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ICSE Class X Mid-term 2025 : Mathematics

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Shaurya Gupta
Vibgyor High School, Haralur Road, Bangalore
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\ \' t I @ m1~nm im HIGH I l I ,, I ' First Term E)(aminat~on ' AY 2024-2025 MATHEMATICS I Grade: X \ \, I I l Max. Mar,ks: 80 I I ' Oat~ : 18/09/20~4 Time Allowed: ~ hours \ INSTRUCTION~: , ' I ' \ I ' \ I ' t \JJ ,, I I Answer s to this paper. must be writt~n on the paper provided separ~tely. You will n~t be ~llowed to .write during the first 15 minutes. \\ 1 4 I I ~s to b~ sp:~_nt' i,n rea~in g the q:~est~9n pape.r. This time \ \ \ l I,\ 1, : . I ' t The time giv~n at the 'head of. this' paper is the time allowed for. writing the '1 ~ l I answe ~ I ,.\ '' , , ':, .I I ''ii , \ . ,., . . . . .. .. , 1 ' 1 1 .~ 4 \ ; I ., I ~~-, '\' I. l ~ l t ' 1 ' I ' \ 1. \ l I I I ' ,r ~' ' ' \ I I 1 \ ~ \ ' ' l I I~ \ } :,~ 11 \ I 1 ' \ l ' 1 l ,,' I 1 :11 :t I /1 ', 1 ' ', ' .' ' l ' l I \ ' I ' \ ', , , \ ' ' '\ I ~ . The i.~t~n.ded,,.ma~~s fc>.'r '.the- ql;lestions ,;o r,'p,r1:s of que stions are!give n along~ide I \, \' ' ' \ 1 }t\ \ I . the ques ' .t ions .. , ' I. ~ ~ Q'' I t\, I -,., ~ 1 y " \' I";l ' I 1t, ~. ' ~ I I \ l I ' ' :I ' ' I 1' I , \ ' ' \ I I \qt'i ' { f 1,_,l '' I , , \ ' '1 \ \ ' ' 1 I , i , I I I ' 1 :\ j I , , I This question. pap~~ contains 9 prin~ed pages . .',~ . w~' Attempt all questions ,from Sec,tion . f'~an~ ~ ~ \ ,\ l I "' I , ' I ' ' I i ; . , I , I ""Y four tjue'stiori,from 'Sectior1 B \ ' \ \ , \ , i "' I ' .~J \ , ~ ! , ~. \ ~I\, ' I( \ ' ' I \ I\ I 1 ! I ' 1 ~~ 11,\ I , ., I ' ., , 1' I 'l I f I ' 1\ ' 1,. ' ( \ ) \ \ ' " L \ ' ' " ' \ 1 ( ' .1 \' 1 \ ! ,\ '\\I I ' I ' ,1 ' ' . ,. '-. \' \ I ' ' ' \ .,. ' ' \ ' ',, ', I ' I I ; ' I 1 I ' 1, ,11 ' .. 1 \ \ ,! I I ' ' ' 1 I I I I ~ ~ \ on the same-sh eet: as the rest of the answ\e.r. Omissic;>n of esse.ntial working t ' ~ will result in the loss of marks. ,.. ... . . i '. : 1 i t ' \ . ' " Geome~ri.~~I fig~re~ to be' constru~te~ 'wll~reye'r ap~lic,ablel. ': \'' f For geom etry, 'fig res are ~o-be copied tq ttje,answer script. ,; \ ,,. / } th 1 All wo'rldng, includin g rough wo.rk,; m.ust be clearly showt{and :must be.' done , I 1 , , I I : ) ~ :'. ' ' , II ' \ I''. )," . I I . I I SECTION A~.. (Attemp't all questionsYrorp t~is S~ction.) ' \ .' ,' ~. I I' . l I \ Question~ ,.. ' I . 'i I l ' ll) ' \ I I ' I / I I 1 \I + \ I, , 1 I ~ ,\ ' J '\\~ \ ' \ [15] I \ \ \, \ , ' I ' , ''.'I I !1. l t / '1 2 , ' \ ' \' I ' : ' 4 i, 1 , , I \ , 1 , '. l t , Reason (R)t Th~ sample space for even numbers on a di.e is I ' r '- l an even' riumbeir\: jg,- : ' ":l, I 1' j I '{2, 4; 6} ' , t "A \ ' '' . ' ,., ori'ly.) . . . ' .I ' i , 1 \i), ' ., 'As'~ertion (A}: dieds 'thro~n once and the pro~ability of getting ' ' 1 . I I,., !' I . ,., I \ I 1t ~hopse t~,. c~rrect a~svver~ to the,'questions from:,\h~ give~ ' 1\ ,1 .) ; ,oPitions . (Do not copy the questio n, write t~e correct i1nswers \ J Io I I. ' 'l I I I 11 y ' . ' !. " ,: ' I ! 11l \ !' I I I:: ' I I ' 1 .. ,l j l ' (a~ (b) ' I I I I I .,, t \' 'I \ \ ' t\ I I ' ,. A is true, R i~}tals~J~ . I ft:. is false, R 11S trtie. 1 , Both A and R/ars true., 1 I 1 \ \I l3oth /\. and R' are false. '' \!, I ' ,, ' I '' in, desce'ndi,ng ! H'j I' I (a) (p) ( ,, I I. j N, ' '. ,, b ,: I \ (bj' ab = ex. (c), .bx \ ac I (q.) I 'cb 'I ax I 't ,, \ )I I I 2 l i I I 1 I 5, Mammwd HIGH (v) The centroid of the triangle whose vertices are (3, -7), (-8, 6) a nd (5, 10) is: (a) (0, 9) (b) (0, 3) (c) (1, 3) (d) (3, 3) \ -2 (vi) -7 . For what possible values of x are the numbers 7 , x, 2 are 1n a G.P? (a) -1 \ I. (b) . 1 (c) Both (a) and (b) (d) None of these I I ,'I fl I ..... \' ' (vii)' .. 30th tetm of th~ A.P. : 1 o; 7, 4, ....... 'is: ~ . I (a) 97 I, '1 t I (b) 77 (c) -77 (d) -87 '. (viii) If (x-a) is a factor of the pqlyribmial p(X)=x~ - ax2 +2x + 2, t.hen the value of a is: f ,. l (a) 1 (b)' -1 (c) 2 (d) '-2 ,' I (ix) The given table shows the distance covered and the time taken by a .train moving at a uniform speed along a straight track. Distance (in m) 60 90 y X 5 I 2 Time (in sec) The values of x and y are: (a) x = 4, y = 150 (b) x = 3, y = 100 \1 3 It .,' HIGH I ,, ,, \ =100 X\ ='4, y (c) 1 \ (d) 1' ,The quadratic equation 2x 2 (x) -fsx + 1 = 0 has: - I ~ . (~) two distinct real roots (b), two equal real ro.ots (c) no real roots 1 \ (d) ' more than ~o real roots ,\ ~ . . (xi) \ ~The:sq! tion set, representi11g lthe followjng number line is: I ' '.' I ~ " \ 'I \ I I I I : . _ , ; ~: :; .:l2;7zJ -, J I .I I > . 3 4 5,: ."6 7 ' (a) ' ' I {x : x E R, -3 s x, < .2} , . , . .-(b). , {x i x E ~>-3 < x 2} , ~ '' " . , ' . 1 1, 1 (c) {x: x ER, -3 s xs 2} (d) {x ; x E R, -3 < x < "2} I I ; . . . t ) ' l ' ... 'I . ... , ,' . \ I t , . \ ,j ' . ..,_) ~ .. \. \ 1 : \''f ' , , '~ ' ' :'\ . ~ .. ' l ,1,.'l\ ' t \I, , I \ The sum invested to .purchas e 15 , shares of;-~' company 6f ,. ;. . . (xii) : ' :... < ' -~ < I ,ao (a) ,, ;. , i ' ' ' I I \ I \ _.. : ~~ \ '\tt (b) . ,go .(c) 1 l nominal value ~7.5 available af a discou~t'of 20 /Q~ i~: 1 , \ ~ - I ~ I I~ ,1350 .. (d) ,goo ' .. ' .. . :' . ,:,.," .,~ (xiii): A-man deposits ,400.per month in a Recurring Deposit Scheme . <. _fo'r,. 1,. year _givjn,g 5% p.a.- simple interest. The interest earned at .. ' ' \, I .. ~ \ .I I the time 0f-maturity is: (b) ,a5 ,1s (c) ,130 (d) ,1so (a) '\\ ' 1c! "'Ii, 1 l l l 1 ll 4 I I .. ' ' l ' . ~- , . . . - --,,l) IW rafcl21 ID ' HIGH (xiv) ' For an Intra - state sale, the CGST paid by a dealer to the Central Government is ,120. If the marked price of the article is '1 ~2000, the rate of GST is: (a) I 6% I 10% (c) 12% (d) 16.67% (xv) The (a) 460 (b) 640 (c) 320 I ;1 ath term of the geometric progress.ion: 5, 10, 20, ..... is: .. .., , I . :1 ! ,, 'l 1I 550 I I . l, \ 2 ] M = 61 1 ~ 4 In [ -1 (i) ' d ) ' ', ' l I ' [4] ~ ' \, I ' ": State the order' of m~trix f\.( . ' ' ,Ir I ; t l1 \ ' ' l I i ,, t ,. (b) ' Find the matri,x M; ." I fl , . ,, (ii) . ,, M /.---r--::;:,'),,, \ \ \ ' '. '' ' '' ' ''I R~ . L = : : : . - - - 5 , - - - - - - t ' S I I l I ' Where Mis a matrix:a nd I is a unit matrix of ord~r 2 x 2 .. (a) I ;I (b) (d) Question 2 ' I ter of the circle. NM is parallel to In the given figure, RS is..a diame . RS and LMRS =,29 . Calculate: (a) LRNM (b) LNRM 5 ' \ [4] I . l .. l l' I{ t, I l I ,I' 1 I . ,,.... ! l ' I\ .~ t .' I I I 'I ' 'I ,, (iii) I I 40 , X '28 f I Question 3 1 I (i) .I (ii) (iii) I. "I . , J ! . '' ' A 1 B D C 6 ' ,i 1 ,~ l l ' ,: .. ,, \ Question 5 ,. t \ ~, 'l ,, I I 1 (i) I I ln th e given circle With centre 0, LA8 C 1ooq,_ LACD = 40 a~d 1 ,1 CT 1,s'a tangent to the bircle at C. Find 'LAoc and LDCT.: ,, A ,. ,1 ;, I ' ,. I ' I\ ' [3] I I I I I I I ' ') ,I I 11 ,, .1 I I \' I 'I \ I l, I I I . I II I},'f ' \ I I I ' ' I \ I a t I ,, I II l \I " ;I \' 1\ I I\ ., I ., ' I , 'l I I ,II I ' I I ,. I I \ ;, ' , .~ ' ' \ I' \ I ., 'I I I eva'Juat~~x ,I\ I [3] .. ' 'I ,, (' ~ ' h ' ' ,. I. ., s.' ' '' l , I I ' l ,'. ~-;,. }' ..: 9 triangle''ABC I\ ' 1 \ I , LC ' [3] .' ,\ I I I. ediar.1s of the m ,\ 1 1 I I' \ I 'I I 11 I ti 'I I \ \ ', ' \' . ' ' I ,. I 'I I ' ' I, 'I l I\ ' ~ 1' " I I 'I \ I " '' ,I , I I ., I, ' ~. ,. ,, , i' .~ I I . ,, 'I h' ,I ~ ,, 11 t, 7 ' 'I ,I ~ 'I \ I I I . l \ 1 I " .. ' .. ' (iii) I,' Q I I ltlD~ iR!~ H(GH J I,, I J f ,! I I ' . ,, ' I r'' ., ,~ II ' I I'' ' , ,; ll, ' i ' ~ In the given fig\jre, O Js ,the centre of the circle. PQ is .the tangent to \the circle at T. Chot.d As. pre,duced meets the tangent at' p.' l ,, 1 , r, . Find: ' ' ~. ' ,1 " ' (a) length of PTt' ~ I I \ t i \ 1 I I ' i : 1 ~I I I 'I \ I I /'1 t"- ~) 1 \ \ II I ' I 1 \ l) ! t ..(b)< LBAT , (c) LBOT , I (~) ,', LABT. ' I, ', I Question 7 (i) \ ' ,\ I ., Question 8.,. 'I l I' I 1 '; t'\ l 1, I. , : ,50.;ao ~60-70 ' ',70-80 ,180,~90 90-100 .. ~. ... 'I . . ,. '. . .. ' ' ' ' No of students 14\ 4',, 8. 19 5 . ' ' Draw a 'histogram for the above data using. a graph paper and . Marks ' \' I I ' ., I ' I , , ,, I \ 1 ' 1 I 1 I ,, I 1. Ii I I I locate the mode. 1 I 8 I \ l '- .. ' ' @ .....,,-=rn. l'-.---,~~IIIQ':1 m HIGH (iii) [4] Using ruler and compasses only: (a) Construct a triangle ABC with BC= 6cm, LABC = 1 20 and AB= 3.5 cm. (b) In the above figure, draw a circle with BC as diamete~. Find a I circumferenc~ of the circle which is point ' P' on the I 1 equidistant from AB and BC. (c) Measure LBCP. Question 9 (i) 37x +,, 26 completely. + 10x2 - x3 ' 1 ' I ,' (ii) [5] Using the Remainder th~orem, factori~e the polynomial [5] Draw an ogive for the fo.llowi'ng frequency distribution . Use your I ,I~ l ogive to es,i~ate: '. :, (a) the me'di.an' ,. I ' (b) the upper Quartile '. ' \ ' ,. .. ' I' \ ',, l ' I ., ' ' I Quartile .. (c) ,. th~ lower ' . ,., .. . ' '. ' \' ' I' \ ' ' .,::, ' ' ,IP '\ \ I '. I 10-1'5':, 5-10.',, I C. I : \ I\' ,I' I 1''W 4 3' .. f- \ ' 1 ,, ~ \, \ Question 10 .. ) 9, \\ I I I , . ~ .7 l - . ' ' .~I '( , , r \\ ' , '1 1 . '1 .', '1, , ' ,t , I , \ ) ( P, ., I , I , 1 _ /\ 1 business concern ~nd during the f~rst yeq,r after,.purch~se ~t ;:' t . ' . recei~ed ~~oo as divide~~\ on .his ~h~res::Find'the rat~,of dividend. ' I _ ~\ I, on ~hares. ii (ii)' q ' h A man bought 500.shares, each qt.face value ~10, of a.'.certain A , , , I ,. ; 1 11 ,1. , . 1 .' I , ' l, \ \ ,, .. " , , t<, 1 Con~truct a regular hexagon of side- 14 ,cnt Cpnstruct a circle f I ,, I (3] 1 I. \'- 1 . circumscribing the h~xagon. ' . ,1 ,, . ,' . , ' . . 9f transaction intra-state fofl~wing the for bill of amount tt:,e '.(i~i). Firi~ ,,I ' , goods. The r~te of GST is 12%. 5 ~ 1 ~ MRP 1 1. I \ ' ' ,, ( ~ i' ' \ l (i) 1' \ i\\. . \ I I ' ') I. , " 6 , I : ' ) '30-35 25-30 20-25 \ 15.::20 .. ,I:_ I Discount ' ,2so ,200 ~150 ,300 30% 40% 32% 20% l ***** 9 I [4]

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