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

Past Year Papers For Class 10

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 wrong answer. Had 4 marks been awarded for each correct answer and 2 marks 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 wrong answer. Had 4 marks been awarded for each correct answer and 2 marks 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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