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ICSE Class X Prelims 2023 : Mathematics (St. Johns Universal School, Mumbai)

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Shaurya Sharma
St. John's Universal School, Mumbai

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UNIVERSAL HIGH SCHOOL Daftary Road, Near Railway Station,Malad Tel:-28881008/9 (East), Mumbai-400097 Second Prelim Examination: 2022-23 MATHEMATICS CLASS: MARKS: 80 X TIME: DATE: 16/01/2023 2 Hours 30 Minutes separately. hnswers tothis paper must be written on the paper provided first 15 minutes. You will not be allowed to write during the This time is The time given at the head spent in reading the question paper. answers. paper is the time allowed for writing the to be of this any FOUR questions from section B. Attempt all questions from section A and must be clearly shown and must be done on the All working,including rough work same sheet as the rest of the answer. in loss of marks. Omission of essential working will result are given in brackets [. of questions The intended marks for questions or parts are provided. tables Mathematical Section A (40 marks) (Attempt all questions from this Question 1 [15] the questions from the given options: the within for 21000 A dealer purchased goods worth 15000 and sold them by the dealer is: the net SGST paid state. If the rate of GST is 12 %, then 219 850 21 800 (d) (c) Choose the correct answers i) section) (a) 360 (b) to 720 The quadratic equation whose ii) (a) (c) iii) x- solution is 6 =0 3x x+x-6= 0 - 2, 3} is : x-x+6= 0 x-x -6=0 (b) - (d) t 3x- 3 and 2x*- 5x the polynomials px of p is: The value remainder. leave the same When (a) - (b) 1 0 (c) +p are divided (d) 1 2 x 3 and yiv) The order of matrix A is is not possible. but BA AB is possible, (a) not possible. (b) BA is possible, but AB possible. is not (c) AB as well as BA (d) AB as well as BA is possible. that of B is 3 x by (x- 4), they 2 1. I For an A.P, if v) (a) vii 10 The (a) reflection (-4, 2) a =5, d=3and =50, then the value tn (b) of 16 point (c) P (b) in 20 Y axis is P(-4, (4, 2) (c) of n is: (d) 21 -2). The co-ordinates of point P are: (4, -2) (d) (-2, 4) B vi)ABCD is a trapezium with Then the AOD COD COB (a) A (b) A A (d) A (c) X AB parallel to AOB triangle similar to A DC. is: D ACB 35 cm. The voume Vi1) A hemispherical bowl has radius (a) 86.5 cm3 (b) 89.8 cm3 (c) water in of For the inequation:2x - 5 s 5x + 4 s 11, xel then solution ix) it 1s: (d) 93.5 92.5 cm3 set is cm3 represented as (b (c) -1 -3 x) a letter is drawn at getting a vowel is: random from If (a) 1/5 2/5 (b) xi) Which of (a) 2 0 4 the following 3/5 (c) is of 0 not (d) 4/5 a diagonalmatrix ? 2 (b) ERROR, the probability word the 0 0 0 0-1 0 0-2| xii) If (a)- 50 (b) 65 The slope of a xiv) (a) joining (c) In the adjoining figure, AB is the The measure of angle BAC is: xii) (a) the mid-point line segment 5 (b) 6 O (c) xv) If the mean is: i30 to X axis (c) is: - (d) 1 observations is 20-40 40-60 Frequency 7 p 10 (b) 11 (c) 22 not defined 54, find the valuc 0-20 Question -3),value of b diameter. Class (a) 14 (2, (d) 90 1 of the following b- 2) and (-2, 4) is (d) 8 A 40 line parallel (b) (6, 7 60-80 of p. 80-100 13 (d) 8 2 25 ab 12 find using properties of proportionthe value of [41 (i) Mr 800 per month deposit account in a bank and deposited he received 15084 at the time of maturity, find the interest Also find the (4] rate of recurring operned a for 18 months. by him. carncd X Soive (iiij interest and give your answer -3= 0 2x2-4x correct per upto three annum. significant figures: [4] 3 Question (5) f From the adjoin ng figure, find: The co-ordinatesof point A. (b) The equation of a line AB perpendicularto 4y and passing through A. (a) The co-ordinatesof (c) point =3x +3 B. [4] 1) An integer is chosen atrandom from 1 to 50. Find the probability is: a) divisible b) c) by that the nutmo 5 a perfect cube a prime number d)not a two digit nuber [4] In a class, weeklv pocket monev of students is as follows: (111) Weekly 40 -50 pocket 50 - 60 60 -70 70- 80 90 - 100 80 - 9o Inoney R) Nurnber of 2 10 14 00 8 students Use the scale: on X axis 2 crm and On Y axis 2 cm 4 students. Draw a histogram and use it to estimate the modal pocket money. Also statethe rmedianclass interval. =10 Section ) = this section) What number should be addedto thepolynomial 3x3 is a factor of the resulting polynornial [5] B (40marks) (Attemptany fourquestionsfrom Question4 6 +2x -19x so that (x+ 3) ? Factorize the resulting polynomial completely. Given: (ii) A [3] =(x:3< 2x- 1<9, xE W}and B ={x:11 s 3x 2 s 23, andB on two different number lines. + x Z} E Represent A (i1i) Find the amount of bill for the following if the rate of CGST is 14 %. Item Marked Price () Discount (%) intra state [3] transactionof goods, [4] A B 7000 20 C 14,700 10 28,200 10 6934.4 32486. 4 -A 5 Question =31, where Iis the unit matrix 9) Given A value of xand (b) If AB= 15, AQ AP = Find [3] I AC. AABC~ AAQP. Prove (a) the order, find y. AABC, LB = 90 . P In (ii) ofsame 3x+ 4, =6, QC = 10x1, [3] x. APQR is inscribed in a circle with centre O. Tangents at Pand R meet at point T. If ZPTR 48 , find ZPOR and zPRQ. (iii) R = Question 6 The (1) following table gives the weight large consignment. Calculate the a Weight No of potatoes 10 Give your answer The 11th in gm to nearest 12 a sample of 100 potatoes taken irom short cut method. 100-110 110-120 18 16 12 14 term of an Arithmnetic term.Find the arithmetic 8th progression is 20. The 15th term is 12 more than progression. (3] 2 = X a (ii) the B Question 7 (i) Find the co-ordinates A(-6, 10 [3] question. Use scale: cm 1 unit. 4), C(0, 4) and D(0, 4) are vertices of a rectangle. a) Reflect point A in axis to A'and reflect A' in axis to A". Plot and write co-ordinates of A' and A". b) Name single transformation which reflects to A'. c) State the geometrical name of the figure AA'A"B. Y Point A(4, 4), B(4, 120-130 whole number. Use graph paper for this (iii) of mean by 50-60 60-70 70-80 80-90 90-100 (in gms) (11) [4] 3) and B(9, of point of trisection 12) respectively. A jar contains some marbles of P and Q of [4] the line segmentjoining [3] green or white colour. The green and white colour marbles together are 36 in number.The probability of selecting a marble is 1/3 and the blue probability of selecting a green marble is 4/9. How many marbles are there of each colour ? e (ii) A blue, [3] circus tent is made of canvas and The diameterand the cone above it. 126 m and mn respectively. The of the canvas used at the 5 rate of is in the form of right circular cylinderand height of the cylindrical part of the tent are total height of the tent is 21 mn. 36 per square metre. Find the total a cost [4] Question (1) A & person on he has to tour has cut down 360 for the daily tour. his expenses. 1f he expenses by 3. Find the The frequency (ii) entrance test isdistributionof the as follows: Score 400 500 600 500 Number Use Scale: 600 700 of 20 candidates 2 cm = scores obtained 10 14 interquartilerange of scores. Number of students who qualified Question 30 axis and 2 1100 129 30 cm =20students oi -15 -30 and Prove: for the test, if 9 Find the sum of first 17 (ii) 22 1000 score. b) The (1) 900 G00 100 marks on one Draw an Ogive and hence a)The estimate: median c) 700 BO0 by 160 6afididates inS8 ternms of an A.P whose 780 fourth is the qualifying and respectively. the n nth SIE ) terms ae 1+Cos0 cOsec V1-Cos0 + cot 1-c09 [3) Sin9 In the figure, AB is a diameter and AC is a such that ZBAC chord 30 .The tangent at C intersects AB produced at D. Prove that BC BD. (iii) = = Question 10 (i) A hollow sphere of internaland external radii 6 cm and8 cm is melted and recast into small cones of base radius 2 cm and height 8 cm. Find the Cones. nmber (ii) f 3 Draw a circle with radius cm. Mark point O as its centre. distance of 5.5 cm from O. From Take a point Pata point P, draw two tangents to the circle Measure and record the length of cach tangent. (iii) A building and a tower are on the same level ground. From the top of the building,the angle of elevation of the top of the tower is 60 and the angle depression of the foot of the tower is 30 , If building is 40 high. find the height of the tower. m 2 t

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