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ICSE Class X Question Bank 2025 : Mathematics

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ST. FRANCIS XA VIERSCHOOL Rehearsal Examination (2024 2025) SUBJECT - MATHEMATICS CLASS-X (Three hours) The time given at the head of this paper is the time allowed for writing the answers. Students should write the Answers in the Test Copies. All working. including rough work, must be clearly shown and must be done on the same page 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 []. TIME: 3 Hrs FULL MARKS: 80 Section A(Attempt All Questions) Question 1 (a) If r, 8, 16, q are in continued proportion, then the value of q +ris (i) (b) [15 x 1= 15] 26 (i ) 66 (i ) 36 (iv) 48 If in two triangle DEF and P R ZD = 2Q and ZR= ZE then, which of following is not true: EF DF PR Po (ii DE FE PO RP (iii) DE QR DF PQ (iv) EF DE RE OR IfA =[3 -2), B= Assertion (A): Product of AB of two matrices A and B is possible. Reason (R): Number of column of matrix is equal to number of row in matrix B. A is true R is false A is false R is true (i) (ii) (i ) Both A and R are true, R is correct reason of A. Both A and R are true, R is incorrect reason for A (iv) (d) cos A The value of 1- tan A+ (i) (e) (ii) (ii ) (h) cos A + sin A (iii) 1+ sin A (iv) 1+ cosA sin A 200 400 550 70 (iv) If a well of radius 4 m has been dug to depth of 14 m then volume of earth dug out is: (iv) 2816 m3 (i ) 704 m (i ) 1408 m (i) 352 m If the ntn term of an A.P. is given by a, = 2n+1, then the sum of first n terms of the A.P is (ii ) n(n + 1) (iv) n(n- 1) n(n-2) (i ) n(n + 2) A dealer in Sikkim sells goods to a consumer in Sikkim worth 80,000. If the rate of GST is 12%, the SGST to be paid is (i) (i) (i ) In the adjoining diagram, O is the centre of the circle and PT is a tangent. The value of x is: (i) (t) 1+ cos A sinA sin A - cos A Z9600 (i ) 6400 (ii ) 2400 (iv) Z4800 (iv) {0, 1} Given x +2<+3 and x is a prime number. The solution set for xis: 3 (i ) {0) (ii ) {1) What must be subtracted from the polynomial +-2x +1, so that the result is exactly divisible by (r-3)? (k) (ii ) 30 -31 30 (iv) 31 (i ) The points which divides the line segment joining points (7, - 6) and (3, 4) in ratio 1:2 internally lies in: Iquadrant () (ii) II quadrant along. The same horizontal line is: 600 (i ) 450 (i) (m) (ii) III quadrant (iv) IVquadrant A light house is 80 m high, the angle of elevation of its top from point 80 m away from its foot (ti) 30 (iv) 900 10 cards are marked with the numbers 1to 10, and then one card is picked up. What is the probability that the card is an odd prime number ? i) 0.6 (ii) 0.5 (iii) 0.4 (iv) 0.3 1 (n) The median of the following observations arranged in ascending order is 64. Find the value of x: 27, 31, 46, 52, x, x+4, 71, 79, 85, 90 60 (o (ii) 62 (ii) 61 (iv) 66 By purchasing 25 gas shares from 40 each a man gets 4% profit on his investment. What rate percent is the company paying ? 6.04% (i) Question 2 sin A (a) Prove that : secA + tan (b) (C) 6.4% (i ) (iii) 6.004% (iv) 60.4% [4 +4 +4 = 12] cos A A-1 Given A=? .B= 10.5 cm, -=1. cosec A+ cotA -1 find4-2AB +B . 1 28 cm From a solid wooden cylinder of height 28 cm and diameter 6 cm, two conical cavities are hollowed out, the diameter of cones are also 6 cm and height 10.5 cm. Find volume and total surface area of remaining solid. 10.5 cm 6 cm Question 3 (a) In the given figure TP and TO are two tangents to the [4 +4+5= 13] circle with centre O, touching at A and C respectively. If ZBCQ = 55 and ZBAP = 60 , find : (i) 2OBA and zOBC, (i) ZAOC (iii) 2ATC. (b) In an arithmetic progression the fourth and sixth terms are 8 and 14 respectively. Find the: (i) first term, (ii) common difference, (iii) sum of first 20 terms. (c) Use graph paper for the following questions: (Take lcm = lunit on both axis) : (1) Plot following points: A(4, 4), B(4, -6), C(8, 0) the vertices of triangle ABC. (ii) Reflect ABC on y - axis and name them A', B',C'. (iii) Write the coordinates of the images A', B' and C'. (iv) Give a geometrical name for the figure AA'C'B'BC. (v) ldentify the line of symmetry of AA'C'B'BC. Section B(Attempt any 4 Questions) Question4 Solve for x, using properties of (a) [3+3+ 4= 10] V2+x+V3-* proportion:+-3-. (b) Cards numbered 2 to 101 are placed in a box. A card is selected at random from the box. A card is (c) selected at random from the bOx, find the probability that the card selected : (i) hasa number which is a perfect square. (ii) has an odd number which is not less than 70. By using ruler and compasses only, construct a quadrilateral ABCD in which AB = 6.5 cm, AD = 4 cm and DAB = 75 . C is equidistant from the sides Ab and AD, also C is equidistant from the points A and B. [3+3+ 4= 10] Question5 (a) A solid sphere of radius 15 cm is melted and recast into solid right circular cones of radius 2.5 cm and height 8 cm. Calculate the number of cones recast. (b) In a GP the first term is 24 and fifth term is 8. Find the 9th term and sum of 5 terms of the G.P. (C) Ashopkeeper purchases a certain number of booksfor 960. Ifthecost per book was 8 less, the number of books that can be purchased for 960 would be 4 more. Write an equation, taking the original cost of each book to be x, and solve it. [3+3 +4= 10] Question6 (a) The daily pocket expenses of 200 students in a school are given below: Pocket expense (in )0-5 5-10 10-15 15-20 20-25 25-3030-35 35-40 No of students 10 14 28 42 50 30 14 12 Draw a histogram representing the above distribution and estimate the mode from the graph. (b Solve the quadratic equation and give the answer correct to 2 decimal places: 4x' - 5x-3 = 0. (c) [4 GivenM=61. State (i)the order of matrix M(i) the matrix M. [3 +3+4= 10] Question 7 (a) The following bill shows the GST rate and the marked price of articles : Rajdhani Departmental Store Item (i) Marked Price 1200 286 Z500 Discount Rate of GST 12% Dry Fruits (1 kg) Nil 5% (ii) Packed Wheat flour (5kg) 10% 12% (iii) Bakery products Find the total GST and the amount paid (including GST) for the above bill. (b (c) A Find the equation of a line passing through the midpoint of A(-4, 6) and B(8, -3) and parallel to the line 6x + 10y + 7 = 0. ABC is right angled triangle with ZABC =90. D is any point on AB & DE is perpendicular to AC. () Prove that A ADE ~ A ABC. (ii) If AC= 13 cm, BC = 5 cm, AE = 4 cm, find DE and AD. D (i i) Find area of AADE:area of quadrilateral BCED. B [3 +3+4= 10] A man invests 4500 in shares of acompany which is paying 7.5% dividend. If Z100 shares are Question 8 (a) available at a discount of 10%, find (i) number of shares (ii) his dividend. (b) Solve the following inequation and write down the solution set. Represent it on the number line. -3+xsx+ 2<+2x,x ER. (c) Using ruler and compass construct a A ABC in which AB = 6 cm, LBAC = 120 and AC= 5 cm. Construct a circle passing through A, B and C. Measure and write down the radius of the circle. A A [3+3+4= 10] Question 9 (a) (b) (c) Rekha opened a recurring deposit account for 20 months. The rate of interest is 9% p.a. and Rekha receives 2441 as interest the time of maturity. Find the amount she deposited each month. If 2x 1 is a factor of both 6x + ax - 4 and bx? 11x +3, find a and b. Hence factorize them completely. In the given figure, O is the centre of the circle. Prove that x + y= z. (5 + 5 = 10] (90,11 Question 10 a) 120f Study the graph and answer each of the following:(Xaxis represent the marks obtained by students in an examination, Y axis represents the number of students) TA00,113) (100,120) 110 a.107) 100 () name the curve plotted, (ii) find the total H6o,96) 90 number of students, (ii ) find the lower quartile, e (iv) find the number of students who obtained Ks0,78) 70 more than 75% marks in the test, (v) find the number of students who did not pass in the test if the pass percentage was 40. (b) From the top of a tower 100 m high a man observes the angle of depression of two ships A P. 30,) and B, on opposite sides of the tower as 45 and 38 respectively. If the foot of the tower and the ships are in the same horizontal line find the distance between two ships A and B to the nearest metre. (10,5) R: ZC 10 20 30 40 60 Marke 60 70 40 90100

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