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ICSE Board Exam 2018 : Mathematics

7 pages, 50 questions, 46 questions with responses, 55 total responses,    2    0
Yash Dudani
Smt. Lilavatibai Podar High School (LPHS), Mumbai
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U U 1 n J I\ 3 q7 U l\ i J T M A T H E M A T c s (T A th is P a p e r m u s t e r s to n sw Yo u w i n is tim T h e tim e g iv A tte m p t A w o r k in a t th e en a tq u t be o he a d ru g n t is s io n T h e in te n d e d o h be a S e c tio w o rk, m A n o r or t z e m a tic a Q u e s tio n (a ) m pt a th e p a p e r p r o v id e d s e a r a te p y ite d u r in g th e a n d jir s t 15 i p d in g th e q u a n re st o y e a lo k in g p f th e w est o n o w ed To r a r ts o t ta b es l q u e s t io n s in a per w r i ts m u te s itin g th e a w S e c tio m n w e rs B t b e d o n e o n th e s a m e a n sw e p q u e s \io n s a re m q u e s t i o Tr o u r ilt r e s t in to S E C T IO N A A tte n t be c e a r ly s to p n a n d h e e t a s th e marlsj. q u e s tio n s a w r n o n a a p e r is th e lim u s q e s s e n tia w M itte s p e n t in r e a P d u rs a n w r d to e f th is fr o m s O o w is to b e e e s tio n s g , in c lu d in g a f o w o \' w " p (4 0 ro v M jr o m ss a re f m a rks g iv e n in b r a ce ts [J id e d a r k s) th is S e c tio n 1 F in d th e v a lu e o y e a r s If th e T 18 5 11 C o p y r ig h t ra te re se r ve f o ' x ' an d y ' i 13 f in te r e s t w as T h is p a p e r c o n s is ts o 10 % p a , fin d th e m a tu r ity f 7 p r in te d p a g e s v a lu e o a n il f th is tank acco un t p a ge T d . W u m ov er (c ) C ards is ? b e a r in g a w n a t ra n (i) a p r im do e nu fr o m m c ar d k e p t in a bag A ity o f g e ttin g a c a r d th e b a g F in d th e p r o b a b i w h ic h is b e r s 2 , 4 , 6 , 8 , 10 , 12 , 1 4 , 16 , 18 n um an d 20 a re i b e r \ t \ , ( ) (iii) a u m b e r th a t is (iv ) a n Q u e s tio n (a ) dd o ltip le o f6 ber n um T h cum 25 F in d th e cm fe r e n c e (i) r d iu s o (i ) v o lu m f th e b a s e (c ) P Q R S is c c f cylincal v e s s e l is a 13 2 cm d its h e ig h t is an y lin d e r f c y lin d e r , a o J f th e e o o 3 ) (2 k + 1 ) a n d If (k u e s t io n a m u 2 (b ) Q b e r d il s ib le b y 4 a n um y c lic q u (u s e (4 k ' 76 = 3 ) a r e th :e e + a d r ila te r a l G iv L en Z co n se cu + F F >R \ QPS = tiv e te r m s o f p A P 7 3 , Z P Q S = 5 5 , a i d v a lu e lin d th e Z P SR 8 2 , = 3 () a If ( x + 2) an d P r o v e th a t V s e T 18 5 11 x c z + 3) e + a re fa c to r s co se c 2 e = o ta fx n 3 + o + a x co 2 + b , n d th e to v a lu e s o f ' ' an d b ' ' (c ) U o s in g frun R u n s s c o re d N f o o u e s tio n h is to g r a m a w d b y 5 0 b a ts m s sc o re b a ts m Q g ra p h p a p e r d ra a E s tim en a te th e m o If th e be r 4] f th e d a ta 5000 6 00 0 7000 8000 90 00 4 0 00 50 00 6 00 0 7000 800 0 9 000 10 0 0 0 4 18 9 6 7 2 4 b e r lin e s tr a 2 e x ig h t lin + 7x 3x s v a lu e o 7 - an 5y 7 - , an E Z x d 4x + a y + 9 0 are p e rp e n d ic u la r to on e fa d g iv e yo u r a n s w e r c o rr e c S E C O N B A tte m p t m ry jo lu qu t to tv (4 0 M e s tio n s a r io d e c im a l p la c e s k s) fr o m t tis S e c t io n Fs o n 5 T h e 4 6 te n r a tio o (b ) n u m 4 0 00 th e r . Iin d th e S o lv (a ) in g th e 4 an o u o sho w n 3000 2 + 1 0 1 3 + 1 0 < 2 4 + 1 0x Q d is tr ib u tio en de en realn u m (b ) fo r th e g iv A m f th e an in f a G P is 16 o is 1 2 8 F in d th e ] r s t te rm an d com m on s e r ie s 2 2 2 5 0 0 in 7 5 0 v e s ts p a id b y th e d th e 7 th te m an , p a n y is 12 % co m , share s a v a c a lc u ila b le a t 10 % te tt la te d is c o u n t If th e d iv id e n d Jci!J ti } i) T h e O i) nu m b er sh a r e s of pl ?c h The an n u a l d iv id e n d (iii) T h e r a te o f r e t u r n h e g e ts n e are st w T 18 5 11 h o le m un as ed r e c e iv e on J Y H N /' r b yu , r ' d M s in v e s tm en t G iv e y o u r a n s w e r c o rr e c t to th e ber 3 J T u m o v er (c ) U g r a p h p a p e r fo se A B C D is Q (b ) (c ) Q (i ) W te d o 2c m A (2 , 2 ), B (2 th e J a x is fA ' d B an l tm it a lo n g b o th - d an (iv ) N a m e th e p o ly g o n , nam e an x d y ax is ) [4 ] 2 ), C (O , 1 ) a n d D (0 , 1 ) it a s A 'B 'C D ' t w o p o in ts \ bic k a r e in v a r ia n t u n d e r th e am ab o v e re fle c o n A ' B 'C D 6 U s in g p r o p e r tie s A P ro v e o f p r o p o r tio n [: l " [ , a = . th a t (1 + co t o , s o lv e . N cose c fo r d c G iv x a [ = B )(1 + t a is p o s itiv x Fi d A C . o + n th a t en o)= s ec + B e 2 [3 ] 10 C Z 7 F in d th e v a lu e o f k fo r w h ic h th e fo llo x O on w n th e c o o r d in a te s o (i ) N e (T a k e s e v e r tic e s a r e R e fle c t q u a a te r a l A B C D u e s tio n (a ) q u a d r ila t e r a l w h o (i) u e s tio n (a ) a e s tio n th is q u r n a m a p ? aw n fo llo w in g d im (i) 2 in g w + 4 k + e qu a o (k 2 n [3 ] h a s e q u a l r o o ts k + 2) = O to a s c a le o f 1 : 5 0 , 0 0 0 , a r e c ta n g u la r p lo t o f la n d A B C D h a s th e e n s io n s A B th e a c tu a l le n g th o = 6cm B C = 8c m f th e d ia g o n a l d is ta n ce an d ll a n g le s a A C o a r e r ig h t a n [3 ] g le s F in d f th e p lo t in k m th e a c tu a l a r e a o f th e p to t in s q k m (c ) A (2 , 5 ), B ( 1 2 ) a n d C (5 8 ) a r e th e , , A B s u c h th a t A M e q u a tio T 18 5 1 n o f th e lin : e M B = 1 : v e r tic e s o 2 F in d th e f co p a s s in g th r o u g h th e p o in ts C a tr ia n g le A B C o r d in a te s o an d M 4 P f 'M ' , ' M H ' is ' a en c e p o in t on fin d th e [4 ] Q u e s tio n (a ) 7 7500 w e re 2 0 le s s c h ild r e n c (b ) 8 d iv id e d , eac q u a lly e h ou w am o n ld h v g a c e r ta in e r e c e iv e n u m d 1 10 0 be r m o re f th e fo llo m e an o in g d is tr ib u o n is 2 4 n d th e w F in d th e o v a lu e o f h th a t B C = , U f c h ild r e n H a d th e r e b e e n g in a l n u m b e r [3 ] f o h ild r e n If th e (c ) o s in g 6 5 cm (i) C i ) C le r ru an d a n m co m A B C L o n s tn c on d c t pa ss o n 120 a c ir c u m ly , c o n s tn c t a AA B C su c su c h th a t D a ' 5 cm an d A B c ir c le o f B C t a c y c lic q u a d r ila te r a l A B C D , s e q u id is ta n t fr o n A B an d B C Q u es (a ) tio n 9 P r iy a n k a h a s sh e a r e c u tT in g e ts 1 5 5 5 0 acco un t w as a s g d e p o s it accou n in te r e s t a t th e tim e o t o f 1 10 0 0 p e r m o fm ah u n th a t 10 % p e r a m ity n d ih e to ta l tim , e fo r w u m If h ic h th e h e ld (b ) ao r @ (iii) F in d A , T 18 5 1 1 a r e s im rea o ila r fA0AdV : A re a o fA o x g 5 T . J & u rn O v er T h e fo llo (c ) w in g fig u r e h e m is p h e r e a h e ig h t o f th e Qu U d an y lin d e r an d c se R e m a in e r th e o 2 3 + 3 2 (b ) at o n e en d ts a so a con e a lid c o n s is tin t th e c o n e a le e a c h o o g o fa r ig h t c ir c u la r c y lin d e r cm F in d th e v o lu m e o f th e so th T he th e r T h e ir c o m m o n r a d iu s is 7 c m f4 ? lid 10 es o n (a ) r e p re s e n 20 T 18 5 11 F in d th e w in g p o ly n om ia l 10 9x In th e fig u r e g iv to fa c to r iz e th e fo llo re m en b e lo w v a lu e o f ' x ' ' 0 ' is th e g iv in g c e n tr e o re a s o n s 6 f th e c ir c le If Q R = O P an d z O RP [4 ] (c ) th g le e an th a t fe e v a tio' o f th e to o w er PT ? " ' " f h c W ' . '" p o f ' ' " 50 w h ia h ia w m d " h ' " Js . . ' 4 to th e n e a r e s t iJa e tr e Q u e s tio n (a ) 11 T h e 4 th te r m d ifr e r e n (b ) U G se A sw e H ce ra y re fi n d th e r th is w s u n qu = an h e ig h t o g iv e o f th e o cm f th e s e r ie s to 8 te r m )o f 60 bo y s cm in g d a ta f 10 is 6 6 F in d th e fir s t te rm an d th e co m m o n m w er e s w a s r e c o rd e 15 o a lo n g abo v e b e lo n g in g to C la s s 10 o fa sc ho o lw as d o n e ax is an d is tr ib u tio n d 2 U cm se = 10 b o y s th e a lo n g r a p h to g th e e s tim o th e r a te th e d ia n Q u a r tile (iii) if a b o v e 15 8 b o y s in th e cm is c la s s w c o n s id e r e ho e d 4 [6 ] o i e s tio n g a r d in g h e ig h t (in w d 1 5 th te m in g (i) th e lo an is d r a w fo llo T 18 5 1 1 en c e p h p a p e r fo T a k in g 2 c m O i) f a n A P is 2 2 d u c te d T h e fo llo co n ax o as th e ta ll b o y s o f th e c la s s ta ll 7 J F in d th e n u m ber o f

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