SUMMATIVE ASSESSMENT – II (2014-2015)
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.
There is no overall choice.
Use of calculator is not permitted.
SECTION-A
(iii)
(iv)
Question numbers 1 to 4 carry one mark each.
1
Express
x
 3y  7 in the form of ax  by  c  0.
4
1
2
Cost of a pen is two and half times the cost of a pencil. Express this situation as a linear
equation in two variable.
1
3
A square and a rhombus are on same base and between same parallels. What is the ratio of 1
their areas ?
4
If the diameter of the base of a closed right circular cylinder be equal to its height ‘h’, find total 1
surface area of cylinder.
SECTION-B
Question numbers 5 to 10 carry two marks each.
5
ABCD is a trapezium with E being any point on side AB. If ADEC and DEBC find the 2
ratio ar (DAE) :ar (BEC).
6
Draw an angle of 55with the help of a protractor. Then, construct an angle 2
5 27
Page 1 of 5
18
, using a compass.
2
7
In the figure, the length of each side of the rhombus PQRS is 15 cm. If diagonal PR24 cm, find 2
the length of the other diagonal QS.
8
Calculate the height of a cone whose slant height is 25 cm and curved surface area is 550 cm2.
2
9
1000 families with 2 children were selected randomly and the following data were recorded :
2
Number of girls in a family
0
1
2
Number of families
111
614
275
If a family is chosen at random, compute the probability that it has :
(i)
10
exactly 1 girl.
(ii)
exactly 2 boys.
A coin is tossed 1500 times with the following frequencies:
2
Head : 655, Tail : 845
Compute the probability for each event.
SECTION-C
Question numbers 11 to 18 carry three marks each.
11
The cost of a toy horse is same as that of cost of 3 balls. Express this statement as a linear
equation in two variables. Also draw its graph.
12
Write the equation 4x6 (1y)3x in the form axbyc and also find the coordinates of the points 3
where its graph cuts the two axes ?
13
In ABC, AD and BE are the medians. If X is the point of intersection of AD and BE, show that 3
ar (ABX)ar (BXC).
14
Two diameters of a circle intersect each other at right angles. Prove that the quadrilateral 3
formed by joining their end-points is a square.
Page 2 of 5
3
15
(a)
Is it possible to construct ABC if perimeter of the triangle is 11 cm, base angles 3
areA 60 andB 70.
(b)
Is it possible to construct EFG, , if EFFG GE 11 cm,E105 and F 90.
(c)
Is it possible to construct XYZ if perimeter is 12.5 cm, X 75 and Y 30.
16
ABCD is a parallelogram and AB is produced to X such that AB BX as shown in the figure . 3
Show that DX and BC bisect each other at O.
17
Draw an angle of 70 with the help of protractor. Now construct angles of (i) 35 (ii) 140, using 3
compass.
18
A dome of a building is in the form of a hemisphere. From inside, it was white washed at the
3
cost of ` 997.92. If the cost of white washing is 400 paisa per square meter, find the volume of
22 

air inside the dome.  Take p 5

7 .

SECTION-D
Question numbers 19 to 28 carry four marks each.
19
Two times of a larger number is equal to three times of the smaller number. Write the linear 4
equation which satisfies this data. Also draw the graph for the same. Does this line pass
through origin ?
20
Write the equations of the lines p and q in following graph :
A student answered equation of line ‘r’ as xy3. Did she answer correctly ? Also, find the
Page 3 of 5
4
area enclosed between lines p, q and r.
21
ABCD is a rectangle. P and Q are points on sides AD and AB respectively. Show that APOQ
1
1
is a rectangle and find ar(APOQ) : ar(ABCD), when it is given that BR BC and DS CD.
4
4
22
In the given figure, AB is a chord of a circle with centre O. AB is produced to C such that 4
BCOB. Also, CO is joined and produced to meet the circle at D. If ACDy and AODx,
prove that x3y. If AOD60, find AOB.
23
Construct KLM in which KL8 cm, K75 and LM KM 4 cm.
24
ABCD is a parallelogram in which P and Q are midpoints of AB and DC respectively. AQ 4
and DP intersect at point X and BQ and PC intersect at point Y. Prove that :
25
26
Page 4 of 5
(i)
APCQ is a parallelogram.
(ii)
BPDQ is a parallelogram.
(iii)
PXQY is a parallelogram.
4
4
An ice cream vendor had to purchase bowls for serving ice cream to the customers at the rate 4
of Rs. 20 per bowl. He had two choices-first a hemispherical bowl of diameter 10.5 cm and
second a cylindrical bowl with diameter 10.5 cm and height of 5.25 cm. The vendor purchased
the cylindrical bowl instead of hemispherical.
(a)
What is the difference in volume of the two types of bowl ?
(b)
What value is depicted in this question ?
A hemispherical dome,
open at base is made from a sheet of fiber. If diameter of 4
hemispherical dome is 80 cm and
27
13
of fibre sheet actually used was wasted in making the
170
dome, then find the cost of dome at the rate of Rs 35 per 100 cm2 (Take 3.14).
A heap of wheat is in the form of a cone whose diameter is 10.5 m and height is
4
3 m. Find its volume. If cost of 1 m3 wheat is ` 10 then find total cost. Also find slant height of
28
heap.
A survey of 2000 people of different age groups was conducted to find out 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.
4
SECTION-E
(Open Text)
(* Please ensure that open text of the given theme is supplied with this question paper.)
29
30
31
Theme :Atithidevo Bhavah
Refer to Table-2 and answer the following questions :
(i)
What is the difference in FTAs from Europe and Australia for the year 2012 ?
(ii)
What is the difference in FTAs from America and Africa for the year 2012 ?
(iii)
What was the FTA from Asia in the year 2012 ?
Consider month-wise percentage share of FTA and answer the following questions :
(i)
Find the mean percentage of foreign visitors in the summer (April – july)
(ii)
Find the mean percentage of foreign visitors in the winter (November – February)
3
(a) Many foreign tourists from different parts of world come to India. What is usually their 4
purpose of visit. State four such purposes.
(b) Calculate the increase in % of foreign tourist arrival in each region in 2012 on the basis of
2011
-o0o0o0o-
Page 5 of 5
3