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ICSE Class X Prelims 2025 : Mathematics (Mount Carmel Convent Anglo-Indian Girls High School (MCC), Tangasseri, Kollam)

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Pre Board-1 2024-25 Grade: 10 Max. Marks:80 Subject: Mathematics Duration: 3 Hours Date: Answers to this paper must be written on the answer sheets 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. This paper contains 09 printed sheets All the questions in SECTION A are to be attempted. Attempt any 4 Question from SECTION B The intended marks for questions or parts of questions are given in brackets [ ] SECTION A (40 Marks) Attempt all questions from this section Question: 1 [15] Choose the correct answers to the questions from the given options. (i) Polynomial x3 2x2 + ax + 12 when divided by (x + 1) leaves a remainder 20, then a is: (a) 31 (ii) (b) -11 (c) 11 (d) None Mohit opened a recurring deposit account in a bank for 2 years. He deposits Rs. 1,000 every month and receives 25,500 on maturity. The interest he earned in 2 years is: (a) Rs.13500 (b) Rs. 3000 (c) Rs. 24000 (d) Rs. 1500 (iii) In the given figure, PQR is a triangle right angled at Q and XY || QR. If PQ = 6 cm, PY = 4 cm and PX : XQ = 1: 2. The length of PR will be P X Y Q R (a) 10 (iv) (b) 12 (d) None In the circle with centre O, if = 20 what is the value of angle (a) 30o (v) (c) 15 Given that sin = (a) 0o (b) 70o 3 2 (c) 60o (d) 50o and cos = 0, then the value of is (b) 90o (c) 60o (d) 30o (vi) A right circular cylinder is filled with water. The water is then poured into another cylinder with half the height and twice the radius of the original cylinder. Statement 1: The volume of water in the new cylinder will be equal to that in the original cylinder. Statement 2: The surface area of the new cylinder is greater than that of the original cylinder. Which of the following is valid? (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. (vii) The mean weight of 9 students is 25 kg. if One more student is joined in the group the mean is unaltered, then the weight of the 10th student is (a) 25 kg (viii) (b) 24 kg (d) 23 kg A girl calculates that the probability of her winning the first prize in a lottery is 0.08. If 6000 tickets are sold, then how many tickets has she bought? (a) 40 (ix) (c) 26 kg (b) 240 (c) 480 (d) 750 Assertion: If A and B are square matrices of order 2, then AB = BA is not always true. Reason: Matrix multiplication is associative. (a) Both assertion and reason are correct and reason is the correct explanation of assertion. (b) Both assertion and reason are correct but reason is not the correct explanation of assertion. (c) Assertion is correct but reason is incorrect. (d) Assertion is incorrect but reason is correct. (x) The table shows the values of x and y, where x is proportional to y x y 6 M 12 18 What are the values of M and N? (a) M = 4, N = 9 (b) M = 9, N = 3 (c) M = 9, N = 4 N 6 (d) (xi) M = 12, N = 0 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: (a) Rs.15 (xii) (b) Rs.30 (c) Rs.150 (d) Rs.165 Sachin buys 1120 shares at Rs. 52 per share and gets dividend of Rs. 1456 then rate of return is: (a) 1.5% (b) 5% (c) 2.5% (d) 2% (xiii) The equation x2 + 2x + 1 = (4 kx)2 + 3 will be quadratic, if the value of k is: (b) k 1 (a) k = 1 (c) Any number (d) Insufficient data (xiv) Select the equation of a straight with slope -2 and which intersects x-axis at a distance of 3 units to the left of origin. (a) 2x y -6 = 0 (b) 2x + y + 6 = 0 (c) 2x y 3 = 0 (d) 2x y + 3 = 0 (xv) If 2 1 2 (a) 15 4 2 , 3 , then the largest value of x is: (b) 4 (c) 3 (d) None of these Question 2 (i) If (x 2) is a factor of 2x3 x2 px 2. a) Find the value of p. b) With the value of p, factories the above expression completely. (ii) In the given figure AC is parallel to x-axis [4] [4] (i) (ii) (iii) (iv) Find the equation of AC. If slope of AB = 2, find the equation of AB. Find the co-ordinates of A. Find the area of ABC. iii) In the given circle ABCD is a cyclic quadrilateral with centre O. Here OD || BC and 0 55 (i) Find . (ii) Find . (iii) Find . (iv) Find BDC. [4] Question 3 39 The sum of first three terms of a GP is (ii) A hemispherical and a conical hole is scooped out of a solid wooden cylinder. Find the [4] volume of the remaining solid where the measurements are as follows. The height of the solid cylinder is 7 cm, radius of each of hemisphere, cone and cylinder is 3 cm. Height of cone is 3 cm. Give your answer correct to the nearest whole number. 22 [Take = 7 ]. 10 and their product is 1. Find the common ratio and the terms. [4] (i) iii) Using a graph paper, plot the points A(6, 4) and B(0, 4). [5] a) Reflect A and B in the origin to get the images A' and B'. b) Write the co-ordinates of A' and B'. c) State the geometrical name for the figure ABA'B'. d) Find its perimeter. SECTION B (40 Marks) Attempt any 4 questions from this section Question 4 (i) A man invests Rs. 9,600 Rs.100 shares at Rs.80. If the company pays him 18% dividend, find (i) the number of shares, he buys, (ii) his total dividend. (iii) his percentage return on the shares. [3] (ii) Solve the following in equation and write down the solution set. [3] 11 8 < 15 + 4 13 + 12, Represent the solution on a real number line. (iii) Prove that tan 1 cot + 1 [4] = 1 + + cot Question 5 (i) In given triangle ABC, line PQ and BC are parallel. If AP: PB = 2:3, find the : (i) length of PQ, if BC= 7.5 cm. (ii) area of APQ : area of ABC. (iii) area of APQ: area of PBCQ. [3] (ii) Swamy deposited Rs.400 at the beginning of every month in a recurring deposit and received Rs.16398 at the end of 3 years. Find the rate of interest given by the bank. [3] (iii) If the mean of the following distribution is 7.5, find the missing frequency f. Variable Frequency 5 20 6 17 7 f 8 10 9 8 10 6 11 7 12 6 [4] Question 6 (i) The line segment joining A (2,3) and B(6, -5) is intersected by the x-axis at the point K. Write the coordinates of the point K. Hence, find the ratio in which K divides AB. [3] (ii) In the figure below, O is the centre of the circle and SP is a tangent. If SRT = 65 , find the values [3] of X, Y and Z. (iii) Prakash bought the following articles from a departmental store: S.No. 1. 2. Item Article A Article B Price Rs.4000 Rs.2400 Rate of GST 18% 5% [4] Discount 5% 5% Find the: (a) Total GST paid. (b) Total bill amount including GST. Question 7 (i) An aeroplane at an altitude of 250 m observes the angles of depression of two boats on the opposite banks of a river to be 45 and 60 , respectively. Find width of the river. Write the answer correct to the nearest whole number. [5] [5] (ii) The daily wages of 80 workers in project are given below: Wages (in Rs) 400 450 450 500 500 550 550 600 600 650 650 700 700 750 Number or workers 2 6 12 18 24 13 5 Use a graph paper to draw an ogive for the above distribution. (Use a scale of 2 cm = Rs. 50 on x-axis and 2 cm = 10 workers on y-axis). Use your ogive to estimate: (i) (ii) (iii) the median wage of the workers. the lower quartile wage of workers. the number of workers who earn more than Rs. 625 daily. Question 8 (i) Two unbiased coins are tossed simultaneously. Find the probability of getting: (i) at least one head, (ii) almost one head, (iii) no head. [3] [3] (ii) 6 is the mean proportion between two numbers x and y and 48 is the third proportional of x and y. Find the numbers. (iii) A sphere of diameter 12 cm, is dropped in a right circular cylindrical vessel, partly filled with water. [4] If the sphere is completely submerged in water, the water level into the cylindrical vessel rises by 3 5 9 cm. Find the diameter of the cylindrical vessel. Question 9 (i) Draw a histogram from the following frequency distribution and find the mode from the graph. Class Frequency (ii) [3] 0-5 2 5-10 5 10-15 18 15-20 14 20-25 8 25-30 5 In an AP of 50 terms, the sum of the first 10 terms is 210 and the sum of its last 15 terms is 2565. Find the AP. [3] (iii) A takes 6 days less than the time taken by B to finish a piece of work. If both A and B [4] together can finish it in 4 days, find the time taken by B to finish the work. Question 10 (i) (ii) (iii) Find the value of p for which the quadratic equation (p +1)x2 6(p +1)x +3(p+9) = 0, p 1 has [3] equal roots. Hence find the roots of the equation. 0 If A = [ 0 1 ], show that (aI + bA)3 = aI + 3a2bA where I is the unit matrix of order 2. 0 [3] Construct , = 6 cm, = 45 and perpendicular from A to BC is 3.5 cm. Construct a circumcircle of the triangle and write the steps of Construction. [4]

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