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ICSE Class X Prelims 2023 : Mathematics (Karnataka ICSE Schools Association [KISA])

7 pages, 53 questions, 34 questions with responses, 41 total responses,

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Indian Certificate of Secondary Education (ICSE), New Delhi

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KARNATAKA ICSE SCHOOLS ASSOCIATION PREPARATORY EXAMINATION (February 2023) Subject: MATHEMATICS Class: X Duration: 2% hours Max. Marks 80 Date : 06/01/2023 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 the paper is the time for writing the answers. Attempt all questions from Section A and any four from Section B. All Orking, 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 loss of marks. The intended marks for the questions or parts allowed questions of questions are given in brackets [( SECTION A QUESTION1 ) The common (a) 9 difference of the A.P whose mth term is 10m - 1, is: (b) 10 (c) 11 (d) 19 (ii) In the given histogram, the upper limit of the modal class 0- (a) 50 (b) 40 (c)60 48 is 48 15 (d) 30 10 20 30 40 50 Class-interval (11) The factors of the given polynomial 3ps+2p-19p+6 are: (a) (p+2) (p-3)(3p-1) (b) (p-2) (p+3)(3p-1) () (p-2) (p-3)3p-1) (d) (p+1) (p+2)(p+3) (v If 88 is the nth term (a) 13 (b) 14 (c) 17 of the arithmetic progression 8,13,18, 23,..then 'n' 1s (d) 16 Pg.1 (V) In the given figure, A ABC is value of 'a A XYZ, the . (a) 3 cm (b) 3.5cm 6 A (c) 4 cm (d) 3.7Scm B A (vi) The solution set for the 7-3xx-15, x given inequation EN is (a) {1,2,3,4,5} (b) 6,7,8.9,... (c) {1,2,3,4,5,5.5} (d) {1<x<5} (vii) The radius of a sphere is 4r, then its volume will be: 4 (a)ur (b) 3 (d) 256 tr' (viii) If 9 and 37 getting a (a) are then the removed from the data (1,4,9,16,25,29,36,37) number which is a probability of composite numberis: 2 b) (c) (0) (ix) in the centre of the circle, AB is 4BAT is point A. If LAOB 100 then In the figure, O = (a) 30 (6) 500 (c) 400 (d) 100 B Pe.2 a chord and AT is the tangent at the (x) If 34 x] +2[y -3] -{10 0]. then: (a) x= 1, y= 0 b) x - I , y= -2 (c) x 2, y= -1 (d) x-2, y=i (s) IfA = and A?= 3I, where I = the order of A is (a) 2 x 2 (b) 2 x3 (c) 1 x 2 (d) 3 x2 (xii) Point P is first reflected in x-axis coordinates of P are: to P'. P is then reflected in y-axis to P"(-2,5). The (a) (2,-5) (b)(-2,5) (c) (-2,-5) (d) (2, 5) (xii) The equation of line whose inclination is 45 and which intersects the (0, -4) is: y-axis at the point (a) x-y=4 (b) x +y = 4 (c) y -x =4 (d) x- y=-4 (xiv) A ladder 15m long just reaches the top of a vertical wall. If the ladder makes of 60 with the wall, then the height of the wall is: an angle (a) 6.5m (b) 7.5m (c) 8.5m d)m 3 (xv) Mr. Sharma purchased goods worth F 40,000 from a shop keeper (within the state). If the rate of GST is (a) 3600 (b) 7200 18%,then CGST is: (c)8000 (d) None of the above Pg.3 Question2 of radius 2emn 6cm. Two hemispheres radius with 8cm height the material Calculate the volume ot and scm are scooped from one of the bases. [4] remaining in the cylinder. (a) A solid cylinder has (b) Prove that vSec20 a +Cosec20 = tan 6 + cot 4] 8 interest. At 1500 per month in a recurring deposit scheme at 6% p.a. (c) Ajay deposits the time of maturity, he receives 38,250. Find the total time of his recurring 4] deposit account. Question 3 (a) Use graph paper for this question. Take 2cm-lunit on both the axes. () Plot the points P (4,3) and Q(-4,-3). From P and Q draw perpendiculars PM and QN in the x-axis. (ii) Write the Co-ordinates of M and N. (iii) Assign special name of the figure PMQN. (iv) Find the area of the quadrilateral PMQN. (v) Write the single transformation that maps P to Q. (b) Write down the equation ofthe line whose gradient isand which passes through P, where P divides the line segmentjoining A(-2, 6) andB(3,-4) in the ratio 2:3. [4] (c) Givena - x+y?+ r2 x2+y2-x2-y2 ,use componendo and dividendo to prove that [4] 2ax a241 SECTION B (Attempt any four questions from this section) Question 4 (a) The following bill shows the GST rates in an Intra state transaction. [3] BILL Articles Marked Price Discount Rate of GST Light 1885 10% 22% Fan 3230 7% 28% Find the total amount to be paid for the above bill. (b) Find the value of 'p', ifthe roots of quadratic equation are cqual. (p+3)x+px+1=0 3 Pg.4 (c) Use graph sheet for this question. Draw a by 30 students and hence estimate (a) the mode (b) the modal class for the Take 2cm-7 25 along the x-axis Pocket Money 125-150 L00- 125 in( ) No. of students 10 h1stogram tor the pocket money received 4 following ditribution. 150-175 175-200 200 225 225 250 8 Question5 (a) IfP= 6 4 and Q- (b) In the given figure AB Findthe matrix M suchthat PQ-2M =0 9cm, PA intersect at P. (i) Prove that APAB~APCD (ii) Find the length of CD (iii) Find the ratio of PB and PD = [31 =7.5 cm and PC= Scm. Chords AD and BC 3 B 7.5 cm (c) (x -2) is a factor of the expression x*+ax -bx +24. When the expression is divided by (x - 3), it leaves the remainder -6. Factorise the expression completely. [4) Question 6 (a) The equation of a line is 3x +4y ) Slope of the line 7 0 . Find [3] (ii) The equation of a line perpendicular to the given line and passing through the intersection ofthe lines x - y + 2 =0 and 3x + y- 10 0 Sne-cose+1 (b) Prove that sin+cose-1 [3 1 sece-tane money, (c) Daya gets pocket money from his father every day. Out of the pocket and so third day on. he saves T2.75 on first day, T3.00 on second day, 7 3.25 on 41 Find: (i) (ii) (iii) The amount saved by Daya on 14th day. 30.00 is saved. On which day The total amount saved by him in 30 days. Pg.5 Question 7 ) A box contains urawn at 17 cards numbered random from the box. Find the i) Even number The volume mixed thoroughly. A card is that the number on the card is 1,2,3,.....17 and I1) prime number are probability iii) divisible by 3 or2 of a metallic cylindrical pipe is 13 1408cm'. Its length is 14cm and its 13] extermal radius is 9 cm. Find its thickness. (C) ln the given figure 'O' is the center ofthe Circle. If 2BAD=75 and BC-CD. Find . () LBOD (i) LBCD (i) 2BOC [41 (iv) 2OBD Question 8 (a) Solve the following inequation. S-1 [3] :xER Represent the solution set on a number line. (b) The mean of the following distribution is 62.8 and Find the sum of all the missing frequencies fi and f2. 0-20 20-40 40-60 Frequency 5 f 10 a is 50. [3] Class (c) In the given figure, ABC is frequencies 60-80 80-100 100-120 8 triangle, right angled at and CD-5cm. Find BD and AB. B and BDLAC. If AD4cm 4] 4 cm Scm m Pg6 Question (a) The volume of a conical tent is 1232m and the area of the base floor is 154m? Calculate () Radius of the floor (4 (i) (ii) Height of the tent Slant height of the tent (iv) Length of the Canvas required to cover this conical tent it its width is 2m. (b) Using frequency distribution table given below draw less than ogive, then from the ogive, find median and inter quartile range. Class interval 10-20 20-30 30-40 40-50 50-60 Frequency 2 4 6 8 10 6) Question 10 (a) Using componendo and dividendo, find the value of x. V12x+1+V2x-3 12x+1-V2x-3 (b) An observer 1.5m tall is 28.5m away from a chimney. The angle of elevation top of the chimney from his eye is 45 . What is the height of the Chimney? (c) Using ruler and compass only, constructa cm and L ABC = 120 . Construct a of the (3 A ABC such that BC: 5cm and AB =6.5 circum-circle of A ABC. 4 Pg.7

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