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MATHS FOR ICSE (with awesomely witty questions)

9 pages, 33 questions, 26 questions with responses, 53 total responses,

Siddharth Chhetri
Sarwan Memorial School (SMS), Banarhat, Jalpaiguri

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SECTION A QUESTION 1. a. b. c. The difference between the compound and simple interest on a sum of money for 2 years at 10% p.a is Rs. 80 . Find the sum of money .Also the amount after 3 years at same rate . [3] Find the value of p if x+2 is a factor of x^3 px +x+q and f(2) = 4.[3] Determine the value of x , such that[4] 2cosec^2 30 + xsin^2 60 tan^2 30 =10. QUESTION 2 a. In a triangle ABC, DE parallel to BC and AD:AB=3:5 [3] 1. Write down AD:DB and DE:BC 2. Prove that TRIANGLE ABC is similar to Triag. ADE. 3. Write down Area of Triag. ADE: Area of Trapezium BCED. b. If A= 3 2 1 1 B= 1 -3 2 4 ,verify that (A-B)^2 is not equal to A^2 -2AB+B^2.[3] c. Find the area enclosed between two concentric circles of radii 3.5 cm and 7 cm . A third concentric circle is drawn outside the 7 cm circle so that the area enclosed between it and the 7 cm circle is same as that between the two inner circles. Find the radius of the third circle correct to one decimal place. Take pi = 22/7. [4] QUESTION 3 a. If P is the solution set of 8x 1 > 5x + 2 x N 7 x 2 3( x + 6) b. c. , and Q is the x N solution set of , where . Represent P Q on a number line.[3] DX deposits Rs . 100 every month in a recurring deposit scheme at 12% per annum for 1 year . Find the amount he will get at the time of maturity. [3] `Compute mean of the following distribution using step deviation method.[4] Class 0-100 100interval 200 Frequen 12 20 cy QUESTION 4. 200300 45 300400 38 400500 35 a. b. In a beauty contest the following girls participated: 1. Katrina Kaif 2. Deepika Padukone 3. Taylor Swift 4. Jacqline Fernandez 5. Jenifer Lopez 6. Kate Winslet 7. Shradddha Kapoor 8. Alia Bhatt 9. Emma Watson 10. Kritty Sanon 1. Find the probability that Bollywood actresses would win the contest. 2. Find the probability of not winning the contest by Hollywood actresses. 3. Find the probability that the singer who sung Wildest dreams and Love story will win. [3] The length of a chord is 10 cm and its distance from the centre is 12 cm .Find the radius of the circle.[3] The image of triangle OXY under reflection in the origin O is the triangle OX Y , where X ( 3 , 4) is the image of X and Y (0 , 5) is the image of Y. (i) Draw a diagram to represent this information and write down the co-ordinates of X and Y. (ii) What kind of figure is the quadrilateral XYX Y ? Give a reason for your answer. c. (iii) Find the co-ordinates of X , the image of X under reflection in the origin, followed by reflection in the y-axis. (iv) Find the co-ordinates of Y , the image of Y under reflection in x-axis, followed by reflection in the origin. [4] SECTION B ATTEMPT ANY FOUR QUESTION 5. a. Date April 1,1997 April 15 May 8 July 15 July 29 Sept.10 Jan 10,1998 Particulars B/F By transfer To cheque By Clearing By Cash To self By cash Withdrawls Deposits Balance 3220.00 2010.00 298.00 4628.00 5440.00 6980.00 8000.00 The following is a page from the passbook of Mr. Naresh s saving bank account. Complete the entries and calculate the interest due to him at the end of the financial year (March 31st, 1998) at the rate of 6%per annum [5] b. A rectangular field is 16 m long and 10 m wide.There is a path of uniform width all around it, having an area of 120 sq.m .Find the width of the path. [5] QUESTION 6 A manufacturing company P sells a Desert cooler to a dealer A for Rs. 8100 including sales tax (under VAT). The dealer A sells it to a dealer B for Rs. 8500 plus sales tax and the dealer B sells it to a consumer at a pforit of Rs. 600. If the rate of sales tax (under VAt) is 8%, find (i) the cost price of the cooler for the dealer A. (ii) the amount of tax received by the Government. (iii) the amount which the consumer pays for the cooler. [3] a. Mrs. Tirkey buy shares of a company for Rs. 8,000 at a discount of Rs. 20 (Par value Rs. 100). The company pays a 6% dividend annually. Find (i) The number of shares bought by Mrs. Tirkey,(ii) her annual income from the shares, and (iii) her annual profit percentage from the shares. [3] b. c. a. Find the centre of the circle passing through the points (6,6), (3,-7), (3,3). Also find its diameter.[4] QUESTION 7. Using ruler and compasses only construct a triangle ABC with sides BC = 2.8 cm, CA = 3.5 cm and AB = 4.5 cm. Draw the incircle to the triangle ABC so that the circle touches the side BC. Measure the radius of the circle.[3] b. c. If A:B = 3:4 and B:C =5:6 ,find A:B:C. [3] A sphere of volume 4312/3 cubic cm . is dropped into a cone , of base diameter 42 cm and height 72 cm, containing water.Calculate: 1. The curved surface area of the cone 2. The rise in level of water in the cone , if the sphere is fully submereged and no water overflows.[4] QUESTION 8 a. A sum of Rs. 1200 becomes Rs 1323 in 2 years at compound interest , compounded annually Find the rate percent .[3] b. Construct the triangle ABC such that BC= 5 cm , BC-AB= 4 cm , angle B= 120 degree .Locate a point X such that angle XAB=90 degree and X is also equidistant from B and C. Find the length of CX. [3] c. Solve for x: x-1/x-2 + x-3/x-4 =10/3. [4] in case, if the question is difficult to understand read this part (x minus 1 divided by x minus 2 plus x minus 3 divided by x minus 4 is equal to 10 divided by 3) QUESTION 9 a. (sec A tan A)^2 = 1-sin A/1+sinA, Prove this identity. [3] b. The mean weight of class 10 of SP School having 35 students is 45 kg .If the weight of the teacher be included , the mean weight increases by 500 grams .Find the weight of the teacher.[3] c. In the figure given alongside, AB=21 cm is the diameter of a semicircle with C as the centre. ABC and CEB are semicircles with diameters AC and CB respectively.[4] QUESTION 10 a. In two concentric circles prove that the chord of the larger circle which is tangent to the smaller circle is bisected at the point of contact.[3] b. The angle of elevation of the top of a hill at the foot of tower is 60o and the angle of elevaton of the top of the tower from the foot of the hill is 30o. If the tower is 50 m hight, what is the height of the hill.[4] c. If x, 5, 10, y are in continued proportion, then find x and y. [3] QUESTION 11 (a) Following table shows the marks of 120 students at I.C.S.E. examination in Mathematics. Draw an b. Ogive for the table: [6] 30 40 50 60 70 80 90 40 50 60 70 80 90 100 1 3 11 21 43 32 9 a. Marks No. of students Use the Ogive to estimate: (i) the lower quartile (Q1) (ii) the upper quartile (Q3) (iii) the lowest marks scored by the top 25% students of the class. (iv) the highest marks obtained by the lower 20%students of the class. b . ) If the points (x , 1) , (1 , 2) and (0 , y +1) are collinear, show that 1 1 + =1 x y . [4]

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