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GITANJALI SENIOR SCHOOL MAYUR MARG, BEGUMPET, HYD- 500016 SUB: MATHEMATICS MARKS: 80 TERM I EXAMINATION 2020-2021 CLASS: IX TIME: 2hr:30min 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, 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 loss of marks. The intended marks for questions or parts of questions are given in brackets [ ]. Mathematical tables are provided. Section A Question 1 (a) At what percent per annum will 3,000 amount to 3,993 in 3 years when interest is compounded annually? (b) Factorise: 1 2 + 2 3 + 2 [3] 2 [3] (c) For solving pair of equation, use the method of Add & Subtract: 23x 29y = 98 29x 23y = 110 [4] Question 2 (a) Solve for x : + = [3] (b) In the figure given below, arc AB = twice arc BC, AOB = 80o, find (i) BOC , (ii) OAC O C A (c) In a right-angled triangle ABC, B [3] ABC = 90 , AC = 10 cm, BC = 6 cm and BC produced to D such CD = 9 cm. Find the length of AD. [4] Question 3 (a) The radius of a circle is 40cm and the length of perpendicular drawn from its center to a chord is 24cm. Find the length of the chord. [3] (b) In the given figure, arc AC and arc BD are two equal arcs of a circle. Prove that chord AB and chord CD are parallel. A B C D [3] (c) The electricity bills of 45 houses in a particular locality are given below. Tabulate the given data and present it as frequency distribution table and cumulative frequency distribution table with one of the classes being 300 400: 748, 567, 890, 231, 150, 458, 356, 762, 386, 824, 525, 663, 724, 841, 315, 641, 156, 712, 156, 317, 814, 547, 879, 456, 463, 664, 175, 584, 515, 487, 871, 511, 522, 454, 247, 819, 412, 326, 445, 311, 321, 545, 344, 266, 351. [4] Question 4 (a) The following table gives a description of the weights obtained by class students of IX. Weights (in kg) 45 48 52 55 46 50 54 No. of students 8 6 7 2 5 9 4 Find the median of weight obtained. [3] (b) Find the length of the perpendicular of a triangle whose base is 24cm and the hypotenuse is 25 cm. Also, find its area. [3] (c) The age of the father is seven times the age of the son. Ten years later, the age of the father will be thrice the age of the son. Find their present ages. [4] Section B Question 5 (a) What sum of money will amount to 93170 in 3 years at 10% per annum, compounded annually? [3] (b) ) In triangle ABC, AB = 12 cm and AC = 9 cm. If M is the mid-point of AB and a straight line through M parallel to AC cuts BC in N, what is the length of MN. (c) If abc = 1, Prove that: 1 1+ + 1 + 1 1+ + 1 + 1 1+ + 1 =1 [3] [4] Question 6 (a) An isosceles triangle ABC is inscribed in a circle. If AB= AC = 12 5 cm and BC = 24 cm. Find the radius of circle. [5] (b) If a, b, c are positive real numbers, show that: 1 . 1 . 1 = 1 [5] Question 7 (a) Factorise: 2 + 1 16 1 7 2 4 + 7 2 [3] (b) Two parallel chords of lengths 64 cm and 48 cm are drawn on the same side of the centre of a circle of radius 40 cm. Find the distance between the chords. [3] (c) The following table shows the weights (in kg) of workers in a factory: weights (xi) 60 62 64 71 75 frequency (fi) 3 5 p 2 1 the mean weight is 64.2. Find the missing frequency p . [4] Question 8 (a) Two parallel chords of lengths 30cm and 16 cm are drawn on the opposite sides of the centre of a circle of radius 17 cm. Find the distance between the chords. [3] (b) In the given figure, ABCD is a parallelogram in which BAD = 80o and CBD = 45O. Calculate: (i) ADB (ii) ABD (iii) CDB . D C 45o 80o A B [3] (c) For solving pair of equation, in this problem use the method of elimination: 1 1 + 7 6 1 2 1 3 =3 =5 [4] Question 9 (a) Using the step-deviation method, find the mean from the following data: xi 18 19 20 21 22 23 24 fi 170 320 530 700 230 140 110 [6] (b) The simple interest on a sum of money for 2 years at 10% p.a. is 1700. Find (i) the sum of money (ii) the compound interest on this sum for 1 years payable half-yearly at the same rate. [4] Question 10 (a) In the given figure, AB = AC, D is midpoint of BC; DP BA and DQ CA. Prove that: (i) DP = DQ (ii) AP = AQ (iii) AD bisects A A P Q C B D [3] (b) The weights (in kg) of 8 children are: 13.4, 11.6, 12.7, 17.2, 14.3, 15.2, 16.5, 9.6 Find the median weight. [3] (c) If 2400 = 2 3 5 , , , . 2 3 5 [4] Question 11 (a) A two-digit number is such that the ten's digit exceeds thrice the unit's digit by 3 and the number obtained by interchanging the digits is 2 more than twice the sum of the digits. Find the number. [5] (b) Draw a frequency polygon for the following data: Expenses No. of families 100 - 150 22 150 - 200 37 200 - 250 26 250 - 300 18 300 - 350 10 350 - 400 5 [5] -------------------------------------------------------------- All the Best ----------------------------------------------------
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