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ICSE Class X Prelims 2025 : Mathematics (Bombay Scottish School, Mahim, Mumbai)

10 pages, 9 questions, 0 questions with responses, 0 total responses,

Navneet Kapoor
St. Xavier's Institution (SXI), Panihati, Kolkata

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. ,. . om&ap 6cotti ' 6ct,ool, a{Jim MENT PR EL IM IN AR Y ASSESS MA TH EM AT IC S : 80 Max. Marks = l0 No. of Qu es tio ns 10 : es sid No. of Printed : 10 Gr ad e : 07.01.2025 Date Du rat ion : 3 ho ur s d separately. be written on the paper provide st mu r pe Pa s thi to s er sw An ite during first 15 minutes. You will not be allowed to wr ding the question paper. This time is to be spent in rea the time allowed for writing answers. this Paper is The time given at the head of cti on B. an y fo ur questions from Se d an A on cti Se m fro s be ion At tem pt al l quest cle ar ly shown, an d mu st be .st mu , rk wo h ug ro g Al l wo rk in g, includin th e re st of th e an sw er . do ne on th e sa m e sh ee t as ll re su lt in los s of ma rk s. ing wi Omission of es se nt ia l work rts of questions are gi.ven in brackets / J. estions or pa Th e intended marks for qu ovl.ded. M ath em ati ca l ta bl es ar e pr I. Se cti on A s Section.) (Attempt all questions from thi Question 1 (15) ns from the given options. tio es qu the to ers sw an ct Choose the corre the correct an sw ers only.) ite wr , ion est qu the py co t (Do no t for a recurring deposit ac co un te in nth mo r pe 00 25 s, sit A ma n de po tur ity , th e ra (i) as int ere st at the time of ma 2 years. If he gets , 6250 of interest is (a) 10% (b) 8% (c) 12% (d) 5% (ii) d of A(-3,-1) an d B(S, 7) divide n joi the ich wh in io rat e Th Assertion(A) : by the line x = 2 is 5 : 3 lin e se gm en t ersection of line x = 2 wi th int of int po e Th : (R) n aso Re AB is (2,0) (a) A is true, R is false. (b) A is false, R is true. n of A. d R is the correct explanatio A. (c) Both A an d Ra re tru e an t the correct explanation of no is R d an e tru are R d an (d) Both A 1 (iii) The centroid of a triangle whose ver tices are ( 3,-5) , (-7 ,4) and (10,-2) 1S (a) (b) (c) (d) (iv) (3, -1.5) (2, -1) (-1,2) (0, -1) A company declares a dividend of 12% on ~ 100 sha res . A ma n buys suc h sha res and gets 15% on his inv estment. The price at which he bou ght the sha res is: (a) ~ 80 (b) ~ 125 (c) t 85 (d) tl0 0 (v) (vi) f ABCDE is a regular hexagon, AB is parallel to x-axis. If the coordinates of the point B are (2,4) the n the equation of BE is: la) y = x + 2 lb) y + "3x = 4 + 24'3 (c) y - 4?,x = 4 - 2../3 (d) y + x = 6 If P and Q are the centres of two circ les intersecting at B and C. ACD is a straight line and LAPB = 130 , find x. [) ! ,, - , A .. ... \ (a) 550 (b) 1150 (c) 2300 (d) 1300 \ 2 (vii) Asser tion (A) : The value of sin A is the great est for fl PQA. p Reason (R ) : The value of sin A does not depen d on the side lengt hs but is a ratio of the side lengths. (a) A is true, R is false. (b) A is false, R is true. (c) Both A and Rare true and R is the corre ct expla natio n of A. n of A. (d) Both A and R are true and R is not the corre ct expla natio bes a (viii) A /l ABC with L.ABC = 90 , AB= 15cm, AC= 17cm, circu mscri circle . The radiu s of the circle is (a} 8.5cm (b) 4cm (c) 3cm (d) 7.5cm (ix) = 3. P(3,4} is a given point , P' is its image when reflected in the line y The equat ion of a line passi ng throu gh P' paral lel to x-axi s is (a) y = 2 (b} X = 2 (c) y = -2 (d) x = -2 (x) th th is If (x + y)th term of an A. P is p and (x-y) term is q then the x term equa l to (a) pq (p+q) (b) 2 (c) (pq)2 (d) (p;q) I (xi) I In rhomb us ABCD, the locus of points equidis tant from A and C is the (I) bisecto r of t.A and LC. (11) perpen dicular bisector of AC. (III) diagonal BD. Which of the above statement(s) is/are true? (a) Only (I) (b) Only (II) (c) (I) and (II) (~ (II) and (III) (xii) If in triangle ABC, PQ II BC , AB II QR and PC intersects QR at 0, then fl PBC is similar to A B (a) (b) (c) (d) /l ORC /l PCA /l OQC llABC (xiii) (I) If the probab ility of an event is p, then the probability of its comple mentar y event is p-1. (II) Probability of an event can be 0. 7. . . (III) The probability that two friends will have same birthda y in the year 2025 is ~ 3 5 Which of the above statement(s) is / are correct? (a) Only II IL\ T"\_..a..L T --d TT \UJ DUUl l i::Ul .U (c) Both II and III (d) Only III 4 (xiT) If on chidi ng 2x3 'ralue of a is: t' - ax+ 5 by 2x + 111 the remai nder is 6 11 then the (a) -2 (b) 10 (c) -9 (d) 3 (xi") )x+-2--0 The value{s) of k far which the quadr atic equat ion (k-3)x2--2(k.-3 has equal roots is 3 (I) 5 (Il) Whic h of the above value( s) is/are correc t? (a) I (bJ n (c) Both I and II (d} Neith er I nor II Queatlon. 2 1f (x - 2) and (x + 1) are the factor s of r3 aand b. i\ ii} + 3%2 + ax+ b, find the value s of f4J nt In the figure given below, XY is the diame ter of the circle , PQ is a tange [4) to the circle at Y, AJCB = so0 and ABX = 70 . Find a) LAYB b) LIXB c) LAYP d) L.APY X (figure not draUJTl to scale) y p 5 Q ' IJ/ 1/2 'Iv iii) (a) Write the fir st four ter ms of the sequence given by ({s) n, n E N (b) If the su m of its first 8 ter ms is k(5+"5 ) , find k. (4) Question 3 i) Points A an d B have coordinat es (7,-3) an d (1,9) respectively. Find the eq ua tio n of perpendicular bisect or of the line segment AB. (4) ii) A golf ball ha s diameter equal to 4 .1 cm. Its surface ha s 150 hemispherical dimples each of radius 2mm. Calculate the total surface are a of the ball wh ich is expose d to the surroundings. Give you r answer co rre ct to the ne are st square cm. (.Take n =3.14) (4] iii) For the Annual Sp ort s Meet of ou r school, students participated in the dis cu s throw competition. The distance thr ow n (in metres) by the pa rti cip an ts is rec ord ed below: Di sta nce in me tre s 12- 13 Nu mb er of stu den ts 3 13- 14 9 14- 15 12 15-16 9 16-17 4 17- 18 2 18-19 1 Us e a gra ph pap er to dra w an ogive for the above distr i"bu ti on. Tal.ce a scale of 2cm = 1 me tre on on e axi s an d 2cm = 5 stu den ts on the oth er a.xis. Hence, usi ng the gra ph est im ate : a) the me dia n. b) the up per quartile. c) the nu mb er of stu den ts wh o thr ew a dis tan ce of 16.Sm an d a bove (5) 6 J on B (Attempt any four} Question 4 Solve the following inequation, write the solution set and represent it on [3} the number line. i) s 1 2x -2-6 < -2 - -3 -< 2 ' x ~ ~ R Find the mean of the following distribution by Short Cut method. Give {31 your answer correct to the nearest gram. ii) Weight (in gm) Frequency iii) 80-85 85-90 90-95 95-100 5 10 12 12 100-105 105-110 I 110-115 8 2 In the figure given below, 0 is the centre of the circle, tangent AB meets diameter CD produced at A. a) Prove MDB ~ MBC. b) If the radius of the circle is 4.5cm and AB = 6cm, find AD 1 I \4\ Queatlon 5 i) ii) There were 50 questions in an examination paper numbered 1 to 50. Write down the probability that the number of question chosen will a) contain atleast one figure 3. b) be a composite number between 20 and 30. (3] c) not be divisible by either 2 or 3. A man has a recurring deposit account of ~1000 per month at 10% per annum. If he gets ~5550 as interest at the time of maturity, find the total [3] time in years for which the account was held. 1 iii) Construct a MBC with BC -= 6.5 cm, AB = 5.5cm, AC = 5cm. Construct th e incircle of th e triangle. Measure an d record th e radius of the incircle. (4] Question 6 i) ii) Use graph sh ee t for this question. Take 2cm '= 1 un it on both the axes. a) Plot A(0,4), B(l,1), C(4,0 ), 0(1,-1) and E( 0,-4) b) Reflect B through th e or igin an d name it as F. W rite down the coordinates of F. c) Reflect B an d C along th e y-axis an d name them as H an d G respectively. Write down th e coordinates ofH an d G. d) Jo in th e points A,B,C,D, ' E,F,G,H an d A in or de r an d write the geometrical name of th e figure formed. e\ Find th e ar ea of th e figur e. (5] A 1.4 m tall girl spots a J .o on moving wi th th e wind in a horizontal lin at a height of 91.4 m from e th e ground. The angle of elevation of the balloon from th e eyes of the girl at th at instant is 6()0. Af te r 6 second th e anr)e of elevation chan s, ges to 32 . Find the speed of the balloon du rin g th at interval. Gi ve your answer rorrect to 3 significant figures. J Find x and y if (3) ii) How many terms of the A. P ~~~ m) \ {5) Qu es tio n 7 i) t 24, 21, 18, ... m us t be take n so th at their ~ A man sold x shares of f 40 paying 8% dividend at a di sc ou nt of 100/o an d invested the proceeds in f 20 shares at a premiu m of 50% an d paying 12% dividend.. If the ch ange in income is tl 92 , find the value of x. (4) 8 l - -- - -- Qu est ion 8 can t . Solve the following equ ati'on and give you r ans we r cor rec t to 3 sig nifi figur es. 2 [3] 2x - lOx + s = o A sho pke epe r bou ght a dis hw ash er at a dis cou nt of 20% fro m a dis hw ash er bei ng ~45 000 . Th e wh ole sal er, the pri nte d pri ce of the d at a dis cou nt of 1O % on the pri nte sh_opkeeper sel ls it to a con sum er the rat e of GS T is 12 % , find : pnc e. If the sal es are int ras tate and ich the sho pke epe r bou ght the a) the pri ce inc lus ive of tax at wh dis hw ash er. sho pke epe r to the Sta te b) the tax (un der GST) pai d by the l3} Go ver nm ent . i) ii) of AB 12 cm . Loc ate the mi d-p oin t M Dr aw a lin e seg me nt AB of len gth poi nt wh ich is Dr aw and des cri be the loc us of a . a) at a dis tan ce of 3 cm fro m AB M. b} at a dis tan ce of 5 cm fro m an d sat isfy bo th the con dit ion s in la) ich wh S R, c} Ma rk poi nts P, Q, \4\ d. (b). Na me the qua dri lat era l for me iii) Qu eat lon 9 A ma the ma tic s apt itu de tes t of 50 il Ma rks No of stu de nts wa s rec ord ed as follows: . 60 -70 8 50- 60 4 70 -80 80 -90 14 19 90 -10 0 5 stu den ts im ate ram for the a~ove da ta an d est tog his a w dra er, pap ph gra a Using [3) the mode. ii) A map has a scale of 1 : 250 ,00 0 a jou rne y of 40 km ? a) Ho w ma ny cm on the ma p is 2 act ua l are a of lake on the ma p is 3cm , wh at is the b) If the are a of a ~ ~~~~? (iii) Prove the identity: [4] sin3 6+ cos 3 9 = sec 6-s tnB tan 6-1 1-2 cos 29 9 Question 10 i) The three sides of a right triangle form three consecut ive even numbers . Fir1d the lengt..hs of the ft\ree sides, rneas11red in cm. [3] ii) Show that point A(3,-2) is a point of trisection of the line segment joining the points (2, 1) and (5,-8). Also, find the coordina tes of the other point of trisection . (3) iii) Using propertie s of proportio n, find x a-x) 3 =a+x - 16 ( a+x a-x [4)

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