Download CTZ3MEM SUMMATIVE ASSESSMENT – I, 2014 MATHEMATICS

CTZ3MEM
SUMMATIVE ASSESSMENT – I, 2014
MATHEMATICS
Class – X
Time Allowed: 3 hours
Maximum Marks: 90
General Instructions:
1.
2.
3.
4.
All questions are compulsory.
The question paper consists of 31 questions divided into four sections A, B, C and D.
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.
There is no overall choice in this question paper.
Use of calculator is not permitted.
SECTION-A
Question numbers 1 to 4 carry one mark each
1
In PQR, if B and C are points on the sides PR and QR respectively such that RB10 cm, 1
PR18 cm, RC15 cm and CQ12 cm, then find whether BC is parallel to QR or not.
2
Evaluate : sin 30 cos 60
1
3
Express cosec 48 tan 88 in terms of t – ratios of angles between 0 and 45.
1
4
For a certain distribution mode and median were found to be 1000 and 1250 respectively. Find 1
mean for this distribution using an empirical relation.
SECTION-B
Question numbers 5 to 10 carry two marks each.
5
Page 1 of 5
Find the smallest natural number by which 1200 should be multiplied so that the square root of 2
the product is a rational number.
6
What is the decimal expansion of the rational number
201
250
2
?
7
Check whether x34x23x2 is divisible by x2.
2
8
In the figure, EFAC, BC10 cm ,AB13 cm and EC2 cm, find AF.
2
9
Prove that :
2
sec4 sec2 tan4 tan2
10
Given below is the distribution of monthly salary of workers in a factory. Calculate the modal 2
salary.
Salary
(inRs.)
4000
to
6000
Number of
21
workers
6000
to
8000
8000
to
1000
0
1000
0 to
1200
0
1200
0 to
1400
0
1400
0 to
1600
0
1600
18000
0 to
to
1800
20000
0
43
72
230
185
110
85
35
SECTION-C
Question numbers 11 to 20 carry three marks each.
11
Find HCF of the numbers 1405, 1465 and 1530 by Euclid’s division algorithm.
12
The perimeter of a rectangular garden, whose length is 4 m more than its width, is 40 m. Find 3
the dimensions of the rectangle.
13
Determine
2x7y14
10x35y35
has
Page 2 of 5
graphically
whether
the
following
pair
of
linear
3
equations 3
(i)
a unique solution,
(ii)
infinitely many solutions or
(iii)
no solution
14
2
Find the zeroes of the quadratic polynomial 3x 2 and verify the relationship between the 3
zeroes and the coefficients.
15
In a quadrilateral ABCD, if ACDB90, then prove that AD AB CD BC
16
The perimeters of similar triangles ABC and PQR are 180 cm and 50 cm respectively. If QR5 3
cm, then find BC.
17
Prove that :
2
2
2
2
3
3
(1cot cosec ). (1tan 
)2
18
If 2 sin A : 3 cos A 3 : 4, then find the values of tan A, cosec A and cos A.
3
19
Find the median age of the life of bulbs from the following data :
3
20
Life time 0-250
(in hours)
250500
500750
7501000
10001250
12501500
Number
of bulbs
10
11
15
10
5
6
In a hospital, age record of diabetic patients was recorded as follows :
Age (in years)
0-15
15-30
30-45
45-60
60-75
Number of patients
5
20
40
50
25
Find median age.
Page 3 of 5
3
SECTION-D
Question numbers 21 to 31 carry four marks each.
21
Is square root of every non-square number always irrational? Find the smallest natural number 4
which divides 2205 to make its square root a rational number.
22
Rahul donated some money and books to a school for poor children. Money and books can be 4
represented by the zeroes (i.e. , ) of the polynomial p(x)x2x2. Akash who is friend of
Rahul, also got inspired by him and donated the money and books in the form of a polynomial
whose zeroes are 12 and 12.Find the polynomial represented by Akash’sdonation ?
Why Akash got inspired by Rahul ?
23
If a polynomial 2x43x36x23x2 is divided by another polynomial 2x23x4, then 4
remainder is pxq. Find the value of p and q.
24
Solve the following system of linear equations graphically :
4
5x 7y 50
5x 7y 20
Also write the coordinates of the points where they meet x-axis. Shade the triangular region.
25
In ABC, AD BC and D lies on BC such that 4 DBCD, then
4
prove that 5 AB25 AC23 BC2
26
In ABC, B90, BDAC, are (ABC)A and BCa, then prove that BD
2
4 A 1 a
27
In PQR, if PQ : QR : PR  8 : 15 : 17, then evaluate.
(i)
(ii)
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cosP. cosRsinP. sinR
ta n P 2 ta n R
1 1 ta n P . ta n R
4
2 A a
4
4
28
29
If sin(AB)1 and tan(AB) 
(i)
tanAcotB
(ii)
secAcosecB.
3
4
, find the value of
Prove that :
c o tA 1 s in A
c o tA 2 s in A
30
1
4

1 2 co sA 1 secA
1 1 co sA 2 secA
For one term, absentee record of students is given. If mean is 15.5, find the missing 4
frequencies x and y.
Number
of
days
Number
of
students
31
0-5
5-10
15
16
10-
15-
20-
25-
30-
35-
15
20
25
30
35
40
x
8
y
8
6
4
70
Pocket money of 100 students is given in the following frequency distribution :
Pocket money
0-20
(in `)
20-40
40-60
60-80
80-100
100-120
120-140
Number
students
6
10
20
30
20
10
of
4
Draw a ‘less than’ ogive and ‘a more than’ ogive for the above data.
-o0o0o0o-
Page 5 of 5
Total
4