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ICSE Class IX Prelims 2025 : Malayalam (Euroschool, Wakad, Pune) : Prelims 2024-25

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f ~~ EuroScho ol ' , . ' ,.~ f ~IATHEM ATics Prrlims, 2024-25 (3 !,ours) t~ GRADE: L\ Maximum Marks: 80 SECTION A (40 Marks) (Attempt all questions from this Section) ..r> j_ Question I (15] Choose the correct answer to the questions from the given options. 1. If x a. + -.ffs = 4 and xy = 1, then find the value of (x + y): 8 b. 2. c. 4 . d. n. The ratio of heights of triangles is 2: 3 and the ratio of their areas is 3: 2. The ratio of their bases is: a. m. 1: 4 s Ifa+b+ c= 'f,a a. 9 b. 2 2: 3 2 c. 4: 9 d. 9: 4 2 + b + c =16,then valueof2 (ab+bc+c a)willbe: . b. c: 25 10 d. 7 1v. Find the factors of 4 (x - a) 2 - 4 (x - a) - 3: a. (2x-a+1 )(2x+a- 3) b. (2x-2a- 3)(2x-2 a+1) c. (x-a+l) (x+a-3 ) d. (x - 2a + 1)( 2x + a - 3) v. Cost of x pen is exceeds twice the cost of pencil (y) by ~12. This statement can be expressed as linear equation: a. v1. x --. 2y = 12 b. x + 2y = 12 c. 2x - y = 12 2x+y = 12 d. Triangles ABC and DEF are congruent by SSS. If AB= 10 cm, BC= 30 cm, AC= 2o" cm, DE= 10 cm, DF = 20 cm, find the length of the side EF: a. 20 cm b. 10 cm c. 30 cm d. 40cm vu. If a line di~ides any two sides of a tJ:iangle in the same ratio t:1:en : a. It will intersect the third side. . b. It divides the third in the same ratio. c. It is parallel to the third side. d. None of these. viii. The median of the data: 155, 160, 145, 149, 150, 147, 152, 144, 148 is: a. ICSE 149 b. 147 c. 1 150 d. 144 ix . . . /\s sc r11 o n: The kn . g1h o l a ch or d w hi ch . , 0 f 5 rm fr om ihc cc is a\ a d1s\ancc n1rc of a ci rc le of ra di us 10 cm is 17 .32 cm . Re as on : Th e pc rpcn . d1cul ar frnrn th e ce nt re of a circle \o a c\10rd bisect s 1h c ch or d. a. Bo th assertion ( A) an d reason (R ) are true and reason (R) is th e co rrect expl anat io of as sertion (A ). n b. B ot h as se rtion (A ) an d re ason (R ) are true but reason (R) is no t th e co1Tect explanation of as serti on (A ). c. Assertion (A ) is true bu t reason (R ) is false . d. A ssertion (A ) is false bu t reason (R ) is tru e. x. Asse1tion: In trian gles A BC an d PQ R , LA = LP, LC = LR an d A C = PR. The tw triang~es ar e co ng ru o en t by A SA_congruen ce. R ea so n: If tw o an gl es an d th e included side of one triangle ar e equal to two angles th e in cl ud ed si de of and th e ot he r triangle, th en the two triangles ar e co ng a. ru ent. B ot h as se rti on (A) an d re as on (R ) are true an d re as on (R ) is th e correct of as se rti on (A ). explanation b. B ot h asse rti on (A ). an d re as on (R ) are tru e b_ut reason (R ) .is ex pl an at io n of as se no t th e c~rrect rti on (A ). c. d. A ss er tio n (A ) is tru e bu t re as on (R ) is fa lse . A ss er tio n (A ) is fa ls e bu t re ason (R ) is tru e. xi . Fi nd th e ar ea of th e eq ui la te ra l tri an gl e of si de 4 cm : a. 6. 82 9 cm2 b. 6. 29 8 cm2 c. 5.92 8 cm.2 xi i. A B C D is a cy cl ic qu ad ril at er al su ch th at A B is a diameter . . of th e ci rc le ci rc um sc rib in g it an d LA D C = 140 , tben LB A C is equal to : d. 6. 92 8 cm2 A V L L -- ~ -- 7 B a. 30 b. 40 50 c. d. 80 . si de of a cu be 1s re du ./c ce d by 25 o, then the ratio of the volumes of th e or ig in al an d th e ne w cu be is : a 64 : 1 b. 4: 3 d. 64: 27 c. 32 : 9 xi v. If se c 4A = co se c (A - 25 . . ") , w he re 4A ts an ac le ut e an g , then th e va lue of A 1s: . 00 a. b. 23" . 98 d. c. 30 Xl ll. IC SE If th e le ng th of ea ch 2 ----. d_l IH~ l 1lS tUIKC l)Ctwccn F111 a. ../ls units 111ll 1winl P(2, 3) is . . ong111 :llll b. 5units li, Qurstion 2 1. AB is a side or a regular pentagon an d 213 units J. TI units -0 BC is a side or a 141 regular hexagon inscribed in a ~ircle with centre 0. Find LAOB, LBOC and LADC. 11 111. Evaluate: [( tan 2 2 o .) + cosec 70 (cot 2 [4] 2 o ) +2tan15 tan45 tan75 ] sec 10 Using the Assumed-Mean method, find the mean weekly wages from the data given ~ [4] below: Weekly wages (in~) 800 820 860 900 920 980 1000 7 14 19 25 20 IO 5 Number of workers Question 3 1. A rectangular tank is 25 m long and 7.5 m deep. If 540 m 3 of water be drawn off the [4] tank, the level of water in the tank goes doWn by 1.8 m. l Calculate: (i) the width of the tank, (ii) the capacity of the tank. 11. Two parallel chords AB and CD are 3.9 cm apart and lie on the opposite sides of the . . . [4) centre of a circle. If AB = 1.4 cm and CD = 4 cm, find the radius of the circle. iii. Solve the simultaneous equations 2x + 3y = 2 and x - 2y = 8 graphicallly: [5] SECTION B (40 Marks) (Attempt any four questions from this Section) Question 4 1. 11. 111. 2../6-../s . . . 1 . h d . S1mphfy by rahona 1smg t e enommator: J,/s + 2,/6 Without multiplying directly, evaluate (9.7) 2 [3] . The sum of the digits of a two-digit number is 12. If the new number formed by reversing the digits is greater than the original number by 18, find the original number. ICSE [3] 3 [4] :: i , 1tt rithi iiuit.ri ;1u:: ',ii,15 1 t1t Qurst ion 5 1. r-' J The adjoining. figure shows a circle with centre O in which a diameter AB bisect s the chord PQ at point R. If PR = RQ = 8 cm and RB = 4 cm, find the radius of the circle 11. 111. Factorise: 2 (ab + cd) - a2 - bz [3] + cz + dz . The differ ence betwe en the sides of a right-angled tri'angle conta ining the right angle is 7 cm and its area is 60cm2 Calcu late the perimeter of the triang le. [ 4] Question 6 1. 11. 111. lf2x - 3y = 10, and xy = 16, find theva lueof 8x3 If13 sin A== 12, find (secA - t.anA) 27y3 . - [3] / [3] The length , bread th and heigh t of a closed wood en box are 20cm , 12 cm and 8 cm. The thickn ess of the wood used to make the box is 10 mm. Find: [4] a) The volum e of the ~ood . b) The cost of the wood requir ed to make the box, if lcm3 of wood costs :{8.50 . Ques tion7 1. / In the given circle with centre 0, AB = BC = CD and LAOB = 40 . Calcu late: (i) LAOD (ii) LAED (iii) LBED. [3] D B 11. ABC be a triangle, right- angle d at Band D be the [3] A midpo int of AC. .Show that DA= DB = DC. D B Ill. !CSE If x = 3 + 2 2, find the value of x 2 + 2. x2 4 C [4] I Qul'stion 8 1. Soh c the following pair or linear equations using any st1itahle method: 8x + Sy = 9 and 3x [3] + 2y = 4. Ic 1 s 24 c 111 and its area cm. F.Ill d Its perimeter. 11. Thl' basl' ol -an 1soscclcs tnang ' is 192 sq. 111. Ir the allitudes from two vertices of a triangle to the opposite A 13) 4 [ ] sides are equal, prove that the triangle is isosceles. C B Question 9 1. 11 . Factorise: 2x 3 + 5 x2y - 12xy 2 [3] The length, breadth and height of a rectangular solid are in the ratio 6: 5: 4. If the total [3] surface area is 5328 cm 2 , find the length) breadth and height of the solid. 111. The following table shows the number of diabetic patients at various age groups. Age (in years) 10- 20 Number of diabetic 3 [4] - 20-30 30 - 40 40-50 50 - 60 6 . 5 14 8 60- 70 2 patients Represent the above data by a frequency polygon. Question 10 / i. Calculate the median for the following distribution: Variate Frequency . 3 6 10 3 4 2 s sin2 30 + cos2 . (31 12 7 15 8 13 IQ 2 tan 30 n. Evaluate: - - - - -45 -4 ---- [3] 2 sin 30 cos 30 +tan 45 s m. In the figure, given below, triangle ABC is right-angled at B: ABPQ and ACRS are squares. Prove th_at: (i) A ACQ and A ASB are congruent. (ii) CQ =BS. ICSE 5 [4]

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