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SUMMATIVE ASSESSMENT – II, 2012
II, 2012
MATHEMATICS /
Class – IX / IX
Time allowed : 3 hours Maximum Marks : 90
General Instructions :
(i) All questions are compulsory. (ii) The question paper consists of 34 questions divided into four sections A, B, C and D. Section-A comprises of 8 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 10 questions of 4 marks each. (iii) Question numbers 1 to 8 in Section-A are multiple choice questions where you are to select one correct option out of the given four. (iv) There is no overall choice. However, internal choices have been provided in 1 question of two marks , 3 questions of three marks each and 2 questions of four marks each. You have to attempt only one of the alternatives in all such questions. (v) Use of calculator is not permitted.
(i)
(ii) 34 8
1 6 2 10 3 10 4
(iii) 1 8
(iv) 2 3
3 4 2
(v)
MA- 1067
SECTION–A /
Question numbers 1 to 8 carry one mark each. For each questions, four alternative choices have been provided of which only one is correct. You have to select the correct choice. 1 8 1
1. x 5, y 2 is a solution of the linear equation : (A) x 2 y 7 (B) 5 x 2 y 7 (C) x y 7 (D) 5 x y 7 x 5 y 2 (A) x 2 y 7 (B) 5 x 2 y 7 (C) x y 7 (D) 5 x y 7 2. (^) In a ABC, AD is a median. E is the mid point of the median AD. If area (BED) 20 cm^2 , then ar ( ABC) will be (A) 10 cm^2 (B) 5 cm^2 (C) 60 cm^2 (D) 80 cm^2 ABC AD AD E ar (BED) 20 2 ar ( ABC) (A) 10 2 (B) 5 2 (C) 60 2 (D) 80 2 3. (^) In the figure, arc ABC of the circle subtends angle of 130 ^ at the centre O. If AB is produced to D, then CBD will be
(A) 60 ^ (B) 65 ^ (C) 70 ^ (D) 130
ABC O 130 ^ AB D
CBD
(A) 60 ^ (B) 65 ^ (C) 70 ^ (D) 130
4. Graph of the equation y 7 is a line (A) parallel to x – axis and at a distance of 7 units from the origin (B) parallel to y – axis and at a distance of 7 units from the origin. (C) making an intercept of 7 with x – axis (D) making an intercept of 7 with both x – axis and y – axis.
10. Find the curved surface area of a closed cylindrical petrol storage tank that is 3.8 m in diameter and 4.9 m high. 3.
11. The following observations have been arranged in ascending order. If the median of the data is 65, find the value of x. 32, 35, 50, 51, x , x 2, 73, 76, 83, 90. 65 x 32, 35, 50, 51, x , x 2, 73, 76, 83, 90. 12. A bag has 3 red and 7 black balls. One ball is taken out of the bag. Find the probability that it is a (i) red ball, (ii) black ball. 3 7 (i) (ii) 13. Prove that equal chords of a circle subtend equal angles at the centre.
OR /
Prove that the line drawn through the centre of a circle to bisect a chord is perpendicular to the chord.
14. Find the value of p, if the mean of the following distribution is 7.5 :
x (^) 3 5 7 9 11 13 y 6 8 15 P 8 4 p 7.
x 3 5 7 9 11 13 y 6 8 15 P 8 4
SECTION-C /
Question numbers 15 to 24 carry three marks each. 15 24 3
15. Find the value of k, if x 2, y 1 is a solution of the equation 2 x 3 y k. Express y in terms of x and find the value of y when x 1 k x 2, y 1 2 x 3 y k y x y x 1 16. (^) ABCD is a parallelogram whose diagonals intersect at O. If P is any point on BO, prove that (i) ar (ADO)ar (CDO) (ii) ar (ABP)ar (CBP) ABCD O BO P (i) ar (ADO)ar (CDO) (ii) ar (ABP)ar (CBP)
17. (^) Construct a triangle ABC in which A 60 , B 90 and ABBCCA11cm.
ABC A 60 , B 90 ^ ABBCCA 11
18. A small indoor greenhouse (herbarium) is made entirely of glass panes (including base) held together with tape. Greenhouse is 30 cm long, 25 cm wide and 25 cm high. (i) What is the area of the glass? (ii) How much of tape is needed for all the 12 edges? (greenhouse) 30 25 25 (i) (ii) 12 OR / A conical tent is to accommodate 11 persons. Each person must have 4 square metre of the space on the ground and 20 cubic metres of air to breath. Find the height of the cone. 11 4 2 20 3 19. The blood group of 20 students are recorded as follows : A, B, O, O, AB, O, A, O, B, A, O, AB, O, A, A, O, B, A, B, O Represent this data is the form of a frequency distribution table. Which is the rarest blood group? 20 A, B, O, O, AB, O, A, O, B, A, O, AB, O, A, A, O, B, A, B, O
OR /
Find the mean of first ten multiples of 3. 3
20. Give the equation of two lines passing through (3, 4). How many more such lines are there, and why? (3, 4) OR / Solve for x : (3 x 11 2
x
18) : What will be the graph of this equation?
x (3 x 11 2 ^ x ^7 2
21. A right triangle ABC with sides 5 cm, 12 cm and 13 cm is resolved about the side 12cm. Find the volume of the solid so obtained. ABC 5 12 13 12
SECTION-D /
Question numbers 25 to 34 carry four marks each. 25 34 4
25. l , m and n are three parallel lines intersected by transversals p and q such that l, m and n cut off equal intercepts AB and BC on p (see figure). Show that l, m and n cut off equal intercepts DE and EF on q also.
p q l, m n AB CD DE EF q
26. (^) Construct a triangle ABC in which BC 7 cm, B 75 ^ and ABAC 13 cm. ABC BC 7 B 75 ^ ABAC 13 OR / Construct a ABC in which B 60 , C 45 and ABACCA11 cm ABC ABBCCA 11 B 60 C 45 27. A part of familys budget on milk is constant and is fixed at Rs 500, while the other is variable and it depends on the need for more milk at the rate of Rs 20 per litre. If extra milk taken is x litre and total expenditure on milk is Rs y , then write a linear equation for this problem. Draw its graph. 500 20 x y 28. A solid cube of side 12 cm is cut into eight cubes of equal volume. What will be the side of the new cube? Also, find the ratio between their surface areas. 12 8
29. (^) In figure ABCD is a cyclic quadrilateral in which AB is extended till F and BEDC. If FBE 20 ^ and DAB 95 , then find ADC.
ABCD AB F BEDC
FBE 20 ^ DAB 95 ^ ADC
30. In equilateral triangle ABC, the mid points of the sides BC, CA and AB are respectively D, E and F as shown in the figure. Prove that DEF is also an equilateral triangle.
ABC BC, CA AB D, E F
DEF
33. Three solid spheres of iron whose diameters are 2 cm, 12 cm, and 16 cm respectively are melted into a single solid sphere. Find the radius of the solid sphere. 2 12 16 34. Construct a histogram and frequency polygon for the following data : Monthly school fee in Rs.
600 – 800 800 - 1000 1000 - 1200 1200 - 1400 1400 - 1600 1600 - 1800 No. of schools 5 12 14 18 10 9
600 – 800 800 - 1000 1000 - 1200 1200 - 1400 1400 - 1600 1600 - 1800
5 12 14 18 10 9
- o O o -
