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ICSE Class X Prelims 2025 : Mathematics (Vibgyor High School, Marathahalli, Bangalore)

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r mD : icrll1i i;1 HIGH VIBGYOR HIGH Second Preliminary Examination A Y 2024-2025 MATHEMATICS Grade : X Max. Marks : 80 Date : 06/0112025 Time Allowed: 3 hours INSTRUCTIONS : Answers to this paper must be written on the paper provided separately. You will not be allowed to write during the first 15 minutes. This time is to be spent in reading the question paper. The time given at the head of this paper is the time allowed for writing the answers. The intended marks for the questions or parts of questions are given alongside the questions. This question paper contains 11 printed pages. Attempt all questions from Section A and any four question from Section B All working, including rough work, must be clearly shown and must be done on the same sheet as the rest of the answer. Omission of essential working will result in the loss of marks. Geometrical figures to be constructed wherever applicable. For geometry, figures are to be copied to the answer script. SECTION A (Attempt all questions from this Section .) Choose the correct answers to the questions from the given Question 1 options. (Do not copy the question, write the correct answers only.) (i) In the given diagram, 0 is the centre of the circle , and PO is a tangent at A . If LABC=50 , then values of x,y and z respectively are : [15] f B (a) 40 ' 80 ' 50 (b) 50 ' 50 ' 65 (c) 50 , 100 '40 {d) 50 , 25 ' 78 (ii) (a) The number of real roots in the equation (x+1 )2-x2 =0 is: 1 {b) 2 (c) 3 (d) 4 (iii) If 17th term of an A.P . exceeds its 10th term by 7. The commo n difference is: (a) 1 (b) 2 {c) 3 {d) 4 (iv) A bag contains 13 red cards, 13 black cards and 13 green cards . Each set of cards are numbered 1 to 13. From these cards, a t, (a) (b) card is drawn at random . What is the probability that the card drawn is a card with an even number? 1 2 6 13 (c) 9 (d) 26 11 39 2 mnr:ru. . .w. - -,,-. ;< HIGH (v) etric The numb er 2048 is which term in the following Geom sequ ence 2, 8. 32 . 128 . .... (a) 9th term (b) 7th term (c) 10th term (d) 6th term (vi) eter of a The co-or dinat es of a point P, wher e PQ is the diam circle whos e centre is (2, - 3) and Q is (1, 4) is: (a) (3 , -10) (b) (2 , -10) (c) (-3, 10) (d) (-2, 10) f I (vii) A In triangle ABC, LBAC = 90 and AD 1- BC . Then (a) 2 BO . CD = BC (b) 2 AB. AC= BC (c) 2 BO . CD= AD (d) 2 AB . AC= AD (viii) In the given figure , the value of x is: L (a) 23 .5 cm (b) 19 cm (c) 24 cm (d) 21 .5 cm 3 HIGH (ix) . lar cone is half of another . . The curved surface area of a right circu If the ratio of their slant heights is 2:1, the ratio right circular cone of their ra d11 1s (a) 34 (b) 1:4 (c) 1 :2 (d) 2:3 (x) At a certain time of day , the ratio of the height of the pole to the length of its shadow is 1 : ./3. then the angle of elevation of the sun at that time of the day is: (a) 30 (b) 45 (c) 60 (d) 90 (xi) Assertion (A): The difference in class marks of the modal class and the median class of the following frequency distribution table is 0. Class 20-30 30-40 40-50 50-60 60-70 1 3 2 6 4 Interval Frequency Reason (R): Modal class and median class are always the same for a given frequency distribution. (a) Both A and Rare correct, and R is the correct explanation for A. (b) Both A and Rare correct, and R is not the correct explanation for A. (c) A is true, but R is false. (d) Both A and Rare true. 4 V I$ iG Y O R HIGH (xii) Matrix A = [~\ ~) such th at Matrix A2 = [~ ~] then the value of k is : (a) 6 (b) -6 (c) 36 (d) 6 (xiii) The mean proportion of (p-q) and (p 3- p 2q) ,if p>q is : (a) p(q-p) (b) p(p-q) (c) -p(p-q) (d) p(-p-q) (xiv) In the diagra m given below , G is the centroi d of MBC. A (3 , -3) , B (2 , -6) , c (x, -6) and G (5 , -5) . Hence , the value of x is: B (2, -6) C (x, -6) D (a) 2 (b) 3 (c) 6 (d) 10 (xv) Mr. Das invests in t100 , 12% shares of Compa ny A availab le at t60 each. Mr. singh invests in t50, 16 % shares of Comp any B availab le at t40 each . Use this inform ation to state which of the followin g statem ents is true . (a) The rate of return for Mr. Das is 12% (b) The rate of return for Mr. Singh is 10% (c) Both Mr. Das and Mr. Singh have the same rate of return of 10% Both Mr. Das and M r. Singh have the same rate of return of 20% (d) 5 Qu est ion 2 nt in Pun jab Na tion al . accou Mrs . Karna has a recurring deposit ~999 0 as inte res t at the s Bank for 3 years at 8% p. a. If she get (i) (4] time of maturity . find : (a) the monthly in sta lme nt. ount . (b ) the ma turi ty valu e of the acc in hei ght and 18 cm in rad ius A girl fills a cylindrica l bucket 32 cm on the gro und and ma kes a with sand . She empties the bucket of the con ical heap is 24 con ical heap of the sand . If the height (ii) [ 4 1 cm . find (a) the radius and (iii) (b) the slant height of the heap. e the expression : Using the properties of proportion solv [4] 2 62( 1 + x) 1+x + x ---= 63( 1 - x) 1 - x + x2 Qu est ion 3 (i) drilateral inscribed in a circle In the given figure , ABCD is a qua to E. If LAD E = 95 and LO SA with centre O and CD is produced [4] = 30 , calculate: (a) LO BC (b) LO AC (ii) [4] Prove the following : sin 0 1- cos0 tan 0 + 1 + case = sec 0 cos ec 0 6 + cot 0 e r- " '"-.---.., .,-,:.1111-=~ '!{1 HIG H iii) ( The given graph with histogram rep resents the marks rec ord ed in a Mathematics aptitude test. Stu dy the graph carefully and answer the following questions. !1 :::. ' : ' : ... 1 '' 1 : " " " .. .. . 1 - - t , ... '.,t: r.f ,, , . ... , ,1' .,,- ,.....,-. ,11.,. 1,, . .... . 1.. .. .. ,. , .. . . ... .,. .. ... .... ~ " ' ' ' " 'f .... ... - , , ,. : : : t - - ... ......... . . : : .: . : : - - -- ~ t - - ' . 1' . 1 t ft . 1 ' I ,., ., ' ' ' ' ' . . ' i' ' : ' : . : . ' '' - 1 . ' . , , , 1 " " ' " ' " ' ' ,, . .. ,. , 1 ".. .." " ,... .. ."..' ' " I" .. ... : . .... 1' ..., ..: ..: .. " , , ... ' 'I: , , ,,. I j"" I" ' I' "" , ' I ,' , ... .. ... , ' .. ,' ... 1-. ...f : : :;: : ; : .. .... , . . . . :-~ ;_: . , , .. . I ' ' '' I . ' .. , 11 ' ' . , . , . . . . . .... . .. . : : : : :; :: ' j ' ' , , ,, . .. . ;, ::: ::1 , ... , ... . . . , "1 1 .,, ... , , - - 11,4:- :1:1 :; : I1 I ,,,,. , , . . ,. ,,.. . , I ,,, . . ,. :~q l , . :.:.: . 1-, .-.-. . ....~ , ,' I' ' I ' I . . , ' I' 1 1 '. : .... ' ,,' .. ,, ... I I . , l I - I - ', ' j 1 , fr '!~ I ' ' ' I : t I " ! ' ' I l I.... j ! I . t : : : : : : I ' I I ' ' " " fl " : : : : : ' : : : : : - : : : : j -- - - I j, i!i::::: i!::::/ 1::::1':: : .::: ::::. :::: ::::::::: ::::::::: I j '' ; I I ' I I , I [5] a t:iilP a HIGH SECT ION B . (Attempt any four quest ions from this section.) hares at t170. He sells the 1oo s h . t 101/o in ~8500 s invest n Sachi b t30. He inves ts t e . shares when the price of each share rises y proceeds in 12% ,100 shares at f125 . Find : [3] o Ques tion 4 (i) (ii) (a) the sale proceeds . (b) the number of t125 he buys. at point s In the given figure, O is the centre of the circle. Tang ents [3] A and B meet at C. If LAGO = 30 , find: I (a) LBCO (b) LAOB (c) LAPB C (iii) [4] Simplify: . A [sinA sm cos A - ~osAA] + cos A [ co~ AA -sm sm sin AA] . Give a special cos name to the resulting matrix with respect to its type . Ques tion 5 (i) n in A solid metallic sphere is cut into 4 identical parts (as show total the diagram). The radius of the sphere is 7 cm. Find the surface area of all the four parts. (Use rr I i I 8 = 227 ) [3] V I iB-: .G Y O R (ii) HIGH Solve the following inequation and represent the solution on the [3] number line . 3.\" --;:- + l.< x + 1t <_ :1 (iii) X I 1 rr 1 ' c U If th e image of the point A (2, 1) with respect to a line mirror PQ is [4] A (5. 2) , find the equation of the line mirror PQ . A(2, 1) M P -- - -- - + - - - -- -+Q A'(5,2) Question 6 (i) Solve the following quadratic equation by using the formula: x 2 - 3(x [3] + 3) = O. Give your answer correct to two significant figures . (ii) The roots of equation (q - r)x 2 - p)x In the given figure I is the incentre of 6ABC . Bl when produced [4] (a) LDCA (b) LDAC (c) LOCI - q) = p + r, that is p, q and rare in A.P . 65 , calculate: (i) =O [3] meets the circumcircle of 6ABC at D. If LBAC Question 7 + (p are equal. Prove that: 2q (iii) + (r = 55 and LACS = A Write the first five terms of the sequence given by ( (a) Is the sequence in A .P. or G.P? (b) If the sum of its first ten terms is p(3 + of p. 9 v13f, n EN /35. find the value [3] - ~1- - ;1 V HIGH (ii) . remainder and facto r . using , omial polyn given a izing factor While , 7 is a factor of . theorem , a student finds that 2,\ + (iii) + Sx 2 (a) 1 l x - 14. th Is the student's solution correct st ating at (Zx (b) factor of the given polynomial? Give a valid reason for your answer. 2x 3 [3] - + ?) is a : The daily wages of 80 workers in a project are given below (4) Cumulative Wages less than(in {) frequency 450 2 500 8 550 20 600 38 650 62 700 75 750 80 ution. Use a graph paper to draw an ogive for the above distrib (Use a scale of 2 cm ={50 and 2 cm = 10 workers) Use your ogive to estimate : (a) The median wage of the workers (b) The lower quartile wage of the workers The number of workers who earn more than ~625 daily. (c) Question 8 (i) balls. The A box contains some green , yellow and white tennis probability of selecting a green ball is [3] and yellow ball is } If the box contains 10 white balls , then find : (ii) (a) Total numb er of balls in the box. (b) Probability of selecting a white ball. is, then the If Zeba were young er by 5 years than what she really than five square of her age (in years) would have been 11 more times her actual age . What is her age now? 10 [3] mo (iii) HIGH In a size transformation , the area of the image of an object of [4] area 4.8 m2 is 30 cm 2 . (a) Calculate the scale factor . (b) Also find the volume of an object, if the volume of the image is 180 cm 3 . Question 9 (i) From the top of a hill , the angles of depression of two consecutive [5] kilometer stones due east are found to be 30 and 45 respectively. Find the distance of the two stones from the foot of the hill upto two decimal places. (ii) Use a graph sheet for this question. Take 1 cm = 1 unit along [5] both x and y-axes . (a) Plot the points : A (0, 5), B (3, 0), C (1 , 0) and D (1 , -5) . (b) Reflect the points B, C and Don the y-axis and name them as B', C' and D' respectively. (c) Write down the coordinates of B', C' and D'. (d) Join the points A, B, C, D, D', C', B', A in order and give a geometrical name to the closed figure ABCDD'C 'B' . Question 10 (i) A shopkeeper marked a pressure cooker at ~1800. The rate of [3] GST on the pressure cooker is 12%. The customer has only t1792 with him and he requests the shopkeeper to reduce the price so that he can buy the cooker in ~1792 including GST. What percent discount must the shopkeeper give? (ii) If a 2 + c 2 , ab+ cd and b 2 + d 2 are in continued proportion.prove [3] that a,b,c and d are in proportion. (iii) Using ruler and compass only, construct a semicircle with diameter BC= 7 cm. Locate a point A on the circumference of the semicircle such that A is equidistant from B and C. Complete the cyclic quadrilateral ABCD such that D is equidistant from AB and BC . Measure LADC and write it down. ***** 11 [4]

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