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ICSE Class X Prelims 2021 : Mathematics (Bombay Scottish School, Mahim, Mumbai)

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BOMBAY SCOTTISH SCHOOL, MAHIM PRELIMINARY EXAMINATION MATHEMATICS GRADE : 10 MAX MARKS : 80 DATE : 25/01/2021 WRITING DURATION : 2 HRS SESSION : 1 NO. OF QUESTIONS : 11 Answers to this paper must be written on the paper provided separately. You will not be allowed to write in the frst 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 questions from Section A and any four from Section B. All working, including 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 result in loss of marks. The intended marks for questions or parts of questions is given in the brackets [ ] SECTION A (40 Marks) Answer all questions from this Section Question 1 a) Using Remainder Theorem, factorise the following polynomial completely 2 x 3 + x 2 13 x + 6 [3] b) Kishore has a recurring deposit account in a bank for 2 years at 8.5% simple interest. If he gets ` 2,550 as interest at the time of maturity, find : [3] i) the monthly deposit ii) the maturity value. c) Calculate the mean and median of the following distribution. Age in years No. of students [4] 12 18 14 17 16 15 13 2 2 5 3 4 6 3 Question 2 2 a) Find x, y if [ 3 0 1 2 ] [ ] + 3 [ ] 1 2 1 = 2 [ ] 3 b) In the figure given below, AB is parallel to DC, BCE = 800 and BAC = 250 Find : i) BAD ii) CBD [3] [3] iii) ADC c) How many terms of the A.P. 6, 11 2 , 5 , . . . . make the sum 25? [4] Question 3 a) Solve the following equation, give your answer correct to 2 significant figures. 4x + 6 [3] + 13 = 0 b) In what ratio does the point ( 4, p) divide the line segment joining the points A (2, 2) and B ( 14, 6) ? Hence find the value of p. [3] c) A retailer buys a television set from a wholesaler for ` 40,000. He marks the price of the television set 15% above the cost price and sells it to a consumer at 5% discount on the marked price. If the sales are intra state and rate of GST is 12%, find : i) the marked price of the television set. ii) the amount of tax paid by the retailer to the Central Government. iii) the amount of tax received by the State Government for the sale of television set. [4] Question 4 a) The figure given below represents a solid consisting of a right circular cylinder surmounted by a cone at one end. Their common radius is 15 cm. The height of the cone is 20 cm and the total height of the solid is 70 cm. Find the total surface area of the solid. (Take = 22 7 ). b) Equation of line L 1 is y = 2 i) ii) iii) [3] [3] Write the slope of line L 2 if L 2 is the bisector of X OY Write the coordinates of point M Find equation of Line L2 c) Use a graph paper for this question. (Take 2 cm = 1 unit on both the axes) Plot the points P (4, 0) and Q (2, 2) i) P is invariant when reflected in an axis. Name the axis. ii) Q is the image of Q on reflection in the axis found in (i) and R is the image of P on reflection in the origin. Write the coordinates of Q and R. iii) State the geometrical name of the figure PQRQ . iv) Find area of the figure PQRQ . [4] SECTION B (Attempt any four) Question 5 a) Find the value(s) of k for which the following equation has real and equal roots. [3] (k + 4) x 2 + (k + 1) x + 1 = 0 b) There are 2 dice, one red and other black. Bothe are rolled simultaneously. Find the probability that : [3] i) each dice shows 5 ii) the number on the black dice is either 2 or 4 iii) the sum is at least 11. c) If 3 + 3 3 3 i) a : b = 76 49 , use properties of proportion to find : ii) [4] 2 2 2 2 2 2 Question 6 a) Solve the following inequation, write the solution set and represent it on a number line. 3 (x 7) 15 7 x > + 1 3 ; x I b) In the figure given below, AB is the diameter of the semicircle. CD AB. i) Prove that ADC CDB ii) Find CD, if AD = 4.5 cm and DB = 8 cm [3] [3] c) If the mean of the following observations is 54, find the value of p using the shortcut method. [4] Class 0 20 20 40 40 60 60 80 80 100 Frequency 7 p 10 9 13 Question 7 a) P (3, 4) , Q (7, 2) and R ( 2, 1) are the vertices of the triangle PQR. Find the equation of the median of the triangle through R. [3] b) The fourth term of an A.P. is 11 and the eighth term exceeds twice the fourth term by 5. Find the A.P. [3] c) Prove the identity : tan 1 cot + cot 1 tan = sec A cosec A + 1 [4] Question 8 a) If a, b, c are in continued proportion, prove that : [4] a 2 b 2 c 2 (a 4 + b 4 + c 4) = b 2 (a 4 + b 4 + c 4) b) The following table shows the distribution of the heights of a group of 200 factory workers. [ 6 ] Height (in cm) No. of workers 145 150 150 155 155 160 160 165 165 170 170 175 175 180 180 185 6 12 20 46 57 37 15 7 Using a graph sheet, draw an ogive for the distribution. Take 2 cm = 5 cm height on one axis and 2 cm = 20 workers on the other axis. Use your graph to estimate the following. i) The median height ii) The lower Quartile iii) The height above which the tallest 25% of workers fall iv) The number of workers who are considered short if 154 cm is considered as standard height. Question 9 a) Mrs. Shetty has a recurring deposit account in a bank of ` 2000 per month at the rate of 10% p.a. If she gets ` 83,100 at the time of maturity, find the total time in years, for which the account was held. b) If A = [ [3] 3 2 7 0 ] ; B =[ 4 5 2 1 ] and C = [ 3 4 5 ] . Find A B 5 C 6 [3] c) The angles of depression of the top and bottom of an 8 m tall building from top of a multi storeyed building are 300 and 450 respectively. Find the height of the multi storeyed building. Give your answer correct up to 2 decimal places. [4] Question 10 a) Point A divides the line segment joining P ( 2, 6) and Q (3, 4) in the ratio 2 : 3. [3] i) Find coordinates of A ii) Find the equation of the line whose gradient is 3 2 and passing through A. b) In the figure given below, PQ = RQ, RQP = 680, PC and QC are tangents to the circle with centre O. Find : i) QOP ii) CPQ iii) QCP [3] c) A grocer bought some baskets of fruit for ` 1500. Five baskets of fruits were lost in the transit. He sold each of the rest for ` 10 more than he paid for them and made neither profit nor loss. Find the number of baskets of fruit bought. [4] Question 11 a) The polynomials a x 3 + 5 x 2 11 x 14 and 3 x 3 + a x 2 4 x + 20 when divided by (x + 2) leave the same remainder. Find the value of a. b) In PQR, MN is parallel to QR and = [3] 2 3 [3] Find : i) MN : QR ii) Area ( OMN) : Area ( ORQ) c) A conical vessel, diameter 36 cm and height 25 cm is filled by a cylindrical pipe of diameter 8 mm. The water flows at the rate of 15 m per minute from the pipe. Find the time taken to fill the vessel completely. Give your answer correct to nearest minute. [4]

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