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CAM BRI DGE PU BLIC SCHOOL_ I( I I ( I(FRI

r-t t pREpARAToRy EXAMINATToN 2ar4-r5

Sub.._Mathematics M a r l<s: B0

Four a l te rna t i ves a re g iven fo r each o f the fo l low ingques t ions / incomple te s ta te rnen ts . on ly one o f them is co r rec t o rmos t appropr ia te Choose the cor rec t answer a long w i th i t s a lphabe t "7 . l f 200P,=

2001 then the va lue o f r i s

b 100 c. 200 d . 502. The fo rm u la to f i nd n th te rm o f H . p i s

a . 1

a .( a . - ( n " 1 ) r i

3. Wh ich among

exper iment?

a . Throw ing a d ie d . Toss ing a co in .b . De te rmin ing the bo i r ing po in t o f wa te r .c . Draw ing a ca rd f rom a we l l shu f f lec j pack o f ca rds .

4 . Cons is tency o r va r iab i l i t y i s de te rmined bv . . . . .

b.( a + ( r r r r ) r t

the fo l l ow ing i s

I ' t

t l l l ' * . n . / t l l ? 2 l . / 1 ,-L . _ - - . - - -

TrL 11.

a po lynom ia I x ' -3x -28 .

c .

d .

in

c " l l l

1 rd( a t ( n - - r ) r t " ' ( o - ( n + t ) r 1

not an example fo r random

a. Var ia t ion

b . Dev ia t io n

5. lf cot/,='! th e n sec}=

^,,5l7:r'r,a.

1 1

6. l f 7 i s a ze ro

be

c . S ta nda rd dev ia t ion

d. Co-e f f i c ien t o f var ia t ion

b

of

a. 4 b . -4 c . -7

7 " D is tance between two po in ts (m, ,s r )

a . .

b

8" The po in t ( -1 .2) can be locateda" lquadrant . b . l l quadrant

, \6Vi-;',t11

tn .n the o ther zero wi l l

d . 0

and (m, ,s2) is

(n1-r), + ("t;t),

quadran t d .i l . Answer the fo l low ing

9. Def ine : "D is t r ibu t ive proper ty o f in te rsec t ion over

lV quadrant .

6L=6union o f se ts"

10. Ment ion t l re re la t iopsh ip among d iv idend , quo t re r r t , rema inder

a nd d iv i so r .

l l . vo rumes o f two spheres a re in the ra t io 64 ' z l ' F ind the ra t io o f

the i r rad i i .

12 .S ta te Tha les theoren" ] 'cen t re O. tf

l -3 .1n f igu re , AB and AC are two tangen ts a c i rc le w i th

Eg=3AEc Find$9g

Geomet rY .

Answer the fo l low ing ques t ions

15 .F ind the LCM and HCF o f the in tegers

them as Produc t o f P r imes '

12 , !5 ,30 bY express lng

16 . |n how many ways can a c r i cke t team o f

t7 p layers in wh ich 5 p layers can bowl?

inc lu de 2 bowle rs '

t l . t ind the Produict of \ [T and" W

18.Show tha t the t r i ang le whose ver t i ces a re (8 , -4) (9 ,5) a nd (0 ,4) is

an i sosce les t r i ang le '

l g .Draw a p lan fo r the record ings fo r the su rveyor ' s f i e ld book g iven

be low: (sca le : 30m=l -cm)I ToD

l l

A

l l l .

eleven de se lected f rom

Each cr icket tea m must

I

i ToE150 )io180 i 90toc

120i oo I 3otoBl u vI

i r rom Al

20.Nine ro t t .n r 'ungoes are mixed wi th 30 good mangoes ' one

mango is chosen a t random. what is the probab i l i ty o f choos ing a

a. ) Good ones b ' ) Rot ten mango?

21.Wr i te two cond i t ions o f a t raversab i l i ty o f network '

.?2. | t (n+1) !=12 (n-1) l 'F ind the va lue o f n

23.S impl i fy by ra t iona l is ing the denominator :

,S..o'." )

t " ' / c

\ ' '5:*;:-diiGr

t - . ,v' lr * v/. jU=i1, , 2 ,3 ,4 ,5 ,G,7 ,8 ,9) . p rove that

24 . l f A { 1 , 2 ,3 ,4 } , B= {2 ,4 ,6 ,B } a n d(AU B) '=A tn

B t .

25 ' ln r igh t ang led t r iang le . BAC= 90" and BM is the a l t i t ude . l f AM=16f \4C. p rove tha t AB=4BC.

26 'The s lan t he igh t o f a f rus tum o f a cone i s 4cm and per imete r o f i t sc i r cu la r ends a re 18 cm and 6 cm. F ind the curved sur face o f thef ru s tu m.

27 .Prove tha t : sec 'e+cose c , @= sec , e . cosec , e28 ' l f m and n a re the roo ts o f the quadra t i c equa t ions x r -3x* r=0 ,

then f ind the va lue o f : . *

29 .The po lynorn ia l 2x3-5x r+x+a and ax , ,+ 2 {3when d iv ided by (x_2)leave the rema inders Rr dnd R, respec t i ve ly . F ind the va f ue o f a i f

(oR)

F ind the quo t ien t and rema inder when x t+x ' -3x+5 i s d iv ided by(x -1 ) us ing syn the t i c d iv i s ion .

30 .How n" rany numbers ress than 50 can be fo rmecJ us ing j . ,2 ,3 ,4and5 w i thou t any repe t i t i on . ? (OR)

t f - l+1 )to l , ,

= * then f ind the va lue x .

So lve the fo l low ing

31 ' The sum o f f i r s t n te r rns o f an -AP i s 3n )+4n F ind the 25 tn te rm o f

th i s A . P .

32 .F ind the s tandard dev ia t ion fo r the fo l low ing da ta

Rr=2 Rr .

tv.

Scores XFreq uency

f

322

375

426

475

522

equaf ,the n33. l f the roots o f rhe eqat ion (b c )x

a' + (c -a )x+(a -b )=g 3 t .

p rove tha t 2b=a+c . (o R)By se l l ing an ar t ic re for 18 "75, a dearer roses as muchcost pr ice . F ind the cost pr ice o f the ar t ic re .

percent as i ts

_//

14.Thc ang l le o f t - l ev 'a t ron o f thc top o f a

hor i zon ta l g round rs found to be 30 '

pos t , thc c l t ' va t ion i t t c reased bY

L5o. l i i nc l the he igh t o { ' [he f ' l ag l ]os t '

f l agpos t f rom a

On wa lk ing 6 n t

point o f e

towards the

(o R)

l f x . s i n ' @= y . Cosu @=s in f l . cos @ and x ' s in A= y ' cos Othen

p rove th a t x ' nY ' = !

35 . l f two c i rc les touch each o ther , then p rove tha t the i r po in t o f

con tac t and the i r cen t res a re co l l i near ' ( bo th cases)

(oR)

Sta te and p rove pv thagorus theorem'

36 .Prove tha t , i f two t r iang Ies a re equ iangu la r , then the i r

co r respond ing s ides a re p ropor t iona l '

37 .ABCD is rhombus . P i s any po in t on BC, AP i s jo ined and p roduced

at O. Then Prove that " * . : i

- ; "

fr .=- -- -->---- -rB

/ -----'------1

/ -/ P-------=-/ < /- - ---->n

f t - - - - - ' * - - c lv

V. So lve the fo l lowing

3B.Given ser ies be 4+ t7+] .6+ . . . . .F ind S3:S6. (oR)

An ar i thmet ic progress ion cons is ts o f th ree terms whose sum is 15

and o f the squres o f ex t remes is 5g. F ind the terms o f progress ion '

39.Draw the graph o f v=x2 and y-x+2 and so lve the equat ion x2-x-2=0 '

40.Two c i rc res o f rad i i 5cm amd z cm have the i r cent res 10 cm apar t '

const ruc t d i rec t common tangents to them. Measure the i r rengths

a nd ment ion the length o f each d i rec t common ta ngents '

41.ABC is r igh t ang led a t c , Let BC=a, AC=b and AB= c and p be the

|engthofperpendicu |ar f romConAB,Provethat

a cP=ab 'Lfir i"

IH\>

. r > \

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