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THE HERITAGE SCHOOL PREBOARD EXAMINATION 2023 CLASS 10 MATHEMATICS Maximum Marks: 80 Timeallowed: Tvo and half hours Answer to this paper must be wrillen on the paper provided separalely. You will not be allowed to write on the puper provided separalely. You will not be allowed lo write during first I5 minutes. The This time is to be spent in reading the question paper. allowedfor writing lhe answers. time given at the head of ihis Paper is thetime Section B. and any four quesiions from Aempl allquestions from Section A must be done on the same work, must be clearly shown, and rough including workings, Al sheet as the rest ofthe answer. The result inloSs of marks. Omission ofessential working will brackels) parts of questions are given in intended marks for questions or Mathematical tables are provided. Section A this section,) (Atlempl all questionsfrom Question I from thc given options. answers to the questions correcct the Choose answer only.) annount question, write the correct the copy includes 10% GST. The (Do not which 6I600 article for Rs Shikha purchases an of SGST is rupees: (a) 2800 (b)3580 (c) 5600 () 6160 Which of the following ICSE as per 2024 equations bas 2 as a root? This paper consists of9 printed pages. Page1 of9 (a) x'- 4x + 5 =0 (b)x +3x -12 == 0 (2x-7x +6 =0 (d)3x?- 6x-2-0 iii. If (x-2) is a factor of 2x x +px -2, the value of p is (a) -11 (c) -2 (d) 5 iv. Ifx,3, 12 and y are in continued proportion then : (a) x= 4/3and y48 (b) x=4/3 and y= 1/48 I (ox=% and y= 48 (d) x = landy =1 The solution set representing the mumber line is: Lat {*:xe R, -3 <x<2} {x:xe R,-3 < x< 2} {x:xe R,-3 <Kxs2} {x:xe R, -3 <x s2} (b) (c) (d) If a matrix P is of the order 1x 2 and matrix Q is of order 2x 1, then the matrix QP will contain: Vayl element. (b) 2 elements. C) 4 elements d) QP multiplication is not possible. vii. If a, = (5n +1) for an A.P. then the common difference is: (a) 1 Ob) 5 (d) 11 Viii. Which of the following is invariant when reflected in the line y +2 =0. (a) (10,2) ICSE as per 2024 This paper consists of 9 printed pages. Page 2 of9 b) (-10, -2) (c) (-2, -10) (d) (-2, 0) ix. The slope of the line x - I =0is: (a) 1 (b) (c) 0 tNot defined. X Kamal buys x number of shares at par of acertain company paying y'% dividend. The rate of return will be: sa Equal to y% (b) Lesser than v% (c) Greater than y% (d) Equal to xv% xi. From the figure given below, Given that the equation of theline AB is y -4 =0. The centroid of the triangle AOB is: (a) (1.5,0) (b) (1.5,8/3) (c) (1.5, 1.5) tl,8/3) Xil. between two and the distance I:50000. factor is cities is: If the scale distance between two actual then the (a) 100000km cit es on map is 2cm, (b)2500km (c) 1000km A tlkm xii. and the cylinder is 44 m a of area surface Ifthe curved n= height of the ICSE as per 2024 cylinder is:(Take printedpages. consistsof9 This paper volume is 22 m The Page3 of9 (a) Im (by3.5 m Bc) 7m X (d) 22 m Thrcc obscrvations x ,y, z arc arangcd in ascending order such that thcir mean is 1000and the median is 800. In such a case the value of (x + z) is: Xiv. Aa 200 (b) 800 (c) 2200 (d) 3200 Assertion(A):7, (-14), 28, (-56), 112 are in GP. Reason (R) : The terms of a G.P. cannot have both positive and negative XV. numberS. (a) Ais true, R is true. (b) A is false, R is true. tcj A is false, R is false. (d) Ais true, R is false. question 2 7cm long and 2 cm diameter. If the A spherical glass vessel has a cylindrical neck amount of liquid it holds diameter of the spherical part is 6cm then calculate the 2 places of decimal. when filled till the brim of the neck. Give your answer to Take =4 7 j. recurring deposit account in PNB for 2 Shikha deposits rupees 500 per month in a rupees 400 per month in a years at 6% p.a. At the same time Rahul deposits p.a. for the sane period. Who recurring deposit account in Bandhan bank at 8% (4] earned more interest and by how much. IfstnB +cose)= x Find the value of sinb. cos0 value of tan + cot.. b. Using the above find the Auestion 3 If-- prove that ax - by CZ - by - cz (a+ b)(x-y) (b+ c)(- 2) =3 (c+ a)(z- ) a tangent to the In the given figure PAQ is point A. If LOBA = 32". Circle, with centre O, at a ICSE as per 2024 az printed pages. This paper consists of9 14] Page 4 of9 Find the values of x, y, z. community market are represented The daily profits in rupees of all the shops in a following questions. graphically as shown below. Study the graph and answer the Shops cfNo i5 iop 20 sa) What is the modal class of the profit? graph. o(b) Estimate the mode trom the graph? (eYWhat is the name of this in the grapl1? What is the total number of shops as shown compared to (0-100)? (300-400) of (e How many more shops made a profit ICSE as per 2024 This paper consists of9 printed pages. [5) Page 5 of 9 SECTION B (Atiempt any four questions from this section.) Question 4 IfA - Findthe value of (A -21)( A31). When I' is the unit matrix of order 2 2. Solve the quadratic equation. -10x t6 = 0for xand give your answer correct to 2 decimal places. (you may use mathematical table for the question) In the figure Given that LACB = 90 and LADC=90 . ii. [3] [31 [4] A then prove that. a b. C AACD~ AABC ABCD~ABAC Hence prove that BC2 BD AC? AD Question 5 A Manufacturer sells a microwave oven to a wholesaler for rupees 15000. The wholesaler sells it to a dealer at a profit of 2500, and the dealer sells itto a customer making a profit of 2700. If the rate of GST is 10% find The price paid by the customer including GST. . The CGST paid by the dealer. [3] Find the mean of thefollowing distribution by short cut mnethod. Class interval Frequency 20-30 30-40 40-50 50-60 8 12 60-70 [3] 70-80 9 In the figure given below, ABCD is a cyclic quadrilateral, and PQ is a tangent to the circle at C. If BD is a dianeter, find the measure of sa zDBC (b)2BCP (e)zBDC ()LADB ICSE as per 2024 This paper consists of 9 printed pages. (4] Page 6 of 9 K [3] If6 is added to its terms ofa GP is 1000. the Find three AP. first in the become terms the The product of then term. added to its third Second term and 7is Question 6 GP. [31 Use agraph sheet for this Thetable question. society. ages of members ofa given below shows the 25-35|35-45 45-55 Age in ycars Number of members 5 of the society 13 55-6565-75 | 75-85 14 find. Draw an Ogive and years. a Median age 60 years and 80 whose age is between members Number of space must have 4m' of Each person accommodate Il persons. calculate. to is breath. Hence Aconical tent 20m' of airto and ground on the the tent. The base area of b The volurne of the 4 tent. tfhetent. w The height of Question 7 Astraigl1t the points P(2, line passes through (4,3). Find: -6)and Q the line PO. (k-1, k t4). The equation of ifPQ passes through line PO. 'k' of value divides the b. The by which x axis ratio The c. elevation street, the angles of a in ground the side of the m high above on the oppositeopposite house another From awindow 10 of house on the the top and the foot and depression of respectively. Find the heightoftheplaces. [5] street are 32 and 45 your answer correct to 2 decimal Give side of thestreet. ICSE as per 2024 printed pages. Th s paper consists of9 Page 7 of9 anot graph A Ketlc ls a S Usc L0) Question 8 Solve the inequation and write the solution set and represent the solution set on the number line. [3] 2x-3 <5x+3 < 2x +3,xE R In the fgure givcn bclow, AC= AB, ZABC=72 . OA and OB arc the 2 tangents. Detennine: b The angle subtended by the chord AB at the centre. [3] Determine ratio in which the point P (m,6)divides the join of A (-4,3) and B (2,8). Also find the value of m. Show that the line AB is perpendicular to a line 6x + 5y = 11. 14] Quession 9 I1. 111. 62(1+x) Using properties of proportion solve for x. [3] If the marked price ofa book is reduced by rupees 5, a person can buy 5 more books for rupees 300. Taking the marked price as 'x, create a quadratic equation and hence find the original marked price. [3] Using ruler and compass only construct, zABC = 60 , Where AB -7 cm, and 1-x+x? 63(1-x) (4] BC= 6 cm. a. Construct the locus of points equidistant from both Aand B. b. Construct the locus of points equidistant from AB and AC. Mark a point P which satisfies both the above conditions in a and b. euestion 10 x+ 2. Find the value of 'a', if (x-a) is a factor of x - ax' + 3] Hence factorize x - ax +x+ 2. fish one out takes shopkeeper The Gopal buysa fish from a shop for his aquarium. biue, 7 black colour fishes. Find orange, 6 at a random from atank containing 5 the probability that the fish is: ICSE as per 2024 This paper consists of 9 printed pages. Page 8 of 9 Orange fish. b fish. Blue or black Is not a blue fish. (3| Kise a graph shect for this question. Take 2 cm =1unit along boththe axes. [4] (a) Plot A (1,4), B (1,1), C (4,1) (b) Reflect Ain yaxis to Afollowcd by reflection inx axis toF. Retlect B in x axis to E followed by reflection in origin toE. Reflcct Cin y axis to Cfollowed by reflcction in x axis to D' Reflect A in x axis to F. Reflect B in origin to B. Reflect Cin x axis to D. (e Join A, B, C, D,E, F,F, B, D', C, E, A, A. Name thefigure formed.
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