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ICSE Class X Prelims 2025 : Mathematics (Vasudev C. Wadhwa Arya Vidya Mandir (VCW AVM), Mumbai)

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ARYA VIDYA MANDIR GROUP OF SCHOOLS Std. X Math Date: 07/01/2025 PRELIMINARY REVIEW - January 2025 MATHEMATICS Marks: 80 Time: 3 hrs 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 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 the loss of marks. The intended marks for questions or parts of questions are given in brackets [ ]. This paper consists of eight printed pages. Section I (40 Marks) (Attempt all questions from this section) Question 1 A. Choose the correct answer to the following questions from the given options : i. A game of chance consists of spinning an arrow that comes to rest pointing at one [15] of the numbers 1,2,3,4,5,6,7 and 8 and these are equally likely outcomes. What is the probability that the arrow point lies on an odd number? (A) 1/2 ii. (B) 1/8 (C) 7/8 (D) 1/4 For an intrastate transaction, a shopkeeper paid 1800 in SGST. then the total amount of GST is __. A. 900 iii. B. 1800 C. 2700 D. 3600 If the replacement set is the set of real numbers, the solution set of the inequation x+3 8 < x-3 5 A. {x : x R; x > 13} C. { x : x R; x 13} B. {x : x R; x < 13} D.{ x : x R; x 13} ..2.. -2Cont Std X Mathematics Preliminary Review January 2025 iv. In the given figure , O is the centre of the circle. The value of x is A.55 v. B.125 D.50 Supriyo has a recurring deposit account in a post office for one and half years at 8% annum simple interest. If he gets 570 as interest at the time of maturity, find the monthly installment. A. 400 vi. C.27.5 B. 500 C. 600 D. 700 Which of the following is a row matrix of order 1 3 A.[2 4 5] vii B. C. D [ 1 3 5 6] Assertion (A): If f(x) is a polynomial and f(a)=0, then (x a) is a factor of f(x). Reason (R): A polynomial f(x) is divisible by (x a) if the remainder obtained by dividing f(x) by (x a) is zero. 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 viii. The roots of quadratic equation 5x2 4x + 5 = 0 are A. Real & Equal B. Real & Unequal C. Not real ix. D. Non-real and equal In PQR, a line joining point X on side PQ and point Y on side PR is parallel to side QR. If the ratio PY : YR is 3 : 5 and length PX = 7 cm, then the length of side PQ is: A. 14 cm B. 14.67 cm C. 18.67 cm D. 18 cm ..3.. -3Cont Std X Mathematics Preliminary Review January 2025 x. Consider the following frequency distribution table: The upper limit of the modal class is A.17 xi. B. 17.5 C.18 D. 18.5 If the centroid of a triangle formed by (4, a) , (b, -5) and (7, 8) is (3, 5), then the values of a and b are respectively: A. 2, 12 xii. B. 30 C. 60 D. 90 B. 137 C. 143 D. -143 The reflection of the point ( -3,0) in the origin is the point A.(0,-3) xv D. 13, -2 The 21st term of AP whose first two terms are -3 and 4 is: A.17 xiv C. 12, -2 The inclination of the line x- 3y + 2 3 =0 is A. 0 xiii B. -12, 13 B. (0,3) C. ( 3,0) D.(-3, 0) The ratio of diameter to height of a Borosil cylindrical glass is 3 : 8. If the actual diameter of the glass is 6 cm, then the curved surface area of the glass is : A.120 B.60 C.96 D.18 Question 2 a. [4] Find the matrix X, such that X = AB + B2 DC ..4.. -4Cont Std X Mathematics Preliminary Review January 2025 b. In the figure given below ED is the chord parallel to the diameter AC of the circle. If [4] CBE = 63 , Calculate DEC. c. Rahul deposited 600 per month in a recurring deposit account. The bank pays a simple interest of 12% p.a. Calculate the: [4] i. The number of monthly installments Amit deposits to get a maturity amount of 11826? ii. The total interest paid by the bank. iii. The total amount deposited by him. a. b. Question 3 Solve the given inequation and Represent the solution on the number line. A straight line passes through the points P(-1,4) and Q (5,-1) . It intersects the coordinate axes at points A and B .M is the midpoint of the segment AB. Find: i) The equation of line PQ ii) The co-ordinate of A and B. [4] [4] y-axis P(-1,4) B M A O x-axis Q(5,-1) ..5.. -5Cont Std X Mathematics Preliminary Review January 2025 c. Points A and B have coordinates (3, 4) and (0, 2) respectively. Plot the following images on the graph paper. [5] (a) A of A under reflection in the x-axis. (b) B of B under reflection in the line AA . (c) A of A under reflection in the y-axis. (d) B of B under reflection in the line AA . (e) coordinates of the point of intersection of A A and BB Section II (40 Marks) (Attempt any four questions from this section) a. Question 4 The data given below shows the marks of 12 students in a test, arranged in ascending order : [3] 2, 3, 3, 3, 4, x, x + 2, 8, p, q, 8, 9. If the given value of the median and mode is 6 and 8 respectively, then find the values of x, p, q. b. Akshay buys 350 shares of 50 par value of a company. The dividend declared by the company is 14%. If his return percent from the shares is 10%, find the market value of each share. [3] c. In the given figure ABC and AMP are right-angled at B and M respectively. Given AC = 10 cm , AP = 15 cm and PM = 12 cm. [4] i. Prove ABC and AMP are similar. ii. Find AB and BP. ..6.. -6Cont Std X Mathematics Preliminary Review January 2025 a. Question 5 Construct an ABC with BC = 6.5 cm, AB = 5.5 cm, AC = 5 cm. Construct the incircle of the triangle. Measure and record the radius of the incircle. b. The probability of selecting a blue marble and a red marble from a bag containing red, blue, and green marbles is and respectively If the bag contains 14 green [3] [3] marbles, then find the total number of marbles in the bag. c. The sum of the radius of the base and height of a solid right circular cylinder is 37 [4] cm. If the total surface area of the solid cylinder is 1628 sq. cm, find the volume of the cylinder. Question 6 a. Prove that, [3] b. If a,b,c,d are in continued proportion, prove that: (a2 + b2 + c2)(b2 +c2 + d2)= (ab + bc + cd)2 [3] c. The sequence 2, 9, 16, ..... is given. [4] (a) Identify if the given sequence is an AP or a GP. Give reasons to support your answer. (b) Find the difference between the sum of its first 22 and 25 terms. Question 7 a. b. ABCD is a parallelogram where A(x,y) B(5,8) C(4,7) and D(2,-4). Find i) The coordinates of A ii) The equation of diagonal BD Solve the following equation for z and give your answer correct up to two significant figures: 4z + 6 + 13 = 0 z [3] [3] ..7.. -7Cont Std X Mathematics Preliminary Review January 2025 c. The weight of 50 workers is given below: [4] weight in kg 50-60 60-70 70-80 80-90 90-100 100-110 110-120 no.of workers 4 7 11 14 5 6 3 Draw an ogive of the given distribution using a graph sheet. Use a graph to estimate the following : 1. The upper and lower quartiles. 2. If weighing 95 kg and above is considered overweight, Find the number of workers who are overweight. Question 8 a. A man invests 22,500 in 50 shares available at 10% discount. If the dividend paid by the company is 12%, calculate: (i) The number of shares purchased. [3] (ii) The annual dividend received. (iii) The rate of return he gets on his investment. Give your answer correct up to the nearest whole number. b. In the figure, not drawn to scale, TF is a tower. The elevation of T from A is x [3] where tan x = and AF = 200 m .The elevation of T from B , where AB= 80 m is y . Calculate: The height of the tower TF c. Prove that [4] ..8.. -8Cont Std X Mathematics Preliminary Review January 2025 Question 9 a. Find the ratio in which P(4, m) divides the line segment joining the points A(2, 3) [3] and B(6, -3). Hence, find m. b. Ram wishes to start a 200m2 rectangular vegetable garden. Since he has 50 m barbed wire, he fences three sides of the rectangular garden letting the compound wall act as the fourth side of the fence. Find the dimensions of the garden. [3] c. Construct a triangle ABC with AB = 5 5 cm, AC = 6 cm, and BAC = 105 . Hence (i) Construct the locus of points equidistant from BA and BC. [4] (ii) Construct the locus of points equidistant from B and C. (iii) Mark the point which satisfies the above two loci as P. Measure and write the length of the PC. Question 10 a. [3] 3 If x 2 is a factor of 2x 2 x px 2. (i) find the value of p (ii) with the value of p, factorize the above expression completely. b. A shopkeeper marked a pressure cooker at 1800. The rate of GST on pressure cooker is 12%. The customer has only 1792 with him and he requests the shopkeeper to reduce the price so that he can buy the cooker in 1792. What percent discount must the shopkeeper give? [3] c. 3080 cm 3 of water is required to fill a cylindrical vessel completely and 2310 cm3 of water is required to fill it upto 5 cm below the top . Find [4] i. radius of the vessel ii.height of the vessel iii.wetted surface area of the vessel when it is half filled with water. -----------------THE END---------------

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