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ICSE Class X Prelims 2025 : Mathematics (Jamnabai Narsee School (JNS), Mumbai)

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Ima Khann
Maneckji Cooper Education Trust School, Mumbai

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This paper consists of 8printed SECTION A(40 pages. Marks) (Attemptall guestions fromthis Section.) Question 1 Choose the [15] correct answers to the questions from the given (Do not copy the questions, () Davina invested the correct answers write options. only.) 5880 in 8%,10 shares at 21.The annual 220 (b)244 income from (a) KO T224 (d)240 (ii) In what ratio does the line x =3divide the join (Y1:2 b)2:1 (c)2:5 (d) 5:2 1 of A (1,2)and B (7, 5). her investment is: ii) Atree trunk of height 12 m is erected with the support of three metal chains. An angleof o0 is made by each metal chain with the tree trunk. Find the length of the metal chain: (a) 32 m (b)10 m {o)24 m 18m (d) iv) A SOlid metallic cylinder Statement 1: The cut is into two identical total volumeof2 equal total surface area of halves halves along is equal to its height (as volume of soltd shown below) metallic cylinder. Statement2: The ( 2 equal halves together is equal tosurface arcaof original solid metallic cylinder. Which of the following is valid? (a) Both the statements are tre, Both the statements are false. (b) Statement 1 (d) Statement In the given find TP: (a) 8V3 1 is truc and statement is false figure, if and statement 2 is false. 2 is true. AT = 16Cm and AB= 12 cm. cm 6 cm (c) 64 cm (b) e & cm (vi) sec'A + cotA- tan'A - cosec (a) A 2 (b) 1 le) -2 (d) o (vii) The scale factor of a picture picture 18 cm, then her is m (b) 2.25 m (a) 14.4 (er1.44 (d) 1.78 andtheactual actual height is: m m 2 height of Rani is 20cm: 1.6 m. If her height inthe Ria deposited 200 per month for 15 months in a bank's recurring deposit account. If the bank pays interest at the rate of 10% per annum, then the interest earned by Ria during this is: period 300 200 (c) 240 (d) 400 (a) e) subtracted from the polynomial What must be divisibleby (a) x+x-2x + 1, so that the result is exactly (x-2)? -9 (b)-7 (c) (x) 7 =5 is a line y Assertion(A): to parallel the x-axis to the x-axis is y =a. ofline Reason(R): The equation explanation of A. are true and R is a corect (a) Both A and R A. a correct explanationof true but R is not (b) Both A and R are parallel (6)A (d) A R is true, is R is false, is false. true. 0.3 then ofxyis? the value 4x (a)-3 (b) 1 3 (d)5 cii) i) The representing the followingnumber set solution 54 xER, line is: -2 -3 -3<x<2 {x: -3 <x<2} (b) {x:xER, <x<2} -3 (c) {x:xER, -3 (d) {x:xER, <x 2} sixmatches is arranged A batsman's is the value ofx? score in 54, then what 25,38, 50,x, 84, 106 (a)60 (c) 58 54 (d) 59 Aby 3 in ascending the value order. If of median is -is (civ) altitudes the point of of a triangle intersect at three perpendicular and the point of sides of intersection of bisectors of intersection of triangle. three Three medians the and centroid orthocenter Circumcenter, and centroid circumcenter, (b) Ortbocenter and orthocenter circumcenter, (c) Centroid, and circumcenter centroid Orthocenter, wvith of the circle is the diameter AB figure, the given () In (xv) value ofx Centre '0'. If 2COB = is the 65 then the is: (532.5e 6)65 (c) 33.5e (d) Question 115 [4) 2 1xM Given Write (a) down the orderof matrix Find thematrix (b) M. M. 80. (i1) After a year [4] he soldthese (b) increase in his (c)the percentage return at in 18%, SOD0in 7%, 100 his dividend) Yohan invested the proceeds (including inyested and each shares at 275 241. 225 shares at for the first year. dividend his Find: (a) year. in the second his annual income investment.9 shares on his original [41 identity: (ii) Prove the following tan A 1-tan A 1-cotA cotA1+secA Question () cosecA 3 (41 In the circle with centre O, ZAOB=70 and ZBEC o =50 , Find: (a) LAEB (b) 2D (c)DAE. 4 D (i ) The surface area ofa cones with solid metallic sphere solid radius of 4 a cm and height Calculate (a) the radius of the sphere, (b) the number of cones recast. (iii is 2464 cm. It is melted and (Take I=22/7) 1 of figure SECTIONB (Attempt any a triangle ABC. AA'CB'BC reflection (40 in the x axis. Marks) fourquestions fromthis Section) 4 Question [4] into 7cm. Use a graph paper to answer the following questions. (Take cm=1 unit on both axes). (4, -6) and C (8, 0), the vertices (a) Plot A (4,4), B on the y-axis and name it as A'B'C'. (b) Reflect ABC A', B'andC (c) Write the coordinates of the images for the (d) Give a geometrical name (e) Name two invariant points under recast deposited Account in a bank and Recurring Deposit Prisha opened a 20,700 at the tm received 2 years. If she findthe rate of interest for per annum. (ii (3] Use properties for the followings proportion of x3+12x If y+27 find x: y 9y2+27 622+8 in grams of a sample 70-80 80-90 90-100 16 18 gives the weights (iii) The following table method. Mean by step-deviation Weights [3] of maturity, 800 permonth (in g)S0:60 60-70 10 12 of 100 books. Calculate 100-110 14 110-120 the (41 120-130 10 12 No. ofbooks Question5 (1) Show that 2x Cxpression In +7 is a factor completely, APQR, LQ=90 5x- llx- 14. Hence factorize of 2x+ and MN I PMN: area MQ =4 cm and QR =12 PR. PM =5 cm, cm 12 cm Find: (a) MN (b) area of A given theorem. using the factor 5 cm 4 the of APRO 5 cm. (3) (31 (ii) A and B are two points on the x-axis and y-axis [4] respectively. 3 -3 -2 23 I 5 4 -2 Y A and B. (a) Write down 3:1. Using section formula that AP: (b) P is a point on AB such P. point coordinates of perpendicular to ofa line passing through P and the equation (c) Find the coordinates.of find PB- Question Solve the following inequationawrite down the solutign and set number line. -ii-1}<ER and give your answer correct (i1) Solve (ii) and histogram carefully questions: following the answer to 3 significant Study respectto frequenoy table with and their the class boundaries corresponding frequenci class (b)State the modal and note down themode ldentify a () the distribution. of people vhose Find the number (d) wages are between of (a) Make 8000 to9000. figures S the repeesent AB it on the real Question7 In the given figure PQRS is a cyclic quadrilateral PQ and SR ~ ATPS ATRQ. SP if TP =15 cm, RQ=3 cm (a) Prove (b) Find (31 are produced to meet at T. and TR=5 cm. (c) Find area of quadrilateral PQRS if area of APTS 54 cm. = () Prove the following sin 1-cos A V1+cos (iii) identity: A 1+cosA A 141 Vande Bharat af 6 a.m. followed by another train Rajdhani express leaves Mumbai is 600 km away in Gon, whlch trains arrive which leaves Mumnbai at 8:00 a.m.Both is 10km/hour, speeds between their difference from Mumbai at same time. If the what is the speed of Vande Bharat? Question 8 () A B (3,3) and (2, -4), Find the equation by (x-3),it of triangle the median (b)the altitude of (31 ABC. throbgh A triangle throush C B yo 14 and when the expression 2x+abx expret 52 Gnd the values of 'a' and .-1 leaves (31 is a A and "B, from two different heights to photograpl an object 'Q" heights are these from of depression each other. The angles which are vertically above of the drone and base the Ifthe horizontall distance between 45 and 30 respectively. 'A' and Bto heights find the vertical distance between meters, the object Q is 60 drone A the nearest Question of triangle f(x2)is a factor ofthe divided (ii) vertices () of: If is (i) C(-1,5) are used meter. 9 toy A is in the shape of a solid oylinder lower base of the cylinder. is drilled out asthat of a cylinder at the of the remaining Given that, A with a hemisphere cone of same radius Find the surface area solid. the radius is 7cm, height of cone is 24 cm. cm (4] (ii) in a test are given below: The marks obtained by 120 students 10-20 20-30 30-40 40-50 50-60 60-7070-8080-9090-100 0-10 Marks 9 5 No. of 16 22 6 11 18 26 4 3 students on a graph sheet. Draw an ogive for the given distribution =10 students. Take 2 cm =10 marks and 2 cm the following: Use the givenscale for ogive to estimate (a) The median. in the test. who obtained more than 75%marks (b) The number of students marks required who did not pass the test if minimum (c) The number of students to pass is 40. (1) 10 of properties Using proportion, solve for x. Question Given that x [3) is positive: 2x+ V4x-1 =4 2x-V4x2-1 (i ) In at O, tangent drawn the given semicircle with centre C. point D meets ABproduced [3] DAB38 Given Find: (a) at DBA b)2C ZBDC. ) 138 the same horizontal A' and 'B on observed from two.points at 'A'and The top of of elevation the angles If the base of the tower. of the on a point the height and line through are 36 and 48 side of thetower meter. which are on the opposite nearest and B to the the distance between A tower is 100 m. Find a (iii) toweri 8 [4] 'B

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