ii, (2014-2015) summative assessment ii mathematics / class xi /...

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II, (2014-2015)

SUMMATIVE ASSESSMENT – II MATHEMATICS /

Class – IX / IX 3 90

Time allowed : 3 hours Maximum Marks : 90

(i)

(ii) 31 4

1 6 2 8

3 10 4

3-3 2 4 1

(iii)

(iv)

General Instructions :

(i) All questions are compulsory.

(ii) The question paper consists of 31 questions divided into five sections A, B, C ,D and E. Section-A comprises of 4 questions of 1 mark each, Section-B comprises of 6 questions of 2 marks each, Section-C comprises of 8 questions of 3 marks each and Section-D comprises of 10 questions of 4 marks each. Section E comprises of two questions of 3 marks each and 1 question of 4 marks from Open Text theme.

(iii) There is no overall choice. (iv) Use of calculator is not permitted.

/ SECTION-A

1 4 1

Question numbers 1 to 4 carry one mark each.

1 2 6

7

xy x y

1

www.tiwariacademy.com


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Express x in term of y : 2 6.7

xy

2 a 3 6x ay

Find a, if linear equation 3 6x ay has one solution as (4, 3).

1

3 64 cm2 16 cm

Area of parallelogram is 64 cm2. If base of the parallelogram is 16 cm, find the height of the

corresponding attitude.

1

4 r h

A cylinder of base radius r and height h is dipped vertically to half the height in a bucket full

of purple paint. Find the area of the surface which gets painted.

1

/ SECTION-B

5 10 2

Question numbers 5 to 10 carry two marks each.

5 ABCD CD P R

(i) ar (PAB) ar (RAB)

(ii) ar (PAB) 8 cm2 ar (ABCD)

P and R are point on side CD of a parallelogram ABCD. Show that

(i) ar (PAB) ar (RAB)

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(ii) If ar (PAB) 8 cm2, find ar (ABCD).

6 P XPZ2(XZYYXZ)

In the given figure, P is the centre of the circle. Prove that XPZ2(XZYYXZ).

2

7 XYZ XA ABXY YB

In the given figure of XYZ, XA is a median and ABXYShow that YB is also a median.

2

8 440 cm3 88 cm2

If the volume of cuboid is 440 cm3 and the area of base is 88 cm2, find the height of the cuboid.

2


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9 7 5 8

In a bottle there are 7 red buttons, 5 green buttons and 8 purple buttons. What is the

probability that randomly drawn button from the bottle is a purple button ? If one extra green

button is put in side the bottle, what will be the probability that randomly drawn button is

purple ?

2

10 2 1850

0 1 2

511 814 575

(i)

(ii)

1850 families with 2 children were selected randomly and the following data were recorded :

Number of girls in a family 0 1 2

Number of families 511 814 575

If a family is chosen at random, compute the probability that it has

(i) exactly 1 girl.

(ii) exactly 2 boys.

2

/ SECTION-C

11 18 3

Question numbers 11 to 18 carry three marks each.



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11 yx1 xy5

y-

Draw the graphs of yx1 and xy5 on the same cartesian plane . Shade the triangle formed by

these graphs and y-axis and also find its area.

3

12 (3,1)

Find the equations of any two lines passing through the point (3,1). How many such lines can be

there ?

3

13 PQR T PS ar (PQT)

1

4ar (PQR)

In PQR, point T is the mid - point of median PS as shown in the given figure. Show that

ar(PQT) 1

4ar (PQR).

3

14 ABCDE O ACD

DEB

3


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In the given figure, ABCDE is a pentagon. Whose vertices lie on the semicircle with centre O.

Find the sum of ACD and DEB ?

15

Draw a right angle. Bisect it and verify the result.

3

16 PQRS O x y

In the figure, PQRS is a parallelogram whose diagonals intersect at O. Find the values of x

and y. Also, find the angles of the parallelogram.

3

17 3


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Two diameters of a circle intersect each other at right angles. Prove that the quadrilateral

formed by joining their end-points is a square.

18 60 7 cm cm

60 circular plates, each of radius 7 cm and thickness one-third of a cm, are placed one above

another to form a solid circular cylinder. Find the total surface area and the volume of the

cylinder so formed.

3

/ SECTION-D

19 28 4

Question numbers 19 to 28 carry four marks each.

19 20x50y200

(a) x- (b) y-

Represent 20x50y200 by a graph. Write the coordinates of the point where it meets :

(a) x-axis (b) y-axis

4

20 4


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Write the equation of the lines drawn in following graph. Also, find the area enclosed

between them.

21 EFGH EG FH, X ar(EXF) ar(EXH)

ar(GXF)ar(HXG)

EFGH is a parallelogram with diagonals EG and FH meeting at a point X. Show that

ar(EXF)ar(EXH)ar(GXF)ar(HXG)

4

22 AB CD O E

EBED EAEC

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In the figure, AB and CD are two equal chords of a circle whose centre is O. When produced

these chords meet at E. Prove that EBED and EAEC.

23 STU ST TU US 10 cm, T60 U 75

Construct STU, if ST TU US 10 cm, T60 and U 75.

4

24 ABCD AB P Q

APABBQ PD QC R PRQ90

In the figure, ABCD is a rhombus whose side AB is produced to points P and Q such that

APABBQ. PD and QC are produced to meet at a point R. Show that PRQ90.

4


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25 A ''V

1

3l2h

1

3h3'' B ''V

1

3r2h''

(a) A B

(b)

(i)

(ii)

(iii)

(iv)

Student A stated the formula for the volume of cone as ''V1

3l2h

1

3ph3'' and the student B as

''V1

3r2h''.

(a) Is the formula used by student A give same answer as student B or not ? If yes, why ?

(b) By stating formula different than as usual which value is depicted.

(i) Truth value

(ii) Social value

(iii) Respect for other views

(iv) Equality

4

26 12 m 1.35 m2

340.20 85 m2 91.80

The cost of papering the walls of the room 12 m long at the rate of Rs. 1.35 per m2 is Rs. 340.20

and the cost of matting the floor at the rate of 85 paisa per m2 is

Rs. 91.80. Find the height of the room.

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27 0.50 cm 6 cm

A hemispherical bowl is made of 0.50 cm thick brass. The inner radius of the bowl is 6 cm.

Find the outer and inner curved surface area and volume of the bowl.

4

28 100

22

10

15

24

29

(a)

(b)

(c)

The table shows the prefered snacks of 100 children :

Prefered Snack Number of children

Lays chips

Crax

Cheese Balls

Uncle chips

Fun flips

22

10

15

24

29

Find the probability that the child chosen at random likes :

(a) crax and funflips

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(b) lays chips and cheese balls (c) only uncle chips

/SECTION-E

( /Open Text)

(* Please ensure that open text of the given theme is supplied with this question paper.)

Theme : Empower to learn

29

How Harshit gets benefitted with these sites ?

3

30 – 1 .

Draw the bar graph for the table – 1.

3

31

Prepare frequency polygon for table 2. Number of question (on trouble bubble) asked during different hours of the day are given. Find median for this data of questions.

4

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