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ICSE Board Exam 2002 : Mathematics

8 pages, 53 questions, 51 questions with responses, 132 total responses,

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Indian Certificate of Secondary Education (ICSE), New Delhi

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MATHEMATICS (Two hours and a half) Answers 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 questions from Section B. All working, i ncluding 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 brackets [ ]. Mathematical tables are provided. S ECTION A (40 Marks) Attempt all questions from this Section. Question 1 (a) The price of a T. V. set inclusive of sales tax of 9% is Rs. 13407/-. Find its marked price. If the sales tax is increased to 13%, how much more does the customer pay for the T. V.? [3] (b) On a certain sum of money, the difference between the compound interest for a year, payable half-yearly, and the simple interest for a year is Rs. 180. Find the sum lent out, if the rate of interest in both the cases is 10%. [3] Question 2 (a) If a : b = 5 : 3, find (5a + 8b) : (6a 7b). [2] (b) Using Factor theorem, show that (x 3) is a factor of x3 7x2 + 15x 9. Hence, factorise the given expression completely. [3] Q uestion 3 [5] (a) In the adjoining figure, the medians BD and CE of a ABC meet at G. Prove that:(i) EGD ~ CGB Prove that:(ii) BG = 2GD from (i) above. (b) The shape of the top of a table in a restaurant is that of a segment of a circle with centre O and BOD = 90 . BO = OD = 60 cm. Find:(i) The area of the top of the table. Find:(ii) The perimeter of the table. Note : Take = 3.14 Question 4 (a) Without using tables, evaluate:3 cos 80 cosec 10 + 2 cos 59 cosec 31 [2] (b) Solve the following inequation, and graph the solution on the number line:2x 5 5x + 4 < 11, X R. [3] Question 5 Using only a ruler and compasses, construct ABC = 120 , where AB = BC = 5 cm. (a) M ark two points D and E which satisfy the condition that they are equidistant from both BA and BC. [2] (b) In the above figure, join AE and EC. Describe the figure: (i) ABCD [1] (b) In the above figure, join AE and EC. Describe the figure: (ii) ABD [1] (b) In the above figure, join AE and EC. Describe the figure: (iii) ABE [1] Question 6 (a) The marks of 20 students in a test were as follows:5, 6, 8, 9, 10, 11, 11, 12, 13, 13, 14, 14, 15, 15, 15, 16, 16, 18, 19, 20. Calculate:(i) The M ean [1] (a) The marks of 20 students in a test were as follows:5, 6, 8, 9, 10, 11, 11, 12, 13, 13, 14, 14, 15, 15, 15, 16, 16, 18, 19, 20. Calculate:(ii) The M edian [1] (a) The marks of 20 students in a test were as follows:5, 6, 8, 9, 10, 11, 11, 12, 13, 13, 14, 14, 15, 15, 15, 16, 16, 18, 19, 20. Calculate:(iii) The M ode [1] (b) Construct a ABC, in which AB = AC = 3 cm and BC = 2 cm. Using a ruler and compasses only, draw the reflection A'BC of ABC, in BC. Draw the lines of symmetry of the figure ABA'C. [6] Question 7 (a) The point P (3, 4) is reflected to P' in the x-axis; and O' is the image of O (the origin) when reflected in the line PP'. Using graph paper, give:(i) The coordinates of P' and O' [1] (a) (ii) The lengths of the segment PP' and OO' [1] (a) (iii) The perimeter of the quadrilateral POP'O' [1] (a) (iv) The geometrical name of the figure POP'O' [1] (b) Find x and y, if: [2] [ x 3x y 4y [2]=[5 ] ] 1 12 (Type in the answers separated by commas. Leave no spaces around the commas.) Question 8 [10] (a) Prove the following identity: 1 sin + cos + 1 sin cos = 2 sin 1 2 cos2 (b) In the given figure, AB is the diameter of a circle with centre O and BCD is 120 . Find: (i) DBA (b) Find: (ii) BAD (c) Find the equation of a line passing through the point ( 2, 3) and having the x-intercept of 4 units. Question 9 (a) The annual salary of M r. Ram Kumar is Rs. 1,91,734/-. He contributes Rs. 875/- per month to provident fund, and pays Rs. 260/- per month as L.1.C. premium. He buys National Saving Certificates worth Rs. 40,000/- and invests Rs. 12,000/- in M utual Funds. He donates Rs. 2,500/- towards the Prime M inister s Relief Fund (eligible for 100% deduction) and Rs. 500/- to a Charitable Trust (eligible for 50% deduction). If Rs. 1000/per month has been deducted by his employer as income tax at source in the first eleven months, find:(i) His taxable income Tax slab:Upto Rs. 50,000 : No tax. [2] Rs. 50,001 to Rs. 60,000 : 10% of the income exceeding Rs. 50,000. Rs. 60,001 to Rs. 1,50,000 : Rs. 1,000 + 20% of the income exceeding Rs. 60,000. Above Rs. 1,50,000 : Rs. 19,000 + 30% of the income exceeding Rs. 1,50,000. Standard Deduction : Rs. 20,000. Rebate in tax : 20% of the total savings or Rs. 14,000, whichever is less. Surcharge : 10% of the total tax payable after rebate. A surcharge of 10% is levied on the income tax payable (after deducting rebate) if taxable income is more than Rs. 60,000/-. S tandard Deduction : Rs. 20,000/Tax Rebate : 20% of money invested in Provident Fund, M utual Fund, L.I.C., P.P.F, National Savings Certificate, etc., subject to a limit of Rs. 12,000/-. (Type in the answers separated by commas. Leave no spaces around the commas.) (a) (ii) The balance of tax he has to pay in the last month of the financial year. [2] (b) A man wants to buy 62 shares available at Rs. 132/- (par value of Rs. 100/-). (i) How much should he invest? [2] (ii) If the dividend is 7.5%, what will be his annual income? [2] (iii) If he wants to increase his annual income by Rs. 150/-, how many extra shares should he buy? [2] Question 10 (a) Solve graphically the simultaneous equations given below. Take the scale as 2 cm = 1 unit on both the axes. x 2y 4 = 0 2x + y = 3 [6] (b) The following table gives the weekly wages of workers in a factory: [1] Weekly wages in Rs. No. of workers 50 - 55 5 55 - 60 20 60 - 65 10 65 - 70 10 70 - 75 9 75 - 80 6 80 - 85 12 85 - 90 8 Calculate : (i) The mean. (b) (ii) The modal class. [1] (b) (iii) The number of workers getting weekly wages, below Rs. 80/- [1] (b) (iv) The number of workers getting Rs. 65 or more, but less than Rs. 85/- as weekly wages. [1] Question 11 (a) Using a ruler and compasses only, construct: (i) The triangle ABC in which AB = 9 cm, BC = 10 cm and ABC = 45 . [3] (a) (ii) Construct a circle of radius 2 cm to touch the arms of ACB in (i) above. [3] (b) A hollow sphere of internal and external diameters 4 cm and 8 cm respectively, is melted into a cone of base diameter 8 cm. Find the height of the cone. [4] Question 12 M r. Shiv Kumar has a Saving Bank account in Punjab National Bank. His pass book has the following entries: Date Particulars April 1, 1997 B/F Withdrawals in Rs. -- Deposits in Rs. Balance in Rs. -- 3220.00 [5] April 15 By transfer M ay 8 To cheque No. 355 July 15 By clearing July 29 By cash Sept. 10 To self Jan. 10, 1998 By cash -- 2010.00 5230.00 298.00 -- 4932.00 -- 4628.00 9560.00 -- 5440.00 15,000.00 698.00 -- 8020.00 -- 8000.00 16020.00 Calculate the interest due to him at the end of the financial year (M arch 31st 1998) at the rate of 6% per annum. (b) An aeroplane travelled a distance of 400 km at an average speed of x km/hr. On the return journey, the speed was increased by 40 km/hr. Write down an expression for the time taken for: (i) The onward journey. (ii) The return journey. If the return journey took 30 minutes less than the onward journey, write down an equation in x and find its value. Question 13 [5] [10] (a) The shadow of a vertical tower AB on level ground is increased by 10 m, when the altitude of the sun changes from 45 to 30 , as shown in the given figure: Find the height of the tower and give your answer, correct to 1/10 of a metre. (b) In the right angle QPR, PM is an altitude. Given that QR = 8 cm and M Q = 3.5 cm, calculate the value of PR. (c) A function f is given by the formula f (x) = 25 4x2. Find: (i) f (3) (c) (ii) Find x, such that f (x) = 0 Question 14 [2] (a) The marks obtained by 120 students in a M athematics test is given below: Marks No. of S tudents 010 5 10 20 9 20 30 30 40 40 50 50 60 60 70 70 80 80 90 90 100 16 22 26 18 11 6 4 3 Draw an Ogive for the given distribution on a graph sheet. Use a suitable scale for your Ogive. Use four Ogive to estimate: (i) The median. (a)(ii) The lower quartile. [2] (a)(iii) The number of students who obtained more than 75% in the test [2] (a)(iv) The number of students who did not pass in the test if the pass percentage was 40. [2] (b) A (1, 4), B (3, 2) and C (7, 5) are the vertices of a ABC. Find: (i) The coordinates of the centroid G of ABC. [2] (b) (ii) The equation of a line, through G and parallel to AB. [2]

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Additional Info : Solved ICSE Board exam paper study guide - ICSE 2002 : MATHEMATICS - I.C.S.E. Free Online Question Paper
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