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VIBGYOR HIGH First Term Examination AY 2020-2021 MATHEMATICS Grade: IX Max. Marks Date : 28/09/2020 : 80 Time Allowed: 2 hour hours 30 minutes _________________________________________________________________________ INSTRUCTIONS: The time given at the head of this paper is the time allowed for writing the answers. This question paper is divided into two Sections. Attempt all questions from Section A and any four questions from Section B. Intended marks for questions or parts of questions are given in brackets along the questions. All working, including rough work, m must ust be clearly shown and should 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 6 pages Omission of essential working will result in loss of marks SECTION- A (40 marks) (Answer all questions from this section) Q. 1 a If 5 tan = 4, find the value of b Three cubes, each with 6cm edge, are joined end to end. Find the total surface area of the resulting Cuboid. [10] [3] [3] c Use Congruency of triangles to find the value of x and y Q. 2 a Compare 9 and 21 b In the given quadrilateral AD = BC, and P, Q, R and S are the midpoints of the sides AB, BD, CD and AC, respectively. Prove that PQRS is a rhombus. [4] [10] [3] [3] . c [4] Given: sec A= Evaluate (i) (ii) cotA+ secA Q.3 [10] [3] a Solve 4x + 3y = 14 and 5x + 7y = 11. Find the values of x - 3y and 5y - 2x b If A= 300, then prove that 3 sinA 4sin3A = sin3A c If two intersecting chords of a circle make equal angles with the diameter passing through their point of intersection, prove that the chords are equal. [3] [4] [10] Q.4 a The radius of the wheel of a car is 40 cm. Find the number of rotations made by the wheel in order to cover a distance of 11 km? [3] b Rishi invested 30000 in a finance company and received 39930 after 1 years.Find the rate of interest per annum Compounded semisemi annually [3] c Find the value of in each of the following. is an acute angle [4] (i) (ii) 3 sec 2 = 2 2 3 4 cot 3 - 4 = 0 SECTION B (40 MARKS) (Answer any FOUR questions from this section) Q.5 a [10] [3] If x = + Find i) iii) x2 + ii) x + b Find the area of a ring ring-shaped shaped region enclosed between two concentric circles of diameter 728 cm and 700 cm. [3] c If the numerator of a fraction is increased by 2 and the denominator by 1, [4] it becomes and if the numerator and denominator of the same fraction are each increased by 1, the fraction becomes . Find the fraction. Q.6 [10] [3] a ABC is a triangle right angled at C and M is mid mid-point point of hypotenuse AB. Line drawn through M and parallel to BC intersects AC at D. Show how that (i) D is the mid -point of AC (ii) MD AC (iii) CM = MA = AB A D C M B b A certain sum of money at compound interest amounts to 9200 in 1 year and to 12167 in 3 years. Find the sum and the rate percent. [3] C In the figure , ABCD is a parallelogram in which X and Y are the midmid points of AD and BC respectively . Prove that AE=EF=FC [4] Q.7 a Mary wants to decorate her Christmas tree. She wants to place the tree on a wooden block covered with colored paper with a picture of Santa Claus on it. She must know the exact quantity of paper to buy for this purpose. If the box has length, breadth and height as 80 cm ,40 cm and 20 cm respectively. How many square sheets of paper of side 40 cm would she require [10] [3] b The lengths of two parallel chords of a circle are 6 cm and 8 cm. If the smaller chord is at a distance 4 cm from th the e Centre, what is the distance of the other chord from the Centre? [3] c Find acute angles A and B, if tan(A tan(A+B +B )= 3 and tan(A-B B )= 1/ 3 0 0 , 0 <A+B 90 , A A>B >B [4] Q.8 a A river 3m deep and 40 m wide is flowing at the rate of 2km per hour. How much water will fall into the sea in a minute? b Calculate the compound interest accrued on 25000 in 3 years, when the rates of interest for successive years are 8%,10%and 12% respectively. c If x and y are rational numbers and and y. = x + y 3, find the value of x [10] [3] [3] [4] Q.9 a A field is 15m long and 12m broad. At one corner of this field a rectangular well of dimensions 8m x 2.5m x 2m is dug and the dug -out soil is spread evenly over the rest of the field. Find the rise in the level of the rest of the field. b In the following figure figure, ABC = 900 , AB =( x + 8 ) cm, BC = ( x + 1 ) cm and AC= (xx + 15 ) cm. Find the lengths of the sides of the triangle riangle [10] [3] [3] C B c A Evaluate (i) (ii) [4] - + ( ) ( ) - 2 cos 700 cosec 200 Q.10 a In how many years will 5000 amount to 6655 at 10 % Compound interest? b Solve [10] [3] [3] 2x - = 9, 3x + = 2. Hence find ind the value of K if x = Ky+ 5 c The external dimensions of a closed wooden box are 2.15m, 1.5m and 1.1m.if the thickness of the wood in the box is 2.5 cm; find: (i) Volume of the wood in the box (ii) The cost of the box, if the wood costs 1.20 per cm3 (iii)Total surface area of the box Q.11 a P , Q , R, and S are the mid points of sides AB, BC , CD and DA respectively of Rhombus ABCD. Show that PQRS is Rectangle. Under what condition will PQRS will be the square? b Find the Value of m [4] [10] [3] [3] c The given figure shows a right right-angled triangle ABC and an equilateral [4] triangle BCD. Find the area of the shaded portion. *****
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