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ICSE Board Exam 2006 : Mathematics

8 pages, 45 questions, 45 questions with responses, 136 total responses,

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Indian Certificate of Secondary Education (ICSE), New Delhi

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MATHEMATICS - 2006 (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. (While attempting this section, type in ONLY the numerical value of the answer, assuming that its unit is the same as that mentioned in the question.) Question 1 (a) Kiran purchases an article for Rs. 5,400 which includes 10% rebate on the marked price and 20% sales tax on the remaining price. Find the marked price of the article. (b) If 3x + 5y 3x 5y = 7 3 , find x : y. [3] [3] (Leave no spaces around the : (colon) symbol.) (c) A person invests Rs. 10,000 for two years at a certain rate of interest compounded annually. At the end of one year this sum amounts to Rs. 11,200. Calculate :(i) the rate of interest per annum. [2] (ii) the amount at the end of the second year. [2] (Type in the answers separated by commas. Leave no spaces around the commas.) Question 2 (a) Show that 2x + 7 is a factor of 2x3 + 5x2 11x 14. Hence, factorise the given expression completely, using the factor theorem. [3] (b) The median of the following observations 11, 12, 14, 18, (x + 4), 30, 32, 35, 41 arranged in ascending order is 24. Find x. [3] (c) [2] In the above figure, BAD = 65 , ABD = 70 and BDC = 45 . Find :(i) BCD (ii) ADB Hence show that AC is a diameter. (Type in the answers separated by commas. Leave no spaces around the commas.) Question 3 [2] [10] (a) M ohan deposits Rs. 80 per month in a cumulative deposit account for six years. Find the amount payable to him on maturity, if the rate of interest is 6% per annum. (b) A rectangular playground has two semicircles added to its outside with its smaller sides as diameters. If the sides of the rectangle are 120 m and 21 m, find the area of the playground. ( = 22/7) (c) Use graph paper for this question. The points A (2, 3), B (4, 5) and C (7, 2) are the vertices of ABC. (i) Write down the coordinates of A', B', C' if triangle A'B'C' is the image of ABC, when reflected in the origin. (ii) Write down the coordinates of A", B", C" if triangle A"B"C" is the image of ABC, when reflected in the x-axis. (iii) M ention the special name of the quadrilateral BCC"B" and find its area. (Type in the answers separated by commas. Leave no spaces around the commas.) Question 4 (a) Without using tables, evaluate:2 tan 53 cot 37 [3] cot 80 tan 10 (b) Given that x R, solve the following inequality and graph the solution on the number line: 1 3 + 4x < 23 [3] (c) Find the mean of the following distribution:- [4] Class interval 20 - 30 30 - 40 40 - 50 50 - 60 60 - 70 70 - 80 Frequency 10 6 8 12 5 9 S ECTION B (40 Marks) Attempt any four questions from this Section. (While attempting this section, type in ONLY the numerical value of the answer, assuming that its unit is the same as that mentioned in the question.) Question 5 (a) In the given figure, AB is the diameter of a circle with center O and OA = 7 cm. Find the area of the shaded region. [3] (b) Prove that sin t an = 1 + sec . [3] 1 cos (c) M r. Ashok has an account in the Central Bank of India. The following entries are from his pass book:Date [4] Particulars Withdrawals Deposits Balance Rs. P. Rs. P. Rs. P. 01.01.05 B/F -- -- 1200.00 07.01.05 By cash -- 500.00 1700.00 400.00 -- 1300.00 -- 800.00 2100.00 500.00 -- 1600.00 -- 700.00 2300.00 600.00 -- 1700.00 -- 300.00 2000.00 17.01.05 To cheque 10.02.05 By cash 25.02.05 To cheque 20.09.05 By cash 21.11.05 To cheque 05.12.05 By cash If M r. Ashok gets Rs. 83.75 as interest at the end of the year where the interest is compounded annually, calculate the rate of interest paid by the bank in his Savings Bank Account on 31st December, 2005. Question 6 (a) In the given figure, AB is a diameter. The tangent at C meets AB produced at Q. If CAB = 34 , find :(i) CBA [1 1/2] (ii) CQA [1 1/2] (Type in the answers separated by commas. Leave no spaces around the commas.) (b) If the lines y = 3x + 7 and 2y + px = 3 are perpendicular to each other, find the value of p. (Leave no spaces in your answer.) (c) Let A = [ 4 2 6 3 ],B=[ 02 1 1 ] and C = [ 2 3 1 1 ] [3] [4] Find A2 A + BC. Question 7 (a) M r. Sanjeev Chopra gets a monthly salary of Rs. 16,000. Savings: Contribution towards Provident Fund: Rs. 45,000 per year. Donations : To Prime M inister's Relief Fund: Rs. 3,100 (eligible for 100% tax exemption) Calculate:(i) M r. Chopra's taxable income. [2] (ii) The tax rebate on M r. Chopra's savings. [2] (iii) The tax M r. Chopra has to pay in the last month of the year, if he has been paying a tax of Rs. 1,200 per month in the first eleven months of the year. Tax slab:- [2] Upto Rs. 50,000 : No tax. 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. (Type in the answers separated by commas. Leave no spaces around the commas.) (b) The shadow of a vertical tower on a level ground increases by 10 m when the altitude of the sun changes from 45 to 30 . Find the height of the tower, correct to two decimal places. [4] Question 8 (a) In the given figure, PT touches a circle with centre O at R. Diameter SQ when produced meets PT at P. If SPR = x and QRP = y , show that x + 2y = 90 . (b) The line segment joining A (2, 3) and B (6, 5) is intercepted by the X axis at the point K. Write the ordinate of the point K. Hence find the ratio in which K divides AB. (Type in the answers separated by commas. Leave no spaces around the commas and the : (colon) symbol.) (c) M r. Ram Gopal invested Rs. 8,000 in 7% Rs. 100 shares at Rs. 80. After a year he sold these shares at Rs. 75 each and invested the proceeds (including his dividend) in 18%, Rs. 25 shares at Rs. 41. Find:(i) his dividend for the first year (ii) his annual income in the second year (iii) the percentage increase in his return on his original investment. (Type in the answers separated by commas. Leave no spaces around the commas.) Question 9 (a) A = { 2, 1 , 1, 2} and f = {(x, 1/x), x A} (i) List the domain of f [1] (ii) List the range of f [1] (iii) Is f a function? Give reasons for your answer. (Type in the answers separated by commas. Leave no spaces around the commas. Do not answer sub-question (iii).) [1] (b) Solve the equation 2x l/x = 7. Write your answer correct to two decimal places. (Type in the answers separated by commas. Leave no spaces around the commas.) [3] (c) A vessel in the form of an inverted cone is filled with water to the brim. Its height is 20 cm and diameter is 16.8 cm. Two equal solid cones are dropped in it so that they are fully submerged. As a result, one third of the water in the original cone overflows. What is the volume of each of the solid cones submerged? [4] Question 10 [10] (a) The daily wages of 160 workers in a building project are given below:Wages in Rs. No. of Workers 0 - 10 10 - 20 20 - 30 30 - 40 40 - 50 50 - 60 60 - 70 70 - 80 12 20 30 38 24 16 12 8 Using a graph paper, draw an Ogive for the above 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. (Type in the answers separated by commas. Leave no spaces around the commas.) (b) In the figure given above, PB and QA are perpendiculars to the line segment AB. If PO = 6 cm, QO = 9 cm and the area of POB = 120 cm2, find the area of triangle QOA. Q uestion 11 (a) Find the coordinates of the centroid of a triangle whose vertices are: A ( 1, 3), B (1, l) and C (5, 1) (Leave no spaces in your answer.) [3] (b) Use a ruler and a pair of compasses to construct ABC in which BC = 4.2 cm, ABC = 60 and AB = 5 cm. Construct a circle of radius 2 cm to touch both the arms of ABC of ABC. [3] (c) A shop keeper buys a certain number of books for Rs. 720. If the cost per book was Rs. 5 less, the number of books that could be bought for Rs. 720 would be 2 more. Taking the original cost of each book to be Rs. x, write an equation in x and solve it. [4]

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Additional Info : Solved ICSE Board exam paper study guide - ICSE 2006 : MATHEMATICS - I.C.S.E. Free Online Question Paper
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