Download SAMPLE PAPER-SA II MATHEMATICS Class – IX Time allowed : 3

SAMPLE PAPER-SA II
MATHEMATICS
Class – IX
Time allowed : 3 hours
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
(iii)
(iv)
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
Question numbers 1 to 4 carry one mark each.
1
Construct an obtuse angle and draw bisector of its supplement.
1
2
If the number of square centimeters on the surface area of sphere is equal to the number of
cubic centimeters in its volume, what is the diameter of the sphere?
1
3
The points scored by a basketball team in a series of matches are as follows : 17, 7, 10, 25, 5, 10, 1
18, 10, 24. Find the mean.
4
The different types of cartoon channels preferred by children among the age group (4-8years) 1
are depicted in the following bar graph :
Find the ratio of the least watched channel to the highest watched channel. Following
SECTION-B
Page 1 of 5
Question numbers 5 to 10 carry two marks each.
5
In the adjoining figure, SQR60 and QSR30. Find the measures of RPQ and SPR. 2
Also, prove that SQ is a diameter of the circle passing through the points P, Q , R and S.
6
Using protractor, draw DEF60. Construct another angle equal to DEF, using compass.
7
In a quadrilateral, three angles are in the ratio of 3 : 3 : 1 and the fourth angle is 80. Find the 2
measure of equal angles.
8
The floor of rectangular hall has a perimeter 150 m. If the cost of painting the four walls at the
rate of Rs. 10 per m2 is Rs. 9000, find the height of the wall.
2
9
Following table shows the birth months of the 80 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 selected at random was born a month in which the
Independence day or Republic day are celebrated.
2
10
Following table shows the birth months of 40 students of class IX :
2
Jan.
Feb.
March
April
May
June
July
Aug.
Sept.
Oct.
Nov.
Dec.
3
4
2
2
5
1
2
6
3
4
4
4
2
A student is chosen at random. Find the probability that student :
(a)
was born in April.
(b)
was born in a month having 31 days.
SECTION-C
Question numbers 11 to 18 carry three marks each.
11
The mean of monthly salary of the 12 employees of a firm is ` 1,450. If one more person joins 3
the firm who gets ` 1,600 per month, what will be the mean monthly salary now ?
12
The following table shows the marks scored by students of a class in a chemistry examination
(max. marks 35)
MARKS
0-7
7-14
14-21
21-28
28-35
No.
OF
4
8
12
2
8
STUDENS
Represent the data using a histogram.
13
P and Q are points on side BC of ABC such that P and Q trisect BC. Show that ar (PQA)ar 3
(PAB)ar (AQC).
If two equal chords of a circle intersect within a circle, prove that the segments of a chord are 3
equal to the corresponding segments of the other chord.
14
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3
15
Construct a triangle whose angles are in the ratio 1 : 3 : 5 and length of side included by last
two angles is 6 cm.
16
In a quadrilateral PQRS, Q 80, R S50and PRS20. Find the measures of 3
P, R and S .
17
If each diagonal of a quadrilateral divides it into two triangles of equal areas, then prove that
quadrilateral is a parallelogram.
18
A solid piece of metal, cuboidal in shape, with dimensions 24 cm, 18 cm and 4 cm is recast into 3
a cube. Calculate the lateral surface area of the cube.
3
3
SECTION-D
Question numbers 19 to 28 carry four marks each.
19
The following data represents the population of girl child (per 1000 boy child) in a state.
Years
Number of Girls
2007-2008
875
2008-2009
900
2009-2010
925
2010-2011
945
2011-2012
1000
(a) Draw a bar graph to represent the above data.
(b) What change in the value over the period of time is depicted by the
state ?
4
20
PQR and XYZ are such that PQXY; PRXZ and PQXY. If
PRXZ, then show that ar(PQR)ar(XYZ)
4
21
In a circle of radius 5 cm, AB and AC are two
ABAC6 cm, as shown in the figure. Find the length of the chord BC.
22
Construct
11 cm.
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ABC
when
B75,
C45
and
the
perimeter
chords
such
of
triangle
the
that 4
is 4
23
In ABC, medians BE and CD are produced respectively to points X and Y such that CDDX 4
and BEEY as shown in the figure. Show that points X, A and Y are collinear. Also, show that
A is the midpoint of XY.
24
In a group of 3 girls, one girl forgot to bring her lunch so, other two girls decided to share 4
their lunch with her lunch box 1st girl lunch box is in the shape of a cuboidal box measures 6
cm  8 cm  15 cm and of 2 nd girls lunch box is cylindrically shaped having radius 7 cm and
height 15 cm.Which box has more surface area and which box has more volume ? Which
22
value is depicted by girls ? (Use 
)
7
A corn cob, shaped somewhat like a cone has the diameter of its broadest end as 4cm and 4
length as 20 cm. If each 1 cm2 of the surface of the cob carries an average of three grains, find
how many grains you would find on the entire cob ?
25
26
A class room is 10 m long, 6.4 m wide and 5 m high. If each student be given 3.2 m2 of the 4
floor area, how many students can be accommodated in the room ? How many cubic metres
of air would each student get ?
27
The sum of radius of the base and height of a solid cylinder is 37 m. If the total surface area of
the cylinder is 1628 m2, find the curved surface area and volume of the cylinder.
4
28
The length of 40 leaves of a plant are measured in millimetres and represented in the table
below :
Length (in mm) Number of leaves
118 – 126
12
127 – 135
7
136 – 144
5
145 – 153
14
154 – 162
2
One leaf is plucked at random. Find the probability that the leaf plucked was of length :
(a)
more than 126 mm and less than 136 mm.
(b)
more than 126 mm.
(c)
less than 154 mm.
4
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SECTION-E
Open Text)
(* Please ensure that open text of the given theme is supplied with this question paper.)
Theme :Energy Consumption and Electricity Bill
29
Form linear equations for the monthly bill amounts of offices of Haryana and Rajasthan for 3
non-domestic category. Then, find the difference between the bill amounts of offices of
located in Haryana and Rajasthan, if both offices consumed 1500 units each in a month.
30
Rahul has a three bedroom flat. He installed three fans and one air conditioner of 1 ton in the 3
house. He observed that the total consumption for light and other electrical appliances
excluding fan and air conditioner is 100 units in a month. He wishes that his consumption of
electricity should be 450 units in a month. Establish a linear equation for the same assuming
that he is using all the fans for 'x' number of hours and air conditioner for 'y' number of hours
(AC
of
1
ton
take
load
of
1900 W).
31
In a household, 5 tubelights of 40 W each are used for x hours and an electric press of 500 W 4
for 4 hours everyday. If 'W' watt-hour is total electric energy consumed by tubelights and
press in a day, then develop a relation between x and 'W' and represent this situation as linear
equation algebraically and draw its graph.
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