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Bombay Scottish School, Mahim PRELIMINARY ASSESSMENT MATHEMATICS Grade : 10 Date : 16.02.2022 Duration : 1 hrs Max. Marks : 40 No. of Questions : 06 No. of printed sides: 09 Answers to this Paper must be written on the paper provided separately. You will not be allowed to write during the first 10 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. Log tables and graph paper will be provided Attempt all questions from Section A and any three questions from Section B. The intended marks for questions or parts of questions are given in brackets f /. SECTION A (Attempt all questions from this Section.) Question 1 Choose the correct answers to the questions from the given options. (Do not copy the question,write the correct answer only.) [10] i) The reflection of point A(-5,4) in the x-axis is a) (5,4) b) (-5,4) c) (-5,-4) d) (-5,0) . f d ii) If a card is drawn from a well shuffled pack o car s, that the card drawn is a red and a king is a) then the probability 7 13 b) 0 c) 1 26 1 d) 13 iii) A right angled triangle ABC with sides 5cm, 12cm and 13cm is revolved about the side of 12cm,the volume of the solid so formed is a) 300TC b) 240TC C) 100TC d) 720TC iv) The slope of a line parallel to x-axis is a) 1 b) 0 c) -1 d) not defined 2 v) In the figure given below, if AB is the diameter of a circle with centre 0, LBCD = 130 , then LDBA is equal to a) 50 b) 40 c) 30 d) 60 vi) sec 0 - tane sine is equal to a) sec 0 b) tan 0 c) 1 d) cos 0 3 vii) In the figure given below, if the lines AB and CD are equally inclined to the coordinate axes and passing through the point (0,-2) B C A D then the equation of line CD is a) y = 2x + 1 b) y+x+2=0 c) y-x + 2 d) y-x-2 0 =0 viii) If point P(3,a) divides the segment joining the points A(7,l) and B(0,8) in the ratio 4 : 3, then the value of a is a) 5 b) -4 c) -5 d) 4 4 ix) Which of the following cannot be the probability of an event? b) 43% c) 0.25 d) 2.7 x) From the histogram given below, the modal class is 40 10 a) 10-15 b) 5-10 c) 20-25 d) 15-20 5 - SECTIONB (Attempt any three questions from this Section.) Question 2 a) b) c) d) Find the equation of a line whose inclination is 60 and y-intercept is -4 [2] A bag contains twenty~ 5 coins, fifty~ 2 coins and thirty~ 1 coins . If it is equally likely that one of the coins will fall down when the bag is turned upside down, what is the probability that the coin i) will be a~ 1 coin? ii) will not be a~ 2 coin? [2] Prove that (1 + cot A - cosec A)( 1 + tan A+ sec A) = 2 [3] In the figure given below,frorn an external point P,tangents PA and PB are drawn to a circle. CE is a tangent to the circle at D.If AP= 15cm, find the perimeter of the triangle PEC. [3] Question 3 a) b) Calculate the ratio in which the line joining A(6,5) and B(4,-3) is divided byy = 2 [2] Find the value of p for which the lines 6x + Sy - 7 = 0 and 2px +Sy + 1 = 0 are parallel to each other. [2] 6 c) Use graph paper for this question. Marks obtained by 100 students in an examination are given below: Marks obtained 0-10 10-20 20-30 30-40 40-50 No.of students 8 10 22 40 20 Draw an ogive for the given distribution taking 2cm = IO marks on one axis and 2cm =10 students on the other axis. Using the graph, determine the median marks. [3] d) From a solid cylinder of height 12 cm and diameter 10 cm, a conical cavity of the same base radius and of the same height is hollowed out. Find the total surface area of the remaining solid.(Take n = 22 ) [3) 7 Question 4 a) b) AB is the diameter of a circle with centre (2,-1). If A(-2,5),find the coordinates of B. In the figure given below, O is the centre of the circle, LBCE AB is a tangent to the circle at C. = [2) 30 and B A Find i) LACD ii) LCOE [2) 7 c) d) b 24 find the value of a. If the mean of the following distri ution 1s ' 40-50 30-40 20-30 10-20 0-10 Marks 5 10 8 a 7 Number of students [3) I The point Pis the foot of a perpendicular from A(-5,7) to the line 2x -3y + 18 = 0 Find: i) the equation of the line AP. ii) the coordinates of P. [3] Question 5 a) A cylindrical container of radius 6cm and height 15cm is filled with ice cream. The whole ice cream is to be distributed to 5 children in equal cones.The height of the cone is 12 times the radius at the base of the cone. Find the radius of each cone. (2] tan A + = tan A sec A+ 1 2 cosec A [2 ] b) Prove that : sec A _ 1 c) In the adjoining figure,diameter AB and chord CD of a circle meet at P. PT is a tangent to the circle at T. CD= 7.8 cm, PD,;, 5cm ,PB= 4cm.Find Al-------+=--_.,..P i) AB ii) the length of tangent PT. 8 d) Use graph paper for this question. Take 1cm = 1 unit on both the axes. Plot the points A(3,5) anf B(- 2 ,_ 41 i) Re~ect A in the x-axis to get the image A' and reflect B in the y-axis,followed by reflection in the origin to get the image B'.Write down the coordinates of A' and B'. ii) Write down the geometrical name of the figure AA'BB'. iii) Name one invariant point under the reflection in the x-axis. Question 6 a) The coordinates of two points P and Qare (2,6) and (-3,5) respectively.Find: i) the equation of PQ. ii) the coordinates of the point where PQ intersects the x-axis. b) c) d) Two dice are rolled together.Find the probability of getting i) the sum of the numbers on the upper-most faces between 5 and 8. ii) a prime number on each dice. [3] [2] [2] , A pilot seated in an aircraft at an altitude of 250m, observes the angle of depression of two boats on the opposite banks of a river to be 45 and 60 respectively.Find the width of the river.Give your answer correct to 3 significant figures. [3] Use graph paper for this question. Using an appropriate scale on both axes, estimate the mode of the given distribution by plotting a histogram. Expenditure (~) 20-25 25-30 30-35 35-40 40-45 45-50 No.of girls 4 7 23 18 6 2 9 [3]
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