2016 10 Sp Mathematics Sa1 Solved 02

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CBSE Sample Paper -02 (solved)

SUMMATIVE ASSESSMENT –I

Class – XMatemat!"s

Time allowed: 3 hours Maximum Marks: 90

#e$eral I$str%"t!o$s&

a) All questions are compulsory.

b) The question paper comprises o 3! questions di"ided into our sections A# $# % and &. 'ou

are to attempt all the our sections.

c) (uestions ! to in section A are one mark questions.

d) (uestions * to !0 in section $ are two marks questions.

e) (uestions !! to +0 in section % are three marks questions.

) (uestions +! to 3! in section & are our marks questions.

,)

There is no o"erall choice in the question paper. -se o calculators is not permitted.

SECTI'N – A

!. &etermine whether the trian,le ha"in, sides cm# / cm and !0 cm is a ri,ht trian,le or not.

+. xpress 0. as rational number in simplest orm.

3. 1ro"e that+

+

!cot 2 !

sin 2− = −

. "aluatesin!/

cos+

°

°.

SECTI'N – B

*. xpress sin/!4 5 tan/!4 in terms o tri,onometric ratios o an,les between 04 and *4.

. 6ind the 7%6 o 9 and 0 by prime actorisation method. 7ence# ind their 8%M.

. + +tan 2 ! a= − # pro"e that ( )3

3 + +sec2 tan 2cosec2 + a+ = − .

/. um o two numbers i 3* and their dierence is !3. 6ind the numbers.

9. The number o students absent in a school was recorded e"ery day or ! days and the raw

data was presented in the orm o the ollowin, requency table.

;o.o students

absent

* / 9 !0 !! !+ !3 !* !/ +0

;o. o days ! * !! ! ! !3 !0 0 ! ! !

<btain the median and describe what inormation it con"eys.

!0. A man ,oes !0 m due east and then + m due north. 6ind the distance rom the startin, point.





SECTI'N – C

!!. how that there is no positi"e inte,er n or which ! !n n− + + is rational.

!+.

A$% is a ri,ht trian,le ri,ht an,led at % and A% = 3 $%. 1ro"e that∠

A$% = 04.!3. The taxi char,es in a city comprise o a ixed char,e to,ether with the char,e or the distance

co"ered. 6or a >ourney o !0 km# the char,e paid is ?s * and or a >ourney o !* km# the

char,e paid is ?s !!0. @hat will a person ha"e to pay or tra"ellin, a distance o +* km

!. asecθ 5 btanθ 5 c = 0 and psecθ 5 qtanθ 5 r = 0# pro"e that

Bbr C qc)+ C B pc C ar )+ = Baq C bp)+

!*. Throu,h the midDpoint M o the side %& o a parallelo,ram A$%&# the line $M is drawn

intersectin, A% in 8 and A& produced in . 1ro"e that 8 = +$8.

!. 6ind the Eeros o the polynomial f Bu) = u+ 5 /u and "eriy the relationship between the Eeros

and its coeicients.

!. sinθ=+ +

+ +

a b

a b

−

+

# ind the "alues o other i"e tri,onometric ratios.

!/. The ollowin, table ,i"es weekly wa,es o workers in a certain or,aniEation. The requency

o class 9D*+ is missin,. t is known that the mean o the requency distribution is .+. 6ind

the missin, requency.

@eekly wa,es B?s) 0D3 3D D9 9D*+ *+D**

;umber o workers 3! */ 0 +

!9. ol"e: ax 5 by = c

bx 5 ay = ! 5 c

+0. @ithout usin, tri,onometric tables# e"aluate

++ + *cosec */ cot*/ tan3+ tan!3 tan3 tan* tan*3 tan

3 3 3° − ° ° − ° ° ° ° °

SECTI'N –

+!. 8et a# b# c and pbe rational numbers such that p is not a perect cube. ! +

3 3 0a bp cp+ + = # then

pro"e that a = b = c = 0.





++. n a FA$%# ri,ht an,led at %# i tanA=!

3# ind the "alue o sinAcos$ 5 cosAsin$.

+3. n the ,i"en i,ure# & GG $% and A& : &$ = * : . 6ind( )

( )

Area &6

Area %6$

∆

∆.

+. 6ind the mean marks o students rom the ollowin, cumulati"e requency distribution:

Mars N%m*er o+ st%de$ts Mars N%m*er o+ st%de$ts

0 and abo"e /0 0 and abo"e +/

!0 and abo"e 0 and abo"e !

+0 and abo"e + /0 and abo"e !0

30 and abo"e * 90 and abo"e /

0 and abo"e ** !00 and

abo"e

0

*0 and abo"e 3

+*. cosecθ C sinθ = l and secθ C cosθ = m# pro"e that ( )+ + + + 3 !l m l m+ + = .

+. 6ind the "alues o a andb so that x 5 x 3 5 / x + 5 ax 5 b is di"isible by x + 5 !.

+. &raw the ,raphs o the ollowin, equations on the same ,raph paper.

+ x 5 y = +H + x 5 y =

6ind the coordinates o the "ertices o the trapeEium ormed by these lines. Also# ind the

area o the trapeEium ormed.

+/. 1ro"e that i in two trian,les# one pair o correspondin, sides are proportional and the

included an,les are equal# then the two trian,les are similar.

+9. n a FA$%# ri,ht an,led at % and ∠A = ∠$#

Bi) s cosA = cos$ Bii) s tanA = tan$





@hat about other tri,onometric ratios or ∠A and ∠$. @ill they be equal

30. A sweet seller has +0 ka>uburis and !30 badamburis. he wants to stack them in such a

way that each stack has the same number and they take up the least area o the tray. @hat is

the number o buris that can be placed in each stack or this purpose

3!. ?ohanIs mother decided to distribute 900 bananas amon, patients o a hospital on her

birthday. the emale patients are twice the male patients and the male patients are thrice

the child patients in the hospital# each patient will ,et only one apple.

Bi) 6ind the number o child patients# male patients and emale patients in the hospital.

Bii) @hich "alues are depicted by ?ohanIs ather in the question

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2016 10 Sp Mathematics Sa1 Solved 02