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ICSE Class X Prelims 2025 : Mathematics

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Maximum marks : 80 Time allowed : Three hours Answer 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 answers. Omission of essential working will result in loss of marks. The intended marks for questions or arts of questions are given in brackets [ ] SECTION A (Attempt all questions from this Section) Question 1 Choose the correct answers to the questions from the options given below. [15] (i) What is the remainder, if we divide 6x3 + x2 2x +4 by x 2? a. 48 b. 52 c. -26 d. 24 (ii) Deepali deposited Rs 100 per month for 12 months in a bank s recurring deposit account. If the bank pays interest at the rate of 9% per annum, then the total amount deposited by Deepali during this period is: a. Rs. 1200 b. Rs. 2400 c. Rs. 1500 d. Rs. 1800 (iii) In the given figure, O is the center of the circle. If SPQ = 60 and PQR =82 , then find RTQ S P R O Q T a. 104 b. 52 c. 75 d. None of these (iv) In the figure given below, PQ is a chord of a circle and PT is the tangent at P such that QPT = 60 . Then PRQ is equal to: Q O R T P a. 135 b. 150 c. 120 d. 110 (v) Yuvaan sitting in an aeroplane observes that the angle of depression of two temples 4km apart are 45 each. If the aeroplane is exactly above the midpoint of the line joining the temples, find the height: a. 1km (vi) b. 1.5 km c. 2 km d. 3 km If a sector of a circle is folded to make the two radii coincide, the surface so formed is 1. Hollow right circular cone 2. Hollow right circular cylinder Which of the following statement is valid? a. only 1 (vii) b. only 2 c. b o t h 1 an d 2 d . n e i th e r 1 n or 2 The mean of the following distribution is : Height in cm 15 18 20 22 25 30 No. of sticks 10 15 10 8 7 10 a. 21.18 b. 21.36 c. 21.54 d. None (viii) A fruit box contains 8 mangoes, 4 apples and 3 melons. One fruit is drawn at random. What is the probability that the fruit drawn is melon or apple? a. (ix) 4 b. 15 2 7 Assertion: Let A = [ 3 ] 5 3 7 c. 15 15 and B = [ 14 8 d. 15 6 ] , if 2A = B, then m=7 and n =3 + Reason: Two equal matrices have the same order and their corresponding elements are also equal 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 of A d. Both A and R are true, and R is incorrect reason for A (x) (xi) (xii) (xiii) (xiv) (xv) If 3A = 4B = 6C, then A : B : C is: a. 5 : 3 : 2 b. 4 : 1 : 2 c. 4 : 5 : 2 d. 4 : 3 : 2 The printed price of an article is Rs.3080. If the rate of GST charged is 10% then the GST charged is : a. Rs. 154 b. Rs 308 c. Rs. 30.80 d. Rs. 15.40 By purchasing Rs 25 shares for Rs. 40 each a man gets 4% profit on his investment. What rate of dividend is the company paying? a. 6.04% b. 6.004% c. 6.4% d. 60.4% The equation x2 + 2x + 1 = (4+kx)2 + 3 will be quadratic, if the value of k is : a. 1 b. k 1 c. any number d. Insufficient data The equation of a line passing through the point ( -2, 3) and having x-intercept 4 units is: a. x + 2y = 8 b. x + 2y = 4 c. 2x + y = 8 d. x+y+4 = 0 The solution set of the following inequation is : 2 3x + 5 < 13 when x Z a. {-1,0,1,2,3} b. {0,1,2,3} c. {0,1,2} d. {-1,0,1,2} Question 2 (i) Find the value of a and b such that the polynomial x3 ax2 13x + b has (x -1)(x -3) as factor. (ii) In the given figure, ABC is a triangle and BC is parallel to the y-axis. AB and AC intersects the y-axis at P and Q respectively. Y B( -2,3) [4] [4] 2 D -2 X -1 P 0 -1 -2 1 2 3 4 A X Q(0, -3) C(-2,-4) Y a. Write the co-ordinates of A b. Find the equation of line AC c. Find the ratio in which Q divides AC In the given figure , PQ is the tangent to the circle at A. AB and AD are bisectors of CAQ and PAC respectively. If BAQ = 30 . Prove that : a) BD is the diameter of the circle b) ABC is an isosceles triangle. (iii) [4] C D B P A Q Question 3 i. The sum of first three terms of a G.P. is 16 and the sum of next three terms is 128. Determine the sum of n terms of the G.P. [4] ii. A solid toy is in the form of a hemisphere surmounted by a right circular cone. The height of the cone is 2 cm, and the diameter of the base is 4 cm. Determine the volume of the toy. If a right circular cylinder circumscribes the toy, find the difference between the volumes of the cylinder and the toy. (Take = 3.14) [4] iii. Study the graph and answer the following questions: [5] (a) Write the co-ordinates of A and B (b) A and B are reflected in the x-axis to A and B respectively. Write the co-ordinates of A and B (c) Name the geometrical figure ABB A ; (d) Measure the angle ABB ; (e) The image of A of A, when A is reflected in the origin. Name the single transformation that maps A to A . SECTION B (Attempt any four questions from this Section) Question 4. (i) Mr. Roy invests Rs 7,500 on buying shares of face value of Rs 100 each at a premium of 50% in a company. If he earns Rs 550 at the end of the year as dividend, find: (a) The number of shares he has in the company (b) Dividend percentage per share [3] (ii) [3] Find the values of x which satisfy the given inequation.Represent the solution set in number line. 1 -2 2 (iii) 2 3 15 , 6 x N. Prove the following trigonometry identity: tan +sec 1 tan sec +1 = sec + tan . [4] Question 5. (i) In the given figure o is the center of the circle. If = 100 and = 40 , find (a) ADC (b) DAC (c) ODA (ii) [3] Mrs. Reena has a cumulative deposit account of Rs 400 per month at 10 percent per annum simple interest. If she gets Rs 30,100 at the time of maturity, find the total time for which the account was held. [3] (iii) [4] Using step deviation method find mean for the following frequency distribution: Class 20-30 Frequency 10 30-40 6 40-50 8 50-60 12 60-70 5 70-80 9 Question 6. (i) The vertices of a PQR are P(0,5) , Q(-1, -2) and R (11,7). Write down the equation Of RQ. Also find : (a) The equation of the line through P and perpendicular to QR. (b) The co-ordinates of the point A, when the perpendicular through P as obtained in (a) meet QR. [3] (ii) In the given figure PQ is a diameter PS is a chord of the circle such that QPS = 30 . The tangent at S intersects PQ produced at R. Find: (a) SQP (b) SRQ (c) Show that QS = QR . [3] (iii) [4] Mrs. Malhotra brought the following articles from a departmental store: S. No 1 2 Item Ceramic cookware Cashew nuts Price Rs 1,200 Rs 600 Rate of GST 18% 12% Discount Rs. 100 Nil Find: (a) Total GST paid. (b) Total Bill amount including GST. Question 7. (i) The angle of elevation of the top of a hill from the foot of a tower is 60 and its angle Of elevation of the top of the tower from the foot of the hill is 30.If the tower is 20 m high find: (a) Height of the hill (b) Distance between the hill and the tower. [5] (ii) [5] The weight of 50 workers is given below: Weight(kg) No of workers 50-60 4 60-70 7 70-80 11 80-90 14 90-100 6 100-110 5 110-120 3 Draw an ogive of the given distribution using a graph sheet. Take 2 cm = 10 kg on one axis and 2 cm = 5 workers along the other axis. Estimate the following : (a) Upper and Lower quartiles . (b) If weighing 95kg and above is considered overweight, find the number of workers who are over weight. Question 8. (i) Two dice are thrown simultaneously. What is the probability of getting: (a) 9 as the sum of the two numbers that turn up? (b) A doublet? [3] (ii) Solve for x : [3] +4+ 10 +4 10 5 =2 (iii) A metallic cylinder has radius 3 cm and height 5 cm. It is made of metal A. To reduce its weight a conical hole is drilled in cylinder as shown and is completely filled with a 3 8 lighter metal B. The conical hole has a radius 2 cm and depth 9 cm. Calculate the ratio of the volume of the metal A to the volume of metal B in the solid. [4] Question 9. (i) A mathematics aptitude test of 50 students was recorded as follows: Marks No. Of students 50-60 4 60-70 8 70-80 14 80-90 19 [3] 90-100 5 Draw a histogram of the above data and locate the mode. (ii) The product of first three terms of a GP is 1000. If 6 is added to its second term and seven Added to its third term, then the terms become in AP. Find the GP. [3] (iii) Find the value of m in terms of p and q such that the quadratic equation 2 2 ( ) + 2( 2 - 2 )x + m = 0 has equal roots and p q. [4] Question 10. (i) A bus covers a distance of 240 km at a uniform speed. Due to heavy rain, its speed gets gets reduced to 10 km/hr and it takes 2 hours longer to cover the total distance. Assuming the uniform speed to be x km/hr, form a quadratic equation and solve it to find the value of x. [3] (ii) 2 0 1 0 Given A =[ ] and I = [ ] and A2 = 9A+ mI. Find m. 1 7 0 1 [3] (iii) Use ruler and compasses for the following question. All construction lines and arcs should be clearly shown and be of sufficient length and clarity to permit assessment. [4] (a) (b) (c) (d) Construct , in which BC =8 cm , AB = 5 cm , = 60 . Construct the locus of points inside the triangle which are equidistant from BA and BC. Construct the locus of points inside the triangle which are equidistant from B and C. Mark as P , the point which is equidistant from AB, BC and equidistant from B and C.

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