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ICSE Class X Prelims 2023 : Mathematics (Bombay Scottish School, Mahim, Mumbai)

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Bombay Scottish School, Mahim PRELIMINARY ASSESSMENT MATHEMATICS Grade : 10 Max. Marks : 80 Date : 16.01.2023 No. of Questions : 10 Duration : 2 hours and 30 mins No. of Printed sides : 08 Answers to this Paper must be written on the paper provided separately. Attempt all questions from Section A and any four questions 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 loss of marks. The intended marks for questions or parts of questions are given in brackets [ ] Mathematical tables are provided. Section A (Attempt all questions from this Section.) Question 1 Choose the correct answers to the questions from the given options: [15] (i) If a polynomial 3x2 -5x + p when divided by (x-2) leaves the remainder 3, then the value of p is (a) -19 (b) 2 (c) 1 (d) -1 (ii) If x [2 3 ] + y [ 1 0 ] = [10 6 ] , then the values of x and y are (a) x = 3, y = -6 (b) x = 2, y = 6 (c) x = 3, y = -4 (d) x = 2, y = -6 (iii) The percentage share of SGST of total GST for an intra-state sale of an article is (a) 75% (b) 50% (c) 25% (d) 100% (iv) If the height of a tree is 3 times the length of its shadow, then the angle of elevation of the sun is 1 (a) 450 (b) 600 (c) 300 (d) 900 (v) The point A(0,-4) is invariant under reflection in (a) both x and y axes (b) origin (c) y-axis (d) x-axis (vi) If probability of an event E is 0.07, then the probability of event E not happening is (a) 0.93 (b) 0.95 (c) 0.89 (d) 0.90 (vii) Which of the following matrix multiplication is not possible? (a) [3 2][2 0 ] (b) [1 (c) [6 4 3 1 ] 2] [ 2 3 1 4 ] [ 1 3 ] (d) [2 4 0 1 ][ 1 3] (viii) The sum of first n terms of the series a,3a,5a .. is (a) n2a2 (b) n2a (c) (2 12 ) (d) na (ix) The equation (x+1)2 2(x+ 1) = 0 has (a) two equal roots (b) no real roots (c) one real root (d) two real roots (x) The solution set of the following number line is 2 (a) {x / - 1 x 4 , x R } (b) {x / - 1 x < 5, x R } (c) {x / - 1 < x 5 , x R } (d) {x / - 1 x 5 , x R } (xi) A cone is surmounted on a flat side of a coin. The cone has same radius as the coin. The surface area of the solid formed is equal to the (a) base area of coin + C.S.A of coin (b) base area of coin + C.S.A of coin + C.S.A of cone (c) T.S.A of cone + T.S.A of coin (d) T.S.A of cone (xii) AB is a diameter of a circle with centre O(-2,2). If point A is (3, -7) then the coordinates of B are (a) (-7,11) (b) (7, -11) (c) (-9,13) (d) (9, -13) (xiii) In the given figure, PA is a tangent to the circle at point A, PB = 16cm, BC = 9cm. The length of PA is (a) 25cm (b) 9cm (c) 20cm (d) 10cm (xiv) In a grouped frequency distribution, the mid values of the classes are used to measure which of the following central tendency? (a) Median (b) Mode (c) Mean (d) all of these 3 (xv) If the slope of the side BC of a rectangle ABCD is 23 , then the slope of the side AB is (a) -3 (b) 23 (c) 2 3 (d) 3 2 Question 2 a) David has a recurring deposit in a bank for 2 years at 6% per annum. If he gets 1200 as interest at the time of maturity, find : i) the monthly instalment. ii) the amount of maturity. [4] b) Prove that: (cosec A - sin A) (sec A - cos A) (tan A + cot A) = 1 c) If M = [1 2 2 1 ] and I is a unit matrix of the same order as that of M, show that M2 2M = 3I [4] [4] Question 3 a) A toy is in the form of a cone mounted on a hemisphere of same radius 3.5cm. The total height of the toy is 15.5cm. Find: i) the slant height of the cone. ii) the total surface area of the toy. Give your answer correct to the nearest whole number. (Take = 227 ) [4] b) Using properties of proportion, find the value of x. 3 +4 + 3 5 =9 3 +4 3 5 c) Use graph paper for this question: Plot P(3,4) and reflect it along the x-axis as P O is the image of O (the origin) when reflected in the line PP . Write: i) the coordinates of P and O . ii) the equation of the line segment PP . iii) the geometrical name of the figure POP O iv) the perimeter of the figure. Section B 4 [4] [5] Question 4 (Attempt any four) a) Solve the following quadratic equation and give your answer correct to 2 significant figures. 4x2 - 5x - 3 = 0 [3] b) Construct a regular hexagon of side 5cm and construct a circle circumscribing the hexagon. Measure and write the length of the circum-radius. c) [3] A line AB meets x-axis at A and y-axis at B. Point P(4,-1) divides AB in the ratio 1:2. i) ii) Find the coordinates of A and B. Find the equation of a line through P and perpendicular to AB. [4] Question 5 a) Solve the following inequation, write the solution set and represent it on the number line. 2x 3 < x + 1 4x + 7 , x W [3] b) In the figure given below, PQRS is a cyclic quadrilateral. PQ and SR produced meet at T. i) Prove: TPS ~ TRQ. ii) If TP = 18cm, RQ = 4cm and TR = 6cm, find PS. [3] 5 c) The expression x3 -kx2 +14x 8 has (x-2) as a factor. [4] i) Find the value of k. ii) With the value of k, factorise the above expression completely. Question 6 a) A box contains 7 blue, 8 white and 5 black marbles. If a marble is drawn at random, then find the probability that the marble drawn is i) black. ii) blue or white. iii) green. [3] b) Two solid spheres of radii 2cm and 4cm are melted and recast into a solid cylinder of height 6cm. Find the radius of the cylinder formed. [3] c) A manufacturer sells an air-fryer to a dealer for 18000 and the dealer sells it to a consumer at a profit of 1500. If the sales are intra-state and the rate of GST is 12%, find i) ii) iii) the amount of GST paid by the dealer to the State Government. the amount paid by the consumer for the air-fryer. the amount of GST received by the Government. [4] Question 7 a) From the top of a 80m tall light house, the angles of depression of two ships on the same side of the light house in horizontal line with its base are 300 and 400 respectively. Find the distance between the two ships. Give your answer correct to 2 significant figures. [4] b) Use graph paper for this question. The following distribution represents the height of 160 students of a school. Height 140-145 145-150 150-155 155-160 160-165 165-170 170-175 175-180 (in cm) No. of 12 20 30 38 24 16 12 8 students Draw an ogive for the given distribution taking 2cm = 5cm of height on one axis and 2cm = 20 students on the other axis. Use the graph to determine: i) The median height. ii) The upper quartile. iii) The number of students whose height is above 172cm. [6] Question 8 a) The second, third and the last term of an A.P are 14, 18 and 114 respectively. Find the first term and the number of terms in the A.P. [3] 6 b) In the figure given below, O is the centre of the circle, ST is a tangent to the circle at D, ABO = 300 and BDS = 660. Find i) DAB ii) DCB iii) ADT c) [3] The following are the marks obtained by 70 students in a class test. [4] Marks No. of students 30-40 10 40-50 12 50-60 14 60-70 12 70-80 9 80-90 7 90-100 6 Calculate the mean by step-deviation method. Give your answer correct to 2 decimal places. Question 9 a) Find the equation of a line parallel to x 2y + 8 = 0 and passing through the point (1, 2). [3] b) Find two numbers such that the mean proportion between them is 12 and the third proportion to them is 96. [3] c) A two digit positive number is such that the product of its digits is 6. If 9 is added to the number, the digits interchange their places. Find the number. [4] Question 10 a) If A = [4 5 3 4 ] i) ii) , B = [7 6 ] and AX = B. Find the order of matrix X matrix X [3] 7 b) c) In the given figure, S is a point on the side QR of PQR such that PSR = QPR. If QP = 8cm , PR = 6cm and SR = 3cm. i) Prove PQR ~ SPR ii) Find the length of QR and PS. [3] Use graph paper for this question. The daily pocket expenses of some students in the class are given below: Pocket expenses in No of students 0-50 50-100 100-150 150-200 200-250 8 10 24 18 6 Draw a histogram for the given distribution, estimate the mode and write the modal class. [4] ______________________________________________________________________________ 8 9

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