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ICSE Class X Prelims 2024 : Mathematics (Childrens Academy, Thakur Complex, Kandivali East, Mumbai)

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Shravya Kanitkar
Children's Academy, Thakur Complex, Kandivali East, Mumbai

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PRELIMINARY EXAMINATION 2023-24 Grade : Date : X Subject : 21/11/2023 MATHEMATICS Marks : Time : 80 2 hr 30 min 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 this paper is the time allowed for writing the answers. This paper consists of 6 printed pages. Attempt all questions from Section A and any four questions from Section B. All workings, 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. All figures in geometry have to be copied in the answer sheet. The intended marks for questions or parts of questions are given in brackets [ ]. SECTION A (Attempt all questions from this Section) Question 1 Choose the correct answers to the questions from the given options: (i) [15] The reflection of a point A in the line l is the point A . Therefore, line l is the __________ of AA . (ii) (a) median (b) perpendicular bisector (c) angle bisector (d) perpendicular The equation of a line which has Y-intercept 4 and is parallel to the line 2x 3y 7 = 0 is: (iii) (a) 2 3 7 = 0 (b) 2 3 + 7 = 0 (c) 3 2 + 7 = 0 (d) 2 3 + 12 = 0 A In the given figure, O is the centre of the circle. If COB = 100 , AOC = 160 , then ACB = (iv) (a) 600 (b) 700 (c) 500 (d) 800 O B C In what ratio, does point P(-4, 6) divide the line joining points A(-6, 10) and B(3, -8)? (a) 7:2 (b) 2:7 (c) 5:2 (d) 2:5 Mathematics/Grade X/ICSE/ Preliminary Examination/ Page 1 of 6 CAT/LD/2023-24 (v) Two right circular cylindrical pots contain the same amount of water. If their diameters are in the ratio, 2 : 3 the ratio of their heights is: (vi) (a) 2:3 (b) 9:2 (c) 9:3 (d) 9:4 If cosec A = 2x and cot A = (a) (c) 2 1 2 1 then the value of 2( 2 (b) 2 (d) 8 1 2 ) is : (vii) Class Interval 10 20 20 30 30 40 40 50 50 60 60 70 Cumulative Frequency 2 5 10 17 22 28 The median class of the above frequency distribution table is (a) 50 60 (b) 40 50 (c) 60 70 (d) 30 40 (viii) A dice is marked with numbers 3 , 2 , 1 , 1 , 2 , 3. The probability of getting a positive integer is (a) (c) (ix) 1 6 2 6 (b) (d) 1 3 1 2 A shopkeeper buys goods worth 4,000 and sells at a profit of 320. If the rate of GST is 10%, then the bill amount is: (x) (xi) (a) 4,400 (b) 4,320 (c) 4,752 (d) 4,720 For the quadratic equation 4x2 + 12x + 9 = 0, the roots are: (a) imaginary (b) 0 each (c) real and distinct (d) real and equal A sequence is a, a, a, a, a, a 1) It is an A.P. 2) It is a G.P. (a) Only 1) is correct (b) Only 2) is correct (c) Both are incorrect (d) Both are correct (xii) In the given figure, PQR ~ PMQ ~ QMR, Q = 90 and QM PR. If PM = 4cm and PR = 13cm, find QM. P (a) 9cm (b) 6cm (c) 8cm (d) 17cm M Q Mathematics/Grade X/ICSE/ Preliminary Examination/ Page 2 of 6 R CAT/LD/2023-24 (xiii) Mr. Subhash sells 150, 100 shares at a premium of 22. His sale proceeds is: (a) 13,800 (b) 18,300 (c) 15,000 (d) 11,700 (xiv) The fourth proportional to 4xy, 2x2y and 8 is: (a) 4x2 (b) 4xy (c) 4x (d) 4y (xv) If A and B are two fixed points, then the locus of a point P such that APB = 90 is a : (a) circle with AP as radius (b) circle with AB as diameter (c) circle with PB as diameter (d) circle with AB as radius Question 2 (i) Mrs. Sen deposits a sum of 2,400 every month in a recurring deposit scheme of a bank. If she receives 30,048 at 8% p.a interest rate calculate the term for which the account was held. (ii) Prove that: sin cos +1 sin + cos 1 = [4] cos [4] 1 sin (iii) When 2x3 + ax2 11x + b is divided by (x 2) and (x 3), it leaves the remainders as 0 and 42 respectively. Find the values of a and b and hence, factorize the given polynomial. [4] Question 3 (i) In the given figure, PT touches the circle at point R, whose centre is O. Diameter SQ meets tangent PT at P. QPR = 60 and QRP = 15 . Find: (ii) G (a) OQR (b) OSR (c) SRT (d) QGR S O Q P T [4] R In a rhombus PQRS, the vertex P is (2, 8) and the vertex R is (8, 3). Find the equation of the diagonal QS. (iii) [4] Use graph paper for this question. Take 1cm = 1unit on both axes. (a) Plot A(-4,0), B(-3,2), C(0,4), D(4,1) and E(7,3) on the graph sheet. (b) Reflect the points B, C, D and E in the X-axis and name the images as B , C , D and E respectively. (c) Join the points ABCDEE D C B A in order. (d) Give a geometrical name for the closed figure formed. Mathematics/Grade X/ICSE/ Preliminary Examination/ Page 3 of 6 CAT/LD/2023-24 (e) Name two points that are invariant when reflected in the line represented by the graph y = 0. [5] SECTION B (Attempt any four questions from this section) Question 4 (i) The following bill shows details of purchases made. Find the total amount to be paid for the bill. Sr. No Bought items 1 Graphic Card 2 Laptop Bag Price per item in 20,000 Quantity Discount GST 1 5% 10% 5,000 1 10% 12% [3] (ii) Solve the given quadratic equation : 7x2 + 2x 2 = 0. Give your answer correct to two decimal places. (iii) [3] Use a graph sheet for this question. For the following distribution, draw a histogram and then use it to estimate the mode. Take 2cm = 500 and 2cm = 5 stores as the scale. Earnings ( ) 4500-5000 5000-5500 5500-6000 6000-6500 6500-7000 No. of stores 20 14 12 5 3 [4] Question 5 (i) A person invests 5,040 in 100 shares, declaring a 16% dividend at 120. Find: (ii) (a) the number of shares purchased. (b) his annual income from the dividend. (c) the rate of returns on his investment. 2 Matrix A is [0 1] and matrix B is [ 2 [3] 1 4 ]. If AB = BA, then find the 0 1 value of . (iii) [3] From a point on the ground the angles of elevation of the bottom and the top of a transmission tower fixed at the top of a 20 m high building are 45 and 60 respectively. Find the height of the tower to the nearest metre. [4] Question 6 (i) Solve the inequation and represent the solution set on a number line. 1 1 1 4 4 4 2 + 2x 3x + < 3 + 2x; x R. Mathematics/Grade X/ICSE/ Preliminary Examination/ Page 4 of 6 [3] CAT/LD/2023-24 (ii) A model of a ship is made to a scale of 1:200 find (a) if the length of the model is 4m, calculate the length of the ship (b) if the area of the deck of the ship is 16,0000m2. Find the area of the deck of the model. (c) If the volume of the model is 200cm3, calculate the volume of the ship in m3. (iii) [3] The 3rd term of an arithmetic progression is 20 and its 8th term is 26. Find its 51st term and the sum of its first 51 terms. [4] Question 7 (i) The monthly income of a group of 320 employees in a company is given below. Draw an ogive of the given distribution on a graph sheet using a scale of 2cm = 1,000 on one axis and 2cm = 50 employees on the other axis. Use the ogive to estimate: Monthly Income (in thousands) No. of employees (ii) 6 7 7 8 8 9 9 10 10 11 11 12 12 13 20 45 65 95 60 30 5 (a) the median income (b) the lower quartile (c) the number of employees whose salary is above 11,500 [6] A train travels at a certain speed for a distance of 63 kilometers and then travels a distance of 72 kilometers at a speed of 6 km/hr more than its original speed. It takes three hours to complete the total journey. What is its original speed? [4] Question 8 (i) A solid right circular cylinder has a radius of 5cm and its total surface area is 660 cm2. Find: (ii) (a) the height of the cylinder. (b) the volume of the cylinder. Using the properties of proportion, solve for x : 5+ 5 5 5 (iii) [3] = 3. [3] The mean of the following distribution is 50 and the total of frequencies is also 50. Find the unknown frequencies a and b. Marks Frequency [4] 0-20 20-40 40-60 60-80 80-100 6 a 8 b 8 Mathematics/Grade X/ICSE/ Preliminary Examination/ Page 5 of 6 CAT/LD/2023-24 Question 9 (i) Identical cards bearing numbers from 16 to 69 are well shuffled. A card is drawn at random from it. Find the probability that the card drawn is: (a) a multiple of 15 (b) a factor of 64 (c) a perfect cube. [3] (ii) Find the sum of 11 terms of the geometric progression 4, 8,16 . (iii) Construct a ABC where AC = 10cm, AB = 6cm and BC = 8cm. [3] (a) Draw the locus of a point that is equidistant from the points A and C. (b) Construct a circle taking AC as the diameter. (c) Locate a point D, such that ABCD is a cyclic quadrilateral and also point D is equidistant from A and C. (d) Measure and record ACD. [4] Question 10 (i) The midpoint of the line segment joining (2a, 4), ( 2, 2b) is (1, 2a + 1). Find the values of a and b. (ii) [3] In the given figure, O is the centre of the circle and AB is the diameter. DO // CB and DCB = 120 . A Calculate: (iii) (a) DAB (b) DBC (c) ADC D O > C > B [3] A conical vessel of radius 6 cm and height 8 cm is completely filled with water. A sphere is lowered into the water and its size is such that when it touches the sides of the vessel, it is just immersed. What fraction of water overflows? [4] ************************THE END************************ Mathematics/Grade X/ICSE/ Preliminary Examination/ Page 6 of 6 CAT/LD/2023-24

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