(2014-2015)
SUMMATIVE ASSESSMENT – II
MATHEMATICS
Class – IX
Time allowed : 3hours
Maximum Marks : 90
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
Question numbers 1 to 4 carry one mark each.
1
If the length of a rectangle is decreased by 3 unit and breadth 1
increased by 4 unit, then the area will increase by 9 sq. units.
Represent this situation as a linear equation in two variables.
2
Cost of 4 pencils is same as that 5 erases. Expresses this statement 1
as a linear equation in two variables.
3
Why PQR having PQ = 6 cm, P = 1350 and Q = 750 can’t be 1
constructed?
4
If the radius of a sphere is 2r, then find its volume.
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SECTION-B
Question numbers 5 to 10 carry two marks each.
5
ABCD is parallelogram and O is the point of intersection of its 2
diagonals. If ar (AOD) = 4 cm2, find ar (AOB).
6
Construct an angle of 1350 at the initial point of a given ray, using 2
compass and ruler.
7
In the figure, BE and CF are medians of ABC. If AB = 6 cm, BC = 8 cm 2
and AC = 4 cm, find the length of EF.
8
A cuboidal water tank can hold 50,000 litres of water. If the length 2
and depth of tank are 250 cm and 10 m respectively, find the breadth
of the tank.
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9
1500 families with 2 children
following data were recorded :
Number
family
of
girls
Number of families
in
a 0
211
were
selected
1
2
814
475
randomly
and
the 2
If a family is chosen at random, compute the probability that it has
:
(i) Exactly 1 girl
(ii)
10
No girl
Following table shows the birth month of the students of class XII.
Jan
Feb Mar
Apr
May
June
5
6
7
4
10
3
July Aug Sept Oct
Nov
Dec
5
10
6
8
8
8
Find the probability that a student was born in August
2
SECTION-C
Question numbers 11 to 18 carry three marks each.
11
Represent
x
 y  4 in the form of y  mx  c and also draw graph of this
2
3
equation.
12
Find the value of k if the graph of the equation 3x + ky = 5 passes 3
through the point (1, 2). For what value of k will the graph pass
through (1, 0)?
13
In the given figure, P is any point on the diagonal AC of a 3
parallelogram ABCD. Line segments EF and GH are drawn through P
parallel to AB and CB respectively. Prove that ar (AEP) = ar (AHP).
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14
In the figure, AB and CB are chords of a circle equidistant from the 3
centre O. Prove that the diameter DB bisects ABC and ADC.
15
Draw any acute angle. Divide it into four equal parts, using ruler 3
and compass.
16
ABCD is a parallelogram and M is the mid-point of CD. Through D, a 3
line segment is drawn parallel to MB to meet CB produced at O and AB
at N as shown in the figure. Prove that :
(i)
AD
(ii) DO
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=
1
CO
2
= 2 BM
17
In the given figure, ABCD is a square. A line segment AE intersects 3
the diagonal BD at O such that AOB = 600. Find the measure of angle
x.
18
The external diameter of a cylindrical shaped iron pipe is 25 cm and 3
its length is 20 cm. If the thickness of the pipe is 1 cm, find the
total surface area of the pipe.
SECTION-D
Question numbers 19 to 28 carry four marks each.
19
Consecutive interior angles of a parallelogram are 30x and 40y. 4
Write a linear equation which satisfies this data. Also draw the
graph for the same.
20
A student wrote the equations of the lines a and b drawn in the 4
following graph as y = 1 and 2x + 3y = 6. Is he right? If yes, write
coordinates of point of intersection lines a and b.
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Also, find the area enclosed between these lines and y-axis.
21
In ABC ; P, Q and R are points on sides AB, AC and BC such that
BP = AP, AQ = AC and
BR = CR. Show that PAQR is a parallelogram.
If ar( PBR) = 4 cm2, find the area of parallelogram PAQR.
22
In the figure, O is the centre of the circle, OC = 5 cm and 4
AB = BC = 2√5 cm
Find the length of AC.
23
Construct ABC in which A = 600, AC + BC = 11.5 cm and AB = 4 cm.
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4
4
24
Show that a quadrilateral formed by joining the mid-points of the 4
consecutive sides of any quadrilateral is a parallelogram.
25
The "Caring old people organisation" needs money to build the old 4
age home which requires 164000 bricks. Bricks measure 10 cm x 8 cm
x 4 cm and cost of brick depends on its volume at the rate of Re 1
per 100 cm3. It requires 4 cylindrical cans of paint of radius 14 cm
and height 30 cm. The cost of paint is Re 1 per 20 cm3. How much
money is required by organization? If “A company gives the money to
organization” then, what common value is depicted by A company and
organisation.
26
A 4cm edge cube is cut into small cubes each of edge 1cm. Calculate 4
the total surface area of small cubes. Also find the ratio of total
surface area of large cube to that of the small cubes.
27
The sum of the radius of the base and height of a solid cylinder is 4
37m. If the total surface area of the solid cylinder is 3256m2, find
the volume of the cylinder.
28
A tyre manufacturing company kept a record of the distance covered 4
before a tyre was replaced.
If you buy a tyre of this company, what is the probability that :
(i) it will need a replacement after it has covered 900 km
(ii) it will last more than 1200 km
(iii) it will need to be replaced between 600 km to 1200 km.
(iv) it will need to be replaced before 600 km.
Distance
More than 900 - 1200 600 - 900 300 - 600 Less than
1200
300
No.of
250
150
220
200
180
tyres
The above table shows the result of 1000 cases, use the data to
answer the above questions.
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SECTION-E
(Open Text)
(* Please ensure that open text of the given theme is supplied with
this question paper.)
Theme : Empower to learn
29
Study the figure -3 and answer the following questions :
(i) Which subject shows that 23% of students were benefitted?
(ii) Which subject shows that 13% of students were benefitted?
(iii) How many students were benefitted in science?
30
Draw the bar graph of users of different languages used on 'LEARNOUT' 3
site.
31
For table 2 on Trouble Bubble prepare a histogram and frequency 4
polygon. At what time maximum numbers of questions are asked?
-o0o0o0o-
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