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ICSE Class X Sample / Model Paper 2026 : Chemistry

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KARNATAKA ICSE SCHOOLS ASSOCIATION ICSE STD. X Preparatory Examination 2026 Subject MATHEMATICS Duration : 3 hours Maximum Marks : 80 Date: 12.01.2026 General Instructions: 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 ______________________________________________________________________________________ Instruction for the invigilators Kindly read aloud the Instructions given above to all the candidates present in the Examination Hall. __________________________________________________________________________________ KISA PREPARATORY_MATHEMATICS 1 of 10 SECTION - A (40 Marks) (Attempt all the questions from this section) Question 1 Choose the correct answers from the given options. (Do not copy the questions; write the correct answers with options only.) [15] i) The fourth vertex D of a parallelogram ABCD whose three vertices are A(-2,3),B(6,7) and C(8,3) is (a) (0,1) (b) (0,-1) (c) (-1,0) (d) (1,0) ii) On a map 4cm represents an actual distance of 1 km.The area on the map, in cm2, which represents 3 km2 is (a) 0.48 (b) 4.8 (c) 48 (d) 48000 iii) If a:b = 9:10,then then value of 2 2 2 2 2 3 2 +3 is 23 (a) 77 (b) 23 77 24 (c) 99 77 (d) 23 __________________________________________________________________________________ KISA PREPARATORY_ MATHEMATICS 2 of 10 iv) Slope of a line is 1.5089,its inclination is (a) 56 24' (b) 26 28' (c) 56 28' (d) 26 24' v) If d=x 13, fd=30,and f=120,then the mean is equal to (a) 13 (b) 12.75 (c) 13.25 (d) 14.25 vi) In the given figure, PT is tangent to a circle with centre O. Chord PQ subtends an angle of 65 at the centre. The measure of QPT is (a) 65 (b) 32.5 (c) 67.5 (d) 130 vii) A quadratic equation whose roots are 2 + 3 and 2 3 is (a) x2 4x + 1 = 0 (b) x2 + 4x + 1 = 0 (c) 4x2 3= 0 (d) x2 1= 0 __________________________________________________________________________________ KISA PREPARATORY_ MATHEMATICS 3 of 10 viii) Assertion(A): The equation of a line through the point of intersection of the lines 2x + 5y = 9 and 5x 2y = 8 and perpendicular to the line 4x + 3y = 7 is 3x-4y+2=0. Reason(R) : If two lines are perpendicular to each other,the product of their slopes is equal to 1 (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 explanation of (A). (d) Both (A) and (R) are true, but (R) is not the correct explanation of (A). ix) If A = then A2 = pA, then the value of p is (a) 2 (b) 4 (c) 2 (d) 4 x) The two missing terms in an AP: __,13,__,3 are (a) 11 and 9 (b) 17 and 9 (c) 18 and 8 (d) 18 and 9 xi) If 2 5 5 + 4 11, Z,then the solution set is (a) {-3,-2,-1,0,1} (b) {-2,-1,0,1} (c) {-3,-2,-1,0} (d) {0,1} _______________________________________________________________________________ KISA PREPARATORY_ MATHEMATICS 4 of 10 xii) A metallic cone having base radius 2.1 cm and height 8.4 cm is melted and moulded into a sphere. The radius of the sphere is (a) 2.1 cm (b) 1.05 cm (c) 1.5 cm (d) 2 cm 1 1 1 xiii) If P(E1) = 6 , P(E2) = 3 , P(E3) = 6 , where E1, E2, E3 and E4 are elementary events of a random experiment, then P(E4) is equal to 1 2 (a) 2 (b) 3 1 (c) 3 3 (d) 4 xiv) ( + ) (1 ) = (a) (b) (c) (d) ________________________________________________________________________________ KISA PREPARATORY_MATHEMATICS 5 of 10 xv) Assertion(A): In the given figure, DE || BC, so that AD = (4x 3) cm, AE = (8x 7) cm, BD = (3x 1) cm and CE = (5x 3) cm then, the value of x is 1. In triangle ABC, if DE || BC, then = (a) (A) is true, (R) is false. Reason(R): (b) (A) is false, (R) is true. (c) Both (A) and (R) are true, and (R) is the correct explanation of (A). (d) Both (A) and (R) are true, but (R) is not the correct explanation of (A). Question 2 i) If A= , B= and 2 5 2 = 5 ,find the matrix C, where C is a 2 by 2 matrix [4] ii) Mrs Kour gifted the following items to her friend on Diwali. The GST rates and the quantity of each items and the marked price are given below: Sl.No. Items Price ( ) Quantity GST Rate 1. Almonds 650 1 5% 2. Diyas 50 2 0 3. Cookies 80 2 18% Find: a) The total amount of SGST paid b) The total amount of the bill [4] iii) f(x) = x3 - ax2 + (a - 3)x + 6, where a is a non-zero real number. When f(x) is divided by (x + 1), there is no remainder. Using the remainder and factor theorem, factorize the above expression completely. [4] Question 3 i) Sachin has a recurring deposit account in a bank for 2 years at 6% per annum simple interest. If the gets 1200 as interest at the time of maturity, then find (a) The monthly installment. (b) The amount of maturity. [4] ________________________________________________________________________________ KISA PREPARATORY_ MATHEMATICS 6 of 10 ii) Two taps running together can fill a tank in 3 1 13 hours. If one tap takes 3 hours more than the other to fill the tank alone then how much time will each tap take to fill the tank? [4] iii) Find the equation of the line PQ in the figure, [5] where P and Q being the mid-points of the parallel sides AD and BC respectively where A(2,-4), B(2,5),C(-6,3),D(-4,6). Also check whether PQ is perpendicular to BC. [5] SECTION - B (40 Marks) (Attempt any four the questions from this section) Question 4 i) Two tangents PA and PB are drawn to a circle with centre O from an external point P. [3] Prove that APB = 2 OAB 2 ii) Solve the quadratic equation 3( + 3) = 0,give your answer correct to two [3] significant figures. iii) In the figure,ABC is a right angled triangle with BAC=90 , [4] Prove that (a) ADB CDA (b) If BD=18 cm,CD= 8 cm,find AD. (c) Find the ratio of area of ADB to area of CDA Question 5 i) Construct a pair of tangents to a circle of radius 4cm when the angle between the tangents is 60 . 7 + 2 [3] 5 ii) If 7 2 = 3 , use the properties of proportion to find (a) : (b) 2 2 2 2 + [3] iii) Find three numbers in GP such that their product is 729 and the sum of the first and the third is 30. [4] _____________________________________________________________________________________ KISA PREPARATORY_ MATHEMATICS 7 of 10 Question 6 i) Rishab invests 4,500 in 8%, 10 shares at 15. He sells the shares when the price rises to 30, and invests the proceeds in 12% 100 shares at 125. Calculate: (a) the sale proceeds. (b) the number of 125 shares he buys. (c) the change in his annual income from dividend [3] ii) The tangents TA and TB are drawn to the circle with centre O. The diameter BC and tangent TA, when produced, meet at D. Given that ABC = 24 , calculate the values of x, y and z. [3] 2 iii) The sum of the first n terms of an AP is given by = (3 ).Find its (a) first term and (b) common difference (c) nth term (d) 20th term [4] Question 7 (i) Use graph sheet for this question.Take 2 cm = 1 unit along the axes. Plot the OAB, where 0 (0,0), A (3,-2), B (2,-3). (a) Reflect the OAB through the origin and name it as OA'B' (b)Reflect the OA'B' on Y- axis and name it as OA"B" (c )Reflect the OA'B' on X- axis and name it as OA'''B''' (d) Join the points AA"B"B'A'A'''B'''B and give the geometrical name of the closed figure so formed. (ii)The following distribution represents heights of 160 students of a school [5] Height (in cm) 140-145 145-150 150-155 155-160 160-165 165-170 170-175 175-180 No . of students 12 20 30 38 24 16 12 8 Draw an ogive for the given distribution taking 2 cm = 5 cm of height on one axis and 2 cm = 20 students on the other axis. Using the graph, determine: [5] ________________________________________________________________________________ KISA PREPARATORY_ MATHEMATICS 8 of 10 (a) The median height. (b) The interquartile range. (c) The number of students whose height is above 172 cm. [5] Question 8 2 i) Prove that 1 + +1 = 2 [3] ii) Find k so that the point P (-4, 6) lies on the line segment joining A (k, 10) and B (3, -8). Also, find the ratio in which P divides AB [3] iii) For the given histogram,construct the frequency distribution table and hence find the mean [4] by step deviation method. Question 9 i) Solve the given inequation and graph the solution set on numberline: [3] ii) Using ruler and compasses only,construct ABC=120 ,where AB=BC=7cm. (a) Mark two points D and E which satisfy the condition that they are equidistant from both BA and BC and D is equidistant from B and C as well. (b) In the above figure join DA and DC and name the figure ABCD. [3] iii) From a solid right circular cylinder with height 12 cm and radius of the base 5 cm, a right circular cone of the same height and the [4] same base radius is removed. Find the volume and total surface area of the remaining solid. [Use = 3.14] ________________________________________________________________________________ KISA PREPARATORY_ MATHEMATICS 9 of 10 Question 10 i) Cards numbered from 11 to 60 are kept in a box. If a card is drawn at random from the box, find the probability that the number on the drawn card is (a )Divisible by 4 or 6 (b) Multiple of 2 and 5 (c) Factors of 60 [3] ii)Two people standing on the same side of a tower in a straight line with it, measure the angles of elevation of the top of the tower at 25 and 50 respectively. If the height of the tower is 70m, find the distance between the two people. [3] iii) In the given figure, AB = 7 cm and BC = 9 cm. (a) Prove ACD ~ DCB. (b) Find the length of CD. [4] **** ALL THE BEST **** ________________________________________________________________________________ KISA PREPARATORY_ MATHEMATICS 10 of 10

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