ulh sfa djna jt lajst s` tfjt sfa well da jdla t` keva ajof `g tfa ofelhrab jb aqujl bumdar `g o``neas b` mjttar eg tfa oabtra fjs 88 `r 86 ofelhrab0 88 = 4  4  :: 86 = 4  4  4  4  ? LOM3 4  4  4  4  ?  :: = 146 o``neas

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EBXATBJXE@BJL _EBKJY@TA MJXF_ O@MYAXEXE@B

:4.

Heveha tfa raotjbkla ebt` qujrtars qujrtars dy hrjwebk hrjwebk tw` tw` strjekft lebas> `ba `g tfa lebas lebas must pjss pjss tfr`ukf p`ebt J.

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E fjva ? pelas `g `g ojrhs. Ajof Ajof pela fjs 8 ojrhs ojrhs jbh ajof ojrh fjs j heggarabt heggarabt lattar lattar `b et. et. Xjnebk j ojrh gr`m ajof pela, E ojb g`rm ?-lattarah w`rhs. Xfasa jra s`ma `g tfa w`rhs E ojb g`rm3 DAK AK@ KJY K@H LEH YEB XJB [AD o`rraot)   [fjt jra tfa lattars eb ajof pela `g ojrhs0 (jll jbswars must da o`rraot) Xfa lattars jra kr`upah3 [KBL AHXY D@JE

:8.

J d`ttla fjs ? typas `g buts ‟ pajbuts, ojsfaw buts jbh jlm`bhs. 81% jra pajbuts. Xfa ojsfaw buts jbh jlm`bhs jra eb tfa rjte` `g 4 3 ?. Xfara jra 75 m`ra pajbuts tfjb ojsfaw buts. F`w mjby buts jra tfara eb tfa d`ttla0 Yaroabtjka `g Ojsfaw jbh Jlm`bh3 : ‟ 81% = 11% 1 ubets = 11% 4 ubets = 44% 81% ‟ 44% = 4?% = 75 buts :99%3 ?99 buts

:1.

[fab H`b wjs tweoa js `lh js Nem, Leb wjs 49 yajrs `lh. [fab tfa rjte` `g Leb―s jka t` H`b―s jka wjs 1 3 ?, Nem wjs :9 yajrs `lh. Eg Leb es tfa `lhast jm`bk tfam, gebh Nem―s jka wfab Leb es 11 yajrs `lh. 49 Leb es :1 yajrs `lhar tfjb Nem. [fab Leb es 11 yajrs `lh, Nem es 89 yajrs `lh.

Leb H`b

1

1

1

1

1

1

Nem

1

1

:9

8

1

1

 

EBXATBJXE@BJL _EBKJY@TA MJXF_ O@MYAXEXE@B

:7.

Xw` dr`tfars wjbt wjbt t` `wb tfa sjma Kubhjm gekureba. Eg d`tf sjva rakuljrly, et well tjna tfa 4 y`ubkar dr`tfar 59 hjys t` jgg`rh tfa gekureba jbh tfa `lhar dr`tfar  `g tfjt tema. F`w l`bk ? must tfay sjva eg tfay o`mdebah tfaer sjvebks s` js t` o`-`wb tfa gekureba0 :

U`ubkar sjvebk rjta3 59 `g tfa o`st @lhar sjvebk rjta3

: 

59∛

=

 :

 `g tfa o`st

79

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: + : =   1 = : O`mdebah rjta3 59  o`st 79 :69 ?7

O`mdebah sjvebks3 ?7 hjys :;.

:6.

JDOH es j raotjbkla. V jbh U jra p`ebts `b JD jbh OH raspaotevaly suof tfjt VU es parpabheouljr t` DH. Eg JV = OU = JH, gebh HVU. _eboa VU jbh DH ebtarsaot jt 59 ¹, tfab HVDU must da j rf`mdus. Xfab HVU = DVU.  Jls`  JVH = 81¹, s` HVU = (:69 ‟ 81) û 4 = 7;.1¹ 

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O

Eg ;9% `g j oljss `g pupels wajr spaotjolas, spaotjolas , ;1% `g tfam lena Mjtfamjt Mjtfamjteos, eos, 69% `g tfam pragar ebh``r kjmas, jbh 59% `g tfam sjeh tfjt tfaer gjv`ureta far` es _peharmjb, jt lajst wfjt paroabtjka `g tfa oljss `g pupels wajr spaotjolas, lena Mjtfamjteos, pragar ebh``r kjmas jbh wf`sa gjv`ureta far` es _peharmjb0 :1%    Jbs3 :1%

wajr spaotjolas lena Mjtf pargar ebh``r kjmas far` es _peharmjb

:5.

‟ :. Xfa sum `g tfa pjka bumdars `b tw` pjkas `g j d``n tfjt es gjoebk ajof `tfar es 8 x   ‟ Axprass tfa smjllar pjka bumdar eb tarms `g  x . Lat tfa smjllar pjka bumdar da : ubet. Xfa `tfar pjka bumdar = : ubet + : 4 ubets + : = 8 x   ‟ ‟ : ‟ :) ‟ :] û 4 Xfa smjllar pjka bumdar = ^(8 x   ‟ = 4 x   ‟ ‟ : 

49.

Jmy fjs 449 ubet-oudas. :19 `g `g tfam jra dlua oudas wfela tfa ramjebebk jra rah oudas. ? _fa wjbts t` duelh j 4:7 ubet  ouda tfjt fjs `bly j sebkla o`l`ur `b ets `utar gjoas. [fjt es tfa gawast bumdar `g ubet-oudas, jbh `g wfjt o`l`ur, h`as Jmy baah eb jhhete`b t` wfjt sfa fjs0 Ebbar o`ra `g 4:7  4:7 om?3 (7 ‟ 4)? = 78 @utar dlua oudas baahah3 4:7 ‟ 78 = :14 (