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ICSE Class X Prelims 2023 : Mathematics (Gokuldham High School & Junior College (GHS), Mumbai)

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Sapna Dimri
Sadhu Vaswani International School (SVIS), Navi Mumbai

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GOKULDHAM HIGHSCHOOL &UNIOR COLGE SECONDARY SECTION 2022-2023 FIRST TERMINAL EXAMINATION MATHEMATICS GRADE: DATE:12.09.2022 Answers to this Paper must be written on thc paper MAX. MARKS: 86 TIME:2 hr. 30) min. separately. You will not be allowed to write during firstprovided 15 minutes. This tme is to be spent in the question papcr. The tine given at the head of this Paper isreading the time allowed for writing the answers. Attempt all questions from Section A and any four All working, including rough work, must be clearly questions from Section B. 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 questions or parts of questions are given in Mathematical tables are provided. brackets || This paper consists of 8 pages SECTION A |40 MARKS] (Attempt all questions from this section) Quesion i Choose and write the correct answers to the questions from the given options: Donot copy the quesiion.] (i) A shopkeeper buys an article for S00and sells it for 1000. The rate of GST is 18%. The rate of SGST and CGST are respectively a) b) c) d) (ii) 9% and i8% 9% and 9% 18%o and 9% 4.5% and 9% When the discriminant of a quadratic equation is zero then the roots of the quadratic equation are a) Infinite b) Equal c) Unequal d) Not real (vi) x 1 =0 are +x+ cquation quadratic The tan )-(1/cos?0) is b) a)I d)realnotC) b) a) cosec*)cosD c) -1 d) roots d) P(36)(37) real none real of of and and the these cqual distinct (Vil) (36) 2 P(36) c) Px b) 36 years. and time instalment monthly the is 3 on if isP calculated scheme, be vill deposit interest recuring Px a)3 then ina (v) A is of the order 2x1,then of AB is of order product 2x3 and the order 2x d) 13x2c)Ix3b)3x1a) matrix matrix isB A (iv) the then the value MATHEMALLCS -3, is x + 2, +5 by remainder 4x-3kx div.ding on 'k'is of If -3) c)3 b) -4 a)4 (iGRADEX i) is 12 its urved then cm, a?b) and the height is + (a is 10cm thenA? = ab N xe 11, +is: 5< set for -1} 1,2} the inequation 1<3x surface the 3:7,then in t h e MATHEMATICS ratio heights their have GRADEX of lateral is samne radii 9:49c)7:3b)3:7a) N3:N7d) of cylinders their {1,2} d) c) b) a) solution d) c)+ab b) a)a mean a +b a a - b proportion {0, {-4, (-2, 1,-3, -1, 2}-2, 0, ratio Two (vii) The (ix) The (x) of (a + b) and of 2A d) c)I b)0 a)A (xi) of cone a the base a) 120t cm d)90%cm?c)Cm?657 b)cm?60tdiameter surface area isThe (xii) MATHEMATICS GRADEX (41) n the given figure is the centre of the circle. Given that LDAC = 40 and ADis diameter of thecircle. Thedegree measure of zABC is a) b) c) d) 40 50 140 220 40d (xiv) If sec A - tan A = k, sec A + tan A is equal to a) 1-(1/k) b) 1k c) 1+.k d) 1/k (xv) The modal class of a grouped frequency distribution is the class interval with the a) lowest frequency b) cumulative frequency c) highest frequency d) average frequency Question 2 (a) Amit deposits ? 500every month in arecurring deposit account for 2:2 years. If the rate of interest is 10% per annum, find the amount he will receive on 14] maturity. (b) Findtwo numbers whose mean proportional is 16 and the third proportional is 128. (c) 14} Prove the following identity: (sinA+cosecA) +(cosA +secA) = 7+ tan'A + cotA (4} MATHEMATICS GRADEX Question 3 (a) and recast into SO4 cones cach of diameter 3.5cm and height 3 cm are melted cylinder and of the a metall1c solidcylinder of same radjs. Find the height 14] its surface area. (b) Find x and y if 14] (c) workers Use a graph sheet for this question. The daily wages of 120 working at a site are given below. along other axis to Use 2cmn=50 along one axis and 2 cm =20workers draw an ogive and hence estimate: 1. 11. Wages () i. the median wages ii. the inter - quartile range of wages is above Ii1. percentage of workers whose daily wage 250 -300 300 -350 No. of workers 15 350 .- 400 400 - 4S0 20 30 450 500 475. 500 - 550 25 (5! 550 - 600 15 SECTION D|40 MARKS] (Attempt any four questions from this section) Question 4 marked price of art1les: {a) The following billshows the GST rates and the BILL: COMPUTERS Articles Marked price Rate of GST 18% Rs 15500.00 Graphic Card 28% Rs 1900.00 Laptop adapter Calculate: (ijthe CGST paid to the Government for Graphic card. (ii)the total GST paid to the govern1ment (iii)the total amount to be paid for the above bill. (3] (b) Solve the following quadratic equation : (x-1) -3x + 4=0 Give your answer correct to three significant figures. 3| GRADE X (c) MATHEMATICS Use graplh sheet for this question. The following frequency distribution table represents the scores obtained by 100 students in an aptitude test. Draw a histogram and hence estimate the mode from it. Take 2cm =10marks along one axis and 2 cm = 10 students along the other axis. Scores No. of students 0 -10 10 -20 20- 30 30 - 40 40- 50 6 10 28 42 14 Question5 (a). Find the matrix Y, if X - 5Y =14 1, where X = 4 2 14| and I is the l3| identity matrix. (b) Factorise the given polynomial completely, using the Remainder Theorem: x +x2 (c). 4x 4 |3) The distance byroad between two towns A and B is 216 km and by rail it is 208km. A car travels at a speed ofxkm/h, and the train travels at aspeed which is 16kn/h faster than the car. ()Calculate ()the time taken by the car to reach town B from A in terms of x. (II)the tine taken by the train to reach town B from A in terms of x. (ii)if the train takes 2 hours less than the car to reach town B, (I)obtain an equation in x and (II) solve it to find the speed of the car. (iii) Hence find speed of the train. 14} GRADEX MATHEMATICS Question 6 (a). lI;2 Is a root of the equation 6x'-x-p =0, find the value ofp. Hence find 3: the other root (b) Solve the following inequation and represent the solution set on the number line. [3| 7<+4x+2<20,xeI (c)- Prove: sin A + coSA sin A-coSA 2 sec A sin A-cosA sia A +cos A sec'A-2 14] Quesion 7 (a) Ashopkeeper buys an article from the wholesaler at aprice of 1200 He pays CGST of R27, the rate of GST being 18%.Find the price at which he sold the article to the consume:. In the figure given below, chord ED is parallel to the diamneter AC of the circle wit centre O. IfZCBE = 54 and ZBCF = 92 , Caiculate 1. ii. LBAE LDEC 920 C E (c) 3} Acircus tent is in the form of a cylinder surmounted by a cone. The diameter ofthe cylindrical portion is 24m and its height is l imif the vertex of the cone is 16m above the ground, find the length of canvas required to make the tent given that the width of the canvas is 2m. Question (a). Solve the following inequation and represent the solution set on a number line: 2x 5 -3<-;;.xER 2 (3| MATHEMATICS GRADE X (b) What nunber shouid be added to 2r + 9r + Zr so that (x+ 3) is a factor of [3| the resulting polynomial? (c). Ahmed has a recurring deposit account in a bank. He deposits 1250 per month for 2years. If he gets 36250 at the time of maturity, find 1. the interest paid by the bank. 14) ii. the rate of interest Question9 (a) Find two consecutive positive integers such that the square of the first |4] decreasced by 17 equals 4 times the second integer. (b) In the given figure, reflex BOD =210 and ZBDC= 35 . Find: 1. ii. 11!. IV. V. LBCD ZBAD 2OBD 2CBD 2COD 210 D 3so) |6} Question 10 (a) Solve for x, using the properties of proportion: (b) x+3x 341 3x'+1 91 Prove that: secA(1-sin'A)-2 tan'A =1 (c) 3; Ifx'-2r +ar tb has a factor (r+2)and leaves a reminder9 when divided by (x+1) ,find the values of a and b. 3:

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