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o Bachani Nagar Malad (E) o Ashok Nagar Kandivli (E) o Thakur Complex Kandivli (E) FIRST SEMESTER EXAMINATION 2016-2017 Grade : X Date : 10/10/2016 Subject : Mathematics ICSE Marks: 80 Time : 2 hr 30 mins. You will not be allowed to write during the 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. This paper consists of 4 printed pages. Attempt all questions from Section A and any four questions 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. All figures in geometry have to be copied on the answer sheet. The intended marks for questions or parts of questions are given in brackets [ ] Section A Attempt all questions from this Section Question 1 (a) If ( x + 1 ) is a factor of (2x + 1 )3 + ( 2k 1 )3, find `k`. (b) Find the area and perimeter of the given figure, if AB = 10, BC = 10, DC = 10, DP = 6. [3] B A P [4] C D (c) Calculate the ratio in which the line joining A (6, 5) and B (4,-3) is divided by the line y = 2 [3] Question 2 (a) Without using trigonometrical tables, evaluate: tan233 cosec257 + sin44 . sec 46 - 2 sin 45 + tan260. (b) [3] Following table gives the marks scored by the students in an examination: Calculate the mean marks. [3] Marks 0 9 10 19 20 29 30 39 40 49 50 59 No. of students 4 6 12 4 8 6 Math/Grade X/ICSE/First Semester Examination/ Page 1 of 5 CAA/RS /2016-17 (c) P and Q are centres of the circles of radius 9 cm and 2 cm respectively. PQ = 17cm. R is the centre of a circle of radius x cm, which touches the given circles externally. Given that PRQ = 900, write an equation in `x` and solve it. [4] Question 3 (a) If A = [ 2 1 4 2 5 ],B=[ ] and I is the identity matrix of same 1 3 3 order. Find A . B + B I. (b) [3] Given: P is an external point to a circle with centre C. PA and PB are two tangents drawn from P to the circle, A and B being points of contact. To prove: APC = BPC. [3] A C P B (c) If 3 3 3 3 +1 + 1 +1 1 = x, then using the properties of proportion prove that: x3-3mx2+ 3x m = 0 [4] Question 4 (a) Mrs. Malhotra had a Saving Bank account in Bank of Baroda . Her passbook had the following entries. Date Particulars Withdrawal Deposit Balance Jan 1, 2015 By Balance -------- --------- 9,600 Jan 8 By Cash -------- 6,000 15,600 Feb 18 To Cheque 10,500 ---------- 5,100 May 19 By Cash --------- 6,300 11,400 July 15 To Self 2,400 ---------- 9,000 Oct 7 By Cash --------- 3,600 12,600 On October 30, 2015 Mrs. Malhotra received her transfer order and closed the account. If the amount of interest on closing the account on 30th October, 2015 is Rs. 310; calculate the rate of interest per annum. Math/Grade X/ICSE/First Semester Examination/ Page 2 of 5 [4] CAA/RS /2016-17 (b) Marks obtained by 200 students in examination 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 5 10 14 21 25 34 36 27 16 12 Draw an ogive for given distribution taking 2 cm = 10 marks on the X- axis and 2 cm = 20 students on the Y axis from the graph. Using the graph determine: (i) the median marks (ii) the number of students scoring above 65 marks (iii) if 10 students qualify for merit scholarship, find the minimum marks required to qualify. [6] Section B Attempt any four questions from this Section Question 5 (a) From a pack of 52 playing cards all cards whose numbers are multiple of 2 are removed. A card is now drawn at random. What is probability that the card drawn is (i) face card (ii) a prime numbered red card (b) [3] On a certain sum, the compound interest in two years amounts to Rs. 4,240. If the rates of interest for successive years are 10% and 15% respectively. Find the sum. (c) [3] In the given figure, QAP is a tangent at Point A and PBD is a straight line, if ACB = 360 , APB = 420 , find ; (i) [4] C BAP (ii) ABD (iii) QAD (iv) BCD D B P A Q Question 6 (a) Solve the given inequation and graph the solution on the number line - 2 12 + 2x 4 3 4 3 + 2x ; X R Math/Grade X/ICSE/First Semester Examination/ Page 3 of 5 [3] CAA/RS /2016-17 (b) Rakesh opens a recurring deposit account in a bank and deposits Rs 600 per month for 20 months. Calculate the maturity value of this account, if the bank pays interest at the rate of 10% per annum. [3] (c) Solve the given quadratic equation by using formula and give answer correct upto two decimal places : 5 (x + 1 )2 + 10( x + 1 ) + 3 = 0. [4] Question 7 (a) The line 2x + 5y 4 = 0 intersect x axis at point A. A line l is drawn passing through A and parallel to 3x 7y + 8 = 0. Find the equation of line l. (b) [3] A hemisphere is surmounted by a conical block of wood. The diameter of their bases is 6cm each and slant height of the cone is 5 cm. Calculate: (i) the height of the cone (ii) the volume of the solid . ( = 3.14) (c) [3] Use graph paper for this question. (i) point A (3,-4) is reflected about the line x = 0 to get image B. write the coordinates of B. (ii) point B is reflected about line y = 0 to get image C. write the coordinates of C. (iii) point C is reflected about y axis to get the image D. write the coordinates of D. (iv) find the perimeter of figure ABCD. [4] Question 8 (a) (b) (c) If 10 x2 23 xy + 9 y2 = 0 , find x : y 3 Given A = [ 0 p, q, and r 0 ], B = [ 0 4 [3] ] and AB = A + B , find the values of [3] A man standing on a window of the first floor of a building observes that the angle of depression of a dust bin which is 10 m from the foot of the building is 450. He climbs to the window of the second floor, directly above the first floor and observes the angle of depression of the dust bin to be 60 0. Calculate the height of the second floor window from the ground . Math/Grade X/ICSE/First Semester Examination/ Page 4 of 5 [4] CAA/RS /2016-17 Question 9 (a) Draw a line segment AB of 6cm. Construct a circle with AB as diameter Mark a point P at a distance of 5 cm from the mid-point of AB. Construct two (b) tangents from P to the circle with AB as diameter. [3] Prove the following identity ; [3] (1 + (c) 1 2 ) (1 + 1 2 ) = 1 2 4 In the figure given below, 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 = 5 cm , PB = 4 cm . Find (i) AB (ii) PT. [4] T A C B D P Question 10 (a) D and E are the mid-points of sides AB and AC of ABC. DE = 4 and BC = 8. If A ( ADE) = 25 sq. cm, then find (b) ( ) [3] ( ABC) Draw ABC such that ABC = 600 and BA = BC = 8 cm. M is the mid-point of BA. Find the locus of a point which is (i) equidistant from BA and BC (ii) 4 cm from M (iii) mark a point P which is 4cm from M and equidistant from BA and BC. [3] (c) If marks and cumulative frequencies of the students are given below, draw histogram of the data and hence find mode. Marks 5-10 10-15 15-20 20-25 25-30 Cumulative frequency 7 16 28 36 42 [4] *******************************THE END************************* Math/Grade X/ICSE/First Semester Examination/ Page 5 of 5 CAA/RS /2016-17
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