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ICSE Class X Prelims 2024 : Mathematics (Don Bosco School, Liluah, Howrah)

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Roshni Agarwal
Don Bosco School, Liluah, Howrah

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PRE-BOARD EXAMINATION ICSE 2024 MATHEMATICS F.M. - 80 TIME:2%HRS provlded separately. Answer to this paper must he wrltten on the paper You will not he allowed to write during first 15 minues. This time ls to be spent In reading the question paper. for wrlting the answers. The tme glven at the hed of thls paper is the tme allowed Sectlon B. Atempt all the questlons from Sectlon Aand any four questions from the same sheet as and must be done on All worklng, Includlng the rough work, must be clearly shown, in loss ofmarks. the rest ofthe answer. Omisslon of essentlal working will result [) The Intended marks for questlons or parts of questlons are given in brackets Muthematlcal tables are provded. SECTION A (Atempt all questlons from this seciion,) Question: not copy the question, write the correct Choose the correct answer to the questions from the given options. (Do [15] answer only.). ()) Which 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 theclements are zero. (c) A matrix of order (m x n) has (m tn) clements. rows arc cqual to number of columns. (d) A matrix is said to be asquare matrix if the number of are real and cqual, then the value of kis (i)The roots of the quadratic equation 3x -6x(d)+ k=0 3 (c) 4 (a) -3 (b) 4 of GST is 18%. Then the price of the (ii) The laxable value of aWoodland leather purse is 3500. If the rate leather purse willhe (a) 4310 (b) 4031 (c) 4130 (d) 4330 (iv) Recurring deposit account is also called as Cumulative Deposit account. (a) Current account (b) Saving account (c) Fized Deposit account (d) (v) How many two digit numbers are divisible by 5? (a) 17 (b) 18 (c) 19 (d) 20 the values of Mand N. (vi) The table shovws the values of x and y, when x is proportional to y. What are M (a) M= 4, N=35 12 28 2 N (b) M= 6, N=49 (c) M=3, N=32 (d) M=6, N= 36 (vii) In the given figure PQ |TR, then by using condition of similarity: (a) T (b) P) (c) T PQ (d) OP 1 ( ) TWo cylindrical pots contain the same amount of Vater. If their diameters are in the raio 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 : Birth Anniversary of Dr. APJ Abdul Kalam (Celebrated on 15h of October) Wnat is the probability that both the event Aand Bare cclcbrated on the same day? What is the name given to such event? P(E) sure event, P(E) = 1l (b) Impossible event, P(E) =0 (c) Sure event, P(E) =0 (d) Complementary event, (x) A rectangle ABCD made in first quadrant, shows re lection in x - axis in the quadrant: (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant (xi) A point whose distance from the centre ofa (a) interior (b) exterior (c) on the circle (d) circle is larger than the radius, lies in diamcter of the circle. (xii)sinA cotA + cosA tan'A =? (a) 1 (b) 2 (c) 0 (d) -1 30 ca (xiii) In the given figure AP + AQ (a) 180 cm (b) 240 cm (c) 120V3 cm (d) (30V3+ 60) cm (xiv) Assertion (A): The slope of the line x = a, is to zero. Reason (R):The angle which a straight line makes equals with the positive direction of x-axis mcasured 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 truc (d) both A and R are falsc. (xv) If the mean of the following distribution is 2.6, then the value ofp is 60 cm X 1 f 3 (a) 2 (b) 3 (c) 2.6 2 4 1 2 (d) 2.8 Question 2: (i) Froma rectangular solid of metal 35cm x 30cm x 24cm, a conical cavity of diameter l4cm and height 24 cm is removed. Find olume (a) the oe of the remaining solid. (b) the surface area of the remaining solid. (ii) 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. (ii) Prove that slnA+coSA sinA-cosA + sinA-cosA sinA+coSA 2 1-2cos2A [4| (4| Question3: (i) Ifq is the mean proportional between p and r, prove that (ii) In the given figure O is the centre of the circle. Tangents at A and B meet at C. If ZACO = 30, find (a) ZBCO (b) reflexXLAOB (c) ZAPB [4] (4| 2 30 P B ) The histogram represents the marks obtaincd by some candidate in an examination. Using the data of the diagrams, calculate the mean marks. [use the assumed mean as 22.5] 20 15 11 C 10 5 (1o,0) 20 30 35 40 X 15 Iarks SECTION-B (Attempt any four questions from this section) Question 4: ) Given x Write (a) the order of the matrix X, (b) the matrix X [3) (ii) Anubhav invests 4500 in 8%,10 shares at15. He sells the shares when the price rises to ?30, and invests the proceeds in 12% 100 shares at125. Calculate: a) the sale proceeds. b) the number of 125 shares he buys. [3] c) the change in his annual income from dividend. (ii) In the given figure AABCand AAMP are right angled at Band Mrespectively.Given AC =10cm, AP = I5cm and PM = 12cm.(a) Prove AABC ~AAMP, (b) Find the length of AB and BC. 3 [4] M P B A Question 5: ()Calculate lower quartile, upper quartile and inter quartile-range from the following frequency distribution. X 25 f 3 31 34 10 40 15 45 10 60 2 50 6 48 [3) (ii) Tanishq buys the following items from a departmental store: Quantity Items Pulse Milk Food Face Cream He pays Rate GST 5% 12% 18% ? 80kg 3 kg 2 kg 7 300/kg 500 ml ? 200 1500to the departmental store. How much rupees did the departmental store return to Tanishq? [3) (ii) In the given figure, AE and BC intersect each other at point D. If LCDE=90 , AB = 5cm, BD = 4cm and CD =9cm, find DE. |41 D Question 6: 1 () Is,a term ofthe G.P. 2187 1 1 ....? Show the working in support of your answer. (ii) The equation of aline is 3x + 4y - 7=0. Find (a) the slope of the line, (b) the equation of a line perpendicular to the given line and passing through the intersection of the line X-y+2 =0 and 3x +y- 10 =0. 31 (ii) A girl fills a cylindrical bucket 32cm in height and I8cm in radius with sand. She empties the bucket on the ground and makes a conical heap of the sand. If the height of the conical heap is 24cm, find (a) its radius and (b) its slant height. (leave your answer in square root form) Question 7: (i) The duration of telephone calls in a week at a school were recorded as below: Time in seconds No. of calls 10-20 20-30 14 30-40 40-50 50-60 60-70 70-80 19 27 43 29 16 Draw a cumulative frequency curve and locate the median. 80-90 90-100 12 5 () From the top of a light house 100 mhigh the angles of depression of two ships on opposite sides of it re 48 and 36 respectively. Find the distance between the two ships to the nearest metre. Question 8: )-2 +Solve the13xfollowing inequation, write down the solution set and represent it on the real number line + 10xs 10<24 + 10%, x Z. (ii) In the given figure, O is the centre of the circle. Prove that a =b+c. D B (iii) Determine the ratio in which the line 3x +y-9 = 0 divide the segment joining the points (0,3) and (2,7). 14| Question 9: () One fourth of a herd of camels was seen in the forest. Twice the square root of the herd had gone t0 mountain and the remaining 15 camels were on the bank of river. Find the total number of camels. (1) Using the properties of proportion,find the value of ta X-a x+b. ifx= 2ab atb. (iii) Construct atriangle ABC in which base BC = 6 cm, AB = 5.5 cm and z ABC= 120 . (a) Construct a circle circumscribing the triangle ABC. (b) Draw cyclic quadrilateral ABCD so that D is equidistant from B and C. Question 10: () Using Remainder theorem, factorise completely the polynomial 3x' + 2x'-19x + 6. 14| (3| (ii) 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 wvill visit the shop on (a) the same day, (b) different days, (c) Consecutive days. (iii) Use a graph paper for this question taking Icm = Iunit along both the X and Y axis. (a) Plot the points A (0, 5), B (2, S), C (S, 2), D (S, -2), E (2, -5) and F (0, -5). (b) Reflect the points B,C, Dand Eon the Y -axis and name them B',C, D' and E' Also write the coordinates. (c) Name the figure BCDEE'D'C'B (d) Name a line of symmetry for the figure formed. |3) 14)

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