chf Ht - I SUMMATIVE ASSESSMENT -1

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1 chf Ht - I SUMMATIVE ASSESSMENT - Nltt/MATHEMATIS 'ch' - IX/ lass - IX rcn:90 Time Allowed : hours Maximum Marks : 90 +q;:q : General Instructions: f I All questions are compulsory. -q,rif t "qf{ l, Gf, 'fro Gif "ajcrtf<fltl -lif f arcn cfil t -G{ if 6 t f.ir,:fi arcn t -'fr if 0 t f.ir,:fi arcn.t; o -G" if f f.ir,:fi rcfi i I The question paper consists of questions divided into four sections A, B, and D. Section A comprises of questions of mark each; Section-B comprises of 6 questions of marks each; Section- comprises of 0 questions of marks each and Section-D comprises of questions of marks each. -q,r if t I There is no overall choice in this question paper ;\i(- {'\i:!( cfil -w:rrt t I Use of calculator is not permitted. -at I SETION - A "'f l ocn l aicncfrr\- Question numbers to carry mark each. = 6../+ se Page of 9

2 Simplify: 6-./+ s./u x-x -x- cfilx- 'FT 'ffi I If the polynomial x-x-x- is divided by x-, then find the remainder. m L.A=80, BD 'ffl!it D, sfilffl: LB 'ffl!it L t- f m LBD =? B In fi gu re LA= 80, BD and D are bisectors of LB and L. Then LBD =? (-,S)q, x-la:t I Find the distance of the point (-, 5) from the x -axis. rgu-g-w{/ SETION - B 5 0ncn rcnclitt"i Question numbers 5 to 0 carry marks each. 5 z = 0.06,t, 'ITT (-;) cfill:jr I If z = 0.06, then find the value of (-;). 6 'W-lT 9 X 5 cfit l:jr I Evaluate : 9 x 5 by using an identity. 7 In the given fig, find x, LPOR and LROQ. Pageof9

3 8 fcti {&&0,S cfit lr tr ll'i:zf- mnt t I Prove that every line segment has one and only one mid-point. 9. et-facqs cfit lnr cm t lr i:rfti:r 0 cm t I -I The base of an isosceles triangle is cm and its perimeter is 0 cm. Find the area. 0 cfilffltj toerr qft '!Pflai'icnT ::sti cfil The perimeter of a triangle is metres and the ratio of sides is : : 5. Find the area of triangle. -lf/setion- oncn aicncfitft Question numbe_rs to 0 carry marks each. -./ 0.Js cfit qf(l qif>{uj I 5-5 Rationalise the denominator of -./ Js 5,._fiq;) ml fflt "R Rfi I Locate../ on the number line. Expand ( - x J. Page of9

4 If (x-) and ( x - ¼) are both factors of a.x + 5x + b show that a = b. 5 n:r,r AB II co, cd II EF t EA. AB aw: LBEF = 50 m, m x, Y afr z cnt ljr In the figure AB II D, D I EF. If EA l. AB and LBEF = 50, find the values of x, y and z. 6 Wf@. POQ 00 't ORLPQ, OS t "T fen OP o?.ll OR lf 't I ftr.& LROS=._ (LQOS-LPOS) p Q In the given figure, POQ is a line, ORl.PQ OS is another ray lying between OP and OR. Prove that LROS = - (LQOS- LPOS) S R p Q 7 f,:r,r l er m <ft f 'Wl'RR OOa:f'i p w: q cnt!,l@'i@:: 't I ftr.& fcfj- aab::ada Page of 9

5 p q In the figure and mare two parallel lines intersected by another pair of parallel lines p and q. Show that AAB ::dda. p q 8 "RB[ AB BE aw F I AAB flifacql r i I A B In figure, BE and F are two equal altitudes of AAB. Prove that AAB is isosceles triangle. A 9 cn 'lfi Tcfilw-rr -re:cn m "5ITTITTcn m? Find the percentage increase in the area of a triangle if its each side is doubled. 0 AAB t, jii0 cm t" afu: ADB ticfi'lo t, LD=90 i BD=6 cm m, -qrrr cfi'f l$ffib ($ =.7) Page 5 of 9

6 A B In the given figure dab is equilateral triangle with side 0 cm and adb is right angled at LD = 90. If BD = 6 cm, find the area of the shaded portion ( Ji =. 7 ) 'gf-f ncfi rcficfilt"i Question numbers to carry marks each. Ji $ 'cfil -q 9 fj c:itt:"@lqll cfiajl' 'Til<IT furq:, qfb-ljcfi<ui cfib 'cfit v;cfi' I 'cfit o\!u 'cfil 'qlcftt furq: I Ji.fi 'cfit fcim >fcfir? ffl-m mort? Varun was facing some difficulty in simplyfying Ji..Ji. His classmate Priya gave him a 7- clue to rationalise the denominator for simplification. Varun simplified the expression and thanked Priya for this goodwill. How Varun simplified.fi Ji? What value does it 7- indicate? J'i =.ll Page 6 of9

7 Rationalize the denominator of and hence find its value, if../ =.. -Etci-Etf'lc:fil cfit ffl'f 'cfmt (06) - (9) cfil lwi I Find the value of (06) - (9), using a suitable identity. 5 cfln cfit a:w«a p(x) = 8x + x - x- t I crft a:ff tf,nfc@ -qc;: I x = 5 cfi"{ l The volume of a cuboid is polynomial p(x) = 8x + x - x -. Find possible expression for dimension of the cuboid. Verify the result by taking x = 5 units. 6 «f-s : x +x +x+0 Factorise : x + x + x m ll, l,la crft t o l R B t I BP afr BQ, B ffl A cfit a:ff R ffl TfQ; f I fcn - (i) aapb :AAQB afr (ii) BP= BQ i I In given figure, line is bisector of an angle LA and B is any point on l. BP and BQ are perpendiculars from B to the arms of LA. Show that (i) aapb =aaqb and (ii) BP= BQ. Page 7 of 9

8 a, b c q;fllfj I Q In the figure, two straight lines PQ and RS intersect each other at 0. If LPOT = 75, find the value of a, b and c. R 9 A.AB if AB =A BDl.A el El.AB f I fci; BD= E t I In AAB, AB= A and BDl.A, El.AB. Show that BD= E. 0 <ft" ll<fiib ilaab ctft B cfit D W-f 7P-TT t I LAB W:LAD R E "ti\ fir.mf, (ff LBE=.!_LBAll B D In the given figure, side B of AAB is produced to D. If the bisectors of LAB and LAD meet at a point E, then prove that LBE =.:. LB A. AAB if LB L amm:cn BD afu D f I 80 +y= x t I y B In AAB, BD and D are internal bisector of L B and L respectively. Prove that Page 8 of9 80 +y=x.

Q4. In ABC, AC = AB and B = 50. Find the value of C. SECTION B. Q5. Find two rational numbers between 1 2 and.

Q4. In ABC, AC = AB and B = 50. Find the value of C. SECTION B. Q5. Find two rational numbers between 1 2 and. SUMMATIVE ASSESSMENT 1 (2013 2014) CLASS IX (SET I) SUBJECT : MATHEMATICS Time: 3 hours M.M. : 90 General Instructions : (i) All questions are compulsory. (ii) The question paper consists of 31 questions