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ICSE Prelims 2016 : Mathematics (The Shriram Millennium School (TSMS), Noida)

6 pages, 39 questions, 12 questions with responses, 27 total responses,

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Prelim Examination- 2015-16 Class: X Subject: Mathematics Time: 2 hrs M.M: 80 MATHEMATICS (Two and a half hours) 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 the paper is the time allowed for writing the answers. Attempt all questions from Section A and any 4 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 answers. Omission of essential working will result in the loss of marks. The intended marks for questions or parts of questions are given in the brackets [ ]. Mathematical tables are provided. Section A (40 marks) Attempt all questions from this section Question 1 3x 4y 5x 6y = a) If 2x 3y 4x 5y , find x: y . [3] b) If the rate of the sales tax is 5%, Simran has to pay `7140 for the steel cupboard. What amount she has to pay if the sales tax is increased by 2%? [3] c) In the fig., AOBP is a quadrilateral of a circle of radius 14 cm. A semi-circle with AB as diameter is drawn. Find the area of the shaded region. [4] Question 2 a) In the given figure, ABCD is a quadrilateral, inscribed in a circle with centre O. Side CD produced to E. If 0 ADE=95 and OBA=30 0 , find: (i) This Paper contains 4 printed pages OBC (ii) OAC [3] Page 1 b) Show that c) (x 1) is a factor of x3 7x2+14x 8 . Hence completely factorise the above expression. [3] The compound interest on a certain sum of money at 5% per annum for two years is `246. Calculate the simple interest on the same sum for three years 6% per annum. [4] Question 3 a) Evaluate b) Solve: x 2 2x 3 < 5, x R and y [ ][ ] [ ] [ ] 3 2 2x 4 8 , if 1 4 1 +2 5 = 4y [3] and mark it on a number line. [3] c) Use a graph paper for this question. (Take 1 cm = 1 unit on both the axes). The point reflected to PP ' P ' in the x axis O ; and ' P ( 2,3 ) is is the image of the origin O when reflected in the line . P ' O ' (i) Give the coordinated of (ii) The lengths of the segments (iii) Assign the special name to the geometrical figure (iv) How many lines of symmetry does and PP ' and ' ' OPO P . OO ' . ' ' OPO P . have? Name them. [4] Question 4 sinA+cosA sinA cosA 2 + = a) Prove the following identity: sinA cosA sinA+cosA 1 2cos2A [3] b) Ashima has a cumulative deposit account in a bank for 5 years at 9% p.a. At the time of maturity she gets `51,607.50. Find the monthly instalment. [3] This Paper contains 4 printed pages Page 2 c) Find the mean of the following distribution: Class Interval 15-19 20-24 25-29 Frequency 3 13 21 [4] 30-34 5 35-39 5 40-44 4 45-49 2 Section B (40 marks) Attempt any 4 questions from this section Question 5 [ ][ ] 0 0 0 0 2sin30 2cos60 tan45 sec60 cot450 sin900 cosec300 cos00 a) Simplify: [3] b) Ruchi invested `45,000 in 15% `100 shares quoted at `125. When the market value of these shares increased to `140 she sold some shares, just enough to raise `8,400. Calculate: (i) The number of shares she still holds. (ii) The dividend due to her on these remaining shares. [3] c) A hollow metallic cylindrical tube has an internal radius of 3 cm and height 21 cm. The thickness of the metal of the tube is cm. The tube is melted and casted into a right circular cone of height 7 cm. Find the radius of the cone correct to one decimal place. [4] Question 6 a) A page from the passbook of Rachit s saving bank account is given below: Date Year 2006 Amount Amount Balance Withdrawn Deposited (in `) (in `) (in `) January 1 By Balance --5,000.00 January 5 By Cash -1,000.00 6,000.00 January 20 To Cheque 700.00 -5,300.00 February 2 To Cheque 500.00 -4,800.00 February 15 By Cash -800.00 5,600.00 April 17 By Cash -400.00 6,000.00 July 1 By Cash -1,000.00 7,000.00 November 15 By Cash -500.00 7,500.00 December 20 To Cheque 1,200.00 -6,300.00 If the interest earned by Rachit at the end of December is `373, find the rate of interest. b) Construct PQ at Particulars PQR=45 Q 0 . Mark a point S on and also to pass through QR S such that [5] QS=4.5 cm . Construct a circle to touch . [5] Question 7 This Paper contains 4 printed pages Page 3 a) Write down the equation of the line whose gradient is and which passes through P, where P divides A(2, 5) the line segment joining and B( 5,9) in the ratio 3:4 . [3] b) Mohan and Sohan are visiting a particular shop in the same week (Tuesday to Saturday). Each is equally like to visit the shop on any day as on another day. What is the probability that both will visit the shop on (i) the same day? (ii) consecutive days? (iii) different day? [3] c) A shopkeeper buys a number of books of `80. If he had bought 4 books for the same amount, each book would have cost `1 less. Taking the original number of books as x x , form an equation in and solve it. [4] Question 8 a) Without using trigonometrical tables, evaluate the following: 4 20 20 203 2 0 20 tan 30 +sin 60 3cos 60 + tan 60 2tan 45 . 3 4 [3] P( 4, 5) b) The line joining and Q on the x (i) The ratio of Q(3,2) and intersects the y-axis at R. PM and QN are perpendiculars from P - axis. Find: PR:RQ (ii) The coordinates of R (iii) The coordinates of M and N . , and AB=6cm,AL=2cm and AC=9cm . Calculate: . [3] c) In the given figure, LM BC CM (i) The length of (ii) ar( ALM) The ratio ar(trap.LBCM) . This Paper contains 4 printed pages [4] Page 4 Question 9 a) 24000 blood donors were registered with Red Cross at Kolkata. The number of donors increased at the rate of 5% every six months. Find the time period at the end of which the total number of blood donors becomes 27783. [3] b) Solve for : 2x+3 3x 2 = 4x 1 3x+2 . [3] c) An airplane, when 300 m high passes vertically above another aeroplane at an instant when the angles of elevation of the two airplanes from the same point on the ground are 60 0 45 and 0 , respectively. Find the vertical distance between the two airplanes. [4] Question 10 a) A circle with centre O is drawn inside a quadrilateral ABCD and touches all its sides. Prove that angles AOB and COD are supplementary. [4] b) The marks of 200 students in an exam were recorded as follows: Marks % 10-20 20-30 30-40 40-50 50-60 60-70 70-80 No. of Students 7 11 20 46 57 37 15 Draw the cumulative frequency table and hence, draw the ogive and use it to find: (i) The median, and (ii) The number of students who score more than 40% marks. 80-90 7 [6] Question 11 a) A lady holds 1,800, hundred-rupee shares of a company that pays 15% dividend annually. Calculate her annual dividend. If she had bought these shares at 40% premium, what percentage return would she have got on her investment? Give your answer to the nearest integer. [3] b) If a, b, c, d are in continued proportion, prove that: [3] 1 c 2+ 1 b d2 = 1 1 b+ d 2+ 2 a c a+ c) Find the equation to the line parallel to (2,3) and (4, 1) . This Paper contains 4 printed pages 3x 4y+6=0 and passing through the mid-point of the join of points [4] Page 5 This Paper contains 4 printed pages Page 6

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