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IX MATHS SUMMATIVE ASSESSMENT – lI General Instructions: i. All questions are compulsory. ii. The questions paper consists of 34 questions divided into 4 sections- A,B,C and D. section A comprises of ten questions of 1 mark each, section B comprises of eight questions of 2 marks each, section C comprises of ten questions of 3 marks each and section D comprises of six question of 04 mark each. iii. There is no overall choice. However, an internal choice has been provided in one question of 2 marks each, three questions of 3 marks each and two questions of 4 mark each. You have to attempt only one of the alternatives in all such questions. iv. Use of calculators is not permitted. However you may ask for mathematical tables.
SECTION – A Question numbers 1 to 10 carry 1 mark each. Select the correct alternative from the alternatives given against each of the following questions (1-10): 1. If the length of the diagonal of a square is 8cm, then is area is : (a) 64cm2 (b) 32 cm2 (c) 16 cm2
(d) 48 cm2
2. Total surface area of a solid hemisphere of radius r is: (a) 3r2
(b) 2r2
(c) 4r2
1 (d) r2 3
(c) (0,y)
(D) (y,y)
3. In the given fig. if ABE = 65o, then ADC is (a) 35o (b) 25o
(c) 65o
(d) 115o
4. Any point on y-axis is of the form: (a) (x,0) (b) (x,y)
5. In a parallelogram ABCD, A = (3x + 15o) and B = (5x - 35o). The measure of D is : (a) 125o (b) 90o (c) 180o (d) none of these 6. The mean of first five whole numbers is : (a) 4 (b) 3
(c) 2
(d) 1
2 7. In the given fig. if CD = 4cm and AOB = COD = 60o, then the chord AB, is equal to (a) 4cm (b) 8cm (c) 2cm (d) data insufficient
8. If the total surface area of a cube is 54x2, then its lateral surface area is: (a) 36x2 (b) 30x2 (c) 27x2 (d) 45x2 9. In a quadrilateral ABCD the angles A,B,C and D are in the ratio 3 : 4 : 5 : 6. The difference between the greatest and the smallest angle is (a) 60o (b) 40o (c) 80o (d) 20o 10. In the given fig. ABCD is a rhombus. If A = 70o, the value of CDB is (a) 70o (b) 55o (c) 65o (d) 75o
SECTION – B Question numbers 11 to 18 carry 2 marks each. 11. The following table shows the weights of 12 workers in a factory. Weight (in kg)
60
63
66
69
72
Number of Workers
4
3
2
2
1
Find the mean weight of the workers. Or The runs scored by 11 members of a cricket team are: 14,29,43,13,31,50,18,0,27,58,34 Find the median score. 12. In the fig. P is a point on the chord BC such that AB = AP. Prove that CP = CQ.
3 13. 10 cylindrical pillars of a building have to be painted. If the diameter of each pillar is 50cm and the height 4m, what will be the cost of painting in the pillars at the rate of Rs. 14 per m2? 14. The diagonals of a rectangle ABCD meet at O. if BOC = 44o, find OAD. 15. In the given fig. O is the centre of the circle. The angle subtended by the area BCD at the centre is 140o. BC is produced to P. Determine BAD and DCB.
16. Prove that: If one side of a cyclic quadrilateral is produced, then the exterior angle is equal to the interior opposite angle. 17. Express y in terms of x in the equation 2x - 3y = 12. Find the points where the line represented by this equation cuts x-axis and y- axis. 18. Draw the graph of the equation y = 2x + 3.
SECTION – C Question numbers 19 to 28 carry 3 marks each. 19. D, E,and F are the mid-points of the sides BC,CA and AB respectively of ABC. Prove that 1 (i) BDEF is a || gm (ii) ar (DEF) = (ar ABC) 4 20. In the adjoining fig. 6, O is the centre of the circle and ABC = 45o. Prove that OA OC.
Or Prove that the line drawn through centre of a circle to bisect a chord is perpendicular to the chord. 21. A farmer was having a field in the form of a parallelogram PQRS. She took any point A on RS and joined it to points P and Q. in how many parts the field is divided? What are the shapes of these parts? The farmer wants to sow wheat and pulses in equal portions of the field separately. How should she do it?
4 Or Construct a right triangle whose base is 12cm and sum of its hypotenuse and other side is 18cm. 22. A metal pipe is 77cm long. The inner diameter of a cross section is 4cm, the outer diameter being 4.4cm. find its (i) Inner curved surface area (ii) Outer curved surface area (iii) Total surface area Or It is required to make a closed cylindrical tank of height 1m and base diameter 140cm from a metal sheet. How many square metre of the sheet are required for the same? 23. What length of tarpaulin 3m wide will be required to make conical tent of height 8m and base radius 6m? assume that the extra length of material that will be required for stitching and wastage in cutting is approximately 20cm (use = 3.14) 24. A river 3m deep and 40m wide is flowing at the rate of 2km per hour. How much water will fall into the sea in a minute? 25. The points scored by a Kabaddi team in a series of matches are as follows: 17,4,8,27,15,10,5,14,8,24,38,10,8,7,18,28 Find the median of the points scored. 26. Following is the frequency distribution of total marks obtained by the students of different sections of a class. 300-350 Marks 100-150 150-200 200-250 250-300 Number of students
60
100
90
80
50
Draw a histogram for the distribution above. 27. The height of 50 students measured to the nearest centimeters, have been found to be as follows: 161 150 154 165 168 161 154 152 150 151 162
164
171
165
158
154
156
172
160
170
153
159
161
170
162
165
166
168
165
164
154
152
153
156
158
162
160
161
173
166
161
159
162
167
168
159
158
153
154
159
(i)
Represent the data given above by a grouped frequency distribution table, taking the class intervals as 160-156, 165-170 etc. (ii) What can you conclude about their height from the table? 28. In countries like USA and Canada, temperature is measured in Fahrenheit, equation that 9 converts Fahrenheit to Celsius. F = C + 32 5 (i) Draw the graph of linear equation above using Celsius for x-axis and Fahrenheit for y – axis. (ii) Is there a temperature which is numerically the same in both Fahrenheit and Celsius? If yes, find it.
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SECTION – D Question numbers 29 to 34 carry 4 marks each. 29. Construct a triangle if its perimeter is 10.4cm and two angles are 45o and 120o. 30. Draw a histogram and frequency polygon for the following distribution: Marks Obtained
0 - 10
10 - 20
20 - 30
No. of students
7
10
6
30 - 40 40 - 50 50 - 60 60 - 70 70 - 80 8
12
3
2
2
31. 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. Or A quadrilateral is a parallelogram if a pair of opposite side is equal and parallel. Prove it. 32. Find at least four solutions for the following linear equations and draw the graph. (i) y = x - 4 (ii) y = 2x 33. In the adjoining fig. 8, ABCD is a rhombus in which BC = 25 cm, and AO = 24cm. find the sum of lengths of the diagonals.
Or Prove that the line segment joining the mid-points of a quadrilateral ABCD form a parallelogram.
34. A dome of a building is in the form of a hemisphere. From inside, it was white-washed at the cost of Rs. 997.92. if the cost of white-washing is Rs. 4.00per square metre, find the volume of 22 the air inside the dome. Take 7
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Answers SUMMATIVE ASSESSMENT – lI 1. B
2. A
3. C
4. C
5. B
6. C
7. A
8. A
9. A
10. B
11. 64.25 or 29
12.
13. 880
14. 68
15. 70
16.
17. (6,0) and (0,-4)
18.
19.
20.
21.
(ii) (i) 968cm2,(ii) 1064.8cm (iii) 2038.08cm2
22. 63m
23. 4000m3
24. 12
27. Yes,No
28.
Or 7.48m2 25. 30.
26. 31.
32. 62
29. 3
33. 523.908m
34.
