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KARNATAKA ICSE SCHOOLS ASSOCIATION ICSE STD. X Preparatory Examination 2025 Subject Mathematics Maximum Marks: 80 Duration: 3 Hours Date: 07.01.2025 General Instructions 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 are provided Instruction for the invigilator Kindly read aloud the Instructions given above to all the candidates present in the Examination Hall. KISA PREPARATORY_MATHEMATICS 1 of 8 SECTION A (Attempt all questions from this section) Question 1 Choose the correct answer to the questions from the given options: (Do not copy the question, write the correct answers only.) [15] (i) ) If 73 is the nth term of the arithmetic progression 3,8,13,18 then n is (a) 13 (b) 14 (c) 15 (d) 16 (ii) If 7m+2n 7m 2n = 5 3 then m: n is (a) 7:8 (b) 2:7 (c) 1:8 (d) 8:7 (iii) A man invests 24,000 on 60 shares at a discount of 20%. If the dividend declared by the company is 10% then his annual income is (a) 2880 (b) 1500 (c) 3000 (d) 5000 (iv) One of the following point is invariant with respect to the line y = 4 (a) (3, 4) (b) (3, -4) (c) (4, 3) (d) (-3, 4) KISA PREPARATORY _MATHEMATICS 2 of 8 (v) If xY = . The order of the matrix Y is (a) 2 x 2 (b) 1 x 2 (c) 2 x 1 (d) 1 x 1 (vi) The sum of the probability of an event and its complementary is (a) 0 (b) 1 (c) < 1 (d) > 1 (vii) In a recurring deposit account, Virat deposits 500 per month for 24 months,if the interest he earns is one-tenth of his total deposit, the rate of interest is (a) 4.8% (b) 9.6% (c) 7.2% (d) 3.2% (viii) In the adjoining figure, O is the centre of the circle and AB is a tangent to it at point B. If BDC = 65 then BAO is (a) 50 (b) 25 (c) 65 (d) 40 (ix) (sin + cos ) (tan + cot ) = (a) sec + cosec (b) sec + cos (c) sec (d) cosec KISA PREPARATORY_MATHEMATICS 3 of 8 (x) The number of solid spheres, each of diameter 6 cm, that can be made by melting a solid metal cylinder of height 45 cm and diameter 4 cm, is (a) 2 (b) 4 (c) 5 (d) 6 (xi) Quadrilateral ABCD is circumscribed to a circle. If AB=6 cm, BC=7 cm, and CD= 4 cm then the length of AD is (a) 3cm (b) 4cm (c) 6cm (d) 7cm (xii) In the given figure, BAC = 90 and AD BC. Then, (a) = 2 (b) = 2 (c) = 2 (d) = 2 (xiii) Sourav purchases an article for 5,310 which includes a discount of 10% on the marked price and 18% GST on the selling price. The marked price of the article is (a) 4,200 (b) 5,000 (c) 5,500 (d) 5,900 KISA PREPARATORY_MATHEMATICS 4 of 8 (xiv) When 2x 3 3x 2 + ax 9 is divided by (x+3), the remainder is 6, then the value of a is (a) 4 (b) -8 (c) -7 (d) -32 (xv) Assertion(A):Given two straight lines 3x 2y = 5 and 2x + ky + 7 = 0 are perpendicular to each other when value of k =3 Reason(R): If AB and CD are two mutually perpendicular lines and their inclination be and respectively then tan = cot (a ) Assertion(A) is true but reason(R) is false. (b) Assertion (A) is false but reason(R) is true. (c) Both assertion (A) and reason(R) are true and reason(R) is the correct explanation of assertion (A). (d) Both assertion (A) and reason(R) are true and reason(R) is not the correct explanation of assertion (A). Question 2 (i) Solve 1 = 3 0 and give your answer correct to two decimal places. (ii) Find the number of terms of a GP whose first term is 3 4 [4] , common ratio is 2 and the last term is 384 and find their sum. (iii) Find the value of x, which satisfies the given inequation and graph the solution set on number line: 5 3 2x 1 < 3, x W 6 2 3 Question 3 [4] [4] (i) A piggy bank contains hundred 50-p coins, fifty 1 coins, twenty 2 and ten 5 coins. If it is equally likely that one of the coins will fall out when the bank is turned upside down, find the probability the coin falling out will be (a) a 50-p coin, (b) of value more than 1, (c) of value less than 5 (d) a 1 or 2 coin. [4] KISA PREPARATORY_MATHEMATICS 5 of 8 (ii) A vessel is in the form of a hemispherical bowl mounted by a hollow cylinder of negligible thickness. The diameter of the hemisphere is 14 cm and the total height of the vessel is 13 cm. Find (a) the capacity of the vessel. (b) the inner surface area of the vessel. [4] (iii) Plot points A(0,4),B(1,2),E(0,1),C(3,3),H(3,0) and reflect B,C,H in the Y axis to D,F,G respectively and reflect E in the X axis to J.Write the coordinates of reflected points. Join A,B,E,D,A and also E,C,H,J,G,F,E in order and name the geometrical figures separately. Take scale as 2 cm = 1 unit on both the axes. [5] SECTION B (Attempt any four questions from this Section.) Question 4 (i) Find x and y if: [3] (ii) Rohit deposits a certain sum of money every month in a recurring deposit account for 2 years. If the bank pays interest at 10% p.a. and Rohit receives 66,250 as the maturity value of the account, what sum of money did he pay every month? [3] (iii) Use ruler and compasses only for this question. (a) Construct ABC, where AB = 3.5 cm, BC = 6 cm and ABC = 60 . (b) Construct the locus of points inside the triangle which are equidistant from BA and BC. (c) Construct the locus of points inside the triangle which are equidistant from B and C. (d) Mark the point P which is equidistant from AB, BC and also equidistant from B and C. Measure and record the length of PB. [4] Question 5 (i) SGST on an AC is 14% and the price of the AC including GST is 57,600. What is the (a) rate of GST? (b) price of AC before GST? (c) amount of GST [3] (ii) The distance between Mumbai and Pune is 192 km. Travelling by the Deccan Queen, it takes 48 minutes less than another train. Calculate the speed of the Deccan Queen if the speeds of the two trains differ by 20 km/hr. [3] (iii) The horizontal distance between two towers is 120 m.The angle of elevation of the top and the angle of depression of the bottom of first tower as observed from the top of second tower are 30 and 24 respectively. Find the height of the two towers and give your answer to three significant figures. [4] KISA PREPARATORY_MATHEMATICS 6 of 8 Question 6 (i) In the given figure, PQ is a tangent to the circle at A. BD is a diameter and O is the centre. If ADB = 30 and DBC = 60 , find : (a) QAB (b) PAD (c) CDB [3] (ii) Find the sum of first n terms of an AP whose nth term is (5n-1).Hence, find the sum of the first 20 terms. [3] (iii) Use remainder theorem to factorise the expression 2x 3 + 9x 2 + 7x 6. Hence solve the equation 2x 3 + 9x 2 + 7x 6 = 0. [4] Question 7 (i) Prove that (sin + cosec )2 + (cos + sec )2 = 7 + tan2 + cot2 (ii) If x+2 + x 3 x+2 x 3 [3] = 5, Use the properties of proportion and solve for x. [3] (iii) The weight of 50 apples were recorded as given below .Calculate the mean weight, to the nearest gram, by step deviation method. Weight in grams 80-85 85-90 90-95 95-100 100-105 105-110 110-115 [4] No.of apples 5 8 10 12 8 4 3 Question 8 (i) In the given figure, O is the centre of two concentric circles with radii 7 cm and 15 cm. If AP and BP are tangents to the circles and AP = 20 cm, find the length of BP. [3] (ii) 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 25 cm. (b) If the open area of loading of the truck is 90 m2 , find the same area of the model in cm2 . (c) If the volume of the model is 7500 cm3 ,find the volume of the truck in m3 . [3] (iii) Points A and B have coordinates (7, 3) and (1,9) respectively.Find (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 perpendicular bisector. KISA PREPARATORY_MATHEMATICS [4] 7 of 8 Question 9 (i) Use graph paper for this question. The marks obtained by 100 students in an English test are given below. Marks 0-10 10-20 No.of students 5 9 20-30 30-40 12 14 40-50 50-60 60-70 70-80 80-90 90-100 20 16 11 6 4 3 Draw the ogive and estimate (a) the median marks. (b) the number of students who did not pass the test if the pass percentage was 50. (c) the upper quartile marks.(Take 2 cm = 10 units on both the axes) [6] (ii) Using ruler and compass construct a triangle ABC in which AB=6 cm, ABC = 120 and BC=5 cm.Construct a circle passing through A,B and C.Measure and write down the radius of the circle. [4] Question 10 (i) In ABC, DE BC. If area of ADE: area of DBCE = 9: 16, find the ratio of AD: DB. [3] (ii) Find the ratio in which the point (3, b) divides the segment joining the points A (7, 1) and B (0, 8). Find the value of b. [3] (iii) Surya invests 4500 in 8%, 10 shares at 15.He sells the shares when the price rises to 30 and invests the proceeds in12% 100 shares at 125.Calculate (a) the sale proceeds (b) the number of 125 shares bought by Surya. (c) the change in the annual income. [4] KISA PREPARATORY_MATHEMATICS 8 of 8
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