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ICSE Class X Prelims 2026 : Mathematics (Euroschool, Wakad, Pune)

6 pages, 42 questions, 0 questions with responses, 0 total responses,

Saurabh Chaudhary
Vibgyor High School, Pune (NIBM Road)

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MATHEMATICS Prelim - 2, 2025-26 (Question Paper) GRADE: X --------------------------------------------------------------------------------------------------------------------Maximum Marks: 80 Time allowed: Three 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 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 and graph papers are to be provided by the school. This paper consists of 6 printed pages. SECTION A (40 Marks) (Attempt all questions from this Section) Question 1 Choose the correct answer to the questions from the given options. (Do not copy the questions, write the correct answers only.) 7 +2 5 (i) If = then m: n is 7 2 (ii) (iii) (iv) (v) ICSE 3 (a) 7:8 (b) 2:7 (c) 1:8 (d) 8:7 The money required to buy 50, 40 shares quoted at 38.50 is (a) 1920 (b) 1952 (c) 1924 (d) 1925 The X-axis divides the line segment joining A(2, 3) and B(5,6) in the ratio (a) 2:3 (b) 3:5 (c) 1:2 (d) 2:1 3 2 A polynomial in x is + 5 24. Which of the following is a factor of the given polynomial so that the value of k is 2? (a) (x + 2) (b) (x 3) (c) (x + 4) (d) (x 4) (sin + cos ) (tan + cot ) (a) (sec + cosec ) (b) (sec + cos ) 1 [15] (c) (vi) sec (d) cosec 1 1 1 The 11th term of the G.P. , 8 4 , , 1....... is 2 (a) 184 (b) 192 (c) 1024 (d) 128 (vii) The marks obtained by 12 students in a monthly test are 11,19,07,13,18,21,09,05,20,17,16,21 then Statement 1: The mean of their marks is 14.75 Statement 2:The mean of their marks when the marks if each student is increased by 3 is 17.25 (a) Both the statements are true. (b) Both the statements are false. (c) Statement 1 is true, and Statement 2 is false. (d) Statement 1 is false, and Statement 2 is true. (viii) Assertion(A): The roots of the equation 2 2 6 + 3 = 0 are unequal and irrational. Reason(R):If D<0 and not a perfect square then roots are unequal and irrational. (a) (A) is true, (R) is false (b) (A) is false, (R) is true (c) Both (A) and (R) are true, and (R) is the correct reason for (A) (d) Both (A) and (R) are true, and (R) is the incorrect reason for (A) (ix) A dealer in Mumbai supplies goods and services worth 5000 to another dealer in Pune. If the rate of GST is 18%, then the tax levied under CGST, SGST and IGST respectively are (a) 450, 450, (b) Nil, Nil, 900 (c) 400, 500, (d) 500, 400, Nil 900 Nil (x) Two triangles are similar. The sides of one triangle are 2cm, 3cm and 4cm. The longest side of the other triangle is 6cm, then the other two sides are (a) 4cm, 5cm (b) 3cm, 4cm (c) 3cm, 4.5cm (d) 3.5cm, 4.5cm (xi) Find the value of a if the straight lines 5x 2y 9 = 0 and ay +2x 11 = 0 are perpendicular to each other 4 1 (a) 5 (b) (c) 5 (d) 5 5 (xii) The solution set for 5 3x 2x +2, x W is : (a) {0,1,2,3) (b) {0,1,2} (c) {1,2,3,.....} (d) { 3, 2, 1,0,1,2,3} (xiii) If [9 2] M = [2], then the order of matrix M is 7 1 5 (a) 1 2 (b) 2 2 (c) 2 1 (d) 1 1 (xiv) If P and Q are the fixed points, then the locus of a point T is such that PTQ= 90 is a (a) Circle with (b) Circle with PQ (c) Circle with TQ (d) Circle with PT as radius as diameter as diameter PQ as radius ICSE 2 (xv) In the given figure, O is the centre of a circle and AOC = 120 , then BDC= ? (a) 30 (b) 45 (c) 60 (d) 15 Question 2 (i) Raina has a cumulative recurring deposit account of 340 per month at 6% p.a. If she pays 7157 at the end of maturity, calculate the total time for which the account was held. (ii) Solve the equation ( 1)2 3 + 4correct to 3 significant figures (iii) In the given figure, AB and DE are perpendicular to BC (a) Prove that ~ (b) If AB= 6cm; DE = 4cm and AC = 15cm. Calculate CD (c) Find the area of : area of Question 3 1 3 2 1 (i) If A = [ ] and C = [ ], find 2 5 + , where I is the unit matrix of order 3 4 3 4 2 2 (ii) Use ruler and compass for the following construction: Construct a where AB= 6cm, AC = 4.5cm and BAC = 120 . Construct a circumcircleof . Measure and write down the length of the radius of circle. (iii) Use graph paper for this question(Take 2cm = 1 unit along both X and Y axis). Plot the points A(0,4), B(2,2), C(5,2), D(0,4) and E(0,0) is the origin. (a) Reflect B, C, D on the Y-axis and name it as B C and D respectively. (b) Join ABCDD C B and A in order and give the geometrical name of the figure SECTION B (40 Marks) (Attempt any fourquestions from this Section) Question 4 (i) The 5th term and the 9th term of an arithmetic progression are 4 and 12 respectively. Find: a) The first term (b) Common difference (c) Sum of 16 terms of AP (ii) Using the properties of proportion, solve for x: +1+ 1 4 1 +1 1 2 = (iii) ICSE Prove the following [4] [4] [4] [4] [4] [5] [3] [3] [4] 3 ( 2 1)( 2 + 1) +1 = 0 (a) (b) 1+ 2 1+sec = sec Question 5 (i) Solve the following inequation, write the solution set and represent it on the real number line 5 3 2x < 3 (ii) (iii) 5 + 10 4 5 + 11 ; x R Given that (x 2) is the factor of the polynomial 2 3 7 2 + 2. (a) Find the value of k (b) Hence factorise the resulting polynomial completely A solid is in the shape of a hemisphere of radius7cm, surmounted by a cone of height 4cm. The solid is immersed completely in a cylindrical container filled with water to a certain height. If the radius of the cylinder is 14cm, find the rise in the water level. [3] [4] Question 6 (i) The toy model of a truck and a real truck are in the ratio 1:60. (a)Calculate the length of the truck in metres if the length of the model is 25cm. (b)If the open area of loading of the truck is 90m2, find the same area of the model in cm2. (c) If the volume of the model is 7500cm3, find the volume of the truck in m3 (ii) Draw Histogram from the following frequency distribution and find the mode from the graph: Class Frequency (iii) 0-5 2 5-10 5 10-15 18 Ice cream Vanilla Butterscotch Strawberry Price per litre 100 150 150 Quantity 10 litres 10 litres 10 litres The GST rate is 18%. Find the : (i) total GST paid (ii) total bill amount including GST Question 7 ICSE 15-20 14 20-25 8 4 Discount 5% 20% 20% [3] [3] 25-30 5 Rishita arranged a party on her birthday in an orphanage. She bought three different types of ice-creams Vanilla, Butterscotch and strawberry as given below: Sr.No 1. 2. 3. [3] [4] (i) From the top of a 120m high tower, a man observes two cars on the opposite sides of a tower and in a straight line with the base of the tower with the angles of depression as 60 and 45 . Find the distance between the two cars. (ii) (a) Determine the ratio in which the straight line x y 2 = 0 divides the line joining (3, 1) and (8,9) (b) Line 4x 5y = 20 meets X axis at A. Find the equation of line passing through A and perpendicular to line 2x + 3y = 6 Question 8 (i) Calculate the mean of the distribution given below using shortcut method: Marks 0-10 10-20 20-30 30-40 40-50 50-60 No. Of 3 8 14 9 4 2 students [5] A man bought 200 shares of a company at 25% premium. If he received a return of 5% on his investment. Find the: (a) Market value (b) Dividend percent declared (c) Number of shares purchased if annual dividend is Rs.1000 (iii) Mr. and Mrs.Shenoy were travelling by car from Delhi to Kasauli for a holiday. Distance between Delhi to Kasuali is approximately 350km(via NH 152D). Due to heavy rain they had to slow down. The average speed of the car was reduced by 20km/hr and the time of journey was increased by 2 hours. Find: (a) original speed of car (b) with the reduced speed, the number of hours they took to reach their destination. Question 9 (i) Ms. Samantha went to a fair and participated in a game. The game consist of a box having number cards with numbers from 01 to 30. The three prizes where as per the table given below: [3] (ii) Prize Wall clock Water bottle Purse (ii) ICSE [2] [3] [3] [4] [3] Number on the card drawn at random is a Perfect square Even number which is also a multiple of 3 Prime numbers Find the probability of winning a: (a) Wall clock (b) Water bottle (c) Purse Using ruler and compass construct a semicircle with diameter BC = 7cm.Locate a point A on the circumference of the semicircle such that A is equidistant from B and C. Complete the cyclic quadrilateral ABCD such that D is equidistant from AB and BC. Measure and write ADC 5 [3] (iii) In the given figure, O is the centre of the circle, PQ is a tangent to the circle at T. Chord AB produced meets the tangent at P. AB = 9cm, BP = 16cm, PTB= 50 , OBA= 45 Find: a) length of PT b) BAT c) BOT d) ABT Question 10 (i) The 4th, 6th and last term of a geometricprogression are 10, 40 and 640 respectively. If the common ratio is positive, find the first term, common ratio and the number of terms of the series. (ii) In the figure given below, O is the centre of the circle and AB is the diameter. If AC = BD and AOC = 72 . Find (a) ABC (b) BAD (c) ABD (iii) Use graph paper to solve the question During the medical check-up of 60 students in a school, weights were recorded as follows: Weight(in kg) Number of students 28-30 2 30-32 4 32-34 10 34-36 13 36-38 26 38-40 9 40-42 5 42-44 2 Use graph paper to draw an ogive for the above distribution. (Use scale of 2cm = Rs.50 on X axis and 2cm = 10 workers on Y-axis. Using ogive estimate: (a) Median (b) Upper quartile (c) The number of students whose weight is above 37kg ICSE 6 [4] [3] [3] [4]

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