RKTZTO6
II, (2013-2014)
SUMMATIVE ASSESSMENT – II
MATHEMATICS /
Class – IX /
IX
3-3½
100
Time allowed : 3-3½ hours
Maximum Marks : 100
(i)
(ii)
32
पच
ाँ
य
1
3
4
6
2
11
4
10
य
मुक्त
(iii)
(v)
General Instructions:
(i)
(ii)
(iii)
(iv)
All questions are compulsory.
The question paper consists of 32 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 10 questions of 3 marks each and Section-D comprises of
11 questions of 4 marks each. Section E comprises of one question from Open Text theme
of 10 marks.
There is no overall choice.
Use of calculator is not permitted.
/ SECTION-A
Page 1 of 15
1
4
1
Question numbers 1 to 4 carry one mark each
1
3 x  4y  8
1
y-
At what point the graph of linear equation 3 x  4y  8 cuts the y-axis?
2
5 x  8y
1
ax  by  c  0
Express 5 x  8y in the form of ax + by + c = 0.
3
ADC75
ABCD
AB
E
1
(xy)
ABCD is a parallelogram in which ADC75 and side AB is produced to point E as shown
in the figure. Find (xy).
7 cm
4
1
Find the total surface area of a solid hemisphere with radius 7 cm.
/ SECTION-B
Page 2 of 15
5
10
2
Question numbers 5 to 10 carry two marks each.
5
PQRS
SR
ar (PTQ)10 cm2
T
2
ar (PQRS)
PQRS is parallelogram and T is any point on side SR. If ar (PTQ)10 cm2, find ar (PQRS).
AB
1
2
In the given figure, AB is a chord of a circle with centre O. if AOB60, prove that AB
1
2
6
AB
O
AOB60
2
diameter.
90
7
2
Using ruler and compass, construct an angle of 90 at the initial point of a given ray.
6237 cm3
8
4.5 cm
Volume of a solid cylinder is 6237 cm3. Find the radius if its height is 4.5 cm.
Page 3 of 15
2
9
2
Find the mean of all positive factors of 18.
x
10
2
2
2
3
x
The probability of guessing the correct answer to a certain question is
guessing the correct answer is
2
3
x
2
. If probability of not
, then find x.
/ SECTION-C
11
20
3
Question numbers 11 to 20 carry three marks each.
11
(i)
4 x  y  8, x -
(ii)
3 x  4y  6, x -
(iii)
3
4x  y  8
3 x  4y  6
(a) Find the point where line 4 x  y  8 meets x-axis.
(b) Find the point where line 3 x  4y  6 meets x-axis.
(c) Find the point where line 4 x  y  8 and 3 x  4y  6 meet each other.
12
Page 4 of 15
3
Gurnam & Akhthar have some money with them. Gurnam says to Akhthar, if give me Rs. 40,
my money will be three times than the money left with you. Represent this situation in linear
equation in two variables. Also find two solutions for this equation.
13
ABCD
D
P
C
DP
CP
AB
P
3
AB
ABCD is a parallelogram. If the bisectors DP and CP of angles D and C respectively meet at P
on side AB, then show that P is the mid-point of side AB.
PQRS
14
PQSR
PSQR
3
P Q
In the figure, PQRS is a trapezium in which PQSR and PSQR. Show that P Q.
A, D, P, C
15
BPD, BCD
B
O
BOD150
BAD
In the given figure, points A, D, P, C and B lie on a circle with centre O. If BOD150, find
the measures of BPD, BCD and BAD.
Page 5 of 15
3
16
PQRS
S
PR
QR
X
3
ar (PQRS)ar (PXQ)
PQRS is a quadrilateral. A line through S parallel to PR meets QR produced in X. Show that ar
(PQRS)ar (PXQ).
AB
17
AO
Page 6 of 15
AC
O
ODAB, OEAC
ADE
DAE
ABCACB
3
In the given figure, AB and AC are two chords of a circle whose centre is O. If ODAB,
OEAC and AO bisects DAE, prove that ADE is an isosceles triangle and ABCACB.
18
3
300 cm
20 cm
` 160
4
Ashima has constructed a cubical water tank with lid for her house with each outer edge 300
cm long. She gets the inner four walls and the lid covered with square tiles of side 20 cm.
Find the amount she spent for tiles, if it is given that the cost of 4 tiles is ` 160.
19
3
15, 28, 72, 56, 44, 32, 31, 43,
31
51.
46
Find the median of the given data :
15, 28, 72, 56, 44, 32, 31, 43, & 51.
If 31 is replaced by 46, calculate the new median.
20
Page 7 of 15
50
3
50
)
I
II
III
IV
V
34
35
36
34
37
70%
70%
The table shows the marks obtained by a student in unit tests out of 50 :
UNIT TEST
I
II
III
IV
V
MARKS (Out of 50)
34
35
36
34
37
Find the probability that the student get 70% or more in the next unit test. Also , the probability that
student get less then 70%.
/ SECTION-D
21
31
4
Question numbers 21 to 31 carry four marks each.
`x
21
`y
2
` 1800
3
4
Cost of 1 chair is ` x and that of 1 table is ` y. Cost of 2 chairs and 3 tables together is ` 1800. Write a
linear equation which satisfies this data. Draw the graph for the same.
`x
22
`y
2
3
`9
Let cost of a pencil and a eraser be ` x and ` y respectively. A girls pays ` 9 for 2 pencils and 3
erasers. Write the given data in the form of a linear equation in two variables. Also, represent it
Page 8 of 15
4
graphically.
23
4
ABCD
(a)
AB
CD
X
Y
ar(AXYD)ar(BXYC)
(b)
In order to guide and help people reach school without any problem being faced in finding
the way to school, students of the school decided to put up a sign board based on main road.
The sign board ABCD is in shape of a parallelogram as shown in figure.
24
(a)
If X and Y are respectively the mid-points of sides AB and CD respectively, show that
ar(AXYD)ar(BXYC).
(b)
What can you say about this gesture of the students ?
(a)
4
(b)
60
(c)
Page 9 of 15
ABC
11 cm
A
B 70 
EFG
EFFG GE 11 cm, E 105
F
90 
XYZ
(d)
12.5 cm, X 75
Y 30 
(a)
State Angle Sum Property of a triangle.
(b)
Is it possible to construct ABC if perimeter of the triangle is 11 cm, base
angles A 60 and B 70
Is it possible to construct EFG, , if EFFG GE 11 cm E 105 and
(c)
F 90
(d)
25
Is it possible to construct XYZ if perimeter is 12.5 cm, X 75 and Y 30
ABCD
APABBQ
AB
PD
QC
P
R
4
Q
PRQ90
In the figure, ABCD is a rhombus whose side AB is produced to points P and Q such that APABBQ.
PD and QC are produced to meet at a point R. Show that PRQ90.
Page 10 of 15
O
26
(i)
A, O, P
(ii)
OAPOMB
(iii)
P, L, O
OLM
AOB
4
M
B
In the given figure, O is the centre of the circle and OLM is perpendicular to AOB prove that :
27
(i)
A, O, P and M are concyclic
(ii)
OAPOMB
(iii)
P, L, O and B are concyclic
12 m
5m
70
1.1 m
m2
Find the length of the cloth 1.1 m wide required to make a conical tent whose height is 12 m
and radius of the base is 5m. Also find the cost of the cloth at the rate of Rs. 70 per sq m.
Page 11 of 15
4
12.6 cm
28
25.2 cm
4
A metallic sphere of diameter 12.6 cm is melted to make a right circular cone of height 25.2
cm. Find the area of the base of the cone.
3 cm
29
1.46 m, 1.16 m
75
8.3 dm
4
100 cm2
An open box is made of wood 3 cm thick. Its external dimensions are 1.46 m, 1.16 m and 8.3
dm. Find the cost of painting the inner surface of the box at 75 paise per 100 cm2.
30
4
I
II
III
IV
I
(a)
II
III
IV
18-29
440
160
110
61
35
30-50
505
125
60
22
18
50
360
45
35
15
9
II
(b)
(c)
I
A survey of 2000 people of different age groups was conducted to find out
Page 12 of 15
their preference in watching different types of movies :
Type I Family
Type II Comedy and Family
Type III Romantic, Comedy and Family
Type IV Action, Romantic, Comedy and Family
Age Group Type I Type II Type III Type IV All
18-29
440
160
110
61
35
30-50
505
125
60
22
18
Above 50
360
45
35
15
9
Find the probability that a person chosen at random is :
(a) in 18-29 years of age and likes type II movies
(b) above 50 years of age and likes all types of movies
(c) in 30-50 years and likes type I movies.
31
4
50-55
12
55-60
8
60-65
14
65-70
10
70-75
6
Draw a frequency polygon and the a histogram for the following table :
Class-intervals
Page 13 of 15
Frequency
50-55
12
55-60
8
60-65
14
65-70
10
70-75
6
य / SECTION-E
(मुक्त प ठ /Open Text)
(* Please ensure that open text of the given theme is supplied with this question paper.)
32
10
Theme-I (Planning a garden) (3+3+4)
(a)
सबसे छोटे वृत्त के लिए आवश्यक ख द उववरक की कीमत ज्ञ त कीलिए ।
(b)
बगीचे के नक्शे में से एक वृत्त को यदृच्छय चुन ि त है, तो प्र लयकत ज्ञ त
कीलिए कक -
(i) इसमें पथ है।
(ii) यह सबसे छोट वृत्त है।
(c)
उस कमरे की दीव रों के रै लखक समीकरण लिलखए, लिसके एक कोने क लनदेश ांक
(0, 70) है।
(a)
Find the cost of the compost fertiliser required for the smallest
circle.
(b)
If one circle is to be chosen at random from the layout plan of
find the probability that
garden,
(i) it has a foot path.
(ii) it is smallest circle.
(c)
Write linear equations of the walls of room which has coordinates of one corner
as (0, 70).
Page 14 of 15
-o0o0o0o-
Page 15 of 15