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FINAL EXAMINATION 2020 21 Std: IX Marks: 80 Date: 01/03/21 Subject: Mathematics Dur. : 2 Hour 30min _________________________________________________________________________ SECTION - A (Attempt all questions) Question 1 a. Compare: 3 and b. Solve the given simultaneous linear equations: 3 ; c. In the given circle with centre O, chord AB=30cm and chord CD=34cm. Find the distance between the chords. 4 Question 2 a. Two joggers ran 15 miles north and then 12 miles west. What is the shortest distance they must travel to reach to their starting point. 3 b. If 3 find the value of c. Plot the points A(0,2),B(3,0),C(0,-2),D(-3,0) on a graph paper. Join ABCD. (i) Give the geometrical name of the quadrilateral ABCD. (ii) Find its perimeter. 4 Question 3 a. A is a point on the y-axis whose ordinate is 4 and B is a point on the x-axis whose abscissa is . Find the length of the line segment AB. 1 3 b. In the given figure, PQ is the side of a regular hexagon and QR is the side of a regular octagon. Find 3 (i) (ii) (iii) c. If find the value of a and b 4 Question 4 a. The mean of 1,2,5,7,11,14,15,16,19 is p and median of 4, 7,8,9,q,13,14,16 arranged in order is 10.Find p and q. b. Evaluate: 3 3 c. In the figure, find the length of (i) PS (ii) QR (iii) PR 4 SECTION - B (Attempt any 4 questions) Question 5 a. Arrange the given numbers in ascending order: 3 b. In the given right triangle ABC,P is a point on side AB such that =45 and =60 , find the length of AP if BC=10cm. (Use 2 3 c. In the given circle with centre O, diameter AB bisects the chord CD at a point E such that CE=ED= 8cm and EB =4cm. Find the radius of the circle. 4 Question 6 a. If find the value of 3 . 3 b. In the given figure, find the sides of c. Solve the given equations using cross multiplication method: 4 Question 7 a. Simplify: 3 b. Evaluate: 3 3 c. In the given figure, find the measure of 4 (i) (ii) (iii) (iv) Question 8 a. The mean of value of b. If arranged in order is Find the 3 and also the median of the observation. find the value of ( ) c. In the given figure, find the value of 3 4 (i) (ii) Question 9 a. Using distance formula show that the points X(-3,-1), Y(-1,0),Z(1,1) are collinear. b. The mean weight of 7 students is 50Kg. Three more students having weights 53Kg, 49Kg and 60Kg join the group. Find the new mean weight. c. Solve the simultaneous equations 3 3 4 Question 10 a. Evaluate: 3 4 b. In the given right triangle ABC, D is the mid-point of BC. Prove that 3 c. In a city, the weekly observations made in a study on the cost of living index are given in the following table: 4 Cost of living index 140-150 150-160 160-170 170-180 180-190 190-200 Number of weeks 5 10 20 9 6 2 Draw a frequency polygon for the data given above. Question 11 a. The marks obtained(out of 100) by 30 students in a class test are given below. 4 44 88 71 26 34 98 63 51 38 56 72 79 83 7 39 43 54 92 33 18 10 96 87 36 17 65 55 44 23 14 Taking class intervals as 0-20,20-40,40-60 construct a cumulative frequency distribution table. State the class mark of the 4th class. (i) (ii) b. Draw the graph of 6 ; and (i) (ii) (iii) Write down the co-ordinates of the point of intersection of the two lines. Find the area of the triangle formed by the lines and the y-axis. Write down the co-ordinates of the vertices of the triangle. 5
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