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ICSE Class X Prelims 2026 : Mathematics (Greenwood High, Bangalore)

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GREENWOOD HIGH SCHOOL, BANNERGHATTA PRELIMINARY EXAMINATION -I- 2025-26 SUBJECT: MATHEMATICS GRADE: X DATE: 24-11-2025 DURATION: 3 HOURS MAX. MARKS: 80 1. Answers to this paper must be written on the paper provided separately. 2. You will not be allowed to write during the first 15 minutes. 3. This time is to be spent in reading the question paper. 4. The time given at the head of this Paper is the time allowed for writing the answers. 5. Attempt all questions from Section A and any four questions from Section B. 6. All working, including rough work, must be clearly shown, and must be done on the same sheet as the rest of the answer. 7. Omission of essential working will result in loss of marks. 8. The intended marks for questions or parts of questions are given in brackets [ ]. 9. Mathematical tables are provided. 10. This question paper consists of 7 printed pages. SECTION A (40 Marks) (Attempt all questions from this Section.) Question 1 Choose the correct answers to the questions from the given options. (i) The greatest even integer of the following equation is 2 + 3 3 3 1 4 (a) {0, 2, 4, 6, 8, 12, 14} (b) 15 (c) 14 (d) {0,1, 2,3, 4, 5, 6, 7, .14} (ii) The mean proportion of (a + b) and (a3 + a2b) is (a) a + b (b) a2 + ab (c) a2 ab (d) a b (iii) A dealer buys a washing machine from a manufacturer for 16000 and sells it to a consumer at 10% profit. If the sales are intra-state and rate of GST is 12%, then the total tax received by the Central Government is (a) 960 (b) 1920 (c) 1056 (d) 2112 Page 1 of 7 [15] (iv) If PQR ~ ABC, PQ = 6 cm, AB = 8 cm and perimeter of ABC is 36 cm, then perimeter of PQR is (a) 20.25 cm (b) 27 cm (c) 48 cm (d) 64 cm (v) A cylindrical metallic wire is stretched to double its length. Which of the following will NOT change for the wire after stretching? (a) Its curved surface area. (b) Its total surface area. (c) Its volume. (d) Its radius. (vi) If x2 + kx + m = (x 2) (x 5) for all values of x, then the value of k and m are : (a) 7, 10 (b) 10, 7 (c) 7, 10 (d) 7, 10 (vii) The sum of first n terms of the series a, 3a, 5a .. is (a) n2 a2 (b) n2 a (c) (2 1) 2 (d) na (viii) If (sin A + cos A)2 + (sin A cos A)2 = k, then k is (a) 1 (b) 2 (c) 0 (d) 4 (ix) Statement 1: The reflection of the point ( 4, 0) in the origin is (0, 4) Statement 2: The reflection of the point (x, y) in the line y = a is the point (x, 2a + ). (a) Both statements are true. (b) Both statements are false. (c) Statement 1 is true and Statement 2 is false. (d) Statement 1 is false and Statement 2 is true. Page 2 of 7 (x) In the given figure AC is a diameter, of the circle with centre O. If = 25 and = 100 , then the value of x is (a) 35 (b) 45 (c) 65 (d) 25 (xi) 1 1 A bag contains red, blue and black balls. Probability of selecting red = 6 , blue = 3, and there are 12 black balls. Then the total number of balls is (a) 24 (b) 30 (c) 36 (d) 42 (xii) Radha deposited 400 per month in a recurring deposit account for 18 months. The qualifying sum of money for the calculation of interest is (a) 3,600 (b) 7,200 (c) 68,400 (d) 1,36,800 (xiii) In the given diagram, O is the origin, and P is the midpoint of AB. The equation of OP is: (a) y = x (b) 2y = x (c) y = 2x (d) y = x (xiv) If 50 + 2 49 + k is divisible by (x + 1) then the value of k is (a) 0 (b) 1 (c) 1 (d) 2 (xv) The median of a series is 10. Two additional observations 7 and 19 are added to the series. The median of the new series is (a) 9 (b) 11 (c) 13 (d) 10 Page 3 of 7 Question 2 (i) A customer paid 2500 (rounded off to the nearest 10) to clear the bill. [4] Note: A 10% discount is applicable on an article if 8 or more such articles are purchased. Article Marked Price ( ) Quantity GST A 240 8 12% B 150 6 18% Check whether the total amount paid by the customer is correct or not. Justify your answer with calculations. (ii) An empty cone of radius 3 cm and height 12 cm is filled with icecream such that the 1 6 th [4] of the lower part of the cone is unfilled (empty) but a hemisphere is formed on the top . Find the volume of the icecream. (iii) [4] In the given figure, DE BC and AD : DB = 4 : 3 (a) Show that ADE ~ ABC (b) Find and (c) Prove that Ar( DEF) : Ar( DEC) = 4 : 11 Question 3 (i) In the adjoining figure of a circle with centre O and diameter AD, BED = 70 and BC is [4] parallel to AD. Find : (a) BAD (b) BOD (c) DBC (d) DCF (ii) Using the remainder theorem and factor theorem, factorize the following polynomial [4] x3 + 10x2 37x + 26. (iii) 40 students enter for a game of shot-put competition. The distance thrown (in metres) is recorded below: Distance 12 - 13 13 - 14 14 - 15 15 - 16 16 - 17 17 - 18 18 - 19 3 9 12 9 4 2 1 (in m) Number of Students Use a graph paper to draw an ogive for the above distribution. Use a scale of 2 cm = 1 m on one axis and 2 cm = 5 students on the other axis. Hence using the graph find (a) the median (b) upper quartile 1 (c) the number of students who cover a distance which is above 16 2 m. Page 4 of 7 [5] SECTION B (40 Marks) (Attempt any four questions from this Section.) Question 4 (i) If a, b and c are in continued proportion, then prove that 3 2 + 5 + 7 2 3 2 + 5 (ii) + 7 2 = Solve the following inequation, write the solution set and represent on the real number line. 3(x 7) 15 7x > (iii) [3] +1 3 [3] , x R. On a map drawn to a scale 1 : 40000, a rectangular plot of land, ABCD had following [4] measurements AB = 6 cm and BC = 8 cm. Calciulate (a) The diagonal distance of plot in km. (b) The area of the plot in sq km. Question 5 (i) (ii) (iii) 2 1 1 55 How many terms of the G. P. 9 , 3 , 2, ..must be added to get the sum equal to 72 ? Prove that (sin 3 ) ( 3 cos ) [3] [3] ( sec A cosec A) = cosec A(cot A 1) Use a graph paper for this question taking 1 cm = 1 unit along both the x and y-axis: [4] (a) Plot the points A(0, 5), B(2, 5), C(5, 2), D(5, 2), E(2, 5) and F(0, 5). (b) Reflect the points B, C, D, and E on the y-axis and name them respectively as B , C D and E . (c) Write the coordinates of B , C , D and E . (d) Name the figure formed by BCDEE D C B. Question 6 (i) A retailer in Jaipur (Rajasthan) buys good from a dealer in Alwar (Rajasthan) at a [3] discount of 20% . The retailer sells it to a customer in Jaipur at the printed price. If the printed price of the goods is 16,000 and GST rate is 8%, calculate (a) the price paid by the customer for the goods. (b) the CGST and the SGST payable by the retailer in Jaipur to the government. (ii) A Mathematics aptitude test of 50 students was recorded as follows : Marks Number of Students [3] 50 - 60 60 -70 70 - 80 80 - 90 90 -100 4 8 14 19 5 Draw a histogram for the above data using a graph paper and find the mode. Page 5 of 7 (iii) Points A and B have coordinates (7, 3) and (1, 9) respectively. Find [4] (a) the slope of AB. (b) the equation of the perpendicular bisector of the line segment AB. (c) the value of p if ( 2, p) lies on it. Question 7 (i) If the sum of first 7 terms of an AP is 49 and that of 17 terms is 289, find the sum of first [3] n terms? (ii) If the equation ( 1 + m2 ) x2 + 2mcx + (c2 a2) = 0 has equal roots, prove that [3] c2 = a2(1+ m2). (iii) In the given figure, O is the centre of the circle and AB is a tangent to the circle at B. If [4] PQB = 55 . (a) find the value of the angles x, y and z (b) prove that RB is parallel to PQ. Question 8 (i) Solve the following inequation and represent the solution set on the number line [3] 2x 5 5x + 4 < 11, x I. (ii) Find the value : tan2 A + cot 2A sec 2A cosec 2A [3] (iii) A vessel in shape of an inverted cone is surmounted by a cylinder has a common radius of [4] 7 cm. It was filled with liquid till it covered one third the height of the cylinder. If the height of each part is 9 cm and the vessel is turned upside down, find the volume of the liquid and to what height will it reach in the cylindrical part. Page 6 of 7 Question 9 (i) A bag contains some identical tokens, on which numbers 35 to 94 are marked. A token is [3] drawn at random. What is the probability that the number on the token is: (a) an even number (b) an odd number and prime (c) multiple of 3 and 5 (ii) Using the properties of proportion, find the value of x . 3 +4+ 3 5 3 +4 3 5 (iii) [3] =9 Mr. Sharma deposited 400 per month in a recurring deposit account for a period of [4] 2 years. At the time of maturity, he received 10,080. Find (a) The rate of interest per annum. (b) How much more interest Mr. Sharma would have earned if he had deposited 100 more per month, at the same rate of interest and for same period. Question 10 (i) Find the ratio in which the line segment joining ( 2, 5) and ( 5, 6) is divided by the line [3] y = 3. Hence, find the point of intersection. (ii) A water tank is located 60 meter from a building (see the figure). From a window in the [3] building, an observer notes that the angle of elevation to the top of the water tank is 60 and that the angle of depression to the bottom of the tank is 30 (a) How tall is the tank? (b) How high is the window? (iii) In the given figure, O is the centre of the circle and TP is the tangent to the circle from an external point T. If PBT = 30 , prove that BA : AT = 2:1 *************************End of Paper**************************** Page 7 of 7 [4] Page 8 of 7

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