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ICSE Class X Prelims 2024 : Mathematics : DMT All In One Prelim Set 01 (21 Prelim Papers)

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ICSE 10 School Prelim Papers DMT TOP SCHOOL ICSE X PRELIM PAPERS 24 SET 01 MATHS https://t.me/ICSE_10_Prelim ICSE 10 School Prelim Papers INDEX S.NO. NAME OF SCHOOL Page 1 ICSE SPECIMEN 2024 001 2 ARYA VIDYA MANDIR 013 3 CHILDREN S ACADEMY 023 4 EUROSCHOOL 029 5 GUNDECHA EDUCATION ACADEMY 041 6 JBCN INTERNATIONAL SCHOOL 048 7 JAMNABAI NARSEE SCHOOL 053 8 KAPOL VIDYANIDHI INTERNATIONAL SCHOOL 061 9 NL DALMIA HIGH SCHOOL 067 10 ORION SCHOOL 075 11 PAWAR PUBLIC SCHOOL 083 12 RAMNIWAS BAJAJ ENGLISH HIGH SCHOOL 090 13 RBK SCHOOL 098 14 SJ PODDAR ACADEMY 105 15 ST FRANCIS SCHOOL 114 16 ST JOHN UNIVERSAL 121 17 SVIS 127 18 THAKUR INTERNATIONAL SCHOOL 137 19 THAKUR PUBLIC SCHOOL 143 20 BHAKTIVEDANT SWAMI MISSION 148 21 VIBGYOR HIGH 157 https://t.me/ICSE_10_Prelim ICSE 10 School Prelim Papers ICSE 2024 EXAMINATION SPECIMEN QUESTION PAPER MATHEMATICS Maximum Marks: 80 Time allowed: Two and half hours Answers to this Paper must be written on the paper provided separately. You will not be allowed to write during 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. 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] (Do not copy the question, write the correct answers only.) (i) 1 = [ 1 2] = [ 0 2 ] 3 Which of the following operation is possible? (a) A B (b) A+B (c) AB (d) BA DMT Page 1 https://t.me/ICSE_10_Prelim ICSE 10 School Prelim Papers (ii) (iii) If 2 + + 6 = ( 2 )( 3) for all values of x, then the value of k is: (a) 5 (b) 3 (c) 2 (d) 5 A retailer purchased an item for 1500 from a wholesaler and sells it to a customer at 10% profit. The sales are intra-state and the rate of GST is 10%. The amount of GST paid by the customer: (iv) (v) (a) 15 (b) 30 (c) 150 (d) 165 If the roots of equation 2 6 + = 0 are real and distinct, then value of k is: (a) > 9 (b) > 6 (c) <6 (d) <9 Which of the following is/are an Arithmetic Progression (A.P.)? 1. 1, 4, 9, 16, . 2. 3, 2 3, 3 3, 4 3, 3. 8, 6, 4, 2, (a) only 1. (b) only 2. (c) only 2. and 3. (d) all 1., 2. and 3. DMT Page 2 https://t.me/ICSE_10_Prelim ICSE 10 School Prelim Papers (vi) The table shows the values of x and y, where x is proportional to y. x 6 12 N y M 18 6 What are the values of M and N? (vii) (a) M = 4, N = 9 (b) M = 9, N = 3 (c) M = 9, N = 4 (d) M = 12, N =0 In the given diagram, ABC ~ PQR and 3 = 8. The value of AB : PQ is: P A B (viii) (a) 8:3 (b) 3:5 (c) 3:8 (d) 5:8 D CQ S R A right angle triangle shaped piece of hard board is rotated completely about its hypotenuse, as shown in the diagram. The solid so formed is always: 1. a single cone 2. a double cone Which of the statement is valid? (a) only 1. (b) only 2. (c) both 1. and 2. (d) neither 1. nor 2. DMT Page 3 https://t.me/ICSE_10_Prelim ICSE 10 School Prelim Papers (ix) Event A: The sun will rise from east tomorrow. Event B: It will rain on Monday. Event C: February month has 29 days in a leap year. Which of the above event(s) has probability equal to 1? (x) (a) all events A, B and C (b) both events A and B (c) both events B and C (d) both events A and C The three vertices of a scalene triangle are always equidistant from a fixed point. The point is: (xi) (a) Orthocentre of the triangle. (b) Incentre of the triangle. (c) Circumcentre of the triangle. (d) Centroid of the triangle. In a circle with radius R, the shortest distance between two parallel tangents is equal to (xii) (a) R (b) 2R (c) 2 R (d) R An observer at point E, which is at a certain distance from the lamp post AB, finds the angle of elevation of top of lamp post from positions C, D and E as , and . It is given that B, C, D and E are along a straight line. Which of the following condition is satisfied? (a) tan > tan (b) tan < tan (c) tan > tan (d) tan < tan A B C D E DMT Page 4 https://t.me/ICSE_10_Prelim ICSE 10 School Prelim Papers (xiii) 1. Shares of company A, paying 12%, 100 shares are at 80. 2. Shares of company B, paying 12%, 100 shares at 100. 3. Shares of company C, paying 12%, 100 shares are at 120. Shares of which company are at premium? (xiv) (xv) (a) Company A (b) Company B (c) Company C (d) Company A and C Which of the following equation represent a line passing through origin? (a) 3x 2y + 5 = 0 (b) 2x 3y = 0 (c) x=5 (d) y = 6 For the given 25 variables: , , . Assertion (A): To find median of the given data, the variate needs to be arranged in ascending or descending order. Reason (R): The median is the central most term of the arranged data. (a) A is true, R is false (b) A is false, R is true (c) both A and R are true (d) both A and R are false Question 2 (i) Shown below is a horizontal water tank composed of a cylinder and two [4] hemispheres. The tank is filled up to a height of 7 m. Find the surface area of the tank in contact with water. Use = 22 7 . DMT Page 5 https://t.me/ICSE_10_Prelim ICSE 10 School Prelim Papers (ii) In a recurring deposit account for 2 years, the total amount deposited by a person is [4] 9600. If the interest earned by him is one-twelfth of his total deposit, then find: (iii) (a) the interest he earns. (b) his monthly deposit. (c) the rate of interest. Find: [4] (a) (sin + )2 (b) ( + )2 Using the above results prove the following trigonometry identity. (sin + )2 + (cos + sec )2 = 7 + 2 + 2 Question 3 (i) If a, b and c are in continued proportion, then prove that: [4] 3 2 + 5 + 7 2 = 3 2 + 5 + 7 2 (ii) In the given diagram, O is the centre of circle circumscribing the ABC. [4] CD is perpendicular to chord AB. OAC=32 . Find each of the unknown angles x, y and z. DMT Page 6 https://t.me/ICSE_10_Prelim ICSE 10 School Prelim Papers (iii) Study the graph and answer each of the following: [5] (a) Name the curve plotted (b) Total number of students (c) The median marks (d) Number of students scoring between 50 and 80 marks DMT Page 7 https://t.me/ICSE_10_Prelim ICSE 10 School Prelim Papers SECTION B (Attempt any four questions from this Section.) Question 4 (i) (ii) If = [ [3] 4 4 ] , find 2 . If 2 = , then find the value of . 4 4 Solve the given equation 2 4 2 = 0 and express your answer correct to two places [3] of decimal. (You may use mathematical tables for this question). (iii) In the given diagram, ABC is right angled at B. BDFE is a rectangle. AD = 6 cm, CE = 4 cm and BC = 12 cm (a) prove that ADF ~ FEC (b) prove that ADF ~ ABC (c) find the length of FE (d) find area ADF : area ABC [4] C 4 cm E F A 6 cm D B Question 5 (i) Shown below is a table illustrating the monthly income distribution of a company with [3] 100 employees. Monthly Income (in 10, 000) Number of employees 0-4 4-8 8 - 12 12 - 16 16 - 20 20 - 24 55 15 06 08 12 4 Using step- deviation method, find the mean monthly income of an employee. (ii) The following bill shows the GST rate and the marked price of articles: [3] Vidhyut Electronics S. No. Item Marked Price Quantity Rate of GST (a) LED TV set 12000 01 28% (b) MP4 player 5000 01 18% Find the total amount to be paid (including GST) for the above bill. DMT Page 8 https://t.me/ICSE_10_Prelim ICSE 10 School Prelim Papers (iii) In the given figure, O is the centre of the circle and AB is a tangent to the circle at B. If PQB=55o. [4] P (a) find the value of the angles x, y and z. (b) prove that RB is parallel to PQ. R O S 55 A Q B Question 6 (i) There are three positive numbers in a Geometric Progression (G.P.) such that: (a) [3] their product is 3375 (b) the result of the product of first and second number added to the product of second and third number is 750. Find the numbers. (ii) The table given below shows the ages of members of a society. Age (in years) Number of Members of the Society 25 35 05 35 45 32 45 55 69 55 - 65 80 65 75 61 75 - 85 13 [3] Use graph sheet for this question. Take 2cm = 10 years along one axis and 2cm=10 members along the other axis. (a) Draw a histogram representing the above distribution. (b) Hence find the modal age of the members. DMT Page 9 https://t.me/ICSE_10_Prelim ICSE 10 School Prelim Papers (iii) A tent is in the shape of a cylinder surmounted by a conical top. If the height and radius of [4] the cylindrical part are 7 m each and the total height of the tent is 14 m. Find the: (a) quantity of air contained inside the tent. (b) radius of a sphere whose volume is equal to the quantity of air inside the tent. Use = 22 7 Question 7 (i) The line segment joining A(2,-3) and B(-3, 2) is intercepted by the -axis at the point M [5] and the y axis at the point N. PQ is perpendicular to AB produced at R and meets the y- axis at a distance of 6 units from the origin O, as shown in the diagram, at S. Find the: (a) P coordinates of M and N 6 S 5 4 3 B (-3, 2) 2 M 1 (b) coordinates of S (c) R slope of AB. (d) equation of line PQ. Q -6 -5 (ii) -4 -3 -2 -1 O 1 -1 N -2 -3 -4 2 3 A (2, -3) The angle of depression of two ships A and B on opposite sides of a light house of height [5] 100m are respectively 42o and 54o. The line joining the two ships passes through the foot of the lighthouse. (a) Find the distance between the two ships A and B. (b) Give your final answer correct to the nearest whole number. (Use mathematical tables for this question) DMT Page 10 https://t.me/ICSE_10_Prelim ICSE 10 School Prelim Papers Question 8 (i) Solve the following inequation write the solution set and represent it on the real number [3] line. 3 2 + (ii) 1 2 > , 3 5 ABCD is a cyclic quadrilateral in which BC = CD and EF is a tangent at A. [3] CBD = 43 and ADB = 62 . Find: (a) ADC (b) ABD (c) FAD F A D 62 E 43 B C (iii) A (a, b), B(-4, 3) and C(8,-6)are the vertices of a ABC. Point D is on BC such that [4] BD : DC is 2 : 1 and M (6, 0) is mid point of AD. Find: (a) coordinates of point D. (b) coordinates of point A. (c) equation of a line passing through M and parallel to line BC. Question 9 (i) Using componendo and dividend, find the value of x, when: [3] 3 + 3 14 = 3 2 + 1 13 (ii) The total expense of a trip for certain number of people is 18000. If three more people join [3] them, then the share of each reduces by 3000. Taking x to be the original number of people, form a quadratic equation in x and solve it to find the value of x. DMT Page 11 https://t.me/ICSE_10_Prelim ICSE 10 School Prelim Papers (iii) Using ruler and compass only construct ABC = 60 , AB = 6 cm and BC = 5 cm. (a) [4] construct the locus of points equidistant from AB and BC. (b) construct the locus of points equidistant from A and B. (c) Mark the point which satisfies both the conditions (a) and (b) as P. Hence, construct a circle with centre P and passing through A and B. Question 10 (i) Using remainder and factor theorem, factorize completely, the given polynomial: [3] 2 3 9 2 + 7 + 6 (ii) Each of the letter of the word HOUSEWARMING " is written on cards and put in a bag. [3] If a card is drawn at random from the bag after shuffling, what is the probability that the letter on the card is (a) a vowel (b) one of the letters of the word SEWING. (c) not a letter from the word WEAR. (iii) Use graph sheet for this question. Take 2 cm = 1 unit along the axes. (a) Plot A (1, 2), B(1, 1)and C (2, 1) (b) Reflect A, B and C about y-axis and name them as A , B and C . (c) Reflect A, B, C, A , B and C about x-axis and name them as A , B , C , A , B [4] and C respectively. (d) Join A, B, C, C , B , A , A , B , C , C , B , A and A to form a closed figure. DMT Page 12 https://t.me/ICSE_10_Prelim ICSE 10 School Prelim Papers ARYA VIDYA MANDIR GROUP OF SCHOOLS PRELIM REVIEW- JANUARY 2023 Std: X MATHEMATICS Marks:80 Date: 06/01/2023 Time: 2 hr ----------------------------------------------------------------------------------------------------------------Answers to this paper must be written on the paper provided separately. 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 the paper is the time allotted for writing the answers. ----------------------------------------------------------------------------------------------------------------Attempt all the questions from Section A and any four questions from Section B All essential working should be clearly shown whenever needed on the same sheet. The omission of the essential working will result in the loss of marks. Do the rough working at the bottom of the paper. The intended marks for questions or parts of questions are given in the brackets [ ]. This paper comprises 10 printed pages. ----------------------------------------------------------------------------------------------------------------Section - A (40 marks) (Attempt all the questions from this Section) Question 1 Choose the correct answers to the questions from the given options: (i) [15] If the discriminant of quadratic equation ax2 + bx + c = 0 is equal to zero, then two equal roots are: (a) 2 (b) 2 (c) (d) 2 2 DMT Page 13 https://t.me/ICSE_10_Prelim ICSE 10 School Prelim Papers -2Contd... Std X Mathematics Prelim Review January 2023 (ii) A shopkeeper buys goods worth 1000 and sells at a profit of 10%. If rate of GST is 5%, then the bill amount is : (a) 1050 (b) 1155 (c) 1080 (d) 1000 (iii) The solution set representing the following number line, is: (a) {x: x R, -3 < x < 3} (b) {x: x R, -3 < x 3} (c) {x: x Z, -3 < x < 3} (d) {x: x Z, -3 x < 3} (iv) Manisha opens a Recurring Deposit Account with the Bank of Assam and deposits 600 per month for 20 months. Calculate the interest accrued, if the bank pays interest at the rate of 10% per annum. (a) 1050 (b) 1000 (c) 1200 (d) 1500 (v) In the given figure, we have ACB = 90 , CD AB, then ACB~ ADC by: (a) SSS similarity rule (b) SAS similarity rule (c) AA similarity rule (d) None of these 3 DMT Page 14 https://t.me/ICSE_10_Prelim ICSE 10 School Prelim Papers -3Contd... Std X Mathematics Prelim Review January 2023 (vi) The curved surface area of a cylinder of height 14 cm is 88 sq. cm. The diameter of the cylinder is: (a) 0.5 cm (b) 1.0 cm (c) 1.5 cm (d) 2.0 cm (vii) If g(x) = x + 1 is a factor of h(x) = 5x3 + px2 - 8x - 12, then the value of p is: (a) -8 (b) 5 (c) 9 (d) 12 (viii) If the nth term of an A.P. is 7 - 4n, then find its 6 (a) 17 (b) 17 (c) 18 (d) 18 th term is: (ix) Drawing of an ogive table is useful in determining the: (a) mode (b) mean (c) median (d) all the three above (x) In the given figure, P (2,4) is the mid point of the line segment AB. The coordinates of A and B are : (a) A (8, 0), B(0, 4) (b) A(0 ,4), B(8, 0) (c) A(4, 0), B(0, 8) (d) A(0, 8), B(4, 0) 4 DMT Page 15 https://t.me/ICSE_10_Prelim ICSE 10 School Prelim Papers -4Contd... Std X Mathematics Prelim Review January 2023 (xi) Two matrices A and B are multiplied to get AB if: (a) Both have same order (b) Both are rectangular (c) Number of columns in matrix A is equal to the number of rows in matrix B (d) Number of rows in matrix B is equal to the number of columns in matrix A (xii) The point (5, -6) on reflection in a line is mapped to (-5, -6). Name the mirror line and write its equation. (a) X- axis, y = 0 (b) Y - axis, x = 0 (c) X- axis, x = 0 (d) Y - axis, y = 0 (xiii) The probability of not winning a game is 0.35. What is the probability of winning? (a) 0.15 (b) 0.25 (c) 0.65 (d) 1.50 (xiv) In the figure given, if AB is a chord of the circle and AC is its diameter such that ACB = 50 . If AT is the tangent to the circle at the point A, then CAB is equal to : (a) 65 (b) 50 (c) 40 (d) 60 5 DMT Page 16 https://t.me/ICSE_10_Prelim ICSE 10 School Prelim Papers -5Contd... Std X Mathematics Prelim Review January 2023 (xv) If x, 9, 5 and 3 are in proportion, then x equals to: (a) 15 (b) 45 (c) 27 (d) 18 Question 2 (i) Using the properties of proportion, find the value of x in the expression: (4) + + + =5 (ii) Find the equation of the line perpendicular to the line joining the points A(2, 4) and B(6, 8) and passing through the point (5,7). (4) (iii) The given figure represents a hemisphere surmounted by a conical block of wood. The diameter of their base is 12 cm each and the slant height of the cone is 10 cm. Calculate : (a) the perpendicular height of the cone, (b) the volume of the solid (Take = 3.14) (4) Question 3 (i) Ritwik deposits 1600 per month for 18 months in a recurring deposit account. If he gets 31080 at the time of maturity. Find: (a) The total interest earned by Ritwik (b) The rate of interest per annum (4) 6 DMT Page 17 https://t.me/ICSE_10_Prelim ICSE 10 School Prelim Papers -6Contd... Std X Mathematics Prelim Review January 2023 2 sin (ii) Prove that: cos sin + 1 cot = sin A + cos A. (4) (iii) Use graph paper for this question. The point R (6, 3) was reflected in the origin to get the image R . (a) Write down the coordinates of R . (b) If M is the foot of the perpendicular from R to the line y = 0, find the coordinates of M. (c) If N is the foot of the perpendicular from R to the line y = 0, find the coordinates of N. (d) Name the figure RMR N. (5) Section - B (40 marks) (Attempt any four questions from this Section) Question 4 3 2 ] and A2 = I, where I is the identity matrix. Find the value of x and y. (i) If A = [ (3) (ii) Solve the inequation and represent the solution set on the number line: (3) 2y 3 y + 1 4y + 7, x Z (iii) By using step-deviation method, compute the arithmetic mean for the following data: Marks obtained 0 10 10 20 20 30 30 40 40 50 50 60 (4) No. of workers 14 22 37 58 67 75 7 DMT Page 18 https://t.me/ICSE_10_Prelim ICSE 10 School Prelim Papers -7Contd... Std X Mathematics Prelim Review January 2023 Question 5 (i) Without solving the following quadratic equation, find the value of p if the roots of the equation px2 (2p 2)x + p = 0 has real and equal roots. (ii) (3) In an intra-state transaction the marked price of an article is 6000. A wholeseller sells it to a dealer at 20% discount. The dealer further sells the article to a customer at a discount of 10% on the marked price. If the rate of GST at each stage is 18%, find the amount of tax(under GST) paid by the dealer to the government. (iii) PA and PB are two tangents of a circle. AC is parallel to PB. Find the angles of ABC. (3) (4) Question 6 (i) If a, b and c are in continued proportion, prove that 1 3 (ii) 1 1 (3) + 3 + 3 = 2 2 + 2 2 + 2 2 The daily profits in rupees of 100 shops in a departmental store are distributed as follows: Profit per shop (in ) No. of Shops 0-100 12 100-200 18 200-300 27 300-400 20 400-500 17 (3) 500-600 6 Draw a histogram of the data given above on the graph paper and estimate the mode. 8 DMT Page 19 https://t.me/ICSE_10_Prelim ICSE 10 School Prelim Papers -8Contd... Std X Mathematics Prelim Review January 2023 (iii) If 2x3 + ax2 + bx 6 has a factor (2x + 1) and leaves the remainder 12 when divided by (x + 2). Calculate the values of a and b. (4) Question 7 (i) Find the sum of n terms of the A.P. 8, 5, 2, -1, to 11 terms. (3) (ii) P(-4, 6), Q(-1, 6) and R(-1, 2) are the vertices of a triangle. (a) Find the coordinates of the centroid G of the triangle. (b) Find the equation of the line through G passing through P. (3) (iii) Construct a circle of radius 3.5 cm with centre O. Construct 2 tangents PT and PR from a point P outside the circle such that TOR = 120 . (4) Question 8 (i) A hollow copper pipe of inner diameter 14 cm and outer diameter 16 cm is melted into another solid cylinder is of same height as that of pipe. Find the diameter of the solid cylinder. (3) (ii) In the given figure, AB and CD are two chords of a circle intersecting each other at a point P, such that AP = CP. Prove that AB = CD. (3) (iii) A man standing on a window of the first floor of a building observes that the angle of depression of a dustbin which is 10m from the foot of the building is 45 . He climbs to the window of the second floor, directly above the first floor and observes the angle of depression of the dustbin to be 60 . Calculate the difference in height between the first floor and the second floor. (4) 9 DMT Page 20 https://t.me/ICSE_10_Prelim ICSE 10 School Prelim Papers -9Contd... Std X Mathematics Prelim Review January 2023 Question 9 (i) Car A travels x km for every litre of petrol, while car B travels (x + 5) km for every litre of petrol. (a) Write down the number of litres of petrol, use by car A and car B in covering a distance of 200km. (b) If car A uses 2 litres of petrol more than car B in covering the 200km, write down an equation in x and solve it to determine the number of litres of petrol used by car B for the journey. (4) (ii) Use graph paper for this question. Marks obtained by 200 students in an examination are given below: Marks No. of Students 0 10 5 10 20 11 20 30 10 30 40 20 40 50 28 50 60 37 60 70 40 70 80 29 80 90 14 90 - 100 6 (6) Draw an ogive for the given distribution taking 2 cm = 10 marks on one axis and 2 cm = 20 students on the other axis. Determine: (a) The median marks (b) The number of students who failed if the minimum marks required is 40. (c) If scoring 85 and above is grade one, find the number of students who secured grade one in the examination. Question 10 (i) Prove that: + + = cot A tan B (3) ..10 DMT Page 21 https://t.me/ICSE_10_Prelim ICSE 10 School Prelim Papers -10Contd... Std X Mathematics Prelim Review January 2023 (ii) Two dice are thrown at the same time. Find the probablity that the sum of two numbers appearing on the dice. (a) 10 (b) Atleast 12 (3) (iii) In the adjoining figure; QR ST and S divides PQ in the ratio 1 : 2. Find: (4) (a) (b) (c) ST if QR = 4.5 cm ______________________THE END__________________________ DMT Page 22 https://t.me/ICSE_10_Prelim ICSE 10 School Prelim Papers DMT Page 23 https://t.me/ICSE_10_Prelim ICSE 10 School Prelim Papers DMT Page 24 https://t.me/ICSE_10_Prelim ICSE 10 School Prelim Papers DMT Page 25 https://t.me/ICSE_10_Prelim ICSE 10 School Prelim Papers DMT Page 26 https://t.me/ICSE_10_Prelim ICSE 10 School Prelim Papers DMT Page 27 https://t.me/ICSE_10_Prelim ICSE 10 School Prelim Papers DMT Page 28 https://t.me/ICSE_10_Prelim ICSE 10 School Prelim Papers EuroSchool Discover Yourself Mathematics (Twoand a half hour) Prelim-1,2023-24 GRADE: X Maximum Marks:80 hours Timeallowed: TwO and hal/ the paper provided separately. Answers tothis Paper mustbe written on during first 15 minutes. Youwill notbe allowed to write question paper. This time is tobe spentin reading the allowed forwriting the answers. time the is Paper this headof the The time given at questions from Section B. Attempt all questions from Section A and any four shown, and must be done on the same All working, including rough work, nust be clearly sheet as the rest of the answer. Omission of essential working will result in loss of marks. Theintended marks for questions or parts of questions are given in brackets [J SECTION A Atempt all questions from this Section |15) Question I Choose the correct answers to the questions from the given options. (Do not copy the question, write the correct answers only.) 1. IfA =[8-3| and B-|4 - 5|; find: A tB DMT Page 29 https://t.me/ICSE_10_Prelim ICSE 10 School Prelim Papers (a) (-12 - 8] (b) [12 -8] (c) [12 8] (d) [12 -2] 2. Ifthe roots of quadratic equation, px(x -2) + 6 = 0are equal, then value ofp is (a) 0 (b) 4 (c) 6 (d) 0&6 The SGST paid by a customer to the shopkeeper for an article which is priced at 500 is 15. The rate of GST charged is: 3 (a) 1.5 % (b) 3% (c) 5% (d) 6% Z40is distributed between two friends such that the product of their shares is 364. The difference of their shares is : (a) Z (b) 10 (c) Z12 (d) 214 5 First four terms of an AP are ..... whose first term is -2 and common difference is - 2 (a) (b) (c) -2,0, 2, 4 -2,4, -8, 16 -2,-4,-6,- 8 (d)-2,-4, -8,-l6 DMT Page 30 https://t.me/ICSE_10_Prelim ICSE 10 School Prelim Papers Themean proportion between x andy is 6. The third proportional 6. (a) yis 48. Then xy =? l:3 (b) :4 (c) l:6 (d) 1:9 of the For the given diagram, which 1. following is true? 18 cm E cm cm 24 4 3 cm 1. AABC ~ ADEF 2. 3 (a) AB DE AB EF 1 A(AABC) 6A(ADEF) 2 A(AABC) 9'A(ADEF) 1 36 4 81 Only 1 (b) 1and 2 both (c) 2and 3 both (d) land 3both The solutionset for the given inequation is: 8 -8s 2x<8,x E W (a) (-4,-3, -2, -1,0, 1,2, 3, 4) (b) (-4,-3, -2, -1) (c) 0, 1, 2, 3} (d) (-8,-7, -6,-5, -4, -3,-2, -1,0, 1, 2, 3, 4, 5, 6,7, 8) DMT Page 31 https://t.me/ICSE_10_Prelim ICSE 10 School Prelim Papers 9. The probabiliy of the sun rising ioits S a ? P(S) =0 (b) P(S) > | (c) P(S)= 1 (d) 10. P(S) <0 The centroid of AABC is Gi6. 7). 1f the orinatS DVINA anc Care (a. 5). (7.9) and (5. 7) respecral. The value of a is: (a) (b) 6 (c) 3 (d) 7 11. The surface area ofa sphere is 154 cm. The voume of pherr i (a) (b) (c) (d) 12. 1 359=cm 3 2 179 1 736, cm 1 1437-cm 3 Shobha has a recurring deposit account in abank tor three vears at the ae of 11%per annum simple interest. She deposited 200 per month. lnteNN received by her at thetime of maturity is : (a) 1212 (b) 122| (c) ?|121 (d) 1221 DMT Page 32 https://t.me/ICSE_10_Prelim ICSE 10 School Prelim Papers If sec 9 13. (a) 7 then value of tan : 26 7 (b) 24 7 (c) 7 24 (d) 23 7 For an A.P. t, = 4,d = -4 then a=? 14. (a) 6 (b) 7 (c) 20 (d) 28 Find the mean 15. (a) 02 = 50.5 and median 45.5 43 (b) 43.2 (c) 43.5 (d) 44 (a) given that mode of the data when it is The the rim of a inner circumference of circular metal tub is 44 cm. -8cm) Find: of he tub (a)The innerradius it's outer adius is 8 cm (b)The volume of the malenal ofl the it 22 7 tigures. Give your answercorect to three sigiticant DMT Page 33 https://t.me/ICSE_10_Prelim ICSE 10 School Prelim Papers (b) Mr. Sharma Selling at 50 shares 80. If the dividend declared is 20o, Amount invested by Mr. Sharma. Percentage return on his investment. () (ii) (c) buying income of 7900 in receives an annual find the: 4 Prove the following identity: sec'A .cosecA (sinA + cosecA) + (cosA + secA)2 = 5 + Q3 (a) (b) u3+3ab2 3a2b+b3 x3+3xy2 3x2y+y3 4 prove that = a In the given figure, AC is a diameter of acircle with centre O. If CD | BE, LAOB = 800 and zACE = 100 Find: LBEC i) ii) iii) ZBCD ZCED 800 (c) Study thc graph and answer cach of the following: (a) Total number of Pupils (b) The median height (c) Height below which first 55 pupils lie (d) Number of pupils betwcen hcight 130.5cmand |70.5 cm DMT Page 34 https://t.me/ICSE_10_Prelim 4 ICSE 10 School Prelim Papers Section B Attempt any four questions 3 find AC + B - 10C (b) Solve the following quadratic equation; 3 7x+ 2x-2 0 Give your answer corect to two places of decimal, DMT Page 35 https://t.me/ICSE_10_Prelim ICSE 10 School Prelim Papers BCFD is parallelogram. and triangle (c) In the given diiagram, ABCis a AD: DB = 4: 5 and EF =15 cm. Find: AE: EC i) iii) DE BC A E 15 cm Q5 (a) The following table gives the petrol prices per litre for a period of 50 days. Price (?) 85 No. of days 90 12 90 - 95 95 100 10 100 - 105 110 105 5 15 Find the mean price of petrolper litre to the nearest rupee using short-cut method. (b) The following bill shows the GST rates and the marked price of articles: BILL: COMPUTERS Articles Graphic card Laptop adapter Marked price 15500 ? 1900 Rate of GST I8% 28% Findthe total amount to bc paid lor the above bill DMT Page 36 https://t.me/ICSE_10_Prelim 3 ICSE 10 School Prelim Papers (c) In the given figure, PAT is diameter BDis a and A at tangent If ofthe circle. LABD = 280 and zBDC=52 , Find: i) ii) iii) iv) LTAD ZBAD ZPAB 2CBD P B 28 52 Q6 (a) a cylinder so formed If the radius of the is 2 cm, find the cylinder. 512 term of aGP are 4 and 8th the and lst The (b) ratio Find:( )the common term (ii)the sum of its first 5 respectively. the daily carnings of for histogram a Draw question. (c) Use graph sheet for this following table and hence estimate the mode of the 54 medical stores in the followingdistribution. cm=5stores along the y Take 2cm=500 units along the X-axis and 2 axis. Daily earnings (2) No. of 3 12 cm respectively. and cm 3 are cone radius and height of the height of the sphere A Cone and a cylinder. The having the same recast into radius are melted and 4500 5000 |4 5000 5500 20 5500 6000 12 6000 6500 6500 - 7000 medical stores DMT Page 37 https://t.me/ICSE_10_Prelim 4 ICSE 10 School Prelim Papers Q7 (a) A(-4, 2), B(6, 4) and C(2, -2) are the vertices of AABC. () the equationof median AD (ii) the equation of right bisector of AB (b) An aeroplane travelled adistance of 400 km at an average speed of x km/hr.on the retum journey,the speed was increased by 40km/hr. Write down an expression for the time () the onwards jourmney (ii) thereturm journey taken for: If the returnjourney took 30 minutes less than theonward jourmey, WIite an equatiOn in x. Q8 Find the value ofx. (a) Solve the following inequation and represent your solution on number line. 3- 2x >xt 1-x the real 2x (b) If AB and CD are two chords of acircle which when produced meet at a point p outside such that B- 5 cn, PA -8 PD cm and CD=2 cn tlhen tind DMT Page 38 https://t.me/ICSE_10_Prelim ICSE 10 School Prelim Papers (c) A(a, b), B ,3) C(8, -6) are the vertices of a AABC. Point such that BD(4,:I DCand is 2 : 1and M(6, 0) is mid-point of AD. Find: 4 coordinates of point D. coordinates of point A. () (i1) Q9 Dis on BC equation of a line passing through Mand parallel to line BC. (a) If a, b, c, d are in continued proportion, prove that: 3 (a'+ b +c)(62 + c + d2) = (ab + bc + cd) (b) In the given figure, line APBmeets the x-axis at A, y-axis at B and co-ordinates of P(-4,2) isa point such that AP : PB = 1: 2, Write down the 3 A and B. B(o. y) P ( - 4 , 2 ) A(x, o) RQ =10 cm, ZPRQ=75 and (c) Construct 2 tr angle POR given base RP = 8 cmn. Find by construction: and QP. The locus of points which are equidistant from QR Q. The locus of points which are equidistant from P and (ii) (ii) (iii) Mark the pointO which satisfies conditions (i) and i) Q10 (a) Using remainder and lactor theorem, factorize completely, the given polynomial: 21'-9x' + 7x + 6 DMT Page 39 https://t.me/ICSE_10_Prelim ICSE 10 School Prelim Papers probability of drawing the If balls. blue some and (b) Abag contains S red balls then find the numbers of ball, red ofa that thrice is bag the a blue ball from bule balls in the bag. x and y axis: both along lcm=lunit taking paper, graph a of help (c) With the (0, -3) Plotpoints A(0, 3), B (2, 3), C(3,0), D(2, -3), Ethem as B'. C' () (i) Reflect points B,C and D on the y axis and name andD' respectively. (iii) (iv) IWrite the cquation of line BD' Name the figure BCDD'C'B'B DMT Page 40 https://t.me/ICSE_10_Prelim 3 4 ICSE 10 School Prelim Papers GUNDECHA EDUCATION ACADEMY, KANDIVALl(E). FIRST PRELIMINARY EXAMINATION -2023-2024 DATE: 04.12.2023 MATHEMATICS CLASS: X Marks:80 Time: 2 Hrs Answer to this paper must be written on the paper provided separately. You will not be allowed to write during first fifteen minutes. This time is to be spent in reading the questio~ paper. . The time given at the head of this paper is the time allotted for writing the answers Attempt all questions from section A and any four from section B. on the same sheet .All working, including rough work, must be clearly shown and must be done as the rest oftlte answer. Omission ofessential working will result in ioss ofmarks. The inter,ded marks for questions or parts ofquestions are given in brackets []. Mathematical tables are provided. SECTION A (40 Marks) Attempt all questions from this section. [ l 5x 1=l 5J : Question 1: Choose the correct answers to the questions from the given options S d by it as Rs. 750. If 1 (i) The tax invoice of a telecom service in Meerut shows cost of services provide ,tf-."ft H the GST rate is 18%, find the amount of bill. 1T (d) t 85 (c) t 135 . (b) t 885 (a) t 785 ,ts th (ii) The 17th term of an AP exceeds its 10 term by 7, the common difference is -i(t,.,) d'+1'cf d) 7 (c) 4 (b) . (a) 1 .. --; 1 id (iii)Is the points (1,-1 ), (5, 2) and (9, 5) are collinear? -:i. / <4-' ~:i,1- G-Io , (d) none of these (c) Cannot find (b) no (a) yes +.' lf' (iv)The solution set of the inequation 4 S 3(x + 2) -10 S 8,x E Wis (~'-~ m~ l:1..1.. ,,,(dJ (3,4) (c)(3,6) (b)(4,2) (a) (1,5) 4 then the d, dividen 18% him pays y compan the If 80. t at shares 100 t on 9600 ~ (v) A man invests number of shares he bought are 1'\ S-.,1}. d) 90 (c) 80 , (b) 120 (a) 100 ' AB is parallel to PR (vi)In the given figure, if PQR is the tangent to a circle at Q whose centre is 0, " and_L~R_:__ 70 then L./108 is equal to 1 1~ ?i' !{t I' I~ p (a) 70 Q Cl c, R (b) 20 (c) 40 GEA/ FIRST PRELIMINARY EXAMINATION -2023-2024 This Paper consists of 7 printe,J pages. .d) 80 Turn Over DMT Page 41 https://t.me/ICSE_10_Prelim ICSE 10 School Prelim Papers 2 CLASS X MATHEMATICS . . . The values of a and b is (vii) The point p (a, b) is invariant, when the reflected m the ongm. 1) {a) (0, O) (b)(O, 2) (c) (3, O) . d) (-l, - n the robability of her (viii) If the probability of Sania winning a badminton match ts 0.87, the P losing the match is 3 (a)0.23 "(6)0.13 (c)l.3 d)0.3 teofradiu s6cmis (ix)The length of the tangent drawn from a point 8 cm away from the centre of circ (a) 28 (b) {7 ef'i{7 d) 10 (x) The remainder on dividing f(x) = 2xZ - 7x - 1 by x + 3 is (a) 20 ~8 (c) 31 d) 48 _(xi)A heap of rice is in the form of a cone of base diameter 24 m and height 3.5 m. Then, the vo1urne of the heap is (a) 105.Sm3 . (b)528m3 (c)l73.5m3 -Pf'noneof these (xii) In MBC, P and Q are points on CA and CB spectively, such that CA= 16 cm, CP = 1O cm. CB = 30 cm and CQ = 25 cm, then (a) PQ is parallel to AB ) PQ is not parallel to AB 31..<( (c)QB ..o CQ (xiii) (xiv) = PA , tx . i~. 1 Ii +-11-1 d) none CP If the discriminant of the equation kx2 -3-./2x + 4-./2 = O is 14, then the value of k is r 1 1 " _Y"'" OOv2 00_ 3 ~ The slope of a line perpendicular to the line passing through the point (2, S) and (-3, 6) i(a)s 1 (a)-5 . (xv) lt~-~ .::----- 1 (b)- (c)-- 5 5 ~)5 - Assertion(A): Frequency is the number of times a particular observation occurs in data. Reason (R): Data cannot be grouped into class intervals such that all observations in that range belong to that class (a)J3<>th A and Rare correct A is true, R is False (c) A is false, R is true (d) Both A and R false \ 'f- y)( 12. y ~.5 ~~?<3-s GEA/ FIRST PRELIMIN ARY EXAMINATION - 2023-2024 Turn Over This Paper consists of 7 printed ~- DMT Page 42 https://t.me/ICSE_10_Prelim ' ICSE 10 School Prelim Papers 2023-24 3 ASS X .MATHEMATICS ple interest. Ifh e gets bankfor 3 years at 9 % p.a. sim a in t oun acc t osi dep ing urr (i) Mr. Ram has a rec of maturity, find Rs 3996 as interest at the time [4] a. The monthly instalment ty. turi ma of t b. The amoun ce. This sauce is pletely filled with chocolate sau com is cm 7.2 ter me dia [4] of l e. (ii) A hemispherical bow cm. find the height of the con 4.8 us adi ofr e con d erte inv poured into an c.o+. -1c,Y\ [4] :::..1 2 ec2 A = tan A + cot A (iii) Prove that sec A + cos _ C-:---~ (I- HO n"-- t I+ CQ t'< -) -\-o.Y\ t (.cfr T l!_o+ '2.) ~4 q n t-t.o+ -+\.. " ' -\ 1_ 7Question 3 le if LABD = 26 CE is the tangent to the circ le. circ the of tre cen the is 0, (i) In the given figure _J (a) .LBDA (b) LB AD (c) ,LP AD 2 2 2 {d) LOOS c) (a - b + c) = a + b + c + b (a+ t tha ve pro , tion por in continued pro (ii) If a, b, c are = I unit on both axes) following questions. (Take 1 cm the r we (5] ans to er pap ph gra a (iii) Use e ABC. C (8, 0), the vertices of a triangl and 6) , B(4 4), , A(4 t Plo a. and name it as A'B'C'. b. Reflect ABC on the Y axis B' and C'. c. Write the coordinates of A', ve joined figure. e a geometrical name for the abo d. Join A A' C' B' B C and Giv from the figure on X axis. e. Name two invariant points SECTIONB .) r questions from this Section fou any pt (Attem Question 4 lJ f~J x M = write (i) Gi ve n~ a. The order of Matrix M b. The matrix M 'lX I u [3] EXAMINATION - 2023-2024 GEA/ FIRST PRELIMINARY This Paper consists of 7 printed pages. Turn Over DMT Page 43 https://t.me/ICSE_10_Prelim .J ICSE 10 School Prelim Papers 2023 -24 4 CLASS X MATHEMATICS . two significant figures. [3] (ii) Solve the given equation x2 - 6x -15 =O and give your answer 10 (iii)In triangle ABC, LABC = LDAC. AB = 8 cm, AC =4 cm and AD = S cm. a. Prove that a ACD ~ a BCA b. Find BC and CD c. Find area of MCD : a BCA. [4] ~estio nS \ 0 (i) Find the mean of fue following distribution by shortcut method. Express your answer correct to [3] two decimal places -40 35 30-35 0-5 5 10 10-15 15 20 20 25 25-30 Marks 2 5 8 16 24 3 15 7 No.Of ~tudents (ii) Solve the following inequation and represent it on the number li:ie: 2x - S Sx + 4 < 11, x E I [3] I (iii)Mr,Ajay invested, 8000 in 7%, 100 shares at, 80. After a year he sold these shares at~ 75 each and invested the proceeds including his dividend in 18% , , 25 shares at 41. Find : a. His dividend for the first year b. His annual income in the second year c. The percentage increase in his return on his original investment. CN11~ v I crZ> [4] 0~ / /Questi on.6 \~ (i) T4e line through P(5, 3) intersects y axis at Q at an angle of inclinatio11 of 45 . find: .j a. Write the slope of the line - b. Write the equation of the line c. Find the coordinates of Q GEA/ FIRST PRELIMINARY EXAMINATION -2023-2024 This Paper consists of 7 printed pages. [3] Turn Over / DMT Page 44 https://t.me/ICSE_10_Prelim ICSE 10 School Prelim Papers r:LASS X MATHEMATICS 2023 -24 5 (ii) [3] CD and EF is a tangent at A. ABCD is a cyclic quadrilateral in which BC= LCB D =43 and LAD B =62 . Find: (a) LAD C F (b) LABO (c) LFAD E mode (iii)Draw the histogram and hence find the paper. Class 10-2 0 interval 5 Frequency for the following frequency distribution usin [4] 20-30 30-40 40- 50 50- 60 60- 70 70- 80 3 12 7 2 6 3 g graph Question 7 [3] th is 128. Find: th (i) The 4 term of a G.P is 16 and 7 term a. First term b. Common ratio c. G.P series. amount to and the marked price of articles. Find the total (ii) The following bill shows the GST rates [3] be paid for the given bill. BILL: COMPUTERS Articles Marked price (Rs) Rate ofG ST (%) Graphic card 15000 18 Laptop Adapter 1900 28 ATI ON - 2023-2024 GEA / FIRS T PRE LIM INA RY EXA MIN This Pap er consists of 7 prin ted pages. Tur n Ove r DMT Page 45 https://t.me/ICSE_10_Prelim ICSE 10 School Prelim Papers 2023 -24 6 CLASS X MATHEMATICS (iii) and FB In the diagram given below if AF= 21 cm, CE= 30 cm 7 cm. Find the volume of the figure. C E 30cm ' I \ I : 0: ,--1 A - E - - - - - - - - f - . - - - - - - . . L :I _;..... I I B I '. ' D [4] ~ue stio n 8 by 120 shooters in a shooting The following distribution represents the scores obtained [5] competition 9080-90 0 70-8 0 0 60-7 50-6 0 40-5 0 30-4 0 0 20-3 10-2 100 0-10 Score ed 3 obtain 4 6 11 18 26 22 16 9 5 Noo f shooters , determine Draw an ogive for the given distribution. Using the graph a. the median b. the upper quartile (i) (ii) depression of two s!iips on opposite From the top of a lighthouse 100 m high, the angles of between the two ships to the sides of it, are 48 and 36 respectively. Find the distance [5] nearest metre. XQuestion 9 lar (i) The line through A(-2, 3) and B (4, b) is perpendicu to the line 2x -4y = 5. find the value of b. [3] a circle circumscribing (ii) Construct a regular hexagon of side 4cm, construct the hexagon. [3] 720. If the cost per book was~ 5 less, then (iii)A shop keeper buys a certain number of books for~ be 2 more. Talcing the original cost the number of books that could be brought fo: 720 would [4] it. of each book to be~ x, write an equation in x and solve 2024 GEA/ FffiST PRELIMINARY EXAMINATION - 20237 printed pages. of sts consi r Pape This Turn Over DMT Page 46 https://t.me/ICSE_10_Prelim ICSE 10 School Prelim Papers " cf,,/\ss X MATHEMATICS 202 3-2 4 7 /4 lio nI O 0 [ ] factorise completely x3 - 7 x2 + 14x - 8 = 3 (i) Use remainder and factor theorem to ity at selected is selected at random. What is the probabil [3]th (ii) A letter of the word "SECONDARY" word a. Not a vowel b. Last 8 letters from English alphabet c. Not a letter from the word DEAR [4] in terms of a and b. (iii)Find the value of x from the equation b= ra+x + ~ ,/a+ x-,/ a-x b+I b-1 j,+ ' b-l b-+ 1 t 2- b .a +:x: __ 1 b+ l-2 b 3 b + 1+1--b" a ~b t I - I i b ,,v +Q j?t 1r"'-- - """:;/2 t-J. - /,. t- ..,_ -2024_ IMI NA RY EXAMINATION - 2023of 7 prmted pages. GEA/ FIRST PREL END This Paper consists DMT Page 47 https://t.me/ICSE_10_Prelim ICSE 10 School Prelim Papers DMT Page 48 https://t.me/ICSE_10_Prelim ICSE 10 School Prelim Papers DMT Page 49 https://t.me/ICSE_10_Prelim ICSE 10 School Prelim Papers DMT Page 50 https://t.me/ICSE_10_Prelim ICSE 10 School Prelim Papers DMT Page 51 https://t.me/ICSE_10_Prelim ICSE 10 School Prelim Papers DMT Page 52 https://t.me/ICSE_10_Prelim ICSE 10 School Prelim Papers DMT Page 53 https://t.me/ICSE_10_Prelim ICSE 10 School Prelim Papers DMT Page 54 https://t.me/ICSE_10_Prelim ICSE 10 School Prelim Papers DMT Page 55 https://t.me/ICSE_10_Prelim ICSE 10 School Prelim Papers DMT Page 56 https://t.me/ICSE_10_Prelim ICSE 10 School Prelim Papers DMT Page 57 https://t.me/ICSE_10_Prelim ICSE 10 School Prelim Papers DMT Page 58 https://t.me/ICSE_10_Prelim ICSE 10 School Prelim Papers DMT Page 59 https://t.me/ICSE_10_Prelim ICSE 10 School Prelim Papers DMT Page 60 https://t.me/ICSE_10_Prelim ICSE 10 School Prelim Papers DMT Page 61 https://t.me/ICSE_10_Prelim ICSE 10 School Prelim Papers DMT Page 62 https://t.me/ICSE_10_Prelim ICSE 10 School Prelim Papers DMT Page 63 https://t.me/ICSE_10_Prelim ICSE 10 School Prelim Papers DMT Page 64 https://t.me/ICSE_10_Prelim ICSE 10 School Prelim Papers DMT Page 65 https://t.me/ICSE_10_Prelim ICSE 10 School Prelim Papers DMT Page 66 https://t.me/ICSE_10_Prelim ICSE 10 School Prelim Papers DMT Page 67 https://t.me/ICSE_10_Prelim ICSE 10 School Prelim Papers DMT Page 68 https://t.me/ICSE_10_Prelim ICSE 10 School Prelim Papers DMT Page 69 https://t.me/ICSE_10_Prelim ICSE 10 School Prelim Papers DMT Page 70 https://t.me/ICSE_10_Prelim ICSE 10 School Prelim Papers DMT Page 71 https://t.me/ICSE_10_Prelim ICSE 10 School Prelim Papers DMT Page 72 https://t.me/ICSE_10_Prelim ICSE 10 School Prelim Papers DMT Page 73 https://t.me/ICSE_10_Prelim ICSE 10 School Prelim Papers DMT Page 74 https://t.me/ICSE_10_Prelim ICSE 10 School Prelim Papers DMT Page 75 https://t.me/ICSE_10_Prelim ICSE 10 School Prelim Papers DMT Page 76 https://t.me/ICSE_10_Prelim ICSE 10 School Prelim Papers DMT Page 77 https://t.me/ICSE_10_Prelim ICSE 10 School Prelim Papers DMT Page 78 https://t.me/ICSE_10_Prelim ICSE 10 School Prelim Papers DMT Page 79 https://t.me/ICSE_10_Prelim ICSE 10 School Prelim Papers DMT Page 80 https://t.me/ICSE_10_Prelim ICSE 10 School Prelim Papers DMT Page 81 https://t.me/ICSE_10_Prelim ICSE 10 School Prelim Papers DMT Page 82 https://t.me/ICSE_10_Prelim ICSE 10 School Prelim Papers DMT Page 83 https://t.me/ICSE_10_Prelim ICSE 10 School Prelim Papers DMT Page 84 https://t.me/ICSE_10_Prelim ICSE 10 School Prelim Papers DMT Page 85 https://t.me/ICSE_10_Prelim ICSE 10 School Prelim Papers (xv) DJ\BCD is a rhombus with coordinates A(3, -1) and C(S,6). The slope of diagonal BO is: -2 (a) 7 [I '" 7 (b) 2 2 A/ (c) 5 (3,-1) (d) 7 M ' / C / (5.6) ,/ B Question 2 Prom a circular cylinder of diameter 10cm and height 12cm, a conical cavity of the (i) same radius and of the same height is hollowed out. f-'ind the volume and the whole ?;Sl 0 surface area of the remaining solid. (rr = 3.14) l4J (ii) ln the given figure DE II BC, AD: DB = 5: 4 l4) Find: (a) DE: BC (b) If AE;::;2.5cm, find AC. (c) A(t.ADE): A( oDBCE) "') (111 p h cos/I sin/I C . A +cos A rove t at:--+--=sm 1-cotA 1-tanA Question 3 (i) (ii) From the top of a tower of height 60m, the angle of depression of the top and bottom of a pole arc 30 and 45 . Find r4l (a) I low far the pole is from the bottom of the tower. (b) The length of the pole. Draw a regular hexagon of side 4cm. Construct its incircle. Measure the radius. (iii) Draw an ogive for the following distribution. 141 l5 I Take Scale on one axis, 2 cm = {l 00 and on the other axis, 2 cm = 50 employees Monthly 600income 700 No. of 40 employee Determine: (a) The median income. (b) The percentage of employees (c) The interquartile range. PPSK 23-24/ l O / MATH EMATICS 700800 68 800900 96 9001000 120 10001100 90 l l 001200 40 12001300 -26 whose income exceeds I 1 80 Pg 4 of 7 DMT Page 86 https://t.me/ICSE_10_Prelim ICSE 10 School Prelim Papers SECTION B (Attempt a11y four questions from this secrion) Question 4 (i) If A= [!1], B Find:AB = [ ]. c = [ 4] + 2C - 4D and D = [;] [3 J (ii) The model of a building is constructed with the scale factor I :30. (a) If the height of the model is 80cm, find the height of building in meters. (b)lf actual volume of the building is 27m 3 , find the volume of the model in cm3 [3] (iii) Solve the quadratic equation and give the answer correct to two significant figures. 4x 2 - 7x + 2 = 0 [4 J Question 5 (i) A mathematics aptitude test of 50 students was recorded as follows: Marks 50-60 60-70 70-80 80-90 90-100 o of 4 8 14 19 5 Students Draw a histogram for the above data using a graph paper and locate the mode. Take Scale: on x - axis 2cm = lOunits, on y - axis, 2cm = 2units (ii) Mr. Rahul goes to a shop to buy a leather coat which costs Z885(list price). The rate of GST is I 8%. I le tells the shopkeeper to reduce the price to such an extent that he has to pay 131 885 inclusive of GST. Find the reduction needed in the price of the coat. (iii) Shobha has a recurring deposit account in a bank for 3ycars at 7.5% p.a. simple interest. [4] if he gets 8325 as interest at the time of maturity, find (a) The monthly installment. (b) The amount of maturity. Question 6 l3 J (i) In a GP, if the third term is 72 and the sixth term is 1944, find the nth term. (ii) A hollow sphere of internal and external radii 6cm and 8cm respectively is melted and recast into small cones of base radius 2cm and height 8cm. Find the number of cones formed. PP K 23-24 /IO/ MATHEMATICS [31 Pg 5 of7 DMT Page 87 https://t.me/ICSE_10_Prelim ICSE 10 School Prelim Papers DMT Page 88 https://t.me/ICSE_10_Prelim ICSE 10 School Prelim Papers DMT Page 89 https://t.me/ICSE_10_Prelim ICSE 10 School Prelim Papers DMT Page 90 https://t.me/ICSE_10_Prelim ICSE 10 School Prelim Papers DMT Page 91 https://t.me/ICSE_10_Prelim ICSE 10 School Prelim Papers DMT Page 92 https://t.me/ICSE_10_Prelim ICSE 10 School Prelim Papers DMT Page 93 https://t.me/ICSE_10_Prelim ICSE 10 School Prelim Papers DMT Page 94 https://t.me/ICSE_10_Prelim ICSE 10 School Prelim Papers DMT Page 95 https://t.me/ICSE_10_Prelim ICSE 10 School Prelim Papers DMT Page 96 https://t.me/ICSE_10_Prelim ICSE 10 School Prelim Papers DMT Page 97 https://t.me/ICSE_10_Prelim ICSE 10 School Prelim Papers .RBK -School 1,,,"r ::k.::t c; by Bcbubna, K ar;iakia Foundation) :,choo' Cc,d,.; MA069 ./ PRELIMINARY EXAM 1 2023-24 Grade: 10 Max. Marks: 80 Subject : Mathematics 1 Dur. : 2 Hours 2 Date: 04/12/23 Number of printed pages : 6 Section A : Attempt all questions from this section. Q.1) Choose the correct answers to the questions from the given options: (15) 1) The 10th term of the A.P. 5,8, 11, 14, ........... is a) b) c) d) 32 35 38 185 _;:,,.; 2) Surya h s 600 shares of Rs.25 of a company. If a conipany announces a dividend of8 le, therr his annual inc;:ome is a) { 48 b) { 480 c) { 600 d) { 1200 3) The value(s) of k for which the quadratic equation 2x 2 a) b) c) d) - kx +k = O has equal roots is (are) 0 only 4 8 only 0,8 4) The mean proportional between - and 128 is a) b) c) d) 64 32 16 d) 8 2 5) If Ramesh opened recurring deposit account and deposited { 800 per month for 1 years, then 2 total money deposited in the account is a) b) c) d) { 11400 { 14400 { 13680 none of these. 1 RBK School ICSE - Grade 1-10 & ISC - Grade 11-12 www.rbkschool.org info@rbkschool.org DMT Page 98 https://t.me/ICSE_10_Prelim ICSE 10 School Prelim Papers DMT Page 99 https://t.me/ICSE_10_Prelim ICSE 10 School Prelim Papers DMT Page 100 https://t.me/ICSE_10_Prelim ICSE 10 School Prelim Papers DMT Page 101 https://t.me/ICSE_10_Prelim ICSE 10 School Prelim Papers DMT Page 102 https://t.me/ICSE_10_Prelim ICSE 10 School Prelim Papers DMT Page 103 https://t.me/ICSE_10_Prelim ICSE 10 School Prelim Papers DMT Page 104 https://t.me/ICSE_10_Prelim ICSE 10 School Prelim Papers A.B.V.M. Agrawal Jatiya Kosh's Seth Juggilal Poddar AcademyucsE) Sub: Mathematics First Prelimirary Examination (2023 -24) STD: X Marks: 80 Date: 28/1 1/2023 Time: 2 hr. 30 mins. Answers to this Paper must be written on the paper provided separately. Youwill not be allowed to write during the first 10 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. Attempt all questions from Section Aand any three questions from Section B The intended marks for questionor parts of questions are given in brackets !) SECTIONA (Attempt allquestions from this Section) Question 1) i) [15] The ratio of the radii of the two cylinders is 2:3 and the ratio of their heights is 5:3. The ratio of their volume is: a) 10: 17 bt 20: 27 c) 17:27 d) 27:20 ii) The locus of a point equidistant from two fixed point is a) The perpendicular of the line segment joining two fixed points. b) The circumference of the circle. The perpendicular bisector of the line segment joining the two fixed points. d) Median of a triangle. DMT Page 105 https://t.me/ICSE_10_Prelim ICSE 10 School Prelim Papers iii) The solution set which represents the given number line is: -4 -3 -2 -1 0 1 3 2 4 a) {0,1, 2, 3} b) {x:x R, -1<x<4} c) {x:x ER,-1<x<4} dYE-1,0, 1, 2,3} iv) The general term of the Arithmetic Progression 16, 12, 8, 4, 0,......... is : a) 10 - 5n b) 5 - n 20- 4n d) 10 -2n v) Rs.15000 and sel!s it to a A shopkeeper buys an article from awholesaler for liability of the consumer at a profit of 5%. If the rate of GST is 18%, then the tax shopkeeper is a) Rs.150 b) Rs.120 ) Rs.135 d) Rs.145 vi) f(x) What number must be added to the polynomial remainder -1 when divided by x - 1: x + 4x so, that it leaves =3x3 a-7 b) -1 c) 7 d) 1 vii) D pentagon and O is the centre of In the figure ABCDE is a value of circle. The numerical the A LABC + 2CDE = a) 180 b) 360 c) 90 d) 270 Page 2 of9 DMT Page 106 https://t.me/ICSE_10_Prelim ICSE 10 School Prelim Papers vii) iX Which of the following s.atement is not true? v ) All the identity matrices are square matrices. b) Allnull matrices are square matrices. c) For the square matrix, the number of rows is egual to the number of d) Asquare matrix, all of whose elements except those in the leading columns. diagonals are zero, is the diagonal matrix. Mx: (a, 2) (5,b) then the values of a and b are a) -5,-2 b) -5,2 c) S, -2 Y5,2 x) re:pectively: Anshika wants to invest Rs.25000in a She buys Rs.100 shares at a Rs.25. Number of shares purchased bycompany. premium of her is: a) 100 b) 2000 c) 250 t 200 xi) If P(2, k) divides the line joining (6,2) and (-2,4) in the ratio 2 : 2, then k = a) 7 c) 2 d) 1 xii) The root of the quadratic equation 4x' = 3x is/are a 4 3 b) 0, c) -3 4 d) 0, 4 3 Page 3 of 9 DMT Page 107 https://t.me/ICSE_10_Prelim ICSE 10 School Prelim Papers Qu xiii) Apole 12m high casts ashadow 123 m on the ground. Find the Sun's elevation a) 60 t 30 c) 45 d) 90 Xiv) The sides AB, BC and CA of triangle ABC, touch at P, Q and R respectively. If PA= 4cm, BP = 3cm and AC=11cm, then R BC = a) 10cm b) 11 cm c) 14 cm d 15 cm The following table shows the frequency distribution. Assertion:To find the Upper limit of the continuous and necessary to calculate themedian class, It's not necessaryto make the data cumulative frequency. Statement: Upper limit of the median class is 17.5 Class Frequency 0-5 13 6-11 12-17 10 15 18-23 24-29 11 a) Both Assertion and b) Assertion is True Statement are True and Statement is tAssertion is False and Statement is False True d) Both Assertion and Statement are False DMT Page 108 https://t.me/ICSE_10_Prelim ICSE 10 School Prelim Papers Question 2) Mr. Ram Gopal invested Rs.8000 i.7% Rs.100shares at Rs.80. After a year, i) he sold these shares at Rs.75 each and invested the proceeds (including his [4] dividend) in 18%, Rs.25 shares at Rs.41. Find: a) His dividend for the first year. b) His annual income in the second year. c) The percentage increase in his return on his original investment. ii) [4] In the given figure, Iis the incentre of AABC. B when produced meets the circumcircle of AABC at D. IfeBAC = 55 & LACB = 65 , A Calculate: a) zDCA b)ZDAC c) zDC! d) zAIC ii) x= Given write down [4] i a) The order of the matrix X b) The matrix X Question 3) i) From a solid cylinder whose height is 8cm and radius is 6cm, aconical the cavity of height 8cm and base radius 6cm is hollowed out. Find [4] volume and total surface area of the remaining solid. ii) [4) The mean of the following frequency table is 50. But the frequencies f1 and f2 in the classes 20-40 and 60-80 are missing. Find the values of fi and f Class 0-20 20-40 40-60 60-80 80-100 Total Frequency 17 f1 32 f 19 120 Page 5 of 9 DMT Page 109 https://t.me/ICSE_10_Prelim ICSE 10 School Prelim Papers ii) Use a graph paper for this question. (Take 10 small divisions =1 Plot the points P(3,2) and Q(-3,-2). From Pand Qdraw unit on bo perpendicular, PM and QN on the X-axis. a) Name the image of Pon reflection in the origin b)Assign the special name tothe geometrical figure PMQN || and find its area. c) Write anytwo invariant points under reflection in the X-axis. SECTION B [Attempt any four fromthis section) Question 4) i) 800 2 The model of aship is made toa scale 1:300. (3) a) The length of model ship is 2m. Calculate the length of the ship. 18O000 b)The area of the deck ship is 180000 m'. 30ox 30o Calculate the area of the deck of the model. c) The volume of the model is 6.5 m . Calculate the volume of the ship. i) Solve the following inequation and represent the solution set [3 on the number line. -1 2x 5 -3 < 2 3SER i) [4] Using ruler and compass only: a) Construct a triangle ABC with the following data: AB = 3.5cm, BC= 6cm and zABC= 120 diameter. b) In the same diagramdraw a circle with BCas circle which is Find apoint P on the circumference of the equidistant from AB and BC. c) Measure zBCP DMT Page 110 https://t.me/ICSE_10_Prelim Page 6 of9 *h xes ICSE 10 School Prelim Papers Question 5) i) Ashima has a cumulative or Recurring deposit account in a bank for 5years at 9%p.a At the time of maturity, she gets Rs.51607.50. Find the monthly instalment. (3] 700 ii) Howmany three-digit natural numbers are divisible by 7? [3] )28 i) (x- 2) is a factor of x + ax' + bx +6. When this expression is divided by (x - 3),it leaves the remainder 3. Find the polynomial. [4) Question 6) i) Mr.Bedivisits the market and the following articles: [3] Medicine costing Rs.950, GST @5% Apair of shoes costing Rs.3000, GST @18% Alaptop bag costing Rs.1000 with a discount of 30%, GST @18%. a) Calculate the total amount of GST paid. b) The total bill amount including GST paid by Mr.Bedi i) The line through P(5,3) intersects y-axis at Q. (3] a) Write the slope of the line. P(5,3) b) Write the equations of the line PQ. o k slope foYm x' c) Find the coordinates of Q. Too eo foY ii) In the adjoining figure, ABC is a right-angled 45 y triangle withzBAC =90 a) Prove that AADB~ ACDA b) If BD=18cm and CD=8cm. find AD. c) Find the ratio of the [4] 8cm area of AADB and area of ACDA 18cm B Page 7 of 9 DMT Page 111 https://t.me/ICSE_10_Prelim ICSE 10 School Prelim Papers Question 7) X i) Solve x+ 7x=7 and give your answer to two significant places. i) From the top of a hill, the angle of depression of two consecutive kilometer stones due east are found to be 30 and 45 respectively. Find the distance of the tw stones from the foot of the hill. i) (3) Ifthe image of the point (2,1) with respect tothe line mirror be (5,2), find the equation of the mirror. [4] Question 8) Construct aAABC, given thatAB = 6cm, BC = 7cm and AC = 5cm. Construct inscribed circle of a AABC and measure its radius. ) (3) The three vertices of a p ralelogram are (3,4)(3,8) and (9,8). Find the fourth vertex. (3] ii) If tan + sin = m and tan - sin = n, show that m - n' = 4ymn [4) Question 9) i) i) A person on tour has Rs.360 for his expenses. If he extends his tour for 4 days, he has to cut down his daily original duration of tour as x, form an expenses by Rs.3. Taking the equation in x and solve it. 40students enter for a game of shot-put competition.The distance (4] thrown(in metres) is recorded below: (6] Distance(in m) 12-13 13-14 14-15 Number of students 3 9 12 15-16 16-17 17-18 18-19 4 2 1 Page &of 9 DMT Page 112 https://t.me/ICSE_10_Prelim ICSE 10 School Prelim Papers scale of ogive for the above distribution. Use an draw to paper graph a Use theother axis. Hence uSing your on students 2cm=5 and 2cm=lm on one axis graph find: a) The median. b) Upper Quartile. of students c) Number who which is cover a distance above 16.5 m. [3) hemisphere of on a mounted Question 10) cone cm. form of a toy is 15.5 the the in of is height Atoy i) The total 3.5cm. at C. radius area. B meet and surface A Tangentsat total circle. Find the X ii) O is the figure, given In the 30 , find ZACO = If a) ZAOB centre ofthe 30 C b) ZAPB c) ZBAC [4] expression: the solve r) proportion 62 (1+ 1 + x+ x 63(1 -x) propertiesof 1 - rt r 2 Usingthe iii) *****FND* DMT Page 113 https://t.me/ICSE_10_Prelim ICSE 10 School Prelim Papers DMT Page 114 https://t.me/ICSE_10_Prelim ICSE 10 School Prelim Papers (v) In the given figure, PQ and RS are perpendicular to base QT. If RS= 2 cm, QS = 3 cm and QT = 9 cm, then PQ equals to (a) 2 cm P (b) 3 cm (c) 4 cm (d) 5 cm (vi) Assertion (A): (cosec A+ sin A) (cosec A-sin A)= cot2 A+ cos2 A Reason (R): cosec2 A = I + cot2 A and sin2 A = I - cos2 A (a) A is true, R is false (b) A is false, R is true (c) both A and i'are true (d) both A and fare false (vii) A die is thrown once. The probability of getting .a prime num (a) 2 3 (b) .:3 (c) -2 1 (d) .:6 (viii) If A (- 1, 0), B (5, -2) and C (2, 8) are vertices of a /J.. ABC, then its centroid is : (a) (- 2, 2) (b) (0, 7) (c) (2, 2) (d) (7, 0) (ix) The co-ordinates of the point (- 4, 2) after reflection in the line y = o-$;fe ; /, (a) (4, 2) (b) (4,-2) (c) (-4, - 2) (d) (-2, - 4) (x) If Rohan invest n0,320 on noo shares at a discount of n4, then the number of shares, he buys is: (a) llO (b) 120 (c) 130 (d) 150 DMT Page 115 https://t.me/ICSE_10_Prelim ICSE 10 School Prelim Papers DMT Page 116 https://t.me/ICSE_10_Prelim Shubh has a recurring deposit account of 500 per month for a period of4 years. If at the (ii) ICSE 10 School Prelim Papers (iii) time ofmaturity, he gets 28,410 then find the rate ofinterest. [4] Let M x [ ] = [1 2] , where M is a matrix. (a) State the order of matrix M. [4] (b) Find the matrix M. Question 3 (i) A spherical ball oflead 3 cm in diameter is melted and recast into three spherical balls. [4] The diameter oftwo ofthese are 2 cm and 1.5 cm respectively. What is the diameter of the third spherical ball? (ii) Points A and B have coordinates (7,-3) and (1, 9)respectively. Find: (a) the slope ofAB, (b) the equation ofthe perpendicular bisector ofthe line segment AB, (c) the value ofp if(-2, p)lies on it. (iii) - 0 The following table shows the distribution ofmarks in History of180 student (- 5rf)-_('. Marks No. of Students 0-10 7 10-20 21 20-30 26 30-40 17 40-50 13 50-60 21 60-70 42 70-80 33 Draw an ogive for the given distribution taking 2 cm = 10 marks on x- axis and 2 cm = 20 students on y - axis. Using the graph, determine: (a) median marks, (b) number ofstudents who scored 75% and above. DMT Page 117 https://t.me/ICSE_10_Prelim ICSE 10 School Prelim Papers Question 4 (i) Solve the following inequation and represent the solution set on the number line. 5 < 2x - 1 :'.S 11, x E: R (ii) (iii) (3] In the figure given below, CD andEC=2cm. II LA and DE II AC. Find Athe length of CL if BE= 4 cm B.-.___________._____._______.L E c 2 2 cot 0 (sec 0-1) + sec 8 (sin e-1) = Prove that: O 1 +sine [3] [ 4] 1 +sec8 Question 5 (i) Cards marked with all 2-digit numbers are placed in a box and are mixed thoroughly. One card is drawn at random. Find the probability that the number on the card is: [3] , (a) divisible by 10 (b) a perfect square number (c) a factor of 60 (ii) Solve the given equation 5 x2 - 6x - 2= 0 and express your answer correct to two places of decimal. [3] In the figure, 0 is the centre of the circle, PQ is a tangent to the circle at A. If LPAB = 58 , find LABQ and LAQB. [ 4] The following table gives the wages (in ) of workers (per day) in a factory: '19.. [3] (iii) Question 6 (i) l Wages (t) ; 130 - 134 Number of Workers 5 134- 138 138 - 142 142- 146 8 14 12 146 - 150 J 11 DMT Page 118 https://t.me/ICSE_10_Prelim Calculate the mean waQe of workers of the factorv usinQ Assumed Mean Method. ICSE 10 School Prelim Papers DMT Page 119 https://t.me/ICSE_10_Prelim ICSE 10 School Prelim Papers DMT Page 120 https://t.me/ICSE_10_Prelim ICSE 10 School Prelim Papers DMT Page 121 https://t.me/ICSE_10_Prelim ICSE 10 School Prelim Papers DMT Page 122 https://t.me/ICSE_10_Prelim ICSE 10 School Prelim Papers DMT Page 123 https://t.me/ICSE_10_Prelim ICSE 10 School Prelim Papers DMT Page 124 https://t.me/ICSE_10_Prelim ICSE 10 School Prelim Papers DMT Page 125 https://t.me/ICSE_10_Prelim ICSE 10 School Prelim Papers DMT Page 126 https://t.me/ICSE_10_Prelim ICSE 10 School Prelim Papers DMT Page 127 https://t.me/ICSE_10_Prelim ICSE 10 School Prelim Papers DMT Page 128 https://t.me/ICSE_10_Prelim ICSE 10 School Prelim Papers DMT Page 129 https://t.me/ICSE_10_Prelim ICSE 10 School Prelim Papers DMT Page 130 https://t.me/ICSE_10_Prelim ICSE 10 School Prelim Papers DMT Page 131 https://t.me/ICSE_10_Prelim ICSE 10 School Prelim Papers DMT Page 132 https://t.me/ICSE_10_Prelim ICSE 10 School Prelim Papers DMT Page 133 https://t.me/ICSE_10_Prelim ICSE 10 School Prelim Papers DMT Page 134 https://t.me/ICSE_10_Prelim ICSE 10 School Prelim Papers DMT Page 135 https://t.me/ICSE_10_Prelim ICSE 10 School Prelim Papers DMT Page 136 https://t.me/ICSE_10_Prelim ICSE 10 School Prelim Papers DMT Page 137 https://t.me/ICSE_10_Prelim ICSE 10 School Prelim Papers DMT Page 138 https://t.me/ICSE_10_Prelim ICSE 10 School Prelim Papers DMT Page 139 https://t.me/ICSE_10_Prelim ICSE 10 School Prelim Papers DMT Page 140 https://t.me/ICSE_10_Prelim ICSE 10 School Prelim Papers DMT Page 141 https://t.me/ICSE_10_Prelim ICSE 10 School Prelim Papers DMT Page 142 https://t.me/ICSE_10_Prelim ICSE 10 School Prelim Papers Zaglu Sinyk Charitable ust's (Regd.) THAKUR PUBLIC SCHOOL fps (Established 2003) (Aliated to the Council forthe ndtan Sclhool Corifcate Exanrinutions, New Delhi) IS0 9001: 2015 CERTIFIED Mathematics Maximum marks: 80 (Twoand a Half hours) Answers to this paper must be written on the paper provided separately 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. Attempt allquestions from Section Aand attempt any four questions from Section B The intended marks for questions or parts of a question are given in brackets [ ]. SECTION- A [Marks 401 (Attempt all questions from this section) Questionl i) [15] IfA =|-1 -2] and 2 Which of the following operation is possible? a) A - B b) A +B c) AB d) BA i) A dealer in Lucknow (U.P.) sells goods worth 50,000 to adealer in Agra (U.P). If the rate of GST is 18%, the CGST is : c) 4,500 b) 6,000 73.000 a) ii) a) d) Nil If x=3 is a root of quadratic equation x- 2kx-6 = 0 then the value of kis : 1 d): b) 2 the angle An observer at point E, which is at a certain distance from the lamp post AB, finds C, Dand iv) It is given that B, of elevation of top of lamp post from positions C, D and E as a, and y. E arc along a straight linc. Which of the following condition is satisficd? (a) tana>tan B (b) tan <tan y (c) tan Y> tan a. (d) tan a< tan B V) tangents is equal to: In a circle with radius R, the shortest distance between two purallel (d) R (c) 2rR (b) 2R (a) R ITPS-Std.10-Mathematics-First Preliminary Examination-04/12/20231 This paper consists of 5 printed pags, 1/5 DMT Page 143 https://t.me/ICSE_10_Prelim ICSE 10 School Prelim Papers The table shows the valucs ofp and q, where p is proportional to . vi) What are the values of S and R? (a) S = 4, R= 9 (b) S =9, R=3 6 17 ciii) The 12 0-ordin 6 12 18 (c) S =9, R= 4 (d) S =12, R=0 1?7 R 6 a) xi vii) The reflection of any point (-3,2) about line y=x is b) (-3.-2) (2.3) a) c) (2,-3) d (3,2) viii) Assertion (A) The first ternm of the G.P with real term is 1 .if the sum of its third and fifth terms is 90 .the common ratio of the G.P. is +3. Reason (R) The constant ratio is called common ratio of the G.P.and it is denoted by r, Generally r = ak+1 ak a) A istrue, R is false. b) A is false, R is true c) Both are true d) both are false ix) The total surface arca of hemispherewith radius 10 cm taking 942 cm? a) b) 94.2 cm? c) 9420cm? =3.14 is. d) 1882cm? Aright-angle triangle shaped piece of hard board is rotated completely about its hypotenuse, as shown in the diagram. The solid so formed is always: 1. a single cone 2. a double cone Which of the statement is valid? (a) only 1. (b) only 2. (c) both 1. and 2. (d) neither 1. nor 2. xi) Which of the following is/are an Arithmetic Progression (A.P)? 1) 2) 3) 5,8,6,15..... 2,4,6.8,..... V3,2V3,3V3,4V3 c) Only 1. Only 2. Only 2.and 3. d) All 1.2and 3. a) b) xii)) Line 3x + 4y = 24 mects x- axis al point Aandy - axis at point B. II thepoint P divides line segment AB internally inthe ratio 2 :1 the co-ordinates of point P are: b)(4,3) (3,4) a) "ePs.std.10-Mathematics-irst 'reliminary Examination-04/12/2023) This paper consists of 5 printed DMT Page 144 2/5 pages. https://t.me/ICSE_10_Prelim ICSE 10 School Prelim Papers kiii) The point P(-6,-3) is reflected in line y+3 =0 to point P'. The co-ordinates of point P' are: a) (-6,3) xiv) a) Xv) b)(-6,-3) c) (6,3) d) (6,-3) n the given figure, z BCA = LCDA = 90 , then the value of BO BD b) AD CA c) BD ) CD AD is: BC lfx is a negative integer, then the solution set for the linear inequation 2+(x+1) >0is: a) {0, -1, -2} b) (-2, -1} ){-1, -2, -3} d) {-2, -3, -4} Question 2 a) Rajinish has a recurring deposit account ina bank of Barodaand deposits 140 per month for 4 years. Ifhe gets 8092 on maturity, find i) the sum deposited ii) the rate of interest ii) simple [4] interest given by the bank. b) 10. In the figure given below, AB IEF ICD. If AB =22.5 cm, EP =7.5 cm, PC = 15 cm [4] and DC = 27 cm. Calculate: (i) EF (ii) AC 225 S c) F In the given figure, AB is parallel to DC, ZBCE= (4] 80 and LBAC = 25 i)2CAD ii)CBD ii) LADC 25 B 80 Question 3 a) An acroplanc, at an altitude of 250m, observe the angles of depression of two boats on the opposite banks of river to be 45 and 60 respectively. If the boats are onthe oppositesides of aeroplane. Findthe width of the river. Write the answer correct to the nearest whole numbers. [4] (TPS-Std.10-Mathematics-First Preliminary Examination-04/12/2023| This paper consists of5 printed pages. DMT Page 145 3/5 https://t.me/ICSE_10_Prelim ICSE 10 School Prelim Papers b) Acylindrical vesselof adiameter 14 cm and height 42 cm is fixed symmetrically inside similar vessels of diameter 16 cm and height 14 cm. The total space betwcen two vessels is cOIk dust 1or heat insulation purpose. How many cubic cms of cork dust will be required? fil ed with A (1, 1),B (5.1), C(4,2) and D (2,2) are vertices of aquadrilateral. Name the quadrilateral14) c) ABCD, A, B, C and D are reflected in the origion on to A', B',C' and D' respectively. SECTION B (Attempt any 4 questions from this section) Question 4 a) A computer mechanit in Delhi charges repairing cost from three different Persons A, B, Cwith certain discounts. The repairing costs and the corresponding discOunts are given below: [3] Name of the persons Repairing cost (in ) Discount % C B A 5,500 6,250 4,800 30 40 30 Iftherate of GSTis 18%, find the total money (including GST) by the mechanic. b)Find the value of mfor which the equation 3x + mx + 2=0has real roots Also, find the roots of the given equation. (3] c) Construct a triangle ABC. with AB=7cm, BC=8cm and LABC=60 .Locate by construction the point psuch that: i) P is equidistant from B and C. ii) Pis equidistant from AB and BC. Measure and record length of PB. [4] Question 5 a) Solve the following inequation and represent the solution set on the number line :4x-19< 2s2 +x,xeR 5 b) 3X 3] Mis the midpoint of the line segment joining the points A(0,4) and B(6,0). M alsodivides the line segment OP in the ratio 1:3. Find i)co-ordinates of Mi)co-ordinates ofP (3] (0, 4) A M (6, 0) Construct atriangle ABC in which AB-5 cm, BC =6.8 cm and median 4.4 cm .Dray incircle of this triangle [4) c) Question 6 1 a) 1 Find the sun of GP:1-+ 2 4 -+......to 9 terms. Aline 5x + 3y + 15 = 0 mects y-axis at point P. Find the co-ordinates of point P. Findthe equation of a line through Pand perpendicular (3) b) to 'x 3y + 4 = 0. [3] ITPS-Std. 10-Mathematics-Fj"st Preliminary bxamination-04/12/20231 This paper consists of 5printed pages. 4/5 DMT Page 146 https://t.me/ICSE_10_Prelim ICSE School Prelim Papers (Use10 praph paper for this qucstion, (able piven below shows thc Heiny thc table, calculate thcmonthly wapcs of ome factory wotkcr, frequencies of workcr, Draw a cumulative frequency cumulative curvc. Use 2cm 2 500, 5tarting the origin at 2 6500 on x- axis, and 2 CIm 10 workcrs on they-axis. d with (4| 6500-7000 Wapes (in .) No. of 7000-75007500)-8000 8000-85002500-9000 9000-9500 9509-190) 18 22 workers. 25 17 (Question 7 a) -4 .B = b) Divide 216 into parts is S040. C= and A-2C 69, find the valuc of a, hand . (31 thrcc parts which arc in A.P. and the product of two smaller 31 In the given ligurc. Ois the centre of the circle The tangents at B and D interscct cach other al c) point P. ITAB is parallel to CD and Find: i) z BOD ABC-55 ii) z BPD [4| B C Question 8 duc west and the Two trains lcavc a railway station at the same lime. Thc first train travels 5km/hr faster second train due north The first trains travels 50 km apart, Iind the spced lhan thc Second Irain. If after 2 hours, they arc [3] of cach train. hc a) (x-1), polynornial x* + 2x- 5ax 7 is dividcd by divded bu thc When b) x + ax - 12x + 16 js remainder is A and when the polynomial of'a' if2A +B 0. Find the valuc (x +2) theremainder is B. 5a2+12c2 3a4-7 4 that: prove proportion, Sb7+12d2 3b4-7d4 in are d |a, b, c and [3] [4] C) Question 9 14(s0c A-tan A)2 = 2 tan A (3] identitics : cosec A (vecA-lan A) the Irove a) Calculate Biehl mclallic splhercs; caclh ol radiuS Z imm, are nicited and cast into a single spherc. b) (3] sphcrc. the radius of the ncw provothat: bx? -3ax + b = 0 (4) -a-2h " C) rrPs-sd. I0-Mathenatics-F'irst Preliminary Examination-04/12/20231 Thispaper consists of Sprinted pages. DMT Page 147 S/5 https://t.me/ICSE_10_Prelim ICSE 10 School Prelim Papers Bhaktivedanta Swami Mission School Pre-Preliminary Examination (2023-24) Mathematics MM: 80 Class: XAB Time: 2Hr. 2 Date: 11.12.23 Answers to this Paper must be written on the paper provided minutes. separately. You will not be allowed to write during first 15 This time is to be spent in reading the question paper. writing the answers. The time given at the head of this Paper is the timne allowed for Section B. Attempt all questions from Section A and any four questions from on the same must be done Allworking, including rough work, must be clearly shOWn, and 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] (Do not copy the question, write the correct answers only.) () A retailer buys an article for 750 and sells it to a customer for some fixed profit. If the customer paid GST of 150to the retailer, the SGST paid by the customer is and to the final purchase price paid by the customer is (ii) (a) 150, 7900 (b) }150, 2750 (c) 75, Z825 (d) 75,1000 Thepoint (3,0) is invariant under reflection in: (a) (iii) The origin (b) X-axis (c) y-axis (d) both x and y axes A lighthouse is 80m height. The angle of elevation of its top from a point 80m away from its foot along the same horizontal line is: (a)60 (b) 45 (c) 30 Page 1 of 9 (d) 90 DMT Page 148 https://t.me/ICSE_10_Prelim ICSE 10 School Prelim Papers line is: The solution sct representing the following number (iv) -3 (a) (x:xE R, -3<x<2} (b) {x:xE R, -3 <x< 2} {x:xE R, -3 <x< 2} {x:xE R, -3 <x< 2} (c) (d) 3 1 -1 -2 Which of the following is/are an Arithmetic Progression (A.P.)? (v) 1. 1, 4,9, 16,......... 2. Vs, 2V5,3N5, 4V5.. 3. 8, 6, 4, 2,....... (a) only 1. (vi) (b) only 2. (c) only 2. and 3. In the given diagram, A ABC ~ A PQR and AD PS (d) all 1., 2. and 3. 7 =. The value of AB:PQ is: 2 P A C (a) 7:2 (vi ) R (b) 2:5 (c) 2:7 (d) 5:7 The radius of aroller 100 cm long is 14 cm. The curved surface area of the roller is: (Take - 22/7) (a) 13200 cm' (b) 15400 cm' (c)4400 cm? (d) 8800 cm? Page 2 of 9 DMT Page 149 https://t.me/ICSE_10_Prelim ICSE 10 School Prelim Papers (viii) For two matrices P and ) Assertion (A): P yields anullmatrix Reason(R) always Null P and O are not (ix) (a) A is true. R is false (b) (c) A is false. R is true (d) matrices A is true,R is true Ais false. R is false west tomorrow. Event A: The sun will set in the Event B:It willrain on Tuesday. Event C: An hour has 60 minutes. probability Which of theabove event(s) has equal to 1? (a) allevents A, B and C (b) both events A and B (c) both events B and C (d) both events A and C (x) (x) intersect The point where three angle bisectors (c)circumcentre (b)incentre (a) orthocentre between two parallel tangents is equal to: In a circle with radius R. the shortest distance (b)2R (a) R (xii) (d) centroid (d) R (c) 2uR Evaluate: (cosec A - sin A) (sec A - cos A): (a) (cos A + sin A) (c) cos A sin A (b)(cos A- sin A) (d) sec A equation of line L is: (xiii) A point P(6,0). when reflected in line L,gives P'(0,0). The (a) x=6 (b) X+6=0 (c) y=3 (d) x=3 Page 3 of 9 DMT Page 150 https://t.me/ICSE_10_Prelim ICSE 10 School Prelim Papers distribution, find the modal class: (xiv) From the following 10 Class 20 16 Frequency () 50 - 60 10 40 - 50 26 (c) 40 - 50 (b) 30 - 40 (a) 10 - 20 40 30 22 20 -30 (d) 50 60 is produced to point E. In the given figure. AD isextended to point F and AB LCDF =? C 106 (a) 1000 (b) 40 60 (c) (d) 80 Question 2 Trisha gets 2400 as interest at the end of 2vears in a recurring deposit account at 8% i) Find the monthly instalment. i ) the amount at the time of maturity. The first term of an A.P is (-5) and the last term is 45. If the sum of the terms of the AP is 120, then find the number of terms andcommon difterence. Page 4of 9 DMT Page 151 https://t.me/ICSE_10_Prelim ICSE 10 School Prelim Papers [4] (Use graph paper for this question) (c () Plot points A(4. 4); B(4,-6) &C(8, 0). (i) B&C Retlect ABCon the x-0 andname it A'. Write down the co-ordinates of A'. B.C'. AAC'BBC. Write the geometric name of the figure (ii) (iv) Question3 (a) circle. Tangents at Aand B meet at C. If In the given figure Ois the centre of the LACO =30 . find (i) APB (ii) LAOB () BCO B b Prove the following identity (sin A +cosec A)t(cos A +sec A)P= 5+ sec-A.cOsec*A Find the mean of the given frequency distribution using step dev iation method. Correct to two decimal. Agein !5-19 20-24 23-29 30-34 35-39 20 38 24 10 40-44 Yrs No of children Pzge 5 of9 DMT Page 152 https://t.me/ICSE_10_Prelim ICSE 10 School Prelim Papers SECTION B (Attemptany 4 questions from this Section.) Question 4: (a) (b) The model of abuilding is constructed with scale factor I :30. building in metres. () fthe height of the model is 80 cm, find the actual height of the find the volume of (i) lf the actual volume of atank at the top of the building is 27m', [3] the tank on the top of the model. A and B are two points on the x-axis and y-axis respectively. P (2, -3) is the midpoint [3] of AB. Find the (c) (i) Coordinates ofA and B. (ii) Slope of line AB. (iii) Equation of line AB. A /P (2,-3) B Using ruler and compasses construct () (ii) (iii) atriangle ABCin which AB = 5.5 cm, BC =3.4 cm and CA = 4.9 cm. the locus of points equidistant from A and C. a circle touching the lineAB at A and passing through C. [4| ohestion 5 (aj In the figure AB =7 cm and BC -9cm. i) Prove AACD ~ADCB (ii) Findthe length ofCD Page 6 of9 DMT Page 153 https://t.me/ICSE_10_Prelim ICSE 10 School Prelim Papers buying 100 shares at Amit Kuimar invests 36.000 in (b) 15% per annum.Find: (i) The number of shares he buys on (111)The percentage return (ii) Hisyearly dividend his investment. correct to the nearest Giveyour answer [31 whole number. and graph the solution Solve the given inequation (c) 20 premium. The dividend is on the number line. [3| 2y- 3<y+1<4y+7; y R. ghestion 6 Attempt this question on graph paper. (a) Marks obtained by 200 students in Marks 0-10 10-20 No. of 5 10 examination are given below: 20-30 30-40 40-50 14 21 50-60 60-70 70-80 80-90 90-100 34 36 27 16 12 25 2 cm=10 marks on one axis and Draw an Ogive for the given distribution taking the graph find: 2 cm =20 students on the other axis. From (i) (i) (iv) (b) the Median Number of students scoring above 65 marks. minimum marks required to If 10students qualify for merit scholarship, find the (6] qualify. elevation of the From two points A and B on the same side of a building, the angles of top of the building are 30 and 60 respectively. If the height of the building is 10m, [4| find the distance between A and B correct to two decimal places. Page 7 of9 DMT Page 154 https://t.me/ICSE_10_Prelim ICSE 10 School Prelim Papers LQrtestion 7 (a) When divided by N-3the polynomials x'-px' txt6 and 2x'-x-(p+3) x- 6 leave the same remainder. Find the value of 'p'. (b, (3| In AABC. AP :PB-2:3. PO is parallel to BC and is extended to Q so that C is parallel to BA. Find: (i) AAPO~AABC (ii) Area AAPO: area AABC. A [3| (c) A shopkeeper bought an article with market price 1200 from the wholesaler at a discount of 10%. The shopkeeper sells this article to the customer on the market price printed on it. If the rate of GST is 6%, then find: (i)GST paid by the wholesaler. (ii) Amount paid by the customer to buy the item. [4| aestion (a) If an office works for 5 days in a week (Monday to Friday) and if two employees of office remain absent in the same week, what is the probability that it is (i) the same day (ii) Consecutive days ? (i) different days (3| (b) Find A--A iB0 Ahemisphcrical bowlofinternal radius 9em is full of liquid. The liquid is to be illed into cy lindrical shaped s1mall botles, cach of diameter Bem and height 4cm. How nany botles arc herded to enpty the bowl? [3| Page 8 of 9 DMT Page 155 https://t.me/ICSE_10_Prelim ICSE 10 School Prelim Papers Question 9 B(3,6) is Calculatethe ratio inwhich theline segment joiningA(-4,2) and (a) divided by [3] point P(x,3). Also find x. surnnounted by a conical block of wood. hcmisphere a represents figure given TIhe (b) the slant bcight of the cone is 5 cm. The diancterof thcir bases is 6 cm cnch and Caleulatc: (i)the height of the cone. [4| (ii)thevolume of he solid. (c) 2. Findthc number Sum of nterms of GPis 381. Its first term is3 andcomnon ratio is |3| of terms and the 7h term. Question 10 (a) A nanon the top of the tower observes a car mnoving at a uniforrn spccdtOwards it. If it 1akes 12 minutes for the angle of depression to change from 3(' to 45,how s0on will [4| thecar reach the tower? Give your answer to ncarest sccond. (b) Comdructah ABCith 3C6.5 cm, AB 5,5 cIn, C 5 cn, CoStruct thc incirclc of the triangle. Measure and recordtheradius of the incircle. [31 The sm of thre numbers in an AP is -12 andtheir product is 36. tind the nunbers DMT Page 156 https://t.me/ICSE_10_Prelim ICSE 10 School Prelim Papers DMT Page 157 https://t.me/ICSE_10_Prelim ICSE 10 School Prelim Papers DMT Page 158 https://t.me/ICSE_10_Prelim ICSE 10 School Prelim Papers DMT Page 159 https://t.me/ICSE_10_Prelim ICSE 10 School Prelim Papers DMT Page 160 https://t.me/ICSE_10_Prelim ICSE 10 School Prelim Papers DMT Page 161 https://t.me/ICSE_10_Prelim ICSE 10 School Prelim Papers DMT Page 162 https://t.me/ICSE_10_Prelim ICSE 10 School Prelim Papers DMT Page 163 https://t.me/ICSE_10_Prelim ICSE 10 School Prelim Papers DMT Page 164 https://t.me/ICSE_10_Prelim ICSE 10 School Prelim Papers DMT Page 165 https://t.me/ICSE_10_Prelim ICSE 10 School Prelim Papers DMT Page 166 https://t.me/ICSE_10_Prelim

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