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ICSE Class X Prelims 2025 : Mathematics

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9-Atharva
Ryan International School ICSE (RIS), Malad, Mumbai
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PRA CTIC E EXA MINA TION 202 4- 2025 o. : Nove mMf' 11. 2024 Suttle ct: Mattt .matl ce Std: X A Maxtmum MMU : tKJ Time e/loW 9d: 1htf f Hour s ~MP entl ety. An~ toth ispa ptHm u$lb ewr itNv lont he~ rp,o You will no1 be allow ed to wrilo durin g first 10 minu tes. This time is to be spen t in readi ng the oues lion pape r. writin g the answ ers. The time given et the helld of this pape r is the time allow ed tot from SecU on 8. Attem pt all ques tions from sectl on A end any four que.stions and mu. t be don on th All worlc lng, Inclu ding roug h worlr , mu t ff c,._r ly ahow n. m shH t th rwst of the answ er. Omis sion of NSe ntl I worl llng wt/I resu lt In IOU of marlc.s. in brac kets [} The Inten ded mark s for ques lions or parts of ques tions sre given Mathematical table s am provi ded. Tl,/s paJH r co,rslsts of JO quut ions on 12 prlnt ~d sida . Section A [ 40 Marl<&) Attempt all questions Que stion 1 (Do not Choose lhe correct answers to the questions from the given options. copy the question, Write the correct answer only.) The marked price of an article is , 5,000. The shopkeeper gives a (i) the discount of 10%. If the rate of GST is 12%, then the amount paid by customer including GST is: a/ f610 0 9 (ii) If x ...bf f504 0 c) ,s,2 12 d) ,6,1 60 = 3 is a root of the quadratic equation (k + 2)x' - kx + 6 the value of k is: a/ 2 b) 4 c)-4 d)- 3 = o. then [15] (iii) covered and the time taken by a . ht track. The given table shows lhe dlst nce 8 9 y ,ira,g lr fn moving at a uniform speed aton 60 Distance (in m) 2 Time taken ( In sec) 90 5 X The values of x and y are: y = 150 b) X = 3, y = 100 C) X 4 ,y: 100 ) X 4, d) (iv) X = 3 ,y 150 (s 1 8 - 1)( I - ~ ) Is: a) 1 (v) If A= (3 c)-1 b)O -zJ and B = (; 1 d)2 i1 Asser1ion (A): Product AB or the two matrices A and B is possible. Reason (RJ : Number of columns or matrix A is equal to numbe r of rows in matrix 8. a) A is true, R is false b) A is false. R is true c) Both A and R are true, and R is incorre ct reason for A d) Both A and R are true, and R is the correct reason for A (vi) The height of the half cone shown in the figure is: a) 1 m b) 15m c)5m . 2. 'd)i,JTI m (vii) Which or lhe tollOW1ng equoUon represent line pa1 lng through origin? J 3~ - (VIII) 2Y + 0 0 b) 2i- 3i 0 C) x d) y 5 -6 1. Sharot of company A. paying 12%, ,100 aharas are at ,ao. 2. Shtrot of company B, paying 12%, ,100 aharot at ,100. 3. Shtrot of company C, paying 12%, ,100 ahares are at ,120. Share of which company/ are al premium? b) Company B Company A o) Company C a) (Ix) d) Company A and C A right-angle triangle shaped piece of hard board Is rotated completely about Ila hypotenuse, aa shown In the diagram. The solid so formed la alway,: 1, Ingle cone 2. double cone Which of the atatement Is valid? a) only 1. b) only 2. C) both 1. and 2. x) d) neither 1. nor 2. 111 cm 3cm In the given diagram, /J, /I/JC Is similar lo /J, Dl:P by the axiom: a) SSS b) SAS c) AAA . l. d RHS lh6 ci,cumcenlre is equidislant (xi) Statement A: For any ,caJene tri8"9~ from the sides of the tn,ngJe. . . 1of the medians of any Statement B: c:.,nin,;d is Ille n,eebr>9 poll1 triangle. . le Is equldlslanl from lhe vertices Of Statement c: tncenlre of eny mang the triangle. a) Alf lho abo,e sta1ements A. B & C are !rue b) An the aboW! statements A.B & Care false c) The statements A & 8 are true a nd C is false d) The statements A & C are false and B is lrue. (xii) A number Is selected at random from lhe numbers 3, 5, 5, 7, 7, 7, 9, 9 9, 9. The probability that the number selected is their mean is; a) (xiii) ji b) i c) f d) ji In the adjoining r,gure, O is the centre of lhe circle, and a semicircle is drawn on OA as lhe diameter. LAPQ:2Q . The degree measur e of .<OAQis; a)25" (xiv) The 4" lerrn from a) 37 xv) b)40" the cJ so en of the seq b) 46 d) 65' d uence: 11, . 8 . 5 c) 0 4 .4 9. is: d)43 The reffection of the point M ( 1 . 3 a) (. 3 . 2) ) '" the line y = . . 1 IS ' b) ( !, 3) c) (1, SJ d) (1, 1) / 0uHIJon 2 (i) ff a. b, ~ are In conooued propottion. prove lhat ..:::':~=a - b + c (4] Hence , ftnd three numbers in conbnued p,oporuon having a swn 19 tnd having lhe aum of their squares 133. (II) Shown below ;s I horizontal water tank composed of I cytinder and two (4] hemispheres. The tank 11 filled up 10 height of 7 m. Find the surf,ce area of lhe tank In contact with water. (Use TT ) 34m (iii) The line segment joining A(2.-3) and 8(-3, 2) Is intercepted by the x- (4) axis at th& point M and they axis at the point N. PO Is perpendicular to AB produced at R and meets the y- axis at a distance of 6 units from the origin 0, as shown in the diagram, at S. Find the: (a) coordinates of M and N (b) coordinates of S (c) slope of AB. (d) equation of Une PO. 2 3 (2, -3) -j - r [4) In the given diagram, ( ) (ii ) O is the centre of citt:le cif'cumscribing the AA .BC. CO is perpendicular 10 chonl AB. 0AC 32" . Find each of the ri no w n angles x. y and z. 11 1, '- l) is a fa do ro l( r -o .r ' + bi + 2) . find the values of a an db and hence factorize lh e expression comple tely. Use graph paper 10 an swer the following qu estion. (Take Ia n = 1unit onboehtheaxes) a) Plot the p001ts A(2, 3) and 8(6, 3). b) Reflect A in the origin to get the image O. c) Reflect A in the x-ax is to get the image C. d) Write the c <>rdinates of C and D. e) Give a geometrical na me fo, the closed fig ure ABCD an d find its area. ij Name an invariant po int fro,n the figure on reflection in Y axis -6 - ///// [4) (5) ( Secdon 8 (40 Marb) (Attempt 1ny four quesrions from this sec:bOn) 0uHtfon 4 {l) ' [3) Shubh1 hH a cunulatrve ttme ~ i t account in S81. She deposits i , 800 per mon1h fo< a period of 2 yeari. If 11 the tme of maturity she gets, 26790, f111d the interest paid by the bank and hence e,5culate tall of inlere11. (ul There are three pos,tive ni.mbeB in Geometric Progres.sion (G.P.) such [3] that their product is 3375. the resutt of the product of first and seoond number added to Che product of second and third number i5 7SO. Find the numbera. (iti) (4) A tent fs in the shape of a cylinder surmounted by a conical top. If the height and radius of the cylindrical part are 7 m each and lhe total height of the tent is 14 m. Find the: (a) the quantity of air conlafned inside the tent.- Y? I' 7 '-' 7 -,, ., ~ (b) radius of a sphere whose volume is equal to the quantity of air inside lhe lent (Use ,r = ,) Question 5 (i) Solve the following inequarion, write the solution set and represent it on (3) a real number line. -1i <i- s3,x ew (ii) If A= rt :J.s=[~1 ;J. C=[_\ ~],Find AC+ B'-IOC f ~\ o" ) s . 7, (3) _,, Z' > n.,., ~ . (iii) 141 d /jJ IB ,G .P oi n1 Ds on , , _ - al J,D fln d. 8 .eJ _, . .. . A (e, b), B( _., 3) ond C( (IS.O)S BCauc:hlhatBO OC 2 , enc,M ,. ,. ,_ ., ., _ ., .. .. o A (b )., _. ,., ._ ot po W l peuir"IO thfough M -,c (CJ OQUabOn Qf e line .., ... .,o ir, eB C . ()'II, d; .co un l 0- ll on 8 f 50 lhat9S avU8ble at A man inve'lts , 22500 in (I) 1 I( th e (3 ) mpany is 12%. ca tcu lat e di vi de nd ~ by th e c;o (U) rchased. The nl.fflbet of ahllres pu ,eoeiYed. b) Th e ennu.l dividend ts on hi t Investment. c) The rate of return he ge number lO the nearest whole Give your anawer correct nd the roots [3] 1 - 3 ( x + 3 ) : 0 and fi x n tio ua eq ic the quadrat (Hi) figures. correct to thtee aignif,cant '8s for thi:S question. Use the mathematical tab ing a scale of the foHowing question tak fo, s se as mp co d an er Uae rul > Solve t J 10m 1cm. and DA. straight fences AB. BC, CO by d de un bo is y cit a in rl< A pa equidistant a point = 63m, LABC = 75 . 0 is BC m. 50 = AB t tha n ve Gi the outline of the B AO = 9()0, Construct If . BC d an AB s ce fen e from th flag post t P on the line BO for the in po a ate loc o Als . CO parl< AB and B. the comers of the park A which Is equidistant from Quulion 7 (i) a scale of 1 : 250. Find: lo de ma is ip sh of l de A mo el is , .em. if the length of th e m od ip, sh the of gth len the a) the m od el is of the ship, if the area of ck de the of ea ar e Th b) 2. 4 m l sh ip del, if the volume of th e c) The volume of the mo . 8. is 1 km ' [3' 131 Oil In lhe given figure. diameter AB and chord CO of a circle meet et P. PT Is a langent to the circle at T. If CO 7 cm. PO 9 cm, PB 6cm. lind a) tho radius b) tho length of tho tangent PT. (iii) Using step-deviation method. calculate the mean for the following l J frequency distribution. Class 0-15 Frequency 15-30 4 30-45 7 45-60 6 60- 75 8 75-90 2 3 Qutatlon 8 (i) (3) Prove that : (sin8 + cos8) (costc6-sec8) = cosec8sec9-2ta n8 (ii) How many terms of the A.P 33,37,41,-- must be taken to get a sum {3] of 1206 ?. . 9. , Std: XA \ 1 1 ~ A p ft In the figure given aboYe. p Is point on AB and 0 '9 point on SC soeh lhatAP: P8 4:3. PO lsparale ttoAC. (a) Find the ratio PO: AC. giving reuon1 for your answers. (b) In 4 ARC. <ARC 90' ond In 4 POS, ,PSO 90' Given OS :: 6 cm. C) Find the kmglh of AR. d) Find the area( 6 PBO) : Area quadrilateral PACO. OuHtio n 9 (/) Ahmed sells different type& of cake in his shop. The co11 of each cake l3) depends on its size. Every smaU coffee cake costs , x and every large coffee cake cosis, (2x +1). Pech spends t 20on 1mal coffH cakes and ,10 on large eoffff cakes. Pedra buys a total of 45 cakes. Write down an equation, in letms of x. then find the number of each type of cakes Pedra buy. (ii) In the figure, PTU is lhe tangent at the point T to the circle QRST and PQR is a straight fine. L POT 100 , L UTS = 55 and PO= QT. find, giving your reasons in full, the size of a) L TSR, b) L TRO, c) L STR 10. [3] \ , ~~ (iii) The follow;ng bill Shaws th articles: e GST rate and the mant.ed Price of the r---- (4) Rajdhani Departmental store S.No llem I ~ a) b) Dry fruits (1Kg) Packed Wheat flour (5kg) c) I Bakery products Mark.ed DtSCoun1 price Rate of GST '1200 ,,oo '286 Nil 5% '500 10% 12% 12% Find the total amount of GST and amount to be paid ( including GST) for the above bill. Question 10 (i) The angle of depression of two ships A and Bon opposite sides of a light house of height 100m are respectively 42 and 54 . The line joining the two ships passes through the foot of the lighthouse. (a) Find the distance between the two ships A and B. (b) Give your final answer correct to the nearest whole number. (Use mathematical tables for this question) C -------~- '"! ): -----,, , ,,' -~2-- - - f ", ', ' .. ' r.'~ ---- -~z:-,~ -11- [5) (SJ (ii) Monthly Income .lJ.!!.!_thousand) No. of workers - 6-7 40 7-8 66 8-9 86 9-10 120 10-11 90 11-12 40 12 13 26 Draw an ogive for the above data and from it. determine: MJ The median income. The number of employees whose income exceeds 11800. l Take_?__cm_= ~ 10,00 on one aixis and 2 cm= 50 employees on the other.) 12

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