(5) Find the resultant shape obtained by connecting points (0, 5) (0, 20) (25, 20) and (25, 5).

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ID : ww-9-olympiad [1] Grade 9 Olympiad For more such worksheets visit www.edugain.com Answer t he quest ions (1) If a cone and hemisphere stands on equal bases, and have the same height.

1 ID : ww-9-olympiad [1] Grade 9 Olympiad For more such worksheets visit Answer t he quest ions (1) If a cone and hemisphere stands on equal bases, and have the same height. Find the ratio of their volumes. (2) ABCD is a cyclic quadrilateral such that AB is a diameter of the circle circumscribing it and ADC = 105º, then f ind the value of BAC. (3) A shopkeeper sells a toy f or $26 and gains 2/ of what it costs him. Find the cost price of toy. (4) If (x + 2) is a f actor of 2x 3 + kx , f ind the value of k. (5) Find the resultant shape obtained by connecting points (0, 5) (0, 20) (25, 20) and (25, 5). (6) A line passe through points (2, 1) and (1, 2). Find the y-intercept of the line. (7) Coin A is f lipped 3 times and coin B is f lipped 5 times. What is the probability that the number of heads obtained f rom f lipping the two coins is the same? (8) A line passe through points (4, 6) and (2, 4). Find the x-intercept of the line.

2 ID : ww-9-olympiad [2] Choose correct answer(s) f rom given choice (9) The a parallelogram ABCD, the bisector of A also bisects the side BC. If AB = 5 cm, f ind the length of side AD. a. 5 cm b. 12 cm c. 10 cm d. can not be determined (10) If Richard drives at two third of his usual speed, he covers a certain distance in one hour more than the time he takes while driving at his usual speed. Find the time taken by him to cover this distance with his usual speed. a. 4 hours b. One hour c. 3 hours d. 2 hours () Which triangle has the maximum area f or a given perimeter : a. Obtuse Angle T riangle b. Equilateral T riangle c. Isoceles T riangle d. Can not be determined (12) AB is diameter of the circle. If A and B are connected to E, circle is intersected at C and D respectively. If AB = 8 cm and CD = 4 cm, f ind AEB. a. 60 b. 65 c. 45 d. 75 (13) Barbara reaches her of f ice 1 minute early by traveling at a speed of 25 km/h and reaches 20 minutes late by traveling at a speed of 20 km/h. By how much time will she be early or late if she travels at 30 km/h? a. 10 minutes early b. 15 minutes early c. 10 minutes late d. 15 minutes late (14) Two circles with centres O and O intersect at two points A and B. A line PQ is drawn parallel to OO through A(or B) intersecting the circles at P and Q. Find the ratio PQ:OO. a. 1:2 b. 2:1 c. 1:1 d. 3:2

3 ID : ww-9-olympiad [3] (15) Two candles have dif f erent lengths and thickness. The shorter lasts 12 hours and the longer 9 hours when both are lit simultaneously. If af ter 5 hours of their being lit together at the same time, both have the same length, then f ind the ratio of their original lengths. a. 16:21 b. 17:22 c. 8: d. 17: Edugain ( All Rights Reserved Many more such worksheets can be generated at

4 Answers ID : ww-9-olympiad [4] (1) 1:2 The volume of a hemishpere of radius 'r' is 2 3 πr 3. The volume of a cone of radius 'r' and height 'h' is 1 3 π r 2 h From these equations we can cancel out the equal terms (remember the heights are also equal) to f ind the ratio as 1:2

5 (2) 15º ID : ww-9-olympiad [5] Consider a cyclic quadrilateral We know the f ollowing - The sum of the opposite angles is 180º i.e ADC + ABC = 180º - The angle subtended by a diameter to a point on the circumf erence = 90º We know that ADC = 105º ADC + ABC = 105º + ABC = 180º ABC = 75º Now consider the triangle f ormed by points A,B,C. We need to f ind BAC We know ABC + BAC + ACB = 180º (as it is a triangle) ABC = 75, and ACB is the angle subtended by the diameter to a point at the circumf erence, C Theref ore ACB = 90º From these, we get 75º + BAC + 90º = 180º BAC = 180º - (75º + 90º) = 15º

6 (3) $22 ID : ww-9-olympiad [6] According to the question, we have been asked to f ind the cost price of a toy. Let's the cost price of the toy be x. Selling Price, S.P. = $26 Gain = 2 of cost price = 2 Gain = Selling Price - Cost Price 2 x = 26 - x x 2 x + x = 26 x( 2 x( ) = 26 ) = x = 13 x = 22 Theref ore, the cost price of toy is $22. (4) -2 We have been told that (x + 2) is a f actor of 2x 3 + kx Thus, when the value of (x + 2) is zero, the value of the polynomial 2x 3 + kx must also be zero. The value of (x + 2) will be zero when x = -2. Thus, if we put x = -2 in the given polynomial, we can equate it to zero and solve the equation to f ind the value of k: 2(-2) 3 + k(-2) = 0 k = -2 Thus, the value of k is -2.

7 (5) Rectangle ID : ww-9-olympiad [7] We can draw these points and connect them on graph paper as f ollowing Now we notice f ollowing in this shape, 1. Opposite sides are equal and parallel to each other 2. All angles are equal and are right angles (90 ). These are the properties of Rectangle, theref ore this shape is a Rectangle

8 (6) 3 ID : ww-9-olympiad [8] Equation of line y = m x + c Substitute f irst point in the equation 1 = 2 m + c m = (1 - c)/2 (1) Substitute second point in the equation 2 = 1 m + c m = (2 - c)/1 (2) Step 4 On equating value of m f rom both equations, (1 - c)/2 = (2 - c)/1 1-1c = 4-2c 1 c = 3 c = 3 (7) 7 32

9 (8) -2 ID : ww-9-olympiad [9] Equation of line y = m x + c Substitute f irst point in the equation 6 = 4 m + c m = (6 - c)/4 (1) Substitute second point in the equation 4 = 2 m + c m = (4 - c)/2 (2) Step 4 On equating value of m f rom both equations, (6 - c)/4 = (4 - c)/2 12-2c = 16-4c 2 c = 4 c = 2 Step 5 m = (6 - c)/4 = 1 Step 6 Equation of line : y = 1 x + c Now when line intersect with x axis, value of y will be 0 0 = 1x + (2) x = -2 (9) c. 10 cm (10) d. 2 hours () b. Equilateral T riangle (12) a. 60

10 (13) b. 15 minutes early ID : ww-9-olympiad [10] Let us assume, the distance traveled by Barbara to the of f ice at the speed of 'S' km/minute in 'T' minutes is 'D' km. We know that, D = S T It is given that, Barbara reaches her of f ice 1 minute early by traveling at the speed of 25 km/h, We know that 1 hour = 60 minutes, Theref ore, speed = 25/60 km/minute Now, D = 25 (T - 1) (1) 60 It is also given that, Barbara reaches 20 minutes late by traveling at a speed of 20 km/h. Theref ore, D = 20 (T + 20) (2) 60 Step 4 From (1) and (2), we get, 25 (T - 1) = 20 (T + 20) (T - 1) = 20(T + 20) 25T - 25 = 20T (25-20)T = 425 T = (425)/(5) T = 85 minutes Step 5 Put T = 85, in (1), we get, D = 35 km Thus, Barbara reaches to of f ice in 85 minutes. Step 6 If Barbara travels at the speed 30 km/h, 35 Then, T = 30/60 = = 70 minutes Step 7 Theref ore, she will be early by (85-70) minutes = 15 minutes

11 (14) b. 2:1 ID : ww-9-olympiad [] Consider the image below We see that the line drawn at point O perpendicular to OO meets the line PQ at a point R A similar line drawn at O meets PQ at a point S Now PA is a chord, and OR is a line perpendicular to it drawn f rom the circle OR theref ore bisects OA, and PR = RA PA = 2 RA By the same reasoning AQ = 2 AS PQ = PA + AQ PQ = 2RA + 2 AS PQ = 2 (RA + AS) But RA + AS is the same as OO Theref ore PQ = 2 OO The ratio of PQ:OO is theref ore 2:1 (15) a. 16:21

Grade 9 Circles. Answer t he quest ions. For more such worksheets visit

Grade 9 Circles. Answer t he quest ions. For more such worksheets visit ID : th-9-circles [1] Grade 9 Circles For more such worksheets visit www.edugain.com Answer t he quest ions (1) ABCD is a cyclic quadrilateral such that AB is a diameter of the circle circumscribing it