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ICSE Class X Prelims 2020 : Mathematics (St. Mary's School ICSE, Mazagaon, Mumbai)

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ST. Mary s School DATE : 06/01/2020 TIME : 2 HRS ; MARKS : 80 SECTION A (40 MARKS) Attempt all questions from this section Question 1 : [ 3 + 3 + 4 = 10 ] 1) Mr. Remit has a recurring deposit account in a post office for 3 years at 7.5% p.a. simple interest. If he gets ` 8,325 as interest at the time of maturity. Find : a) The monthly instalment b) The amount of maturity. 2) In the figure, DBC = 580, BD is a diameter of the circle. Calculate : a) BDC 3) If x = b) BEC c) BAC + 1 + 1 + 1 1 , Using properties of proportion show that : x 2 2 a x + 1 = 0 Question 2 : [ 3 + 3 + 4 = 10 ] 1) In the given figure, O is the centre of the circle. The tangents at B and D intersect each other at point P. If AB is parallel to CD and ABC = 550, find BOD and BPD. 2) Let A = [ 4 6 2 0 ] ; B=[ 3 1 2 2 ] and C = [ 1 1 3 ] . Find A 2 A + B C 1 3) Points A and B have coordinates (7, 3) and (1, 9) respectively. Find : a) The slope of AB b) The equation of perpendicular bisector of line segment AB. c) The value of p if ( 2, p) lies on it. TEL : 9819019521 Page | 1 Question 3 : [ 3 + 3 + 4 = 10 ] 1) Solve the following inequation and represent the solution set on the number line. 3 2 1 2) Solve the following equation : ( 2 + 3) Prove the following : 1 + 1 3 1 2 < 1 6 ; x R ) 3 ( + 1 1 ) 2=0 = 2 sec 2 A Question 4 : [ 3 + 3 + 4 = 10 ] 1) Salman invests a sum of money in ` 50 shares, paying 15% dividend quoted at 20% premium. If his annual dividend is ` 600, calculate : a) The number of shares he bought b) His total investment. c) The rate of return on his investment. 2) The sum of three numbers in A.P. is 15 and the sum of the squares of the extreme terms is 58. Find the numbers. 3) A card is drawn from a well shuffled pack of cards. Find the probability that the card drawn is : a) Face card b) Ace and King c) A red and a king d) A red or a king SECTION B (40 MARKS) Attempt any four questions from this section Question 5 : [ 3 + 3 + 4 = 10 ] 1) Solve and graph the solution set of : x + 5 4 (x 1) and 3 2 x < 7 ; x R 2) A 20 m high vertical pole and a vertical tower are on the same level ground in such a way that the angle of elevation of the top of the tower as seen from the foot of the pole is 600 and the angle of elevation of the top of the pole as seen from the foot of the tower is 300, find : a) the height of the tower b) the horizontal distance between the pole and the tower. TEL : 9819019521 Page | 2 3) A plane left 30 minutes later than the scheduled time and in order to reach its destination 1500 km away in time, it has to increase its speed by 250 km/hr from its usual speed. Find its usual speed. Question 6 : [ 3 + 3 + 4 = 10 ] 1) 4 x 3 b x 2 + x c leaves remainders 0 and 30 when divided by (x + 1) and (2 x 3) respectively. Calculate the values of b and c. Hence, factorise the expression completely. 2) Show that the line segment joining the points ( 5, 8) and (10, 4) is trisected by the coordinate axes. 3) Find mean by step deviation method. Question 7 : [ 3 + 3 + 4 = 10 ] 1) A model of a ship is made to the scale of 1 : 300 a) The length of the model of the ship is 2 m. Calculate the length of the ship. b) The area of the deck of the ship is 1,80,000 m2.Calculate the area of the deck of the model. c) The volume of the model is 6.5 m3. Calculate the volume of the ship. 2) A vessel is in the form of an inverted cone. Its height is 8 cm and the radius of its top, which is open is 5 cm. It is filled with water up to its rim. When lead shots, each of which is a sphere of radius 0.5 cm are dropped in to the vessel, one fourth of the water flows out. Find the number of lead shots dropped in the vessel. C.I. 63 70 70 77 77 84 84 91 91 98 98 105 105 112 Frequency 9 13 27 38 32 16 15 3) A mathematical aptitude test of 50 students was recorded as follows. Draw a histogram for the given date using a graph paper and locate the mode. Marks 50 60 60 70 70 80 80 90 90 100 No. of students 4 8 14 19 5 TEL : 9819019521 Page | 3 Question 8 : [ 3 + 3 + 4 = 10 ] 1) P and Q are centres of circles with radii 2 cm and 9 cm respectively. PQ = 17 cm and R is the centre of a circle of radius x cms, which touches the above circles externally. Given that : PRQ = 900 ; write an equation in x and solve it. 2) Find the sum of 10 terms of the geometric progression : 1 + 3 + 3 + 3 3 + . . . . . 3) Find the value of x : cos (2 x 6)0 = cos2 300 cos2 600. Question 9 : [ 3 + 3 + 4 = 10 ] 1) The given figure shows a circle with centre O such that chord RS is parallel to chord QT, PRT = 200 and POQ = 1000. Calculate measurements of the following : QTR, QRP, QRS and STR 2) Use a graph paper for this question. Take 2 cms = 1 unit on both the axes. a) Plot the points A (1, 1) , B (5, 3) and C (2, 7) b) Construct the locus of points equidistant from A and B. c) Construct the locus of points equidistant from AB and AC. 3) The surface area of a solid metallic sphere is 2464 cm2. It is melted and recast in to solid right circular cones of radius 3.5 cms and height 7 cm. Calculate : a) The radius of the sphere. Question 10 : b) The number of cones recast (Take = 22/7) [ 3 + 4 + 4 = 10 ] 1) The midpoint of the line segment joining (2 a, 4) and ( 2, 2 b) is (1, 2 a + 1). Find the values of a and b. 2) For a dealer A, the list price of an article is ` 9000, which he sells to dealer B at some lower price. If the rate of GST is 18% and the dealer B paid a tax under GST equal to ` 324 to the government, find the amount paid by the dealer B (inclusive of GST). TEL : 9819019521 Page | 4 3) Construct a triangle ABC in which base BC = 5.5 cms, AB = 6 cms and ABC = 1200. a) Construct a circle circumscribing the triangle ABC. b) Draw a cyclic quadrilateral ABCD so that D is equidistant from B and C. Question 11 : [ 4 + 6 = 10 ] 1) ABC is a right angled triangle with angle ABC = 900. D is any point on AB and DE is perpendicular to AC. Prove that : a) ADE ACB b) If AC = 13 cm, BC = 5 cm and AE = 4 cm. Find DE and AD. c) Find area of ADE : area of quadrilateral BCED 2) Marks obtained by 100 students in mathematics test are given below : Marks 0 -10 10-20 20 -30 30 40 40 50 50 60 60 70 70 80 80 90 90 100 No. of students 3 7 12 17 23 14 9 6 5 4 Draw the Ogive for the given distribution taking 2 cm = 10 units on both axes. Use the Ogive to estimate : i) the median ii) Lower quartile iii) Number of students who obtained more than 85% marks in the test. iv) Number of students failed if pass percent was 35. Please note this question paper of St.Marys school is retyped without any changes done in it. Solutions to 12 prelim papers (Mumbai schools) available after 1 st Feb 2020. For details Whatsapp on 9819019521 TEL : 9819019521 Page | 5

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