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# Maths Past Year Paper SA-1(Set -2) - 2015, Class 10, CBSE Class 10 Notes | EduRev

## Class 10 : Maths Past Year Paper SA-1(Set -2) - 2015, Class 10, CBSE Class 10 Notes | EduRev

``` Page 1

SUMMATIVE-ASSESSMENT-1 2015-16
SUBJECT –MATHEMATICS
CLASS-X                                                                                  zzdr-130

Time allowed: 3 hours                                Maximum Marks: 90

General Instructions:
1. All questions are compulsory
2. The question paper consists of 31 questions divided in to four sections A,B,C and D
3. section –A comprises of 4 questions of 1 mark each,
Section  -B comprises of 4 questions of 2 mark each.
Section  -c comprises of 4 questions of 3 mark each
Section  -D comprises of 4 questions of 4 mark each
4.use of calculator is not permitted.
5. An additional 15 minuts time has been allotted to read this question paper only.

SECTION A
Directions: 4 question of 1 mark each
1. Find a quadratic polynomial having zeroes as
3
?
?
and
2
?

2. Write the formula for the mid-point of a class interval .
3. If Sin A=
3
4
5 ,calculate cos A
4. Given an example of a pair of similar fugures.

SECTION-B
Directions: 6 questions of 2marks each.
5. Find the zeroes of
2
t -15 and verify the relationship between the zeroes and Coefficients
6. Determine whether the following system of linear equation has a unique solution, no
solution or infinitely many solution.
4x-5y=3
8x-10y=6
7. In the given figure DE//BC. Find Ec

Page 2

SUMMATIVE-ASSESSMENT-1 2015-16
SUBJECT –MATHEMATICS
CLASS-X                                                                                  zzdr-130

Time allowed: 3 hours                                Maximum Marks: 90

General Instructions:
1. All questions are compulsory
2. The question paper consists of 31 questions divided in to four sections A,B,C and D
3. section –A comprises of 4 questions of 1 mark each,
Section  -B comprises of 4 questions of 2 mark each.
Section  -c comprises of 4 questions of 3 mark each
Section  -D comprises of 4 questions of 4 mark each
4.use of calculator is not permitted.
5. An additional 15 minuts time has been allotted to read this question paper only.

SECTION A
Directions: 4 question of 1 mark each
1. Find a quadratic polynomial having zeroes as
3
?
?
and
2
?

2. Write the formula for the mid-point of a class interval .
3. If Sin A=
3
4
5 ,calculate cos A
4. Given an example of a pair of similar fugures.

SECTION-B
Directions: 6 questions of 2marks each.
5. Find the zeroes of
2
t -15 and verify the relationship between the zeroes and Coefficients
6. Determine whether the following system of linear equation has a unique solution, no
solution or infinitely many solution.
4x-5y=3
8x-10y=6
7. In the given figure DE//BC. Find Ec

8. Sin 2A=2 sin A is true when A=?
(a)
0
0
(b)
0
3 0
(c)
0
4 5
(d)
0
6 0
9. Express sin
0
6 7 +cos
0
7 5 in terms of trigonometric rations of angles between
0
0 and
0
4 5
10. Find mode of the given distribution
Family size  1-3 3-5 5-7 7-9 9-11
No. of families 7 8 2 2 1

Or
The following table gives the literacy rates (in percentage) of 35 cities. Find the mean literacy
rate.
Literacy rate (in %)                                             number of cities
45-55                                                                                  3
55-65                                                                                 10
65-75                                                                                 11
75-85                                                                                  8
85-95                                                                                  3

SECTION –C
Directions: 10 QUESTIONS OF 3MARKS EACH
11. Prove that 5 is an irrational number.
12. If a and ? are the zeroes of the polynomial
2
x -5x+k and a - ? =-1.
Find the value of k.
13. Determine a and b for which the following system of linear eqations has infinitely amny
solutions
2x-(a-4)y=2b+1
4x-(a-1)y+5b-1
14. If the areas of two similar triangles are equal, Prove that they are congruent.
15. PQR is a right angels triangle right angled at p.m is a point on QR such that PM ? QR.show
that
2
P M =QM.MR
16. Prove that:
s e c 0 1
s e c 0 1
?
?
+
se c 0 1
s e c 0 1
?
?
=2cosec 0
17.  If tan A=cotB,

Prove that A+B=
0
90

Page 3

SUMMATIVE-ASSESSMENT-1 2015-16
SUBJECT –MATHEMATICS
CLASS-X                                                                                  zzdr-130

Time allowed: 3 hours                                Maximum Marks: 90

General Instructions:
1. All questions are compulsory
2. The question paper consists of 31 questions divided in to four sections A,B,C and D
3. section –A comprises of 4 questions of 1 mark each,
Section  -B comprises of 4 questions of 2 mark each.
Section  -c comprises of 4 questions of 3 mark each
Section  -D comprises of 4 questions of 4 mark each
4.use of calculator is not permitted.
5. An additional 15 minuts time has been allotted to read this question paper only.

SECTION A
Directions: 4 question of 1 mark each
1. Find a quadratic polynomial having zeroes as
3
?
?
and
2
?

2. Write the formula for the mid-point of a class interval .
3. If Sin A=
3
4
5 ,calculate cos A
4. Given an example of a pair of similar fugures.

SECTION-B
Directions: 6 questions of 2marks each.
5. Find the zeroes of
2
t -15 and verify the relationship between the zeroes and Coefficients
6. Determine whether the following system of linear equation has a unique solution, no
solution or infinitely many solution.
4x-5y=3
8x-10y=6
7. In the given figure DE//BC. Find Ec

8. Sin 2A=2 sin A is true when A=?
(a)
0
0
(b)
0
3 0
(c)
0
4 5
(d)
0
6 0
9. Express sin
0
6 7 +cos
0
7 5 in terms of trigonometric rations of angles between
0
0 and
0
4 5
10. Find mode of the given distribution
Family size  1-3 3-5 5-7 7-9 9-11
No. of families 7 8 2 2 1

Or
The following table gives the literacy rates (in percentage) of 35 cities. Find the mean literacy
rate.
Literacy rate (in %)                                             number of cities
45-55                                                                                  3
55-65                                                                                 10
65-75                                                                                 11
75-85                                                                                  8
85-95                                                                                  3

SECTION –C
Directions: 10 QUESTIONS OF 3MARKS EACH
11. Prove that 5 is an irrational number.
12. If a and ? are the zeroes of the polynomial
2
x -5x+k and a - ? =-1.
Find the value of k.
13. Determine a and b for which the following system of linear eqations has infinitely amny
solutions
2x-(a-4)y=2b+1
4x-(a-1)y+5b-1
14. If the areas of two similar triangles are equal, Prove that they are congruent.
15. PQR is a right angels triangle right angled at p.m is a point on QR such that PM ? QR.show
that
2
P M =QM.MR
16. Prove that:
s e c 0 1
s e c 0 1
?
?
+
se c 0 1
s e c 0 1
?
?
=2cosec 0
17.  If tan A=cotB,

Prove that A+B=
0
90

Or
If A,B,C are interior angles of a ? ABC, show that

2
s ec
B C
2
? ? ?
? ?
? ?
-1=
2
c o t
A
2
? ?
? ?
? ?

18.  Evaluate :
5
2
5 c os
0
6 0 +
0
4 s e c
0
3 0 -
0
t a n
0
4 5
_______________________________________
2
si n
0
3 0 +
2
c o s
0
3 0

19. The length of 40 leaves of a plant are measured correct to nearest millimeter and the data
obtained is represented in the table below:
Find the median length of the leaves
Length (in mm) no. of leaves
118-126
127-135
136-144
145-153
154-162
163-171
172-180
3
5
9
12
5
4
2

20. The following distribution gives the daily income of 50workers of a factory
Daily income (in Rs) No. of workers
100-120
120-140
140-160
160-180
180-200
12
14
8
6
10
Convert the distribution above a less than type cumulative frequency distribution and draw its
ogive.
SECTION –D
Directions: 11 question of 4 marks each
21.  (a) Find the HCF of 1305, 1365 by using Euclid’s division algorithim.
(b) Also deduce the LCM of 1305 and 1365.
Page 4

SUMMATIVE-ASSESSMENT-1 2015-16
SUBJECT –MATHEMATICS
CLASS-X                                                                                  zzdr-130

Time allowed: 3 hours                                Maximum Marks: 90

General Instructions:
1. All questions are compulsory
2. The question paper consists of 31 questions divided in to four sections A,B,C and D
3. section –A comprises of 4 questions of 1 mark each,
Section  -B comprises of 4 questions of 2 mark each.
Section  -c comprises of 4 questions of 3 mark each
Section  -D comprises of 4 questions of 4 mark each
4.use of calculator is not permitted.
5. An additional 15 minuts time has been allotted to read this question paper only.

SECTION A
Directions: 4 question of 1 mark each
1. Find a quadratic polynomial having zeroes as
3
?
?
and
2
?

2. Write the formula for the mid-point of a class interval .
3. If Sin A=
3
4
5 ,calculate cos A
4. Given an example of a pair of similar fugures.

SECTION-B
Directions: 6 questions of 2marks each.
5. Find the zeroes of
2
t -15 and verify the relationship between the zeroes and Coefficients
6. Determine whether the following system of linear equation has a unique solution, no
solution or infinitely many solution.
4x-5y=3
8x-10y=6
7. In the given figure DE//BC. Find Ec

8. Sin 2A=2 sin A is true when A=?
(a)
0
0
(b)
0
3 0
(c)
0
4 5
(d)
0
6 0
9. Express sin
0
6 7 +cos
0
7 5 in terms of trigonometric rations of angles between
0
0 and
0
4 5
10. Find mode of the given distribution
Family size  1-3 3-5 5-7 7-9 9-11
No. of families 7 8 2 2 1

Or
The following table gives the literacy rates (in percentage) of 35 cities. Find the mean literacy
rate.
Literacy rate (in %)                                             number of cities
45-55                                                                                  3
55-65                                                                                 10
65-75                                                                                 11
75-85                                                                                  8
85-95                                                                                  3

SECTION –C
Directions: 10 QUESTIONS OF 3MARKS EACH
11. Prove that 5 is an irrational number.
12. If a and ? are the zeroes of the polynomial
2
x -5x+k and a - ? =-1.
Find the value of k.
13. Determine a and b for which the following system of linear eqations has infinitely amny
solutions
2x-(a-4)y=2b+1
4x-(a-1)y+5b-1
14. If the areas of two similar triangles are equal, Prove that they are congruent.
15. PQR is a right angels triangle right angled at p.m is a point on QR such that PM ? QR.show
that
2
P M =QM.MR
16. Prove that:
s e c 0 1
s e c 0 1
?
?
+
se c 0 1
s e c 0 1
?
?
=2cosec 0
17.  If tan A=cotB,

Prove that A+B=
0
90

Or
If A,B,C are interior angles of a ? ABC, show that

2
s ec
B C
2
? ? ?
? ?
? ?
-1=
2
c o t
A
2
? ?
? ?
? ?

18.  Evaluate :
5
2
5 c os
0
6 0 +
0
4 s e c
0
3 0 -
0
t a n
0
4 5
_______________________________________
2
si n
0
3 0 +
2
c o s
0
3 0

19. The length of 40 leaves of a plant are measured correct to nearest millimeter and the data
obtained is represented in the table below:
Find the median length of the leaves
Length (in mm) no. of leaves
118-126
127-135
136-144
145-153
154-162
163-171
172-180
3
5
9
12
5
4
2

20. The following distribution gives the daily income of 50workers of a factory
Daily income (in Rs) No. of workers
100-120
120-140
140-160
160-180
180-200
12
14
8
6
10
Convert the distribution above a less than type cumulative frequency distribution and draw its
ogive.
SECTION –D
Directions: 11 question of 4 marks each
21.  (a) Find the HCF of 1305, 1365 by using Euclid’s division algorithim.
(b) Also deduce the LCM of 1305 and 1365.

22. Prove that 2 3 ? 5 is anirrational number.
23. Solve graphically the following system of equations:
X+2y=5
2x3y=4
24. Yash scored 40 marks in a test ,getting 3 marks for each right answer and losing 1 mark for
each incorrect answer, then Yash would have scored 40marks. How many question were
there in the test?
25. Solve the following by substitution method:
3x+4y=10
2x-2y=2
26. Prove that if a line is drawn parallel to one side of a triangle to intersect the other two sided
in distinct points, then the other two sides are divided in the same ration.
27. In the given figure ,
OA.OB=OC.OD
Show that ? ? = ? c and ? B= ? D

Or
If AD and PM are medians of triangles ABC and PQR, respectively where
?
ABC ?
?
PQR,
Prove that
A B
P Q
=
A D
PM

28.  If sec ? +tan ? =p Show that
2
2
p 1
p 1
?
?
=sin ?

29. If tan ? +sin ? =m, and Tan ? -sin ? =n. Show that
2
m -
2
n = 4 m n

30. The annual profits earned by 30 shops of shopping complex in a locality give rise to the
following distribution:

Profit in lakhs (RS) no. of shops (frequency)
More than or equal to5
More than or equal to 10
More than or equal to 15
More than or equal to 20
More than or equal to 25
More than or equal to 30
30
28
16
14
10
7
Page 5

SUMMATIVE-ASSESSMENT-1 2015-16
SUBJECT –MATHEMATICS
CLASS-X                                                                                  zzdr-130

Time allowed: 3 hours                                Maximum Marks: 90

General Instructions:
1. All questions are compulsory
2. The question paper consists of 31 questions divided in to four sections A,B,C and D
3. section –A comprises of 4 questions of 1 mark each,
Section  -B comprises of 4 questions of 2 mark each.
Section  -c comprises of 4 questions of 3 mark each
Section  -D comprises of 4 questions of 4 mark each
4.use of calculator is not permitted.
5. An additional 15 minuts time has been allotted to read this question paper only.

SECTION A
Directions: 4 question of 1 mark each
1. Find a quadratic polynomial having zeroes as
3
?
?
and
2
?

2. Write the formula for the mid-point of a class interval .
3. If Sin A=
3
4
5 ,calculate cos A
4. Given an example of a pair of similar fugures.

SECTION-B
Directions: 6 questions of 2marks each.
5. Find the zeroes of
2
t -15 and verify the relationship between the zeroes and Coefficients
6. Determine whether the following system of linear equation has a unique solution, no
solution or infinitely many solution.
4x-5y=3
8x-10y=6
7. In the given figure DE//BC. Find Ec

8. Sin 2A=2 sin A is true when A=?
(a)
0
0
(b)
0
3 0
(c)
0
4 5
(d)
0
6 0
9. Express sin
0
6 7 +cos
0
7 5 in terms of trigonometric rations of angles between
0
0 and
0
4 5
10. Find mode of the given distribution
Family size  1-3 3-5 5-7 7-9 9-11
No. of families 7 8 2 2 1

Or
The following table gives the literacy rates (in percentage) of 35 cities. Find the mean literacy
rate.
Literacy rate (in %)                                             number of cities
45-55                                                                                  3
55-65                                                                                 10
65-75                                                                                 11
75-85                                                                                  8
85-95                                                                                  3

SECTION –C
Directions: 10 QUESTIONS OF 3MARKS EACH
11. Prove that 5 is an irrational number.
12. If a and ? are the zeroes of the polynomial
2
x -5x+k and a - ? =-1.
Find the value of k.
13. Determine a and b for which the following system of linear eqations has infinitely amny
solutions
2x-(a-4)y=2b+1
4x-(a-1)y+5b-1
14. If the areas of two similar triangles are equal, Prove that they are congruent.
15. PQR is a right angels triangle right angled at p.m is a point on QR such that PM ? QR.show
that
2
P M =QM.MR
16. Prove that:
s e c 0 1
s e c 0 1
?
?
+
se c 0 1
s e c 0 1
?
?
=2cosec 0
17.  If tan A=cotB,

Prove that A+B=
0
90

Or
If A,B,C are interior angles of a ? ABC, show that

2
s ec
B C
2
? ? ?
? ?
? ?
-1=
2
c o t
A
2
? ?
? ?
? ?

18.  Evaluate :
5
2
5 c os
0
6 0 +
0
4 s e c
0
3 0 -
0
t a n
0
4 5
_______________________________________
2
si n
0
3 0 +
2
c o s
0
3 0

19. The length of 40 leaves of a plant are measured correct to nearest millimeter and the data
obtained is represented in the table below:
Find the median length of the leaves
Length (in mm) no. of leaves
118-126
127-135
136-144
145-153
154-162
163-171
172-180
3
5
9
12
5
4
2

20. The following distribution gives the daily income of 50workers of a factory
Daily income (in Rs) No. of workers
100-120
120-140
140-160
160-180
180-200
12
14
8
6
10
Convert the distribution above a less than type cumulative frequency distribution and draw its
ogive.
SECTION –D
Directions: 11 question of 4 marks each
21.  (a) Find the HCF of 1305, 1365 by using Euclid’s division algorithim.
(b) Also deduce the LCM of 1305 and 1365.

22. Prove that 2 3 ? 5 is anirrational number.
23. Solve graphically the following system of equations:
X+2y=5
2x3y=4
24. Yash scored 40 marks in a test ,getting 3 marks for each right answer and losing 1 mark for
each incorrect answer, then Yash would have scored 40marks. How many question were
there in the test?
25. Solve the following by substitution method:
3x+4y=10
2x-2y=2
26. Prove that if a line is drawn parallel to one side of a triangle to intersect the other two sided
in distinct points, then the other two sides are divided in the same ration.
27. In the given figure ,
OA.OB=OC.OD
Show that ? ? = ? c and ? B= ? D

Or
If AD and PM are medians of triangles ABC and PQR, respectively where
?
ABC ?
?
PQR,
Prove that
A B
P Q
=
A D
PM

28.  If sec ? +tan ? =p Show that
2
2
p 1
p 1
?
?
=sin ?

29. If tan ? +sin ? =m, and Tan ? -sin ? =n. Show that
2
m -
2
n = 4 m n

30. The annual profits earned by 30 shops of shopping complex in a locality give rise to the
following distribution:

Profit in lakhs (RS) no. of shops (frequency)
More than or equal to5
More than or equal to 10
More than or equal to 15
More than or equal to 20
More than or equal to 25
More than or equal to 30
30
28
16
14
10
7

More than or equal to 35 3
Draw both ogives for the above data and hence obtain the media profit.
31. If the median of the distribution given below is 28.5, find the value of x and y
Class Interval Frequency
010
10-20
20-30
30-40
40-50
50-60
5
x
20
15
y
5
Total 60

```
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