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PRE-BOARD EXAMINATION ICSE 2024 MATHEMATICS F.M. -80 TIME: 2% HRS Answer to this paper must be written on the pauper provlded separately. You will not be allowed to write during 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 the questions from Section Aand any four questions from Section B. All working, including the 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 resulr in loss of marks. The intended marks for questions or parts of questions are given in brackets [J Mathematical tables are provided. SECTION A (Attempt all questions fromthis section.) Question l: Choose the correct answer to the questions from the given options. (Do not copy the question, write the correct [15] answer only.). YWhich of the following statement is NOT correct (a) Two matrices are added only when they are of same order. (b) A matrix is said to be zero matrix if all the elements are zero. (c) A matrix of order (m x n) has (m + n) elements. (d) A matrix is said to be a square matrix if the number of rows are equal to number of columns. YThe roots of thequadratic equation 3x- 6x + k=0 are real and equal, then the value of kis (a) -3 (b) 4 (c) -4 (d) 3 (in The taxable value of aWoodland leather purse is leather purse will be (a) 4310 (b) 4031 3500. If the rate of GST is 18%. Then the price of the (c) 4130 (d)4330 (wRecurring deposit account is also called as (a) Current account (b) Saving account (c) Fixed Deposit account (d) Cumulative Deposit account. Y Howmany two digit numbers are divisible by 5? (a) 17 (b) 18 (c) 19 (d) 20 iy The table shows the values of xand y, when x is proportional to y. What are the values of Mand N. M |12 14 28 21 N (a) M=4, N=35 (b) M=6, N= 49 (c) M-3, N=32 () M=6, N= 36 (yiYPQIn the given figure PQ |TR, then by using condition of similarity: OP0Q (a) RT (b) RT OR OT OF 0Q (c) OF oT PQ_OP _0T (d) RT OR 00 (yiD Two cylindrical pots contain the same amount of water. If their diameters are in the ratio 2 : 3, the ratio of their height is: (a) 4:9 (b) 9:2 (c) 9:3 (d) 9:4 ix Event A: Celebration of Children's Day in India Event B: Bith Anniversary of Dr. APJ Abdul Kalam (Celebrated on 15th of October) What is the probability that both the event Aand Bare celebrated on the same day? What is the name given to such event? (a) Sure event, P(E) = 1 (6) Impossible event, P(E) =0 (c) Sure cvent, P(E) =0 (d) Complementary event, P(E) =. YArectangle ABCD made in first quadrant, shows reflection in x - axis in the quadrant: (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant sY Apoint whose distance from the centre of a circle is larger than the radius, lies in (a) interior (b) exterior (c) on the circle (d) diameter of the circle. (iiy sinA cot'A + cosA tan A =? (a) 1 (b) 2 (c) 0 (d) -1 30 cm (i) In the given figure AP +AQ (a) 180 cm (b) 240 cm (c) 120V3 cm (d) (30V3 +60) cm 60 em (Xi Assertion (A) : The slope of the line x = a, is equals to zero. Reason (R): The angle which a straight line makes with the positive direction of x-axis measured in the anticlockwise direction is called the angle of inclination of the line. (a) A is true R is false (b) A is false R is true (c) both A and R are true (d) both A and R are false. 6If the mean of the following distribution is 2.6,then the value of pis 2 f (a) 2 3 3 (b) 3 (C) 2.6 (d) 2.8 hestion 2: i) From a rectangular solid of metal 35cm x 30cm x 24cm, a conical cavity of diameter 14cm and height 24 cm is removed. Find (4] (a) the vae of the remaining solid. (6) the surface area of the remaining solid. G Akash opened a recurring deposit account in a bank and deposited 150 per month for 8 months. If he received 1236 at the time of maturity, find the rate of interest per annum. stnA+cosA slnA-coSA (ii) Prove that sinA-cosA sinA +coSA 1-2cos A [4) LQrestion 3: (i) Ifg is the mean proportional between p and r, prove that p -g+r -=q (ii) In the given figure O is the centre of thecircle. Tangents at A and B meet at C. If ZAC0= 30, find (a) ZBCO (b) reflexLAOB (c) ZAPB (4] 14] ji The histogrann represents the marks obtained by some candidate in an examination. Using the data of the diagrams, calculate the mean nmarks. [use the assumed mean as 22.5] 20 15 TT 11 10 (10,) 15 25 20 30 40 \arks SECTION-B (Attempt any four questions from this section) Mestion 4: YGiven 2 X-. Write (a9 the order of the matrix X, (by the matrix X Anubhav invests 4500 in 8%, 10 shares at 15. He sells the shares when the price rises to 30, and invests the proceeds in 12% 100 shares at125. Calculate: La the sale proceeds. b the number of 125 shares he buys. re th change in his annual income from dividend. (iYinthe given figure AABCand AAMP are right angled at Band Mrespectively. Given AC =10cm, AP = 15cm and PM = 12cm.(a) Prove AABC ~AAMP, (b) Find the length of AB and BC. vooestion&: erCalculate lower quartile, upper quartile and inter quartile-runge from the following frequency distribution. 25 34 31 8 40 15 10 45 10 (Gi) Tanishq buys the following items from a departmental store: Rate Items Quantity Pulse Milk Food 50 9 6 3 kg 80kg 2kg 300/kg GST 5% 12% 200 18% 500 ml Face Cream 48 [3 He pays EIs00 to the departmental store. How much rupees did the departmental store return to Tanishq? [3] (iii) In the given figure, AE and BC intersect each other at point D. 14] If LCDE = 90, AB = Scm, BD = 4cm and CD =9cm, find DE. B Question1 6: (i) Is0aterm ofthe G.P. 1 1 .....? Show the working in support of your answer. [3 (ii) The equation of aline is 3x +4y-7=0. Find (a) the slope of the line, (b) the equation of aline perpendicular to the given line and passing through the intersection of the line X-y+2=0 and 3x + y- 10=0. [3] ( S Agirl fills a cylindrical bucket 32cm in height and 18cm in radius with sand. She empties the bucket on the ground and makesa conical hcap of the sand. If the height of the conical heap is 24cm, find oits radius and 6) its slant height. (lcave your answer in square root form) bOuestion 7: GY Theduration of telephone calls in a week at a school were recorded as below: Time in seconds 10-20 20-30 30-40 40-50 50-60 60-70 70-80 No, of 5 14 19 27 43 29 16 calls Draw a cumulative frequency curve and locate the median. 80-9090-100 2 |5] ) rom the top of a light house 100 mhigh the angles of depression of two ships on opposite sides of it are 48 and 36 respectivcly. Find the distance between the two ships to the nearest metre. Question 8; ) Solve the following incquation, write down the solution set and represent it on the real number line -2+ 10x S 13x + 10<24 + 10x, xE Z. ) nthegiven figure, O is the centre of the circle. Prove that ab+c. 31 [31 YiY Determine the ratio in which the line 3x +y-9=0 divide the segment joining the points (1,3) and (2,7). Question 9: (DOne fourth of a herd of camels was seen in the forest. Twice the square root of the herd had gone to mountain and the remaining 15 camels were on the bank of river. Find the total number of camels. ifx= 2ab (0 Using the properties of proportion, find the value of * +**D *-b a+b. (iYConstruct atriangleABC in which base BC=6 cm, AB = 5.5 cm and < ABC= 120 . aConstruct acircle circumscribing the triangle ABC. (bYDraw cyclic quadrilateral ABCD so that Dis equidistant from Band C. [3| [3| 14) Question 10: iY sing Remainder theorem, factorise completely the polynomial 3x3 +2x? -19x + 6. (3| GY Two persons are visiting a particular shop in the same week (Monday to Saturday). Each is equally likely to visit the shop on any one day as on another. What is the probability that both will visit the shop on (aYthe same day, bifferent days, te) Consecutive days. (3| YUse a graph paper for this question taking 1cm =1 unit along both the Xand Yaxis. ((a Plot the points A(0, 5), B(2, 5), C(5, 2), D(5, -2), E(2, -5) and F(0, -5). (bY Reflect the points B, C, Dand Eon the Y-axis and name them B', C, D' and E' Also write the coordinates. or Name the figure BCDEE'D'CB' (YName a line of symmetry for the figure formed.
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