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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 2 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) The abscissa of the point P is 3 and the ordinate of the same point P is the cube of the abscissa. Find the reflection of the point P about X axis. 2) Find k if ( x k ) is a factor of p(x) = x5 k2x3 + 2x + k 3 3) The length of a rectangle is 3 times the breadth and the length of its diagonal is Find the sides of the rectangle. 4) In the given figure, find Area ABG : Area ( ABF ) . 90 units. 5) Area of the square ABCD = 144 cm2. Find the perimeter of the quadrilateral PQRS formed by joining the midpoints of the consecutive sides of ABCD in order. 6) The mean of 10 observations is 24.2. If each observation is decreased by 5, then find the mean of the new set of observations. Page 1 of 6 SECTION B [2 6=12] 7) Find the product using appropriate identity: ( 2 p + 2 2 q + r) (2p2 + 8q2 + r2 4pq 2 2 qr 2 rp) 8) In the given figure, ABC = 65 , DAC = 35 . Prove that CF > AF. 9) In the given figure, O is the center of the circle. Chord BC = Chord BE and reflex AOC = 260 . Find the measure of CBE. 10) The radius of a sphere is reduced by 50%, then find the ratio of the surface area of the original sphere to the new sphere. 11) The daily cost of milk supplied to 25 houses in a locality are given below: Cost in ` 40-50 50-60 60-70 70-80 80-90 90-100 No. of houses 4 5 3 5 2 6 If one of the houses is chosen at random, find the probability that (i) the milk bill of the house is less than `70. (ii) the milk bill of the house is atleast `70. 12) A solid sphere of diameter 24cm is melted and recast into smaller cones of radius 3cm and height 6 cm. Find the number of cones so formed. Page 2 of 6 SECTION C [3 10=30] 13) Find the area of a triangle whose sides are 13cm, 14cm and 15cm. Also find the length of the altitude drawn to the longer side. 14) Simplify : (5x + 3y)3 + (5x 3y)3. 15) Find the missing frequency m of the given data if the mean marks scored is 55. Also find the mode. 10 30 50 70 90 Marks 7 m 10 15 10 No. of students 16) Show that the line segments joining the mid points of the opposite sides of a quadrilateral bisect each other. OR Two parallel lines l and m are intersected by a transversal p . Show that the quadrilateral formed by the bisectors of interior angles is a rectangle. 17) Construct a triangle ABC in which BC = 6cm, B = 60o and AB + AC = 8cm. OR Construct a triangle PQR in which Q = 45o, QR=4.5cm and PQ PR = 2.5 cm. 18) Prove that the equal chords of a circle subtend equal angles at the center. 19) In ABC, D is the mid point of AB. If P is any point on BC and QC DP meets AB in Q. Prove that ar ( BPQ) = 1 ar ( ABC) 2 20) Evaluate: 625 256 1 4 3 64 25 1 0.064 1 3 Page 3 of 6 21) In the given figure, O is the origin. OABC is a trapezium in which OA = 10 cm, BM = 3 cm, and OM is 2 OA . 5 Find (i) the co-ordinates of the vertices of trapezium OABC. (ii) area of the trapezium OABC. 22) In the adjoining figure, CB = CA = AD and DAE=75 . Find the value of y 75 SECTION D [4x8=32] 23)Simplify the given equation and express it in the form ax + by + c = 0. 5( x 2) + 3 (y + 1) = 43 + 3y Without drawing a graph, (i) Find the co-ordinates of two points which lie on this line. (ii) Write the nature of the graphical representation of this equation. OR The parking charges of a car in a mall for first two hours is `50 and `10 for subsequent hours. (i) Frame a linear equation in two variables and express it in the form ax + by + c = 0. (ii) Without drawing a graph, a) Find 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. 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 . Page 4 of 6 25) Find the values of a and b if 5 2 5 2 a b 5 . 5 2 5 2 26) A metal pipe is 77cm long. The inner radius is 4cm and the outer radius is 5 cm. Find (i) Total surface area of the pipe (ii) Volume of the metal used (use = 22 ) 7 27) In the given figure, OA = OD and 1 2 Prove that BCA CBD . 28) In the figure PM = PN = MQ = NR. Perpendiculars are drawn at M and N to intersect at X. (i) How many circles will pass through the points P, Q and R? (ii) If one such circle passes through P, Q and R, identify the center of this circle. Justify. (iii) What type of quadrilateral is XMPN? Justify. 29) The volume of a cuboid is x 3 13x 2 32x 20 cubic units and its height is (x+1) units. Find the length and breadth of the cuboid. Page 5 of 6 30) Draw a histogram for the given 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 ********* Page 6 of 6

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