SUMMATIVE ASSESSMENT –I (2011)

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460012

MATHEMATICS / xf.kr
Class – IX /
& IX
Time allowed: 3 hours
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Maximum Marks: 90
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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 10
questions of 4 marks each.
(iii)
Question numbers 1 to 10 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 choice 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.
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(i)
(ii)

(iii)
(iv)
(v)

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Section-A
Question numbers 1 to 8 carry one mark each. For each question, four
alternative choices have been provided of which only one is correct. You have
to select the correct choice.

Page 1 of 11

1

1.

The simplified form of
(A) 13

2

13 5
1

13 3

is :

8

15

(B)

13 15

15

(B)

13 15

1

2 15

(C) 13 3 

(D) 13

1

13 5
1

13 3

(A) 13
2.

3.

2

8

1

(D) 13

Which of the following is a polynomial in one variable :
(A) 3x2x

(B)

(C) x3 y3 7

(D) x 

(A)

3x2x

(B)

(C)

x3 y3 7

(D)

3 x  4

1
x

3 x  4

x 

1
x

Which of the following is a quadratic polynomial ?
(A) 3x35x4
(C) x2 

1
3
x

(B)

x2 

(C)
If

53x2x27x3

(D) (x1) (x1)

(A) 3x35x4

4.

2 15

(C) 13 3 

1
3
x

(B)
(D)

53x2x27x3

(x1) (x1)

x
y
 1, (x, y  0), then, the value of x3y3 is :
y
x

(A) 1

(B) 1

x
y
 1, (x, y  0)
y
x

(C) 0

(D)

1
2

x3y3

Page 2 of 11

(A) 1
5.

(B) 1

(C) 0

1
2

(D)

Value of x in the figure below is :

(A) 80

(B) 40

(C) 160

(D) 20

(B) 40

(C) 160

(D) 20

x

(A) 80
6.

In ABC, if ABAC, B50, then A is equal to :
(A) 40

(B)

ABC
(A)
7.

50

(C)

ABAC, B50
40

80 

(D) 130

A

(B) 50

(C)

80

(D)

130

A square and an equilateral triangle have equal perimeters. If the diagonal of the square is
12 2 cm then area of the triangle is :
(A)

24

2 cm 2

(B)

24

3 cm2

(C)

48

3 cm2

(D)

64

3 cm2

(D)

64

3

12 2
(A)
8.

24

2

2

(B)

24

3

(C)

2

48

3

2

2

The side of an isosceles right triangle of hypotenuse 5 2 cm is :
(A) 10 cm

(B)

8 cm

(C)

5 cm

(D) 3 2 cm

5 2
(A) 10

(B)

8

(C) 5

(D)

3 2

Page 3 of 11

Section-B
Question numbers 9 to 14 carry two marks each.
9.

If x32 2 , then find whether x
x32 2

10.

x

1
is rational or irrational.
x

1
x

Without actually calculating the cubes, find the values of 553253303.
553253303

11.

If xy8 and xy15, find x2y2.
xy8

12.

xy15,

In the given figure, if  POR and  QOR form a linear pair and ab80, then find the
value of a and b.
 POR

13.

x2y2

 QOR

ab80

a

b

In figure, BE, BDCE and 12. Show ABC  AED.

BE, BDCE

12

ABC  AED.

Page 4 of 11

OR

In the figure given below AC > AB and AD is the bisector of  A. Show that  ADC >  ADB.

AC > AB

14.

A

 ADC >  ADB.

AD

Find the co-ordinates of the point which lies on y–axis at a distance of 4 units in
negative direction of y–axis.
(A) (4, 0)

(B)

(4, 0)

y–
(A) (4, 0)

(C)

(0, 4)

(D) (0, 4)

(C)

(0, 4)

(D) (0, 4)

4
(B)

(4, 0)

Section-C
Question numbers 15 to 24 carry three marks each.
15.

Represent 2 on the number line.
2

OR
p
Express 18.48 in the form of where p and q are integers, q  0.
q

18.48

16.

p
q

p

q

If x  5  2 6 then find the value of x 2 

q

1
x2

0

.

Page 5 of 11

1
x2  2
x

x 52 6

17.

If x 

1
1
 7 , then find the value of x 3  3 .
x
x

x

1
7
x

1
x3  3
x

OR

Factorise : x33x210x24
x33x210x24
18.

Using suitable identity evaluate (998)3.
(998)3

19.

In the given figure, lines AB and CD intersect at O. If AOC BOE 70 and
BOD 40 , find BOE and reflex EOC .

AB

CD

BOE

O

AOC BOE 70

BOD 40

EOC

OR

In the following figure, PQST, PQR  115andRST  130 .
Find the value of x.

Page 6 of 11

PQST PQR  115

RST 130

x

20.

In the given figure, ABC is a triangle with BC produced to D. Also bisectors of  ABC
and  ACD meet at E. Show that BEC 
ABC

BC
BEC 

E

1
BAC .
2

 ABC

D

 ACD

1
BAC
2

21.

In the given figure, sides AB and AC of ABC are extended to points P and Q
respectively. Also  PBC <  QCB. Show that AC > AB.
ABC
 PBC <  QCB.

AB

AC

P

Q

AC > AB.

Page 7 of 11

22.

In the given figure, ACBC,  DCA  ECB and  DBC  EAC.
DBCEAC and hence DCEC.
ACBC,  DCA  ECB

 DBC  EAC

Show that

DBCEAC

DCEC.
23.

The degree measure of three angles of a triangle are x, y, and z. If z 

xy
2

then find the value of z.
x, y,
24.

z

xy
2

z

z

The perimeter of a triangular ground is 900 m and its sides are in the ratio
3 : 5 : 4. Using Heron’s formula, find the area of the ground.
900

3:5:4

Section-D
Question numbers 25 to 34 carry four marks each.
25.





1



x  2 5 2  2 5

If
x2y2.





1





1

x  2 5 2  2 5

2



1

and

2

1









1









y  2 5 2  2 5 2

1

then evaluate

1

y  2 5 2  2 5 2

x2y2

OR
If a 

3  2
3  2
and b
, find the value of a2b25 ab .
3  2
3  2

Page 8 of 11

3  2
3  2

a 

26.

b

3  2
3  2

Rationalize the denominator of

a2b25 ab

4
2  3  7

4
2  3  7

27.

4a29b22a3b.

Factorize : (a)

a2b22(abacbc)

(b)

(a)
(b)
28.

4a29b22a3b.
a2b22(abacbc)

If (x5) is a factor of x32x213x10, find the other factors.
x32x213x10

29.

(x5)

Factorize a7ab6.
a7ab6
OR

If ax3bx2x6 has x2 as a factor and leaves remainder 4 when divided by x2,
find the values of a and b.
ax3bx2x6

x2
a
30.

(x2)

4

b

In the given figure, PQR is an equilateral triangle with coordinates of Q and R
as (2, 0) and (2, 0) respectively. Find the coordinates of the vertex P.

Page 9 of 11

PQR

Q

R

(2, 0)

(2, 0)

P

31.

In the adjoining figure, the side QR of PQR is produced to a point S. If the bisectors of
 PQR and  PRS meet at point T, then prove that QTR 

1
QPR .
2

Page 10 of 11

PQR

QR

QTR 

T

32.

 PQR

S

 PRS

1
QPR .
2

In the following figure, the sides AB and AC of ABC are produced
to D and E respectively. If the bisectors of  CBD and  BCE meet
at O, then show that BOC  90 

ABC
 BCE

33.

AC

O

D

E

BOC  90 

 CBD
A
2

BE and CF are two equal altitudes of a triangle ABC. Using RHS congruence rule, prove that
the triangle ABC is isosceles.
ABC

34.

AB

A
.
2

BE

CF

RHS

ABC

In a triangle ABC, ABAC, E is the mid point of AB and F is the mid point of
AC. Show that BFCE.
ABC

ABAC

E

AB

F

AC

BFCE.

Page 11 of 11