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ICSE Prelims 2013 : Mathematics (Greenwood High International School, Bengaluru)

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Yugal Reddy
Greenwood High International School, Bengaluru

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First Preliminary Examination 2013 2014 Grade: X Date: 2/12/13 Mathematics Time: 2 Hours Max. Marks: 80 Answer to this paper must be written on the paper provided separately. 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. _________________________________________________________________ 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 the loss of marks. The intended marks for questions or parts of questions are given in the brackets [ ]. _________________________________________________________________ SECTION A [40 Marks] (Attempt all questions from this Section) Question 1 (a) A man won a lottery of Rs 50000. 30% was paid as income-tax and the balance deposited in a bank 1 paying at 10% p.a., the interest compounded biannually. What sum will he get after 1 years? 2 [3] (b) Without using tables evaluate: 2 2 2 cot 58 tan 32 cosec 58 3 3 tan 77 [3] 5 tan 13 3 tan 37 tan 45 tan 53 (c) Draw a histogram and a frequency polygon on the same graph and estimate the mode for the following frequency distribution: 80 - 90 Class Interval 30 - 40 40 - 50 50 - 60 60 - 70 70 - 80 3 Frequency 2 8 10 5 4 Question 2 D C (a) In the given figure, O is the centre of the circle. If chords AC and BD intersect at right angles at E and OAB = 35 , calculate the measure of EBCE . [3] O A Page 1 of 5 35 B [4] (b) If [ 5 1 2 y +1 ] 2 [ 1 2 x 1 3 2 ] [ = 3 8 7 2 ] , find the values of x and y. [3] (c) Smita has a Recurring Deposit Account in a bank of Rs 2000 per month at the rate of 10% p.a. If she gets Rs 83100 at the time of maturity, find the total time for which the account was held. [4] Question 3 3 2 (a) What number should be added to 2x 3x 8x such that the resulting polynomial leaves the remainder 10 when divided by 2x + 1? [3] 3 and which passes through P, where P 2 A divides the line segment joining A ( 2, 6) and B (3, 4) in the ratio 2 : 3. [3] 8 cm (b) Write down the equation of the line whose gradient is (c) ABC is a right angled triangle at A. Find the area of the shaded region, given that AB = 8 cm and BC = 10 cm. (Take = B 22 ) 7 10 cm C [4] Question 4 2 (a) Solve the equation 4x 7x + 2 = 0 and give your answer correct to 2 decimal places. [3] (b) If (a + 2b + c), (a c) and (a 2b + c) are in continued proportion, prove that b is the mean proportional between a and c. [3] (c) Attempt this question on graph paper. The points (3, 0) and ( 1, 0) are invariant points under reflection in the line L1 while the points (0, 3) and (0, 1) are invariant points on reflection in line L2. (i) Name the lines L1 and L2. (ii) Plot and write down the images of the point P (3, 4) on reflection in L1 and L2. Name the images as P and P respectively. (iii) State or describe a single transformation that maps P to P . (iv) Name the geometrical figure P P P and find its area. [4] SECTION B [40 Marks] (Attempt any four questions from this Section) Question 5 (a) In the given figure, PM is the tangent to the circle and PA = AM. Prove that: Page 2 of 5 M P A B (i) PMB is isosceles. (ii) PA.PB = MB 2 [3] (b) Solve the following inequation. Write the solution set and represent it on the number line: 5 12 +1 x 5+ 3 x , where x R. 6 [3] (c) The manufacturing cost of a refrigerator is Rs 15000. The manufacturer sells it to the wholesaler at profit of Rs1000. The wholesaler sells it to the retailer at a profit of Rs 1000. The retailer sells it to the consumer at a profit of Rs 1500. If the rate of VAT is 12%, find: (i) Amount of VAT received by the Government. (ii) Amount paid by the customer. [4] Question 6 1 (a) Prove that (cos ec sin ( sec cos ) = [3] (tan + cot ) (b) A family has three children. Find the probability that the family has: (i) atleast one girl child (ii) atmost one girl child (iii) exactly one girl child (c) Construct a triangle ABC in which base BC = 6 cm, AB = 5.5 cm and ABC (i) Construct a circle circumscribing the triangle ABC. (ii) Draw a cyclic quadrilateral ABCD so that D is equidistant from B and C. [3] = 120 . [4] Question 7 (a) A model of a building is constructed with a scale factor 1 : 30. (i) If the height of the model is 80 cm, find the height of the building in metre. 3 (ii) If the actual volume of the building is 27 m , find the volume of the model. [3] (b) A (10, 5), B (6, 3) and C (2, 1) are the vertices of a triangle ABC. L is the midpoint of AB and M is 1 the mid-point of AC. Write down the co-ordinates of L and M. Show that LM = BC. 2 [3] (c) The entries in a Savings Bank Account Passbook are given below: 2003, Date Particulars Jan 1 Feb 1 Feb 12 April 5 April 15 May 9 June 4 B/F By Cash To Cheque By Cash To Cheque By Cash By Cash Withdrawals (in Rs) ----5000.00 --4250.10 --3500 Page 3 of 5 Deposits (in Rs) Balance (in Rs) --11500.00 --3749.50 --1500.00 1500.00 14000.25 25500.25 20500.25 24249.75 19999.65 21499.65 22999.65 Calculate the interest for six months (January to June) at 4% p.a. [4] Question 8 2 (a) Find the value of k for which the quadratic equation 2 x 3 kx + 2 = 0 has real roots. [3] (b) A company with 4000 shares of nominal value of Rs 110 each declares an annual dividend of 15%. Calculate: (i) the total amount of dividend paid by the company. (ii) the annual income of Shruti who holds 88 shares. (iii) If she receives only 10% on her investment, find the price Shruti paid for each share. [3] (c) The angle of elevation of the top of a hill AB from the foot of a tower CD is 60 and the angle of elevation of the top of the tower from the foot of the hill is 30 . If the tower is 30 m high, find: (i) the height of the hill. (ii) the distance between the hill and the tower. Question 9 (a) Given [ 2 1 3 4 ] X= [] 7 6 (i) Write the order of the matrix X. B D C . 60 30 A [4] [3] (ii) Find matrix X. (b) The points A (7, 3) and C (0 4) are two opposite vertices of a rhombus ABCD. Find the equation of the diagonal BD. [3] (c) The surface area of a solid metallic sphere is 1256 cm2. It is melted and recast into solid right circular cones of radius 2.5 cm and height 8 cm. Calculate: (i) the radius of the sphere. (ii) the number of cones recast. (Take = 3.14) [4] Question 10 (a) The value of a flat worth Rs 500,000 is depreciating at the rate of 8% p.a. In how many years will its value be reduced to Rs 389344? [3] 2 mab x+ ma (b) Solve using the properties of proportion: If x = , find the value of + a+b x ma x+ mb [3] x mb (c) A two digit number is such that the product of the digits is 14. If 45 is added to the number then its digits interchange their places. Find the number. [4] Question 11 (a) Compute the mean for the following data by step-deviation method. Marks Frequenc Page 4 of 5 [4] y 12 19 35 47 58 65 84 100 Less than 10 Less than 20 Less than 30 Less than 40 Less than 50 Less than 60 Less than 70 Less than 80 (c) Attempt this question on graph paper. The following table shows the daily wages of 160 workers in building project: Wages (in Rs) 0 - 10 10 - 20 20 - 30 30 - 40 40 - 50 50 - 60 60 - 70 70 - 80 No of Workers 12 20 30 38 24 16 12 8 Draw an ogive for the given distribution. Use your ogive to estimate: (i) The median wage of the workers. (ii) The upper quartile wage of the workers. (iii) The lower quartile wage of the workers. (iv) The percentage of workers who earn more than Rs 45 a day. Page 5 of 5 [6]

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