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ICSE Class X Board Exam 2025 : Mathematics

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BRIGADE, BRILLIANT butterflies Transforming caterpillars into Date : 30.12.2024 Full Marks : 80 Class- X (ICSE) Time :3 hrs Mock Test- 2 Mathematics General Instructions: ) Answers fothis paper must be writen separately on the paper provided. ii) You will not be allowed to write during the first 15 minutes. ii)This time is to be spentfor reading the question paper. iv) The time given at the head of this paper is the time allowed for writing the answers. ) Section-Ais compulsory. Attempt any four questions from Section -B. vi) The intended marks for questions or parts of questions are given in brackets I. Section-A |40 marks! (Attempt all questions fromthis Section) Question 1:Choose the correct answer to the questions from the given options: |15] i) Dev bought an electrical fan which has a marked price of T800. Ifthe GST on the Goods is 7%, then the SGST is : b) Rs. 28 a) Rs. 24 c) Rs. 56 d) Rs. 80 ii)If-4x > 8y, then b) x > -2y a) x > 2y c) x <2y d) x < 2y i) Ten times the 10h term of an A.P. is equal to twenty times the 20h term of the same A.P. The 30h term of this A.P. is: c) 20 b) 40 a) 0 d) 2x (30 + 10) iv) Which of the following equations has imaginary roots? b) 2x- 5x +9= 0 a) x'+ 10x 3 =0 d) 5x' 8x-1 = 0 c) x+ 5x + 4= 0 = v) ABCD is a cyclic quadrilateral with AB||CD. ZBAD= 105 .Then LABC a) 105 vi) c)90 b) 75 sin A + sin? (90 - A) is equal to : a) -1 c) 2 b) 1 d)45 d)-2 Vi) (sec A - cos A)-(sec A + cos A) is equal to : d) -4 c)-2 a)4 b) 2 white and remaining are blue. A ball are 8 red, are 4 which of balls Viil) Abag contains 24 blue is : is drawn at random, the probability ofit to be d) 2 c) 1 b) 0.33 a) 0.5 80; the inter-quartile range is: iX) For numbers 10, 20, 30, 40, 50, 60, 70c)and d) 50 10 60 - 20 b)6030 a) 10 60 x) If2sin A= /3: then: 0 a) 2 cos A+ 1=0 b) 1- sin A= c) cos A =/3 d) 2cosA =1 model of the room is 96 The floor area ofa room is 96 m and area of the floor in the cm . The scale factor is : d) 1:100 c) 1:10 b) 100: 1 a) 10:1 Xi) xii) The inclination of a line passing through the points (4, 3) and (5, 4) with + x axis is : c)45 b) - 1 a) 1 xiii) The geometric mean between 8 and 32 is: b) 256 c) 40 a) 24 xiv) Ifa+b-c a) 35 b+c-a C+a-b d) 45 d) 16 and a+ b +=7; the value of x+ y+ z is: b) Xv) Two integers differ by 2 and sum of their squares is 52. c)-4 or 6 a)4 and 6 b) 4 or 6 d) 42 The integers are: d)4 and-6 or 6 and 4 Question -2 i) If(x-9):(3x + 6) is the duplicate ratio of 4:9, find the value ofx using properties of proportion. (4] i1)Ifx a sec A cos B, y=b sec Asin B and z=ctan A; show that: -=1. (4| iii) Solve for x using the quadratic formula. Write your answer correct to two significant figures: (x-1)- 3x + 4 = 0. [4] Ouestion-3 i) Thenumbers 6, 8, 10, 12, 13, and x are arran od in an ascending order. If the mean of the observations isequal tothe median, find the value of x. [4] ii) Find the value of 'a' for which the followins noints A (a, 3), B(2, 1) and C (3, a) are collinear. Hence, find the equation of the line. [41 iii) Use graph paper to answer the following auestions, (Take 2 cm =lunit on both axis). (A) Plotthe points A(-4, 2) and B(2, 4). [1] (B) A is the image of A when reflected in the Y-axis. Plot it on the graph paper and write the coordinates of A,. [1] coordinates of B,. (C) B, is the image of Bwhen reflected in the line AA,. Write the (1| (D)Write the geometric name of the figure ABA, B1. 1| (E) Draw the diagonals in that figure. [1] Section -B 140 marksl (Attempt any four questions) Question -4 i)AB and CDare two chords of a circle intersecting at P inside of that circle. Prove that: AP X PB = CP X PD. (31 ii) Two solid spheres of radii 2 cm and 4 cm are melted and recast into a cone of height 8 cm. Find the radius of the cone so formed. [31 iii) Rohit invested 9,600 on 100 shares at 20 premium paying 8% dividend. Rohit sold the shares when the price rose to 160. He invested the proceeds (excluding dividend) in 10% 50 shares at 40. Find the : (A)Original number of shares. [) (B) Sale proceeds. [1] (C) New number of shares. [1] (D) Change in the two dividends. [1] Question-i i) Given x3+12x 6x2+8 y+27 Using componendo and dividendo find x : y. [3] 9y2427 ii)Find a if the twopolynomials ax+ 3x-9 and 2x + 4x + aleaves the same remainder when divided by x + 3. [3] ii) If A i= and B-lo 16] find x and y when A2 = B. (4] Question-6 i) The weights of 50 apples were recorded as given below. Calculate the mean weight. to the nearest gram, by the short-cut method: [31 Weight 80 85 85 90 90-9595 in grams No. of 10 100 100 105 105 110 12 110 4 115 3 apples i) In the given figure, M is thecentre of the circle. Chords AB and CD are perpendicular to each other. If ZMAD=xand zBAC = y: A (A)express ZAMD in terms of x. [1] (B) express LABD in terms of y. [1] (C) prove that: x =y. [1] iii) From a rectangular solid of metal 42 cm by 30 cm by 20 cm, a conical cavity of diameter 14 cm and depth 24 cm is drilled out. Find : (A) The surface area of the remaining solid. [2] (B) The volume of remaining solid. [1] (C)The weight of the material drilled out if it weighs 7 gm per cm'. [1] Question -1 of getting : i) Acard is drawn from a well-shuffledpack of 52 cards. The probability (A)Odd black card. |1| (B) Red jack. [1] (C) A facecard. [1] consisting of a rectangle and ii)) Thegiven figure shows the cross-section of a water channel volume of water discharged find the a semi-circle. Assuming that the channel is always full. per second. Give your through it in one minute if water is flowing at the rate of 20 cm answer in cubic meters correct to one place of decimal. |3| K...21cn. 7cm chord through the point a and tangent a between angle i1)Prove that : The equal to an angle in the alternate segment. (4] of contact is Question-8 To an observer C, 40 m from face. cliff vertical a on B and i)Two climbers are at points A ground, A is 'at an elevation of 45 and B of60 . What is thefoot of the cliff, on the level [3] the distance between the climbers? line perpendicular to ii)Find the equation of the straight the line x + 2y = 4, which Through the point (-7, 11). (3] of 9x* - mx nx + 8: factor a is 4 9xGiven, iii) remainder and factor theorem. 2] (A)Find the value of mand n using the (B) Factorize the given polynomial completely. [2] Question-9 2V3 2X# 0. [3] 4y3= x:+ for Solve i) [3] i) Verify : tan'0 + cos0 - 1 = tan'0.sin"0. tinned rasgullas. The tin container is sells Sweets "Madanlal shop 11) A famous sweet height 16cm, and it can hold 20 spherical sealed. 14cm, diameter with shape in cylindrical filled and then sweetened liquid such that the can is and 6cm diameter tasgulas of the can contains. (Take, TF3.14) 4| liquid sSweetened much how out rnd Question-10 X-y=1and x + y =5 (i) Given the equations oftwo straightlmes, L1 andLz are Find: Respectively. If L, and L, intersects at point Q(3, 2). [2] (A)The equation of lineL3 which 1s parallel to L and has y-intercept 3. (B) The value of k, if the lineL3 meets the line L at a point P (k. 4). [21 (C) The coordinate of Rand the ratio HQQR, if line L2 meets x-axis at point R. [1] ii) Draw an ogive for the given data. [5l Class Frequeney 0-15 15-30 5 30 45 7 45 60 2 60-75 75 90 11 St. Joseph's Comvent, Chandannagar Pre- ICSE Examinations Date :03.01.2025 F.M=80 Subject : MATHEMATICS Section A( answer all ) 1. Choose the correct answers from the given options : (15J a) (k+ 3),(k + 2),(3K - 7) and (2K- 3) are in proportion. The value of k is : () k= -5 or k= -1 (1) k = 5 or k = -1 (iv) k = -5 or k = 1 b) The point that lies on the perpendicular bisector of the line joining A(- 2, - 5) and B(2, 5) Is: (i) k = 5 or k = 1 ) (0,0) (0) (0,2) (M) (2, 0 ) (iv) (-2,0) c) A tank of diameter 14 m has been dug to a depth of 21 m. The capacity of the tank is: ) 147O m (i) 2850 m (ii ) 3234 m (iv) 3540 m d) When 6X + 2X - X + 2 is divided by (X+ 2),the remainder is: () 56 ( )36 (ii) 44 (iv) -36 e) Roshni keeps Rs thousand monthly for 18 months in recurring deposit account that pays 6% per annum. Select the correct option from the fllowing statements: A: she gets rupees 855 as interest B: her total deposit without interest is Rs.18,000 C: her maturity value is Rs. 18850 () Only A is true ( ) Ais false, B is true ( ) All are true (iv) A is true,C is false f) The probability of a player winning a particular game is found to be 0.48. So the probability of losing the game is : (iv) 16/ 25 () 1 ( ) 0.42 (ii) 13 / 25 9) P{ -4, 0) is reflected to P(4,0). The reflector is : (i) the line y = 0 () The line x = 0 ( i) The line y=4 (iv) The line x = 2 A-7em. h) From the diagram given alongside, the length of PT is: (iv) 10cm ( i) 3V7cm i) Given that Sin A + Sin' A=1. Value of Cos A + Cos Ais: () 3cm () 1 (i) 12cm (iv) 3 (ii) 2 ( ) V2 j) POR and XYZ are two triangles such that aPQR ~AYXZ. <P= 50 and < R= 75 Measurement of < X is : () 50 (iv) 45 (i ) 75 (ii) 55 k) Mr. Shah bought some disCOunt shares of a company quoted at Rs120. If the percentage of discount is 25%, the face value of the share is : (iN) Rs. 160 () Rs.90 () Rs.100 (ii) Rs. 150 ) The number line is represented by the expression: (){-4 <X<1, x R) (){-4> x>1, x R} (v) (1 <x< -4, x R} (i) {1 >x> - 4, xER) m)P is a point inside a triangle such that PA = PB = PC = 13cm. P is called the of the triangle. ) incentre () centroid (i) circumcenter (iv) orthocenter ) If %A, a and 2 are in A.P, then value of ais : () 11/8 ( ) 7/8 (ii) 3/8 (iv) 5/8 )The nature of root of the equation is imaginary. The value of m can be : )> t4v3 () > +2v6 (ii) < t4V3 (v) > +4v2 Cont (21 divided by ( x - 3 ),leave the same 2. a) x- px? + x +6 and 2x- x- (p +3) x -6, when Remainder. Find the value of p y-axis at B. Find: b) Zx -3y + 12 0 is a line that cuts x-axis at Aand point of AB. ) the co ordinate of the point P which is the mid perpendicular to the given line and passingg through P (W) Equation of a line c) In the gven figure <ORS= 58 and <QOR =110 (i) <QPS. () <ORQ Find the angles () <QSR Sa) The sum of 3 terms of a G.P is 49/2. The product of the first and third term is 343. Find the three numbers. nb) Aright circular solid cone of base diameter 28 cm and height 21cm is cut lengthwise. into two equal halves. Find the total surface area of the two pieces and the cost of painting the outer surfaces of both the pieces at RS, 5 per cm' c) Use graph paper for the following . Take lcm = 1 unit on both the axes. ) Plot A(4,4) , B(4, -6), and C(-3,4). ( ) Reflect A through origin to A' ( ) Reflect Bon theline x= 0,to B' (iv) Reflect C on the line y = 0 to C' (v) Join AB'BC and name the geometrical figure thus formed [4+4+5] Section B( Answer any FOUR of Rs. 1400. /4.a) Mohit bought some Rs.50 shares quoted at Rs.72. He gets an annual income calculate: , If the company pays dividend at the rate of 14% p.a (ii) Rate of returm on his investment (ii) His investment (i) No of shares bOught b) Solve the in equation and plot the solution on the number line: -3 +x s+2 s + 2x c) Prove: sec A-1 sec A+ 1 ; xE R sec A +1 = 2 cosec A V sec A- 1 [3+3+4] 5.a) ABCD is a cydic quadrilateral . AT is a tangent. <ABC = 112 and <BAT = 38 Find the measure of <ACD <ADC and <CAB. years paying interest at 8% p.a. He gets b) A man has a recurring deposit acCount for three monthly installment and the maturity amount Rs.3996 as interest at the time of maturity. Find the distribution by Step deviation method. c) Calculate the mean of the following Class Frequency 10- 15 5 15- 20 20 - 25 11 25- 30 20 30-35 23 35 - 40 18 lont 40- 45 13 45 -50 4 [343+4] [3] /6.a) A(4,7), B(-3,5) and C(7,1) forms the vertices of triangle ABC. Find: () the equation of the median through A ( ) the gradient of the line perpendicular to AC. Given that (A+ B) = A+ B.Evaluate x and B= c) Sum of 5th and gh term of an A.P is 30. If the 25 term is 3 times the 8th term. find the [3+3r4] first three terms of the A.P 7.a) The angle of elevation of the top of a tower AB as observed from The base of abuilding CD is 45 while that of building CD as observed from B is 36 . Find the height of the building and the distance between the buildings in nearest metre. b) From the folowing distribution, representing daily wages of a group of employees find () median (i) interquartile range and (ii) no. of people earning above Rs.470 daily, with the help of an ogive. Class Frequency 250 - 300 300- 350 15 8 350 - 400 400- 450 20 28 450 - 500 10 500- 550 7 (s+ 5] ..0 ,p. They are well shuffed and 8.a) 16 ards are marked with alphabets from a, b, c,.. One card is drawn at random. Find the probability of getting a ard having a letter in the word' median (1) having a consonant (i ) Havinga letter which is not in the word" Mathematics" a + b2+ c b)a, band c are in continued proportion. Prove that : a+b+ c c) Draw a histogram for the following distribution and find the mode. Class Frequency 41 - 50 5 51 - 60 18 61 -70 20 71 - 80 32 = a-b+c 81 -90 91 - 100 12 25 101 - 110 10 [343+4] 5 In the diagram,PS is parallel to QR. PQ = 12 Cm and QR = 9cm. 9. a) Prove : (0) 4 POR~A PSR ( ) Length of PS and RS (il) Area of A PQR : area of A PSR b) The table shows the GST bill of a shop. Calculate the total GST paid and the total amount to be paid by the customer. Item Mustard ol Dry fruits Quantity Cost/ unit 2 lit Rs. 160/lit 1kg Rs. 600 Discount 2% GST rate Ni 12% c) ConstrUct a triangle ABC wth AB =6.2cm and BC = 5cm. <B =45 Draw the locus of a point equidistant from AC and BC and at a distance of 2.5cm from the vertex B, that locates inside the triangle. [3+3+4]

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