Download 9 std MATHS -2

ZBTORAM
SUMMATIVE ASSESSMENT – II (2015-2016)
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
In the given figure, O is the centre of the circle with chords AP and BP being produced to R
and Q respectively. If QPR35, find the measure of
AOB.
1
2
Calculate the volume of a cuboid whose dimensions are 3.6 cm, 8.2 cm and 11 cm.
1
3
Find the mean of first 10 odd numbers.
1
4
The class - marks of a continuous distribution are 2.05, 2.15, 2.25, 2.35, 2.45, 2.55 and 2.65. 1
Find the class - interval corresponding to 2.25 ?
SECTION-B
Question numbers 5 to 10 carry two marks each.
5
Page 1 of 5
In the given figure, if O is the centre of the circle, OBA30 and COA140, find BOC.
2
6
Draw an angle of an equilateral triangle, using protractor. Bisect it using compass.
7
Find the length of each side of a rhombus whose diagonals are of lengths 2
6 cm and 8 cm.
2
Find the volume of sphere whose surface area is 616 cm2.
Teachers and students are selected at random to make two teams of 20 members each on 2
sports day to participate in the event of ''Tug of War''. The numbers of volunteers are as
follows :
TEACHERS
STUDENTS
Male
Female
Male
Female
12
18
20
10
Find the probability that the person chosen at random
(a)
is a male
(b)
is a female student.
8
9
10
11
12
13
Page 2 of 5
2
2
1900 families with 2 children were surveyed and the following data were recorded :
Number of girls in a family
0
1
2
Number of families
511
814
575
If a family is chosen at random, compute the probability that it has
(i)
exactly 1 girl.
(ii)
exactly 2 boys.
SECTION-C
Question numbers 11 to 18 carry three marks each.
The weights (in kg) of 15 students are 31, 35, 27, 29, 32, 43, 37, 41, 34, 28, 36, 44, 45, 42 3
and 30. Find the median of the data. If the weight 44 kg is replaced by 46 kg and 35 kg is
replaced by 37 kg, find the new median.
The numbers 2, 3, 4, 4, 3x1, 3x1, 7, 7, 8 are written in ascending order. If the median is 5, 3
find x. Hence find mode.
PQRTS is a pentagon. A line through T meets QR produced in U such that SR  UT. Show 3
that ar (PSUQ)ar (PQRTS).
14
In the figure, AB and CD are two parallel chords of a circle with centre O and radius 13 cm 3
such that AB10 cm and CD24 cm. If OP is perpendicular to AB and OQ is perpendicular to
CD, determine the length of PQ.
15
Draw an angle of 90 using protractor. Now using compass and ruler, construct angles of 45 and 22 3
18
.
2
16
In ABC, A  60, B 70 and C 50 . Points D, E and F are the mid-points of the sides 3
BC, AC and AB respectively. Find the measures of the angles of the triangle formed by
joining the mid-points of the sides of ABC.
17
In the given figure, ABCD is a quadrilateral and E, F G and H are respectively the mid – 3
points of its sides. Prove that the area of the parallelogram EFGH formed by joining the mid –
points of the sides of the quadrilateral is half the area of the quadrilateral.
18
The radius and height of a cylinder are in the ratio 5 : 7. If its volume is 4400 cm3, find the 3
radius of the cylinder.
SECTION-D
Question numbers 19 to 28 carry four marks each.
19
20
Page 3 of 5
Draw a histogram and frequency polygon to represent the following grouped frequency 4
distribution :
Ages
20-24
25-29
30-34
35-39
40-44
45-49
50-54
(in years) :
Number
of
10
30
26
46
52
32
14
teachers :
ABCD is a rectangle. P and Q are points on sides AD and AB respectively. Show that APOQ 4
is a rectangle and find ar(APOQ) : ar(ABCD), when it is given that BR
1
1
BC and DS CD.
4
4
21
If two circles intersect in two points, prove that the line through their centres is the
perpendicular bisector of the common chord.
4
22
Construct SUT, if perimeter is 9.4 cm, U 40and T 100.
4
23
Prove that the bisectors of angles of a parallelogram form a rectangle.
4
24
On his birthday, Deepak bought 72 balloons to celebrate his birthday with the small children of his 4
colony. If the total surface area of all ballons is 44352 cm2, what volume of methane gas will be used
to fill all the balloons ? Which value is depicted by Deepak ?
25
Eight identical solid metallic cubes each of edge 'a' units and surface area S are melted to form 4
a new cube with surface area S'. Find :
(a)
edge of the new cube.
(b)
ratio of S and S'.
26
The radius and slant height of a cone are in the ratio 4 : 7. If its curved surface area is 792 cm 2, 4
find its radius and height.
27
Find the inner curved surface area and weight of a lead pipe 7 m long, if the external diameter
of the pipe is 4.4 cm and the thickness of the lead is 2 mm and 1 cubic cm of lead weighs 11
grams
4
28
The given table shows the marks obtained by 50 students out of 100 in a history examination :
Marks obtained No of students
0 – 25
9
25 – 50
8
50 – 75
23
75 - 100
10
Total
50
A student is chosen at random,
(a)
Find the probability that he has obtained 75 or more marks.
(b)
If 50% are passing marks, find the probability of the student failing in examination.
(c)
Find the probability that the student has obtained less than 75 marks.
4
Page 4 of 5
SECTION-E
(Open Text)
(* Please ensure that open text of the given theme is supplied with this question paper.)
Theme : Childhood Obesity in India
29
Two friends examined their BMI as 27 and 31, however both have equal height of 150 cm.
Determine weight of both friends. Also state the health status of both friends.
30
Rahul works out every day. He burns 200 kilo calories everyday through walking and 3
running . His workout is given by the following equation 4x8y200
(a)
Write two solutions of the above equation.
(b)
Is (0, 0) a solution of the above equation.
31
4
Refer the open text and answer the following questions :
(a)
What is the maximum calorie intake recommended through fats per day ?
(b)
Frame a linear equation to establish a relation between total calorie intake and
maximum calorie intake recommended through fats in a day and plot the graph.
-o0o0o0o-
Page 5 of 5
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