fiq,f tt qua :rr - ii, summative assessment- iif tt qua_:rr - ii, summative assessment- ii...

fiq,f�tt qua_:rr - II,

SUMMATIVE ASSESSMENT- II MATHEMATICS/ 11fu@'

Class - IX / c6� - IX

Time allowed : 3-3½ hours

: 100

Maximum Marks : 100

(i) umWR�f1

(ii) � WR 1Pl' if 32 WR l � ffl � at, �, '«, �-a-�� if zjcJ 7P1I % I �-at if 4 WR

i�� 13lcficfil%, �-GJif 6Wffi��ii, 23lcfit �--«if lOWRi

� � if, 3 3lcfi t, �-C: ii 11 WR ,g- ��ii, 4 3lcfi t -a-� �-� cfiT WR

1Jw� Wfi"{Uf -q,:3n?:11fur��cfil% I

(iii) �WR1Prifc!iWm��t1

(v) ii<?J�i.12< cfiT WWT qffi � I

General Instructions:

(i) All questions are compulsory.

(ii) The question paper consists of 32 questions divided into five sections A, B, C ,D and E.

Section-A comprises of 4 questions of 1 mark each, Section-B comprises of 6 questions of 2marks each, Section-C comprises of 10 questions of 3 marks each and Section-D comprises of11 questions of 4 marks each. Section E comprises of one question from Open Text theme

of 10 marks.

(iii) There is no overall choice.(iv) Use of calculator is not permitted.

�-at/ SECTION-A

of 15

1

2

3

4

Question numbers 1 to 4 carry one mark each

� � (3, 4), � fl•ilcfi<u1 3y = ax+ 7� 3TTffi§f in:� t, <TT a cfil liR � �I

If the point (3, 4) lies on the graph of linear equation 3y =ax+ 7, find the value of a.

Linear equation x - 2 = 0 is parallel to which axis ?

�ABC cfil � 14 cm2 t I GfR 'lf'l1 BC cfil l=ff� AD t ITT ar (�ACD) ��I Area of �ABC is 14 cm2 . If AD is median to side BC, find area (�ACD).

Calculate the amount of air inside a conical tent with base radius 7 m and height 12 m.

�-Gf / SECTION-B

Question numbers 5 to 10 carry two marks each.

1

1

1

1

5 fc.nm �� EFGH if, LEHG ch1UT LHGF cfi1 fcr_frr t LGFE = 70° a211 HEJ.EF % I LEHG 3m: 2

LHGF � i:rrtl ��I

6

In a quadrilateral EFGH, LEHG is thrice of L'.HGF, LGFE = 70° and HE..LEF. Find the measures of LEHG and L'.HGF.

Construct an angle of 135° at the initial point of a given ray.

of 15

7 '1TT��Tt,AB3w:BC�O��fl m�fcn LABCcfiTBO� 2

cfi«IT t I

9

B

In the given figure, AB and BC are two chords equidistant from the centre 0. Prove that BO bisects LABC.

B

The diameter of a metallic ball is 4.2 cm. If the density of the metal is 8.9 g per cm3, find the mass of the ball.

0, 1, 1, 2, 0, 1, 2, 0, 0, 1, 2, 2, 0, 2, 1, 0 , 1, 1, 0, 2.

� � � � isll(isll@ � �I

Two coins were tossed 20 times. Each time the number of "Heads" occuring was noted down

as follows:

0, 1, 1, 2, 0, 1, 2, 0, 0, 1, 2, 2, 0, 2, 1, 0 , 1, 1, 0, 2.

of 15

2

10

Prepare a frequency distribution table for the data.

i:i;;i�fucfi i:rrif

��"mclcf>l�

(i) 30 � m� � t

(ii) 20 � cfill "ffic f I

A B

75 55

C D E F

37 29 10 37

Given below are the seats won by different political parties in a polling outcome of a state assembly elections.

Political Party A B C

Seats Won 75 55 37

What is the probability that the party selected have

(i) more than 30 seats.

(ii) less than 20 seats.

�-"« / SECTION-C

Question numbers 11 to 20 carry three marks each.

D E F

29 10 37

2

11 � 1"lR � 3:rriT cfiT fcfiwn F·F=if(1f@a t : � fcfi@l-llc< cfil fcfiwn 10 �- afu: � � cfll" 3

� efi � � fcfiMll-llc!{ 8 <i. i1 cl".:r cf>l � � y fcfiMl•-Bc{ 61 afu: � fcfiwn x �- m, "dT

� � � fl•-Ocfi{OI � afu: "3W-flT 3Tiffi§f �I

of 15

12

The auto fare in a city are as follows : For the first kilometer it is Rs. 10 and for subsequent distance is Rs. 8 per km. Taking the distance as y km. and total fare as Rs. x, write a linear equation for this and draw the graph. Also find the fare of 15 km.

� f� .!m -m'ITT i, ��3M if� 2 cfiT eR:T � � % 3m m if 3 cfiT � � 3

4

�ii tB � cfil 'U 1:R'q@� Jil'-llc:fi(OI ct �'ll�l �'U � 'GT ��I

A fraction becomes .! when 2 is subtracted from the numerator and 3 is added to the denominator. 4

Represent this situation as a linear equation in two variables. Also find two solutions for this.

13 ABCD � "9TI� t_ � � AC 311{ BD 1 'tffiJR O 1R � cfi"@ t I � ar 3

(�DOC) = ar(�AOB) t cl) � fot;" LBDA = LDBC % I

B

ABCD is a quadrilateral with diagonals AC and BD intersecting at 0. If ar (�DOC) = ar(�AOB) ; show that LBDA = LDBC.

B

of 15

14 �STU cfil' � � "lfR � � :fill31T cfiT <fl1T 11.4 cm 3ffi 3TT'l:W cfilUT 45° 3ffi 120° f I

Construct �STU if sum of the three sides is 11.4 cm and base angles are 45° and 120° .

3

15 � @fi;olls flriFr cli1 � � � � � 5.2 cm 't I � � GT cfil1JIT � �� 3

� I � ey;:JTcfi1 llfdaj�.J � cflm'R WIB�I

Construct an equilateral triangle of side 5.2 cm each. Now construct angle bisectors of any two angles. Their intersecting point lies where ?

16 m � � if, 0 � cfiT � 't oll{T L'.BCO = 50° 't I "lfR OD � "WlTffi: BC 't o?.ff AM .l BC %, ell x 3

3ffiy��I

17

A

0 is the centre of a circle in the given figure and L'.BCO = 50°. Find x and y, if BC is parallel to OD and AM ..L BC.

A

�3TT<ITI ABCD�f6rcnufo-n:�cfi"IBf1"lffu L'.OAD=68° %, ell L'.BOC��I

The diagonals of a rectangle ABCD intersect at 0. If LOAD= 68° , then find L'.BOC.

of 15

3

18 � ¢fllA if;- � cfiT o1".ffif 1.4 m 3W: � 2 m t I � 15 � if fcncRl � � ( cficR) 3

cfit1TT I (,r= 22 �)7

19

20

The diameter of garden roller is 1.4 m and it is 2 m long. How much area will it cover in 15

revolutions (,r = 22)

7

�I �I �

I �I�> �I�>�>�> �I �I �I�> �I�>

�>�>�I�>�>�>�> -31%f, �> �> �> �>�>�I�>

�. i=iF-f, �. � �, �, �. i=iF-f, �.�I� fcror2if lll�f"'*.9i:fi � � ��t1 �mf£1i:fia1��fcn��cfiT�

(a) �if;-�if � 2fT I

(b) �if,� if ��ti

Following is the data about the months of births of 40 students in class IX

Feb, Jan, July, June, March, Feb, Feb, Feb, Nov, Jan, Jan, Dec, May, June, June, July, June, Nov, Dec, June, July, June, August, Dec, June, March, July, July, June, Dec, Sep, March, Jan, Dec, June, Dec, Sep, March, Jan, Nov.

One student is chosen at random. Find the probability that the student chosen :

(a) Was born in the month of June.

(b) Was not born in the month of June.

f1Yfo1forn � -t- wm:, � itll{iilll:\11 � cfft" (� ,&.llll\1f'315! -t-) ��I

el'lt� iiill:iiiiiln'II

5 3

15 15

25 12

35 18

of 15

3

3

45 9

55 3

For the following information,

(without histograms)

CLASS-MARK FREQUENCY

5 3

15 15

25 12

35 18

45 9

55 3

�-� / SECTION-D

Question numbers 21 to 31 carry four marks each.

21

of 15

construct a frequency polygon

4

y

4 p

s 3

q

1 X

-4-3-2-1 1 3 ,..1

�2 A

v r

-4

Write the equations of the lines drawn in the following graph. Also, find the area enclosed between them.

y

4 p s 3

q 1

X

-4-3-2-1 1 . 3 --1 ,-2 -

r ,J

-4

22 � � � f<t:i fi:fim m 1:f{ Wll<JT TT<TT � � m � � � ccRUT � �:isihl-flj41dl wrr t- 1 � 4

� cfi1" � ffi � � "Q;cfl ,(-11-ilcfi{UI � cf� � 5, � y-'3-l&f 1:f{ -3m: ccRUf X-� 1:f{ � �

� *1•.f1i:fi<01 cfiT 31Tffig � 1 w� m, fi:fim m it 20 � cfiT � WTR 1:f{ � ccRUT \fl- �

�I

You know that the force applied on a body is directly proportional to the acceleration produced in the body. Write an equation to express this situation and plot the graph of the equation, taking constant as 5, force on y-axis and acceleration on x-axis. Also, find acceleration produced in a body, if force

of 15

applied on it is 20 units.

23 � -:ill•l{<i<titll ,mr''�.,�··��<fft�i:r.:��Tf<ll�l�3llcfiRf;r� 4

t � fcPlnt 4m, 4m 3lR Sm f I � f;r� <l11 � � f;mif l=fr:r <fi1 m � � i:r.: cm if

�I� "flt "ft� �'ffiTTT cfi1 chB �� "®%?

24

An awareness slogan "SAY NO TO SMOKING" was displayed on one of the walls of the flyover. It is of triangular shape whose dimensions are 4m, 4m and Sm. Construct the above triangle by taking dimensions as 'cm' in place of 'm'. What values are depicted to the people of the country with respect to this slogan?

(b) ilABC<fil �zj'l-lcf-;,"@ t � BC=7 cm, L'.B=45° 3fu: AB-AC=lO cm %1

(d) ilDEF <l11 � °tj'l-lcl t � EF=5.5 cm, L'.E=75° 3fu: DE-DF=2 cm t' I

Give reasons

(a) Construction of an angle of 22.5° is possible with the help of ruler and compass.

(b) It is not possible to construct a �ABC, given that BC= 7 cm, L'.B = 45° and AB-AC= 10cm

(c) We can construct an angle of 67.5° using ruler and compass.

( d) Construction of ilDEF, if EF = 5.5 cm, L'.E = 75° and DE-DF = 2 cm is possible

4

25 ABCD � cJ.f % I AB i:r.: � M � W-nR % �AM= MB t' 1 � AD 3lR � � CB i:r.: � P 4

3ltt Q � W-nR f � CM J_ PQ t I � ar(D.CPM) = ar(D. CQM) t I

of 15

26

Q

ABCD is a square. M is the point on AB such that AM = MB. P and Q are points on sides AD and extended CB such that CM .l PQ. Show that ar(�CPM) = ar(�CQM).

Q

(a) BJ:rrcfilcfiTUT-$T:f1f�I

(b) q<{T �ABC cfiT �'ID� t 7W; � cfiT 1ffilITT 11 cm 3W � cfiTUT LA

= 60° cf LB = 70° t I

(c)

90° lr I

q<{T �EFG cfiT � zj'lfq "tr, 7W; EF + FG + GE = 11 cm, LE= 105° 3W LF =

(d)

LY= 30° �1

(a) State Angle Sum Property of a triangle.

cm, LX= 75° 3m:

(b) Is it possible to construct �ABC if perimeter of the triangle is 11 cm, baseangles LA = 60° and LB = 70°

(c) Is it possible to construct �EFG, , if EF + FG + GE = 11 cm LE= 105° andLF= 90°

of 15

4

( d) Is it possible to construct /J.XYZ if perimeter is 12.5 cm, LX = 75° and LY= 30°

27 7 cm � � 1l;cfl �(!1rflcfiR � � 2.5 km/ hr cfft 7Tfu � w-ft � cfi{ � 3-ll*llcfiR � if -;;ff'® t 4 ��25m311'{�22mtl �if�tR�rrr,:ft-cfiT�fcITTRT��?

Water is flowing at the rate of 2.5 km per hour through a cylindrical pipe of radius 7 cm into a rectangular tank of length 25 m and 22 m width. In 5 hrs how much is the rise in level of water in the tank?

28 1l;cf) eRJcfiR � <fil w � '9"f-TT °ft 1.4 � >I"@ � cfil" � � 'l-1U lriIT I � � <fil � if 28 PHc 4

�' "ITT� <li" � 9i1 � #c:.ll-flc.( i:f ��I

A cubicle water tank is filled by tap water at the rate of 1.4 litres per second. Find the length of an edge of the tank in centimeters if the tank is completely filled in 28 minutes.

29 1l;cfl � cf>l" � 3lT"( � if 4 : 3 q,T 3fjCI@ t TI� � � 550 cm t I � 1R � eyqJU 4

<� am f@�foti4"i •) qi)� q,T � 6.60 �- >ffir qlf � it 5os2 �- i I ofilR (fil � aw

-��I

The length and breadth of a hall are in the ratio 4 : 3 and its height is 550 cm. The cost of decorating its wall on diwali (including doors and windows) at Rs 6.60 per square metres is � 5082. Find the length and breadth of the room.

30 � cfl&TT � 60 forrnf$rr <fir lTT� 'llR 40 kg �I � cfiT � 'llR 50 kg t � ("j�fcfilff cfiT 4

30 kg 't1 �a.,T � � aTR (!1�fofitff cfft � � �I

31

of 15

(a) The mean weight of 60 students of a class is 40 kg. The mean weight of boys is 50 kg,while that of the girls is 30 kg. Find the number of boys and girls in the class.

f10fctf©d mmT � fefim � ct fcwi£ � ct IX cfi"an ct 40

fcrwf$rr ct � q,T lfl6 � ll'1T * :

4

�cfi"TllIB" f.ffilf'qaj'<tt�

� 3

� 4

� 2

3ffi1 2

� 5

� l

� 2

'� 6

� 3

3� C,

4

� 4

� 4

,:ffe � fcrm� cnT � � �' i'lT � � � fcfi fcrm� cfil

-;;r,:q-

(a) 3nfun: � � q1S[ � 1);311 ti

(b) 31 KcITl 9T0 1TT6 � t3TI %1

(c) 30 RcJB 9T0 1TT6 if �m ti

The given table shows the month of birth of 40 students of class IX of a particular section in a school.

of 15

of 15

Month of Birth Number of Students

January 3

February 4

March 2

April 2

May 5

June 1

July 2

August 6

September 3

October 4

November 4

December 4

If one student is chosen at random, find the probability that the student is

born:

(a) in the later half of the year

(b) in the months having 31 days

(c) in the month having 30 days

�-� / SECTION-E

(� 'lffo /Open Text)

(* Please ensure that open text of the given theme is supplied with this question paper.)

32 Theme-I (Planning a garden) (3+4+3)

(a) ��;,-;i:�if;nrq-flli:fil{�ef)T��m

i1��efi7-�'lft-��I

(b) ;nf"ofi+Refi7-00U�� Bi:flcfi{QI �' ��'fiTf.Rl<Tiofi (70, 0) �I

(i) x- are,� tiiiF1iq:i; tr

(ii)y-3fe:f�BiiHia:i; i1

(a) From the layout plan of garden, find the area of the circular ring in which

maximum plants are shown. Also find the cost of compost for this ring.

(b) Write linear equation of the walls of room which has coordinates of one corner

as (70, 0).

(c) Esha is standing on a footpath. Find the probability that she is

a footpath which is

(i) parallel to x-axis

(ii) parallel to y-axis

-oOoOoOo-

standing on

of 15

10

fiq,f tt qua :rr - ii, summative assessment- iif tt qua_:rr - ii, summative assessment- ii...

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