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Class 9 Exam 2015 : Mathematics (Vibgyor High School, Marathahalli, Bangalore)

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Vibgyor High School, Marathahalli, Bangalore

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VIBGYOR High Second Term Examination 2014-2015 MATHEMATICS Grade: IX Date Max. Marks : 23.03.15 : 80 Time Allowed : 2hrs30 minutes INSTRUCTIONS: 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. The intended marks for the questions or parts of questions are given alongside the questions. All work, including rough work, must clearly be shown and must be done on the same sheet as the rest of the answer. Omission of essential working will result in loss of marks. This paper contains 7 pages. _________________________________________________________________________ SECTION A (40 Marks) Attempt all questions from this section Question1. a) Mr .Kumar borrowed Rs. 15000 for two years. The rate of interest for the two successive years are 8% and 10% respectively .If he repays Rs. 6200 at the end of the first year find the outstanding amount at the end of the second year. [3] 1 b) Solve the following inequation and represent the solution set on the number line : [3] c) If A = and , find A2 5A + 7I I= [4] Question 2 a) From a pack of 52 playing cards, jack, queen and king of clubs are removed and then well shuffled. From the remaining cards a card is drawn , find the probability of getting : i. a face card ii. a black card iii. a king [3] b) If x3 + ax2 + bx +6 has a factor (x 2 ) and leaves the remainder 3 when the expression is divided by ( x 3 ) . Find the values of a and b. [3] c) Rahul opened a recurring deposit account in the bank and deposited Rs.300 per month for two years. If he received Rs.7725 at the time of maturity, find the rate of interest per annum. [4] Question 3 a) Mr. Patrick invested Rs.52000 on Rs.100 shares at a discount of Rs.20 paying 8% dividend. At the end of one year he sells the shares at the premium of Rs.20. Find : i) the annual dividend. ii) the profit earned including his dividend. [3] b) Find the two numbers whose mean proportional is 24 and third proportional is 1536. [3] 2 . c) Solve : + = , x -5 , 3 [4] Question 4 a) Use graph paper for this question. ( Take 1cm = 1 unit on both the axes ) i) Plot A(4, 4) B(4, -6) and C(8, 0) ii) Reflect ABC on the y-axis and name it as A B C iii) Write the co-ordinates of the images A , B , C [3] b) A shopkeeper announces a discount of 10% on the TV set .The marked price of the TV is Rs 22,000. How much will the customer have to pay for buying the TV set if the rate of sales tax is 8%? [3] c) From a thin metallic piece, in shape of a trapezium ABCD in which AB || CD and BCD = 900, a quarter circle BFEC is removed. Given AB = BC = 3.5 cm and DE = 2 cm, calculate the area of the remaining part of the metal sheet. [4] Section B (40 marks) Attempt any four questions Question 5 a) Using properties of proportion , solve for x : =3 [3] 3 , show that 6X X2 = 9I, where I is the unit matrix. b) If X = [3] c) A two digit number is such that the product of its digits is fourteen. If 45 is added to the number then the digits interchange their places. Find the number. [4] Question 6 a) Hamid buys an article for Rs.1, 696. The rate of sales tax is 6%. He asks the shopkeeper to reduce the price of the article to such an extent that he does not have to pay anything more than Rs.1, 696 including the sales tax .Calculate the deduction needed in the cost-price of the article. [3] b) A dividend of 9% was declared on Rs.100 shares selling at a certain price. If the rate of return is 7 %, calculate : i) The market value of the share. ii) The amount to be invested to obtain an annual dividend of Rs. 630. [3] c) Mrs. Kumar has an account with The Bank of India .The following entries are from her passbook : Date Particulars Withdrawals Deposits(Rs.) Balance(Rs.) (Rs.) 08.02.09 B/F 18.02.09 To self 12.04.09 By cash 15.06.09 To self 08.07.09 8,500.00 By cash 4,000.00 2,238.00 5,000.00 6,000.00 Complete the above page of her pass-book and calculate the interest for the six months, February to July 2009, at 4.5% per annum. 4 [4] Question 7 a) Construct an isosceles triangle with base 5 cm and vertical angle 40 . Draw its line of symmetry. [3] b) Two dice are rolled together. Find the probability of getting i) A sum of 13 ii) A sum less than 5 iii) A sum greater than 7 [3] c) Solve the given inequations. A={y: } B={y: } Write down the elements of A B and represent it on number line. [4] Question 8 a) Calculate the area of the shaded region, if the diameter of the semi-circle is equal to 14 cm. b) If M [3] X = [ ] i) State the order of matrix M ii) Find matrix M [3] 5 c) A shopkeeper buys a camera at a discount of 20% from the wholesaler, the printed price of the camera being Rs. 1600 and the rate of sales tax being 6%. The shopkeeper sells it to the buyer at the printed price and charges the tax at the same rate. i) The price at which the camera can be bought. ii) The VAT paid by the shopkeeper. [4] Question 9 a) A model of a ship is made to the scale 1 : 160 . Find : i) The length of the ship , if the of its model is 1.2 m ii) Area of the deck of the ship, if the area of the deck of its model is 1.2 m 2. iii) The volume of the ship, if the volume of its model is 1.2 m3. [3] b) Vivek invests Rs 4,500 in 8%. Rs. 10 shares at Rs. 15 . He sells the shares when the price rises to Rs. 30, and invests the proceeds in 12% Rs. 100 shares at Rs. 125 . Calculate : i) The sale proceeds. ii) The number of Rs.125 shares he buys. iii) The change in his annual income from dividend. [3] c) The simple interest in 3 years and compound interest in 2 years on a certain sum at the same rate are Rs.1, 200 and Rs. 832 respectively. Find i) The rate of interest ii) The principal iii) The difference between the compound interest and simple interest for 3 years. [4] Question 10 a) A shopkeeper 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. 6 Taking the original cost of each book to be Rs. x , write an equation in x and solve it . [3] b) An isosceles right angled triangle with ABC = 90 . A semi-circle is drawn with AC as the diameter. If AB = AC, then find the area of the shaded region. [3] c) If b then using the properties of proportion prove that b2x + x 2ab = 0. [4] Question 11 a) Shekar has a recurring deposit account in a bank for 5 years at 10% per annum simple interest. If he gets Rs. 30,100 at the time of maturity, find the monthly installment. [3] b) In ABC, ACB = 90 and CD is perpendicular to AB. Prove that : CD2 = AD x AB c) Using the factor theorem factorize completely the following polynomial : 3x3 + 2x2 19x + 6 ********** 7 [3] [4]

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