Sample Solution Paper 4 - Term- 1 Mathematics, Class 7 Class 7 Notes | EduRev

 Page 1


  
 
CBSE VII | Mathematics 
Sample Paper 4 - Solution  
 
     
CBSE Board 
Class VII Mathematics 
Term I 
Sample Paper 4 - Solution 
Time: 2 ½ hours                          Total Marks: 80 
 
Section A 
 
1. Correct answer: A 
For example: 
(a) 56 + 73 = 129  
(b) 113 + 82 = 195 
 
2. Correct answer: B 
A proper fraction is a fraction that represents a part of a whole. 
 
3. Correct answer: B 
On a number line when we add a positive integer we move to the right  
Towards or away from origin depends on the number to which it is added. 
 
4. Correct answer: A 
An improper fraction is a combination of whole and a proper fraction. 
 
5. Correct answer: B 
Average of both  
=
60 20
40
2
?
? 
 
6. Correct answer: B 
A variable takes on different numerical values; its value is not fixed. Variables are 
denoted usually by letters of the alphabets, such as x, y, z, l, m, n, p, etc.  
 
7. Correct answer: C 
Total runs = 36 + 35 + 50 + 46 + 60 + 55 = 282. 
     To find the mean, we find the sum of all the observations and divide it by the  
     number of observations. 
     Therefore, in this case, mean = 
282
47
6
? 
 
 
 
 
Page 2


  
 
CBSE VII | Mathematics 
Sample Paper 4 - Solution  
 
     
CBSE Board 
Class VII Mathematics 
Term I 
Sample Paper 4 - Solution 
Time: 2 ½ hours                          Total Marks: 80 
 
Section A 
 
1. Correct answer: A 
For example: 
(a) 56 + 73 = 129  
(b) 113 + 82 = 195 
 
2. Correct answer: B 
A proper fraction is a fraction that represents a part of a whole. 
 
3. Correct answer: B 
On a number line when we add a positive integer we move to the right  
Towards or away from origin depends on the number to which it is added. 
 
4. Correct answer: A 
An improper fraction is a combination of whole and a proper fraction. 
 
5. Correct answer: B 
Average of both  
=
60 20
40
2
?
? 
 
6. Correct answer: B 
A variable takes on different numerical values; its value is not fixed. Variables are 
denoted usually by letters of the alphabets, such as x, y, z, l, m, n, p, etc.  
 
7. Correct answer: C 
Total runs = 36 + 35 + 50 + 46 + 60 + 55 = 282. 
     To find the mean, we find the sum of all the observations and divide it by the  
     number of observations. 
     Therefore, in this case, mean = 
282
47
6
? 
 
 
 
 
  
 
CBSE VII | Mathematics 
Sample Paper 4 - Solution  
 
     
8. Correct answer: C 
an equation is a condition on a variable. The condition is that two expressions 
should have equal value. Note that at least one of the two expressions must contain 
the variable. 
 
9. Correct answer: D 
When the sum of the measures of two angles is 90°, the angles are called 
complementary angles. 
 
10. Correct answer: B 
A median connects a vertex of a triangle to the mid-point of the opposite side. 
 
11. Correct answer: D 
The tests of congruency are 
SSS 
SAS 
AAS,SAA,ASA (all same) 
 
12. Correct answer: A 
First convert both the distances to the same unit. 
So, 3 km = 3 × 1000 m = 3000 m. 
Thus, the required ratio, 3 km : 300 m is 3000 : 300 = 10 : 1. 
 
Section B 
 
13.  
(a)   
  
? ? ? ? ? ? ? ? 8 4 8 4
8 4 8 4
12 4
? ? ? ? ? ?
? ? ? ? ?
? ? ? ?
 
(b)   
  
? ? ? ? ? ? 3 7 19 15 8 9
3 7 19 15 8 9
15 2
? ? ? ? ? ?
? ? ? ? ? ?
? ? ? ?
 
 
 
Page 3


  
 
CBSE VII | Mathematics 
Sample Paper 4 - Solution  
 
     
CBSE Board 
Class VII Mathematics 
Term I 
Sample Paper 4 - Solution 
Time: 2 ½ hours                          Total Marks: 80 
 
Section A 
 
1. Correct answer: A 
For example: 
(a) 56 + 73 = 129  
(b) 113 + 82 = 195 
 
2. Correct answer: B 
A proper fraction is a fraction that represents a part of a whole. 
 
3. Correct answer: B 
On a number line when we add a positive integer we move to the right  
Towards or away from origin depends on the number to which it is added. 
 
4. Correct answer: A 
An improper fraction is a combination of whole and a proper fraction. 
 
5. Correct answer: B 
Average of both  
=
60 20
40
2
?
? 
 
6. Correct answer: B 
A variable takes on different numerical values; its value is not fixed. Variables are 
denoted usually by letters of the alphabets, such as x, y, z, l, m, n, p, etc.  
 
7. Correct answer: C 
Total runs = 36 + 35 + 50 + 46 + 60 + 55 = 282. 
     To find the mean, we find the sum of all the observations and divide it by the  
     number of observations. 
     Therefore, in this case, mean = 
282
47
6
? 
 
 
 
 
  
 
CBSE VII | Mathematics 
Sample Paper 4 - Solution  
 
     
8. Correct answer: C 
an equation is a condition on a variable. The condition is that two expressions 
should have equal value. Note that at least one of the two expressions must contain 
the variable. 
 
9. Correct answer: D 
When the sum of the measures of two angles is 90°, the angles are called 
complementary angles. 
 
10. Correct answer: B 
A median connects a vertex of a triangle to the mid-point of the opposite side. 
 
11. Correct answer: D 
The tests of congruency are 
SSS 
SAS 
AAS,SAA,ASA (all same) 
 
12. Correct answer: A 
First convert both the distances to the same unit. 
So, 3 km = 3 × 1000 m = 3000 m. 
Thus, the required ratio, 3 km : 300 m is 3000 : 300 = 10 : 1. 
 
Section B 
 
13.  
(a)   
  
? ? ? ? ? ? ? ? 8 4 8 4
8 4 8 4
12 4
? ? ? ? ? ?
? ? ? ? ?
? ? ? ?
 
(b)   
  
? ? ? ? ? ? 3 7 19 15 8 9
3 7 19 15 8 9
15 2
? ? ? ? ? ?
? ? ? ? ? ?
? ? ? ?
 
 
 
  
 
CBSE VII | Mathematics 
Sample Paper 4 - Solution  
 
     
(c)   
  
23 41 11 23 41 11
7 29
? ? ? ?
? ? ? ?
 
(d)   
  
? ? ? ? ? ? ? ? 39 24 15 36 52 36
39 24 15 36 52 36
0 20
? ? ? ? ? ? ?
? ? ? ? ?
??
 
(e)   
  
231 79 51 399 159 81
101 159
? ? ? ? ? ?
? ? ? ?
 
  
14. The numbers in ascending order are: 
Team A scored: – 40, 10, 0 
Total score = – 40 + 10 + 0 = – 30    
Team B scored: 10, 0, – 40 
Total score = 10 + 0 + (– 40)= – 30 
? The scores of both teams are equal. 
Yes, we can add integers in any order. As we had observed that the scores obtained 
by both teams in successive rounds were numerically equal but different in order, 
yet total score of both teams were equal.   
 
15. (i)
3 2 5 3 10 3 7
2
5 5 5 5 5
??
? ? ? ? ? 
 
   (ii) 
? ? 4 8 7
7 4 8 7 39 7
44
8 8 8 8 8 8
??
?
? ? ? ? ? ? 
 
 
 
 
 
Page 4


  
 
CBSE VII | Mathematics 
Sample Paper 4 - Solution  
 
     
CBSE Board 
Class VII Mathematics 
Term I 
Sample Paper 4 - Solution 
Time: 2 ½ hours                          Total Marks: 80 
 
Section A 
 
1. Correct answer: A 
For example: 
(a) 56 + 73 = 129  
(b) 113 + 82 = 195 
 
2. Correct answer: B 
A proper fraction is a fraction that represents a part of a whole. 
 
3. Correct answer: B 
On a number line when we add a positive integer we move to the right  
Towards or away from origin depends on the number to which it is added. 
 
4. Correct answer: A 
An improper fraction is a combination of whole and a proper fraction. 
 
5. Correct answer: B 
Average of both  
=
60 20
40
2
?
? 
 
6. Correct answer: B 
A variable takes on different numerical values; its value is not fixed. Variables are 
denoted usually by letters of the alphabets, such as x, y, z, l, m, n, p, etc.  
 
7. Correct answer: C 
Total runs = 36 + 35 + 50 + 46 + 60 + 55 = 282. 
     To find the mean, we find the sum of all the observations and divide it by the  
     number of observations. 
     Therefore, in this case, mean = 
282
47
6
? 
 
 
 
 
  
 
CBSE VII | Mathematics 
Sample Paper 4 - Solution  
 
     
8. Correct answer: C 
an equation is a condition on a variable. The condition is that two expressions 
should have equal value. Note that at least one of the two expressions must contain 
the variable. 
 
9. Correct answer: D 
When the sum of the measures of two angles is 90°, the angles are called 
complementary angles. 
 
10. Correct answer: B 
A median connects a vertex of a triangle to the mid-point of the opposite side. 
 
11. Correct answer: D 
The tests of congruency are 
SSS 
SAS 
AAS,SAA,ASA (all same) 
 
12. Correct answer: A 
First convert both the distances to the same unit. 
So, 3 km = 3 × 1000 m = 3000 m. 
Thus, the required ratio, 3 km : 300 m is 3000 : 300 = 10 : 1. 
 
Section B 
 
13.  
(a)   
  
? ? ? ? ? ? ? ? 8 4 8 4
8 4 8 4
12 4
? ? ? ? ? ?
? ? ? ? ?
? ? ? ?
 
(b)   
  
? ? ? ? ? ? 3 7 19 15 8 9
3 7 19 15 8 9
15 2
? ? ? ? ? ?
? ? ? ? ? ?
? ? ? ?
 
 
 
  
 
CBSE VII | Mathematics 
Sample Paper 4 - Solution  
 
     
(c)   
  
23 41 11 23 41 11
7 29
? ? ? ?
? ? ? ?
 
(d)   
  
? ? ? ? ? ? ? ? 39 24 15 36 52 36
39 24 15 36 52 36
0 20
? ? ? ? ? ? ?
? ? ? ? ?
??
 
(e)   
  
231 79 51 399 159 81
101 159
? ? ? ? ? ?
? ? ? ?
 
  
14. The numbers in ascending order are: 
Team A scored: – 40, 10, 0 
Total score = – 40 + 10 + 0 = – 30    
Team B scored: 10, 0, – 40 
Total score = 10 + 0 + (– 40)= – 30 
? The scores of both teams are equal. 
Yes, we can add integers in any order. As we had observed that the scores obtained 
by both teams in successive rounds were numerically equal but different in order, 
yet total score of both teams were equal.   
 
15. (i)
3 2 5 3 10 3 7
2
5 5 5 5 5
??
? ? ? ? ? 
 
   (ii) 
? ? 4 8 7
7 4 8 7 39 7
44
8 8 8 8 8 8
??
?
? ? ? ? ? ? 
 
 
 
 
 
  
 
CBSE VII | Mathematics 
Sample Paper 4 - Solution  
 
     
16.  
(i)  
3 21 1
74
5 5 5
? ? ? 
(ii) 
1 4 1
41
3 3 3
? ? ? 
 
 
17. We may arrange the marks obtained by group of student in a science test in an  
 ascending order as following –39, 48, 56, 75, 76, 81, 85, 85, 90, 95 
(i) Highest marks = 95 Lowest marks = 39 
(ii) Range = 95 – 39  = 56 
(iii) Mean marks =
? ? 85 76 90 85 39 48 56 95 81 75
10
? ? ? ? ? ? ? ? ?
 
730
73
10
?? 
 
18. Scores of 15 students in mathematics test are – 
19, 25, 23, 20, 9, 20, 15, 10, 5, 16, 25, 20, 24, 12, 20 
 By arranging these scores in an ascending order 
 5, 9, 10, 12, 15, 16, 19, 20, 20, 20, 20, 23, 24, 25, 25 
Mode of a given data is that value of observation which occurs for the most number 
of times and the median of the given data is the middle observation while the data is 
arranged in an ascending or descending order. 
As here are 15 terms in the given data so the median of this data will be 8th 
observation. 
Hence, median = 20 
Also we may find that 20 occurs 4 times (i.e. maximum number of times). 
 So, mode of this data = 20. 
 Yes, both are same. 
 
 
 
 
Page 5


  
 
CBSE VII | Mathematics 
Sample Paper 4 - Solution  
 
     
CBSE Board 
Class VII Mathematics 
Term I 
Sample Paper 4 - Solution 
Time: 2 ½ hours                          Total Marks: 80 
 
Section A 
 
1. Correct answer: A 
For example: 
(a) 56 + 73 = 129  
(b) 113 + 82 = 195 
 
2. Correct answer: B 
A proper fraction is a fraction that represents a part of a whole. 
 
3. Correct answer: B 
On a number line when we add a positive integer we move to the right  
Towards or away from origin depends on the number to which it is added. 
 
4. Correct answer: A 
An improper fraction is a combination of whole and a proper fraction. 
 
5. Correct answer: B 
Average of both  
=
60 20
40
2
?
? 
 
6. Correct answer: B 
A variable takes on different numerical values; its value is not fixed. Variables are 
denoted usually by letters of the alphabets, such as x, y, z, l, m, n, p, etc.  
 
7. Correct answer: C 
Total runs = 36 + 35 + 50 + 46 + 60 + 55 = 282. 
     To find the mean, we find the sum of all the observations and divide it by the  
     number of observations. 
     Therefore, in this case, mean = 
282
47
6
? 
 
 
 
 
  
 
CBSE VII | Mathematics 
Sample Paper 4 - Solution  
 
     
8. Correct answer: C 
an equation is a condition on a variable. The condition is that two expressions 
should have equal value. Note that at least one of the two expressions must contain 
the variable. 
 
9. Correct answer: D 
When the sum of the measures of two angles is 90°, the angles are called 
complementary angles. 
 
10. Correct answer: B 
A median connects a vertex of a triangle to the mid-point of the opposite side. 
 
11. Correct answer: D 
The tests of congruency are 
SSS 
SAS 
AAS,SAA,ASA (all same) 
 
12. Correct answer: A 
First convert both the distances to the same unit. 
So, 3 km = 3 × 1000 m = 3000 m. 
Thus, the required ratio, 3 km : 300 m is 3000 : 300 = 10 : 1. 
 
Section B 
 
13.  
(a)   
  
? ? ? ? ? ? ? ? 8 4 8 4
8 4 8 4
12 4
? ? ? ? ? ?
? ? ? ? ?
? ? ? ?
 
(b)   
  
? ? ? ? ? ? 3 7 19 15 8 9
3 7 19 15 8 9
15 2
? ? ? ? ? ?
? ? ? ? ? ?
? ? ? ?
 
 
 
  
 
CBSE VII | Mathematics 
Sample Paper 4 - Solution  
 
     
(c)   
  
23 41 11 23 41 11
7 29
? ? ? ?
? ? ? ?
 
(d)   
  
? ? ? ? ? ? ? ? 39 24 15 36 52 36
39 24 15 36 52 36
0 20
? ? ? ? ? ? ?
? ? ? ? ?
??
 
(e)   
  
231 79 51 399 159 81
101 159
? ? ? ? ? ?
? ? ? ?
 
  
14. The numbers in ascending order are: 
Team A scored: – 40, 10, 0 
Total score = – 40 + 10 + 0 = – 30    
Team B scored: 10, 0, – 40 
Total score = 10 + 0 + (– 40)= – 30 
? The scores of both teams are equal. 
Yes, we can add integers in any order. As we had observed that the scores obtained 
by both teams in successive rounds were numerically equal but different in order, 
yet total score of both teams were equal.   
 
15. (i)
3 2 5 3 10 3 7
2
5 5 5 5 5
??
? ? ? ? ? 
 
   (ii) 
? ? 4 8 7
7 4 8 7 39 7
44
8 8 8 8 8 8
??
?
? ? ? ? ? ? 
 
 
 
 
 
  
 
CBSE VII | Mathematics 
Sample Paper 4 - Solution  
 
     
16.  
(i)  
3 21 1
74
5 5 5
? ? ? 
(ii) 
1 4 1
41
3 3 3
? ? ? 
 
 
17. We may arrange the marks obtained by group of student in a science test in an  
 ascending order as following –39, 48, 56, 75, 76, 81, 85, 85, 90, 95 
(i) Highest marks = 95 Lowest marks = 39 
(ii) Range = 95 – 39  = 56 
(iii) Mean marks =
? ? 85 76 90 85 39 48 56 95 81 75
10
? ? ? ? ? ? ? ? ?
 
730
73
10
?? 
 
18. Scores of 15 students in mathematics test are – 
19, 25, 23, 20, 9, 20, 15, 10, 5, 16, 25, 20, 24, 12, 20 
 By arranging these scores in an ascending order 
 5, 9, 10, 12, 15, 16, 19, 20, 20, 20, 20, 23, 24, 25, 25 
Mode of a given data is that value of observation which occurs for the most number 
of times and the median of the given data is the middle observation while the data is 
arranged in an ascending or descending order. 
As here are 15 terms in the given data so the median of this data will be 8th 
observation. 
Hence, median = 20 
Also we may find that 20 occurs 4 times (i.e. maximum number of times). 
 So, mode of this data = 20. 
 Yes, both are same. 
 
 
 
 
  
 
CBSE VII | Mathematics 
Sample Paper 4 - Solution  
 
     
19.  
(i) 5p + 2 = 17 
  Put p = 1 in L.H.S 
  (5 × 1) + 2 = 7 ? R.H.S 
 
  Put p = 2 in L.H.S 
  (5 × 2) + 2 = 10 + 2 = 12 ? R.H.S 
   
  Put p = 3 in L.H.S 
  (5 × 3) + 2 = 17 = R.H.S 
  Hence p = 3 is a solution of the given equation. 
 
 (ii) 3m – 14 = 4 
  Put m = 4, 
  (3 × 4) – 14 = – 2 ? R.H.S 
  
  Put m = 5 
  (3 × 5)  – 14 = 1 ? R.H.S 
 
  Put m = 6 
  (3 × 6) – 14 = 18 – 14 = 4 = R.H.S 
  Hence, m = 6 is a solution of the given equation.