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CBSE Class 9 Exam 2025 : Mathematics

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Sri Kumaran Children s Home - CBSE Class: IX Date:21.02.2019 Annual Examination 2018 - 2019 Subject: Mathematics SET 1 Marks: 80 Time: 3 Hrs. General Instructions : 1. All questions are compulsory. 2. The question paper consists of 30 questions in sections A, B, C & D. 3. Section A comprises of 6 questions of 1 mark each, Section B comprises of 6 questions of 2 marks each, Section C comprises of 10 questions of 3 marks each and Section D comprises of 8 questions of 4 marks each. SECTION A [1 6=6] 1) Check whether p(x) = 2 2x 3 5 2x 2 7 2 is a multiple of g ( x ) x 1 . 2) The mean of 30 observations was 188. It was detected on rechecking that the value of 150 was wrongly copied as 105 for computation of mean. Find the correct mean. 3) The figure shows the construction of x . What should be the measure of MB? 4) The abscissa of a point P is 2 . The ordinate of the same point is cube of abscissa. What is the reflection of this point about Y-axis? 5) ABFG is a parallelogram with GF = 8 cm and EF = 6cm. Find the area of GOF. 6) The diagonals of a parallelogram ABCD are d1 and d2 . Write the relation between d1 and d2 if the parallelogram ABCD is (a) rectangle (b) rhombus. P. T. O. 1 SECTION B [2 6=12] 7) Two coins are tossed simultaneously 250 times and the outcomes are recorded as below: Outcomes Two heads One head Two tails Find the probability of getting: a) a tail (b) no head Frequency 125 65 60 (c) atleast one head (d) atmost two tails 8) Factorize using suitable identity: 2 2 x 3 8 y 3 125 30 2 xy . 9) How many cones of radius 7cm and height 8cm should be melted to form a large cone of diameter 28cm and height 20cm. 10) In the given figure S is any point on the side BC of ABC . Prove that AB + BC + CA > 2AS. 11) If the radius of the sphere is reduced by 50%, find the ratio of the new volume to the original volume. 12) In a quadrilateral ABCD, B = 4 D . Is ABCD a cyclic quadrilateral? Justify. SECTION C [3 10=30] 13) Evaluate :- 64 125 2 3 1 256 625 1 4 1 0.064 3 1 P. T. O. 2 14) EFGH is a parallelogram. A is any point on EH. B is the foot of the perpendicular from G to AF. Show that Ar ( Paralle log ramEFGH ) AF GB 15) Simplify:- 5a 3b 3 (5a 3b) 3 16) In the given figure, O is the origin. ABCD is a rectangle in which AB = 9cm and CB = 4 cm. OD = 2 CD . 3 Find a) the vertices of the rectangle ABCD. b) the Ar ( DEC ) . 17) In the figure, AB CD. x : y = 3: 2 and y + z = 1000, Find a and p. 18) Show that the line segments joining the mid-points of the opposite sides of a quadrilateral bisect each other. OR Show that the bisectors of the angles of a parallelogram form a rectangle. 19) Prove that equal chords of a circle subtend equal angles at the centre. 20) Construct a triangle ABC in which BC = 5cm, B = 600 and AB + AC = 9cm. OR Construct a triangle PQR in which Q = 450 and PQ PR = 2.5cm and QR = 4.5cm. 21) Find the area of a triangle whose sides are 13cm, 14cm and 15cm. Also find the length of the altitude drawn to its smallest side. 22) If the mean of the following data is 40.4, find y. Hence find the mode of the data. x f 10 3 20 8 30 12 40 5 3 50 y 60 7 70 5 P. T. O. SECTION D [4x8=32] 23) Find the values of a and b if 5 2 5 2 5 2 a b 5 . 5 2 24) If x 3 ax 2 bx 6 has x - 2 as a factor and leaves a remainder 3 when divided by x - 3 , then find the values of a and b. 25) If the volume of the cuboid is x 3 6x 2 11x 6 cm3 and its height is x - 1 cm, find its length and breadth. 2 (3x 6y) 2(2x y) 11 and express it in the form of ax + by + c = 0. 3 Without drawing a graph i) find the coordinates of two points which lie on this line. ii) find the coordinates of the point where this line intersects the X-axis. 26) Simplify OR The parking charges of a car in a mall for first 2 hours is `50 and `10 for subsequent hours. Frame a linear equation in 2 variables and express it in the form of ax + by + c = 0. Also without drawing a graph find a) the charges for parking a car for 4 hours b) If `100 is the total charge find the time for which the car was parked. 27) In the given figure OA = OD and 1 = 2. Prove that BCA CBD . 28) XN and XM are the perpendicular bisectors of BC and AB respectively. 1) How many circles will pass through A, B and C? 2) If one such circle passes though A, B and C what is the centre of this circle? Justify. 3) Are the points X,N,B and M concyclic? Justify. P. T. O. 4 29) A metal pipe is 77cm long. The inner radius is 4 cm and the outer radius is 5 cm. Find (i) Total surface area of the pipe 22 ) 7 (ii) Volume of the metal used (use = 30)Draw a histogram for the following data: Class mark 125 135 145 155 165 175 Frequency 8 12 4 7 10 14 OR Draw a frequency polygon for the given data. Height (in cm) 150-153 154-157 158-161 162-165 166-169 170-173 No. of persons 7 6 15 10 5 6 ****** 5

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