CBSE Class 9 Mathematics SA1 2011 Question Paper

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SUMMATIVE ASSESSMENT I (2011)

-iln |ii I
MATHEMATICS / nlin
Class IX / IX

Time allowed: 3 hours Maximum Marks: 90
lii ln - s i- lin- sa

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 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 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.

i-i l i
(i) i| li r|
(ii) ; - s r, lr i ii , , nii - i-i ni r| i - s r l-
- i r , i - c r l- - z r , i - a r l-
- s r nii i - a r l- - r|
(iii) i - i s n rl~| r ri ii i l~i - r| l~ i
r|
(iv) ; - i; i| i l l~ r| r, l inl l~ z i -, s i s
i - i i z i - l n r| - - l~ i |
(v) - i in ln r|

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.
460021
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1.
If then x is equal to :
(A) 49 (B) 2 (C) 12 (D) 7
x
(A) 49 (B) 2 (C) 12 (D) 7

2.
Zero of the polynomial p (x) where p (x) ax, a 0 is :
(A) 1 (B) a (C) 0 (D)
p (x) ax a 0
(A) 1 (B) a (C) 0 (D)

3.
If (x3) is a factor of x
3
3x
2
kx12, then value of k is :
(A) 3 (B) 3 (C) 0 (D) 4
(x3) x
3
3x
2
kx12 k
(A) 3 (B) 3 (C) 0 (D) 4

4.
Select the correct statement from the following :
(A) Degree of a zero polynomial is 0
(B) Degree of a zero polynomial is not defined
(C) Degree of a constant polynomial is not defined
(D) Zero of the zero polynomial is not defined

(A)
(B)
(C)
1 1
12 24
49 x
1 1
12 24
49 x
=
1
a
=
1
a
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(D)

5.
Lines are parallel if they do not intersect is stated in the form of :
(A) an axiom (B) a definition
(C) a postulate (D) a proof

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

6.
If ABQR, BCPR and CAPQ then :
(A) ABCPQR (B) CBAPRQ
(C) BACRPQ (D) PQRBCA
ABQR, BCPR CAPQ
(A) ABCPQR (B) CBAPRQ
(C) BACRPQ (D) PQRBCA

7.
Q is a point on side SR of PSR as shown in the figure below such
that PQPR. Show that PS > PQ.

PSR SR Q PQPR
PS > PQ
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8.
The sides of a triangular plot are in the ratio 4 : 5 : 6 and its perimeter is 150 cm. Then
the sides are
(A) 4 cm, 5 cm, 6 cm (B) 40 cm, 50 cm, 60 cm
(C) 8 cm, 10 cm, 12 cm (D) 120 cm, 150 cm, 180 cm
4 : 5 : 6 150
(A) 4 , 5 , 6 (B) 40 , 50 , 60
(C) 8 , 10 , 12 (D) 120 , 150 , 180

Section-B

Question numbers 9 to 14 carry two marks each.

9.
If , then find the value of

10.
Factorise : 27p
3
p
2
p.
27p
3
p
2
p

11.
Evaluate (101)
3
, using a suitable identity.
(101)
3

12.
In the figure given below, if PSRQ then prove that PRSQ.
3 2 2 x
2
2
1
x
x

3 2 2 x
2
2
1
x
x

1
216
9
2
1
4
1
216
9
2
1
4
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PSRQ PRSQ.

13.
In the figure below, ABCD is a square and P is the midpoint of AD. BP and CP
are joined. Prove that PCB PBC.

ABCD P, AD BP CP
PCB PBC

OR

Let OA, OB, OC and OD be the rays in the anticlockwise direction starting from
OA, such that AOB COD 100, AOD BOC80. Is it true that
AOC and BOD are straight lines. Justify your answer by drawing the figure.
OA, OB, OC OD; OA
AOB COD 100 AOD BOC80 AOC
BOD

14.
Locate and write the coordinates of a point :
(A) above xaxis lying on yaxis at a distance of 5 units from origin.
(B) below xaxis lying on yaxis at a distance of 3 units from origin.
Z Z
Z Z
Z Z Z Z
Z Z Z Z
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(C) lying on xaxis to the right of origin at a distance of 5 units.
(D) lying on xaxis to the left of origin at a distance of 2 units.

(A) x 5 y
(B) x y 3
(C) x 5
(D) x 2

Section-C

Question numbers 15 to 24 carry three marks each.

15.
If and , then find the value of the rational number p.
p

OR

If 5
x3
.3
2x8
225, then find the value of x.
5
x3
.3
2x8
225 x

16.
Find p and q, if
3 1
p q 3
3 1
.
3 1
p q 3
3 1
p q

17.
Factorise : 343p
3
64q
3
125p
3
q
6
420p
2
q
3
.
343p
3
64q
3
125p
3
q
6
420p
2
q
3
.
OR

The polynomials kx
3
3x
2
8 and 3x
3
5xk are divided by x2. If the remainder in
each case is the same, find the value of k.
x2 kx
3
3x
2
8 3x
3
5xk k

7

5
x
5
p 7
x
7

5
x
5
p 7
x

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18.
If a
2
b
2
c
2
90 and abc20, then find the value of abbcca.
a
2
b
2
c
2
90 abc20 abbcca

19.
In the figure given below, if ABCD, P is the midpoint of BD, prove that P is
also the midpoint of AC.

ABCD BD P P AC

OR

In ABC, B45, C55 and bisector of A meets BC at a point D.
Find ADB and ADC.
ABC B45, C55 A BC D ADB
ADC

20.
In figure, if ABDC, BDC30 and BAD80, find x, y and z.

ABDC BDC30 BAD80 x, y z

Z Z Z Z Z
Z Z Z Z Z
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21.
ABC is an isosceles triangle with ABAC, D and E are the points on BC such
that BECD. Prove that ABD ~ ACE.

ABC ABAC D E, BC BECD.
ABD ~ ACE.

22.
In the figure given below, if PQRS and ZPXM50 and ZMYS120, find the
value of x.

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PQRS ZPXM50 ZMYS120 x

23.
In the given figure, find the value of x.
x

24.
An isosceles triangle has perimeter 30 cm and each of the equal sides is
12 cm. Find area of the triangle.
30 12

Section-D

Question numbers 25 to 34 carry four marks each.

25.
Evaluate after rationalizing the denominator . It is being given that

OR

Express as a fraction in simplest form.

25
40 80
| |
|
\ .
5 2.236 and 10 3.162

25
40 80
| |
|
\ .
5 2.236 10 3.162
1 32 0.35 .
1 32 0.35 .
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26.
Find the values of a and b if :
a b

27.
Find the value of 8a
3
27b
3
90ab125 if 2a3b5.
8a
3
27b
3
90ab125 2a3b5.

28.
Factorise : 2y
3
y
2
2y1
2y
3
y
2
2y1

29.
Without actually calculating the cubes, find the value of :
(i) (12)
3
(7)
3
(5)
3

(i) (12)
3
(7)
3
(5)
3

OR

The polynomials p(x)ax
3
4x
2
3x4 and q(x)x
3
4xa leave the same
remainder when divided by x3. Find the remainder when p(x) is divided by
(x2).
p(x)ax
3
4x
2
3x4 q(x)x
3
4xa x3
p(x) (x2)

30.
If the co-ordinates of a point M are (2, 9) which can also be expressed as
(1x, y
2
) and y>0, then find in which quadrant do the following points lie :
P (y, x), Q (2, x), R (x
2
, y1), S (2x,3y).
M (2, 9) (1x, y
2
), y>0

P (y, x), Q (2, x), R (x
2
, y1), S (2x,3y)
7 3 5 7 3 5
a 5b
3 5 3 5

7 3 5 7 3 5
a 5b
3 5 3 5

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31.
In given figure, the bisectors of ABC and BCA of ABC
intersect each other at point O. Prove that BOC90 .

ABC ABC BCA O
BOC90 .

32.
Prove that the two triangles are congruent if any two angles and the included side of
one triangle is equal to any two angles and the included side of the other triangle.

33.
In right ABC in given figure, right angled at C, M is the midpoint
of hypotenuse AB, C is joined to M and produced to a point D such
that DMCM. Point D is joined to point B. Show that
(i) AMC BMD (ii) DBC is a right angle

Z Z
Z
A
2
Z
Z Z
A
2
Z
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ABC C M
AB C M D
DMCM D B
(i) AMC BMD
(ii) DBC

34.
In figure below, two isosceles triangles ABC and DBC have a common base BC.
Prove that the line joining their vertices is the perpendicular bisector of the base.

BC ABC DBC

~

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Page 1 of 12

SUMMATIVE ASSESSMENT I (2011)

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5 2.236 and 10 3.162

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