Important Instructions for the School Principal

Important Instructions for the
School Principal
(Not to be printed with the question paper)
1) This question paper is strictly meant for use in school based SA-I, September-2012 only.
This question paper is not to be used for any other purpose except mentioned above under
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Note:
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Page 1 of 11
I, 2012
SUMMATIVE ASSESSMENT – I, 2012
MA1-062
/ MATHEMATICS
IX / Class – IX
3
90
Time allowed : 3 hours
Maximum Marks : 90
(i)
(ii)
34
8
1
6
3
10
(iii)
1
2
10
4
8
(iv)
2
3
4
3
2
(v)
General Instructions:
(i)
(ii)
(iii)
(iv)
(v)
All questions are compulsory.
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.
Question numbers 1 to 8 in Section-A are multiple choice questions where you are required
to select one correct option out of the given four.
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.
Use of calculator is not permitted.
Page 2 of 11
SECTION–A
1
8
1
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.
7
8
1.
1
(A)
0.775
(B)
0.875
The decimal which represents the fraction
(A)
0.775
(B)
0.875
(C)
.0875
(D)
0.845
7
is :
8
(C)
.0875
(D)
0.845
2.
1
2
(A)
2
6x 5 x 1
(B)
3 x x1
1
13
2
(C)
2
(D)
5 x x
x
Expression which represents a polynomial is :
6x25 x 1
13
2
x
(A)
(C)
3.
2
3 x x1
(D)
2
5 x x
1
1
9596
(A)
8120
Value of 9596 is :
(A)
8120
4.
(B)
3
3
2
8a b 12a b6ab
(A)
(2ab)
(B)
8210
(C)
9210
(D)
9120
(B)
8210
(C)
9210
(D)
9120
1
2
(B)
(C)
(2ab)
(D)
(8ab)
One of the factor of 8a b 12a b6ab is :
(A)
(2ab)
(B)
(8ab)
(C)
(2ab)
(D)
(8ab)
3
5.
(8ab)
3
2
AOB
2
1
x
(A)
50
(B)
30
(C)
40
(D)
In the given figure, the value of x for which AOB is a straight line is :
60
(A)
60
50
(B)
30
(C)
40
(D)
Page 3 of 11
6.
ABC
B50
ABAC
1
A
(A)
50
(B)
130
(C)
80
(D)
70
In the given figure ABC is isosceles triangle in which ABAC. If measure of
B50, then measure of A is :
(A)
7.
50
(B)
130
(C)
80
(D)
70
1
(0, 5)
(A)
x-
(B)
y-
(C)
II
(D)
IV
(B)
(D)
on the y-axis
in the IV quadrant
The point (0, 5) lies :
(A)
on the x-axis
(C)
in the II quadrant
8.
1
(A)
(0, 1)
(B)
(1, 0)
Co-ordinates of the origin are :
(A)
(0, 1)
(B)
(1, 0)
(C)
(0, 1)
(D)
(0, 0)
(C)
(0, 1)
(D)
(0, 0)
/ SECTION-B
9
14
2
Question numbers 9 to 14 carry two marks each.
5 2  3  2  5  2  .
9.
2
Find the product of 5 2  3  2  5  2  .
10.
2x2x1
11.
Find the remainder when 2x2x1 is divided by 2x1.
1 3 1 2
1
1 3
a  a b ab2
b
8
4
6
27
2x1
2
2
Page 4 of 11
Factorise :
12.
P
1 3 1 2
1
1 3
a  a b ab2
b
8
4
6
27
R
Q
PQQR
2
Q PR
If Q is a point between P and R such that PQQR, prove that Q is mid-point of
PR.
13.
PQRS, PAB70
ACS100
BAC
2
CAQ
In the given figure PQRS, PAB70 and ACS100. Find the measure of
BAC and CAQ.
/ OR
PQR
PQS50
QPR
PT
PSQR
x
PRT30
In the figure, PT is the bisector of QPR in PQR and PSQR. Find the value of
x, when PQS50 and PRT30.
14.
90 cm
54 cm
2
Page 5 of 11
The longest side of a right triangle is 90 cm and one of the remaining two sides is
54 cm. Find its area.
/ SECTION-C
15
24
3
Question numbers 15 to 24 carry three marks each.
15.

Evaluate :

2
5  2   8  3
2
5  2   8  3
3
2
2
/ OR
x2 
x84 3
256
x2
256
If x84 3 , find the value of x 2  2 .
x
16.
1
1
2x  4x   8 3   32  5
3
x
1
1
If 2x  4x   8  3   32  5 , find the value of x.
17.
3
3
(8) (15) (7)
3
3
Without actually calculating the cubes, find the value of (8)3(15)3(7)3.
/ OR
x
If x 
18.
y
9
2
x3 
xy4
y3
8
y3
y
3
and
xy4
find
.
x 
9
2
8
3
a2b2c2
(abc)15, (abbcca)35
If (abc)15, (abbcca)35 find a2b2c2.
19.
ACDE
BAC70
ADCE
x
3
y
DEC55
In the given figure, ACDE and ADCE find x and y, when it is given that
BAC70 and DEC55.
Page 6 of 11
/ OR
ABCD, BAC72
CEF40
CFE
In the given figure ABCD, BAC72 and CEF40. Find CFE.
20.
AC A
ABCD
ABAD
3
C
CDCB
If diagonal AC of a quadrilateral ABCD bisects A and C, then prove that
ABAD and CDCB.
21.
CDDAABBC > 2AC.
3
Page 7 of 11
In the figure, prove that CDDAABBC > 2AC.
22.
PSPR, TPSQPR
3
PTPQ
In figure PSPR, TPSQPR. Prove that PTPQ.
23.
CBF100, DCB45
BDA110
3
ABD, DCE
BAC
In the given figure, CBF100, DCB45 and BDA110.
Find the
measure of ABD, DCE and BAC.
Page 8 of 11
24.
10 cm
ABC
D
3
DBC
BD8 cm
[ 3 1.732]
In the given figure ABC is equilateral with side 10 cm and DBC is right angled
at D. If BD8 cm, find the area of the shaded portion. [ 3 1.732]
/ SECTION-D
25
34
4
Question numbers 25 to 34 carry four marks each.
25.
1
x2  2
x
1
If x53 3 find x 2  2 .
x
4
x53 3
/ OR
a8 5 b
If a  8 5 b 
8 5
8 5

8 5
8 5
a
b
8 5
8 5

, determine the rational numbers a and b.
8 5
8 5
Page 9 of 11
4
26.

2
 216  3
Evaluate :
4
2
 216  3
27.

1
3
 256  4
1
3
 256  4


2
4
1
 243  5
2
1
5
 243 
4
5(2ab)2(2ab)4
2
Factorise : 5(2ab) (2ab)4
28.
3
4
x38x25x14
4
3
(3x2y) (3x2y)
Simplify : (3x2y)3(3x2y)3
29.
Factorise : x38x25x14
30.
PQRS
4
P(3, 4), Q(3, 4), R(3, 4)
S
Three vetices of a rectangle PQRS are P(3, 4), Q(3, 4), R(3, 4). Plot the
points in the Graph and find the coordinates of the missing vertex S.
31.
ABDC, BDC35
BAD80
x, y
4
z
In the given figure, ABDC, BDC35 and BAD80. Find x, y, z.
32.
ABC
AC
AB
BE
CF
4
ABC is an isosceles triangle in which altitudes BE and CF are drawn to equal
sides AC and AB respectively. Show that the two altitudes are equal.
/ OR
Prove that the angles opposite to equal sides of an isosceles triangle are equal.
Page 10 of 11
33.
ABC
BC
D
D
AB
4
AC
ABC is a triangle and D is the mid-point of BC. The perpendicular from D to AB
and AC are equal. Prove that the triangle is isosceles.
34.
BD
AB > AC
CD
B
C
4
D
BD > CD
In the given figure, BD and CD are bisectors of B and C respectively meeting
at D and AB > AC. Prove that BD > CD.
-oOo-
Page 11 of 11