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SUMMATIVE ASSESSMENT – II, 2012

II, 2012

MATHEMATICS /

Class – IX / IX

Time allowed : 3 hours Maximum Marks : 90

3 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-1002

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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. How many linear equations in x and y can be satisfied by x 1 and y 2 ?

(A) Only One (B) Two (C) Infinitely many (D) Three

x y x1 y2

(A) (B)

(C) (D) 3

2. In the figure, If ABDC and HFAB, then which of the following is true ?

(A) ar (GHF)(DHFC) (B) 3 ar (GHF)2 ar (DHFC) (C) ar (GHF)(HEF) (D) None of these

ABDC HFAB

(A) ar (GHF) ar (DHFC) (B) 3 ar (GHF)2 ar(DHFC)

(C) ar (GHF) ar (HEF) (D)

3. In the given fig O is centre of circle, ACO 35 and ABO 45, then BOC is

(A) 80 (B) 160 (C) 90 (D) 70

O ACO = 35 ABO45 BOC

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(A) 80 (B) 160 (C) 90 (D) 70

4. The graph of y 6 is a line : (A) parallel to x - axis at a distance 6 units from the origin (B) parallel to y - axis at a distance 6 units from the origin. (C) passing through the point (6,0) (D) passing through the origin.

y6

(A) x 6

(B) 6 y

(C) (6,0)

(D)

5. The class mark of the class 130 - 150 is :

(A) 130 (B) 135 (C) 140 (D) 145

130 - 150

(A) 130 (B) 135 (C) 140 (D) 145 6. In a cylinder, radius is doubled and height is halved, curved surface area will be :

(A) halved (B) doubled (C) same (D) four times

(A) (B) (C) (D)

7. If A&B are the only two outcomes of an event and P(A) 0.32 then value of P(B) would

be :- (A) 0.38 (B) 0.68 (C) 0.78 (D) 0.32

A B P(A) 0.32 P(B)

(A) 0.38 (B) 0.68 (C) 0.78 (D) 0.32 8. Volume of right circular cone of radius 6cm and height 7cm is

(A) 1892 cm3 (B) 66cm3 (C) 264cm3 (D) 132cm3

6 7

(A) 1892 3 (B) 66 3 (C) 264 3 (D) 132 3

SECTION-B /

Question numbers 9 to 14 carry two marks each.

9 14 2

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9. ABCD is parallelogram, AEDC and CFAD If AB16cm, AE8cm, CF10cm, find AD.

ABCD AEDC CFAD AB16 , AE8

CF10 AD

10. A solid shotputt is a metallic sphere of radius 4.9cm. Find the volume of the shot

putt.

4.9cm

11. The following observations have been arranged in ascending order. If the median of the

data is 63, find x 29, 32, 48, 50, x, x+2, 72, 78, 84, 95

63 x

29, 32, 48, 50, x, x+2, 72, 78, 84, 95 12. Out of the past 250 consecutive days, its weather forecasts were correct 175 times.

(i) What is the probability that on a given day it was correct ? (ii) What is the probability that it was not correct on a given day ?

250 175

(i)

(ii)

13. Prove that if chords of congruent circles subtend equal angles at their centres, then the

chords are equal.

OR/

Suppose you are given a circle. Give a construction to find its centre.

14. For a particular year, following is the distribution of age of primary school teachers in

district

Age(in years) : 15 –20 20 –25 25 –30 30 –35 35 –40 40 –45 45 –50

No of teachers : 10 30 50 50 30 6 4

Answer the following questions (a) What is the class size ?

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(b) Which age group represents the lowest no. of teachers ?

15 –20 20 –25 25 –30 30 –35 35 –40 40 –45 45 –50

10 30 50 50 30 6 4

(a)

(b)

SECTION-C /

Question numbers 15 to 24 carry three marks each.

15 24 3

15. Give the equations of two lines passing through (2,14). How many more such lines are

there and why ?

(2,14)

16. The side AB of parallelogram ABCD is produced to any point P. A line through A and

parallel to CP meets CB produced at Q and then parallelogram PBQR is completed. Show that ar (ABCD) ar (PBQR)

ABCD AB P PBQR

CP A CB

Q ar (ABCD)ar (PBQR)

17. Draw a line segment AB5cm. From the point A draw a line segment AD6cm making

an angle of 60. Draw perpendicular bisector of AD.

AB5 A 60 AD6

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AD

OR/

Draw a line segment of 10 cm. Divide it into four equal parts. Write the measure of each part.

10

18. Three cubes of edge 12cm are joined together (end to end). Find the volume of the

resulting cubiod.

12 3

OR/

Curved surface area of a solid cone is 308 cm2 and its slant height is 14cm. Find (i) radius of base (ii) total surface area of the cone.

308 2 14

(i) (ii)

19.

Find the mean ( x ) of first ten prime numbers and hence show that 10

ii 1

x x

0.

( x ) 10

ii 1

x x

0

20. Find three different solutions of the equation : 4x3y12 from its graph.

4x3y 12

21. The height of a cone is 16cm and the base radius is 12cm. Find curved surface area and the

volume of cone (3.14)

12 16

3.14

22. If the diagonals of a parallelogram are equal then show that it is a rectangle.

OR/

Show that the diagonals of a rhombus are perpendicular to each other.

23. In the figure ABC, is an isoceles triangle in which ABAC, AD bisects exterior angle PAC

and CDAB. Prove that ABCD is a parallelogram

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ABC ABAC, PAC AD

CDAB ABCD

24. Marks obtained by 90 student in a particular subject out of a total of 100 are given below,

find the probability that a student selected obtained marks 60 or above and a student selected obtained less than 40.

Marks out of 100

0 – 20 20 – 30 30 –40 40 –50 50 –60 60 –70 70 and above

No. of students 7 10 10 20 20 15 8

90 100 60

40

100 0 – 20 20 – 30 30 –40 40 –50 50 –60 60 –70 70

7 10 10 20 20 15 8

SECTION-D /

Question numbers 25 to 34 carry four marks each.

25 34 4

25. In the figure ABCD is a parallelogram and AP, CQ are perpendiculars drawn from

vertices A and C on diagonal BD. Show that

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(i) APBCQD (ii) AP CQ

ABCD BD A C AP CQ

(i) APBCQD (ii) AP CQ

OR/

ABCD is a quadrilateral in which L, M, N and O are the mid points of the sides AB, BC, CD and DA respectively as in the figure below. Show that

(i) ONAC and ON 1

2 AC

(ii) ON LM (iii) LMNO is a gm.

ABCD L, M, N O AB, BC, CD DA

(i) ONAC ON1

2 AC

(ii) ON LM

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(iii) LMNO

26. Construct a triangle ABC in which BC 7cm, B75 and ABAC 13cm.

ABC BC7 B75 ABAC13

27. Draw the graph of xy 3 and 2x2y8 on the same axes. What does the graph of

these lines represent ?

xy3 2x2y8

28. A metal pipe is 77cm long. The inner diameter of a cross – section is 4cm, the outer

diameter being 4.4cm. Find the total surface area of the metal used.

77 4 4.4

29. In, the figure, if a line interacts two concentric circles with centre O at A,B,C and D, prove

that ABCD

O A, B, C D

ABCD.

30. Show that the line segments joining the mid points of the opposite sides of a quadrilateral

bisect each other.

31. The following linear equation converts Fahrenheit temperature to celcius

F

9

5

C32

(i) If the temperature is 40C what is the temp in Fahrenheit ?

(ii) If the temperature, is 95 F what is the temp. in celcius ? (iii) Is there a temp which is numerically of same value in Fahrenheit and celcius ? If

yes find the temperature.

F 9

5

C32

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(i) 40C

(ii) 95 F

(iii)

32. ABCD is a cyclic quadrilateral whose diagonals interest at E. If DBC70, BAC30,

find BCD. Further, if ABBC, find ECD.

ABCD E DBC70,

BAC30 BCD ABBC ECD

33. A godown measures 45m25m10m. If 8000 wooden crates each measuring

1.5m1.25m0.5m are stored in the godown. Find how many more such crates can be stored in the godown.

45 25 10 8000

1.5 1.25 0.5

OR/

A hemispherical tank is made of iron sheet 1cm thick. If the inner radius is 1m then find the volume of the iron used to make the tank.

1 1

34. A random survey of number of children of various age groups playing in a park was

found as follows :

Age (in years) Number of children

1 – 2 5

2 – 3 3

3 – 5 6

5 – 7 12

7 – 10 9

10 – 15 10

15 - 17 4

Draw the histogram of above data.

1 – 2 5

2 – 3 3

3 – 5 6

5 – 7 12

7 – 10 9

10 – 15 10

15 - 17 4

- o O o -