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ICSE Class X Board Exam 2025 : Mathematics

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Name NiLAbha..Ral. Code No. : .MCXNOA PATHFINDER Where Aspiration Meots Suocess BoardsGrad Mock Test-1 MATHEMATICS ICSE - X:2024-'25 Maximum Marks:80 Time allowed: Three hours separately Answers to this paper must be written on the paper provided You will not be allowed to write during the first15 minutes. This time is to be spent in reading the question paper. answers. The time given at the head of this paper is the time allowed for writing the Attempt all questions from Section A and any four questions from Section B. All working, including rough work, nmust be clearly shown, andmust be done on the same sheet as the rest of the answer. Ommission of essential working will result in loss of marks. The intended marks for questions or parts of questions are given in brackets [ ]. Mathermaticaltables are provided. SECTIONA (40 MARKS] (Attempt all questions from this Section.) [1x15=15] Question 1. Choose the correct answers to the questions from the given options: (Do not copy the question, write the correct answers only). The marked price of an articleis1800, the billprice including GST is 12016. The rate of GST is (a) 12% (c) 18% (b) 5% (d) 12.5% () When the polynomial 3x2x +5x-7 is divided by x+2, the remainder is (c) 19 (a) -49 b) 10 (i) Forthe quadraticequation 5x-6x +7= 0, the roots are (a) real (b) real and equal (c) distinct (d) 0, (d) not real [4 2] then AB is () If matrix A=(5 10] and matrix B= 1 3 201 (a) 30 ) (20 30] [30] (c) 40 () [30 40] M The median of 7, 8,4,3 and 10 is (a) 3 (b) 7 (c) 8 (d) 4 (V) Ifthe lines 3y ax-6 and 3y =5-X are parallel to each other, then the value of 'a' is (a) 1 (b) 5 (c) 3 (d)1 Turn Over AMothemotiet Mock Tost sis terms five first product of its |ICSE-X 202425 (d) 81 ()243 GPis 3, The () The 3rdterm ofa (b) 729 (a) 27 numberlineis g following representingthe (vi) The solution set r - st -1<x<5) eR, () (x:x -1<x<5} (x:xeR, (9) (a) (x:xeR -1sx<6) (o)xxeR, -1sxs5} ,then'n' is 13, 18.... 8, 3, (d)16 A.P the of n () If 73 is the n-th term (c) 15 8.196, nd2.196. The (b) 14 (a) 13 are 0 x -6x- 18 = (x) The roots of the quadratic equation roots correct to 2 figures are (c) 82,-2.2 d) 8.190,-2.190 (b) 8.0, -2.0 (a) 8.19, -2.19 years at5% p.a. simple 2 for account deposit (Xi) Asum of 75000 is invested innarecurring (d) 76250 on maturity is (c) 7500 (b) 7500 (a) 1,26,250 interest. Ths 45 . Then the value of <ACB ie <BDC= and 70 <ABD= 65 , (X1) In the given fiqure, <BAD = ATL 65 707 (a) 90 (xi) The ratio of volumes of two spheres is 1:27, then the ratio of their radii willbe b) 1.9 (c) 3:1 (a) :1 () 1:3 ( v) For agiven triangle, Assertion(A): Toconstruct a circumcircle, construct the perpendicular bisectors of at least two S Reason (R):Thelr point of intersection is equidistant from the sides of the triangle. (a) (A) is true, (R) is false (b) (A) is false, (R) is true (c) 45 (a) 70 (c) Both (A)and (R)are true (o) Fora given horizontal, Assertion (A): The angle of (d) Both (A) and (R) are false felevation is equal to the angle of Reason (R):They form verticaly opposite angles. depression. (a) (A) is true, (R) is false (b) (A) is false, (R) is (c) Both (A) and (R) are true true (d) Both (A)and (R) are Mock Test oUESTION PAPER Question 2. () (41 Avessel is in the form of an inverted cone. Its height is 11 cm and the radius of its top is open is2.5 cm. It is filled with water upto its rim. When lead shots, each of which is a sphere of 0.25which cm radius are dropped into the vessel, 25 of the water flows out. Find the number of lead shots dropped. [4] (i) For the given sequence 2, 4.5, 7, 9.5, 12, ... Find () (a) the general term (b) the 20th term (c) the sum of first 20 terms. [4] Question 3. () Prove that: ( ) sin0 1-cot0 cOs = sin 1- tan0 + cos [4] In the given circle with diameterAB, find the value ofX. [4] (ii) Use graph sheet for this question. Take 2 cm =1 unit along the axes. [5] (a) PlotA(1, 2),B(1:1) and C(2, 1) (b) Reflect A, B and Cabouty-axis and name them as A', B' and C. (c) Reflect AB, C, A B' and Cabout x-axis and name them as A", B", C",A"", B"" and C"" respectively. (d) Join A, B, C, C B AA" B", C",C, B, A' and Atomake it a closed figure. SECTIONB (Attempt any four questions from this Section.) Question 4. () Rani invests for 2 years in a recurring deposit account and gets 52,500 on month, find the,rate of interest. () Find mean of the following distribution using the short-cut method: maturity. If she invests 2000 per [3] [3] Class interval35- 4040-45 45-50 50- 55 55- 60 Frequency (t) Given that a +3ab 6 5 3 63 b+3a?b 62 Using componendo and dividendo, finda:b. [4] 3 QUESTION PAPER. Mathematics : Mock Test1 ICSE-X: 2024- 25 meets PT at P SQ when produced Diameter R. at O centre [3 In the given figure, PT touches a circle with 90 . = 2y + KSPR = X and KQRP = y show that x Question 5. Px NDER T R : (i) Solve the following inequation and graph the solution on the number line 2x-5<5X+4<11, x eR [3) (ii) In the given figure, find ^y-axis A 3 B 2 X-axis -1 0 (a) the co-ordinates of the points A, Band C (b) the equation of the line'AP(|| BC) () the co-ordinaes ofthe points XandYWhere line AP meets the x-axis and y-axis respectively. () the ratio in,which point Adivides the line segment XY. Question 6. 0 Solve the quadratic eouation 5x-5= 0and give your answer correct to two decimal places. (Usemathemateal tables if pecessary) i) The first terro, the last tefm and the common difference of an Arithmetic Progression are 98, 1001 and respectively. Find the following for the given Arithmetic Progression : (a) numbenof tegis 'n. (b) sum of the n' terms. (i) In the given figure, ABC isa triangle with <EDB= <ACB.Prove that AABC ~ AEBD. B :4024-25 Mathemotics : Mock Test1 EC = 8 cm, BD =10 cm and area of (a) lengthofAB ABED =81 cm , calculate IfBE =12 cm, GUESTIOH PAPER AABC (b) area of stion 7. 0 The egiven graph represents ahistogram. Study the graph carefully and 4) answer the following questions: (51 Scale:X axis 5 div. = 20 unit Yaxis 5 diy, =1unit 80 class (2) Make afrequency table with respect to the boundaries and their corresponding frequencies. (b) State the model class. (C) ldentify and note down the mode of the distribution. (0) Write down the class mark of the model class. of elevation of the straight line with it, measure the angles a in tower a of side same between the the on distance Opeople standing height of the tower is 70 m, find the the If respectively. [5) 50 and 25 or ne tower as two people. 5 QUESTION PAPER ICSE- X:2024-25 Mathematics : Mock Test1 Question 8. I3] Theorem: f(x)= 6x 7x-7X+0. Factor of help the with expression orise the ) Iwo dice are thrown simultaneously. What is the probability of gettin9 (i) [3] a doublet? radius of wire of length 100 cm. Find the a into drawNn then and [4] melted ASold sphere of lead of radius 1cm is (a (b 9 as the sum of the two numbers that turn up ? the wire. Question9. of contact. tothe given circle. The pointT is the point tangent a is PT and secant a [3] is PAB figure, Inthe given Given PT=6 cm,AB = 5 cm, find AP. I N D E B 4/5cm 6 cm 56 at 10% premium. The dividend on the shares is () Aman invests 30,800 in buying shares of nominal v ue 18% per annum. Calculate : (a) the number of shares he buys. (b) the dividend he receives annually (c) the rate of interest he gets onhis money, [3] (G) Draw an ogive for the followingfrequencydistribution, Jse your ogive to estimate Marks (x) Number of 0-10 5 students () 10-20203030 -40 40- 5050 - 60 60- 70 70- 80 16 22 26 18 80- 90 90 -100 11 (a) the median, and (b) the number of students who obtained more than 75% marks 4 3 14] Question 10. The marked1price of an article is ?15,000. The dealer buys it at a of 25% and sells it to the retailer at a discount of 15% on the market price. lf rate of GST is 12%, finddiscount the GST paid by the dealer. () Find the equation of aline passing through the point of intersection of 4x+ 2y =7 with the y-axis and parallel to y- 7x + 5=0. 13] (i ) Use ruler and compasses only: (a) Construct a AABC with BC = 6cm, <ABC = 120 and AB =3.5, (b) In the above figure, draw a circle with which Is equldistant from AB and BC. BC as dlameter. Finda point'P' on the circumference of the circle (c) Measure BCP 14 6/

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