Class 7 Math: CBSE Sample Question Paper Solutions Term I – 3 | Mathematics (Maths) Class 7 PDF Download

 Page 1


  
 
CBSE VII | Mathematics 
Sample Paper 3 - Solution  
 
     
CBSE Board 
Class VII Mathematics 
Term I 
Sample Paper 3 - Solution 
Time: 2 ½ hours                          Total Marks: 80 
 
Section A 
 
1. Correct answer: A 
(128 ÷32)÷ (-4) 
 = 4 ÷ (-4) 
 = -1 
 
2. Correct answer: A 
Total cost = 2.40 × 10 
 = Rs. 24 
 
3. Correct answer: B 
The given observations can be arranged in ascending order as 
4, 6, 9, 10, 11, 12 and 18 
Here, number of observations = 7 (odd) 
Median = Middle observation = 10 
 
4. Correct answer: A 
2x + 3 = 7 
If we will transpose 3 to RHS, then the term with variable will remain on one side 
and the constants will be on other side. 
So, the first step is to transpose 3 to RHS. 
i.e. 2x = 7 – 3 
 
5. Correct answer: C 
?BCA = 180° - 150° = 30°                      (linear pair angles) 
Also, ?B = ?BCA = 30°                           (Angles opp. to equal sides are equal) 
? ?A = 180° - 30° - 30° = 120°            (Using angle sum property of triangle) 
 
6. Correct answer: B 
Increased amount =  
12
Rs. ×54=Rs. 6.48
100
  
 
 
 
Page 2


  
 
CBSE VII | Mathematics 
Sample Paper 3 - Solution  
 
     
CBSE Board 
Class VII Mathematics 
Term I 
Sample Paper 3 - Solution 
Time: 2 ½ hours                          Total Marks: 80 
 
Section A 
 
1. Correct answer: A 
(128 ÷32)÷ (-4) 
 = 4 ÷ (-4) 
 = -1 
 
2. Correct answer: A 
Total cost = 2.40 × 10 
 = Rs. 24 
 
3. Correct answer: B 
The given observations can be arranged in ascending order as 
4, 6, 9, 10, 11, 12 and 18 
Here, number of observations = 7 (odd) 
Median = Middle observation = 10 
 
4. Correct answer: A 
2x + 3 = 7 
If we will transpose 3 to RHS, then the term with variable will remain on one side 
and the constants will be on other side. 
So, the first step is to transpose 3 to RHS. 
i.e. 2x = 7 – 3 
 
5. Correct answer: C 
?BCA = 180° - 150° = 30°                      (linear pair angles) 
Also, ?B = ?BCA = 30°                           (Angles opp. to equal sides are equal) 
? ?A = 180° - 30° - 30° = 120°            (Using angle sum property of triangle) 
 
6. Correct answer: B 
Increased amount =  
12
Rs. ×54=Rs. 6.48
100
  
 
 
 
  
 
CBSE VII | Mathematics 
Sample Paper 3 - Solution  
 
     
7. Correct answer: C 
?
28
2
33
 
So the multiplicative inverse is
3
8
. 
 
8. Correct answer: D 
The triangle ABC is a right angled triangle,  
By Pythagoras theorem, we have: c
2
 = a
2
 + b
2 
 
9. Correct answer: B 
21b - 32 + 7b - 20b  
= 21b + 7b - 20b – 32  
= 8b – 32 
 
 
10. Correct answer: D 
  
 
11. Correct answer: A 
The two triangles can be proved to be congruent by using SAS congruency criterion. 
The corresponding equal parts in triangles ABC and ADE are 
  
 
12. Correct answer: C 
Let the whole number be x. 
Twice of the whole number = 2x 
9 added to twice of the whole number = 9 + 2x 
From the given information, we have: 
9 + 2x = 31 
2x = 31 - 9 
2x = 22 
x = 11 
Thus, the required whole number is 11. 
 
 
 
 
 
Page 3


  
 
CBSE VII | Mathematics 
Sample Paper 3 - Solution  
 
     
CBSE Board 
Class VII Mathematics 
Term I 
Sample Paper 3 - Solution 
Time: 2 ½ hours                          Total Marks: 80 
 
Section A 
 
1. Correct answer: A 
(128 ÷32)÷ (-4) 
 = 4 ÷ (-4) 
 = -1 
 
2. Correct answer: A 
Total cost = 2.40 × 10 
 = Rs. 24 
 
3. Correct answer: B 
The given observations can be arranged in ascending order as 
4, 6, 9, 10, 11, 12 and 18 
Here, number of observations = 7 (odd) 
Median = Middle observation = 10 
 
4. Correct answer: A 
2x + 3 = 7 
If we will transpose 3 to RHS, then the term with variable will remain on one side 
and the constants will be on other side. 
So, the first step is to transpose 3 to RHS. 
i.e. 2x = 7 – 3 
 
5. Correct answer: C 
?BCA = 180° - 150° = 30°                      (linear pair angles) 
Also, ?B = ?BCA = 30°                           (Angles opp. to equal sides are equal) 
? ?A = 180° - 30° - 30° = 120°            (Using angle sum property of triangle) 
 
6. Correct answer: B 
Increased amount =  
12
Rs. ×54=Rs. 6.48
100
  
 
 
 
  
 
CBSE VII | Mathematics 
Sample Paper 3 - Solution  
 
     
7. Correct answer: C 
?
28
2
33
 
So the multiplicative inverse is
3
8
. 
 
8. Correct answer: D 
The triangle ABC is a right angled triangle,  
By Pythagoras theorem, we have: c
2
 = a
2
 + b
2 
 
9. Correct answer: B 
21b - 32 + 7b - 20b  
= 21b + 7b - 20b – 32  
= 8b – 32 
 
 
10. Correct answer: D 
  
 
11. Correct answer: A 
The two triangles can be proved to be congruent by using SAS congruency criterion. 
The corresponding equal parts in triangles ABC and ADE are 
  
 
12. Correct answer: C 
Let the whole number be x. 
Twice of the whole number = 2x 
9 added to twice of the whole number = 9 + 2x 
From the given information, we have: 
9 + 2x = 31 
2x = 31 - 9 
2x = 22 
x = 11 
Thus, the required whole number is 11. 
 
 
 
 
 
  
 
CBSE VII | Mathematics 
Sample Paper 3 - Solution  
 
     
Section B 
 
13. Given that, m||p and t is the transversal 
We know that, if two parallel lines are cut by a transversal, each pair of alternate 
interior angles are equal. 
So, ? a = ? z (pair of alternate interior angles) 
 Thus, ? z = 57
o
. 
  
14. The numbers in ascending order are: 
11, 12, 12, 12, 19, 23, 33, 34, 34, 45, 46, 49, 50, 55, 56, 65, 67, 78, 81, 87, 98 
As the number of observations (21) are odd, 
Median = middle observation = 11
th
 observation = 46 
Mode is the observation that appears most often. 
Here, 12 appears maximum number of times (thrice). So, 12 is the mode. 
 
15. 725 × (-35) + (-725) × 65 
 = 725 × (-35) - 725 × 65 
 = 725 x (-35 - 65)         [Using distributive property] 
 = 725 × (-100) 
 = -72500 
 
16. Sum of 38 and -87 = 38 + (-87) = 38 - 87 = -49 
 
 Subtracting (-134) from -49, we get 
 -49 - (-134) = -49 + 134 = 85 
 
 
17. Average score = mean score 
? ? ? ? ? ? ? ? ? ?
?
?
?
Sum of all observations
Mean=
Total number of observations
12 23 10 77 15 78 90 54 23 10 1
11
393
11
35.7
 
  
 
18. Pie filling made in 1 minute = 9.2 kg 
Pie filling made in 6 minutes = 6 × 9.2 kg = 55.2 kg 
 
Page 4


  
 
CBSE VII | Mathematics 
Sample Paper 3 - Solution  
 
     
CBSE Board 
Class VII Mathematics 
Term I 
Sample Paper 3 - Solution 
Time: 2 ½ hours                          Total Marks: 80 
 
Section A 
 
1. Correct answer: A 
(128 ÷32)÷ (-4) 
 = 4 ÷ (-4) 
 = -1 
 
2. Correct answer: A 
Total cost = 2.40 × 10 
 = Rs. 24 
 
3. Correct answer: B 
The given observations can be arranged in ascending order as 
4, 6, 9, 10, 11, 12 and 18 
Here, number of observations = 7 (odd) 
Median = Middle observation = 10 
 
4. Correct answer: A 
2x + 3 = 7 
If we will transpose 3 to RHS, then the term with variable will remain on one side 
and the constants will be on other side. 
So, the first step is to transpose 3 to RHS. 
i.e. 2x = 7 – 3 
 
5. Correct answer: C 
?BCA = 180° - 150° = 30°                      (linear pair angles) 
Also, ?B = ?BCA = 30°                           (Angles opp. to equal sides are equal) 
? ?A = 180° - 30° - 30° = 120°            (Using angle sum property of triangle) 
 
6. Correct answer: B 
Increased amount =  
12
Rs. ×54=Rs. 6.48
100
  
 
 
 
  
 
CBSE VII | Mathematics 
Sample Paper 3 - Solution  
 
     
7. Correct answer: C 
?
28
2
33
 
So the multiplicative inverse is
3
8
. 
 
8. Correct answer: D 
The triangle ABC is a right angled triangle,  
By Pythagoras theorem, we have: c
2
 = a
2
 + b
2 
 
9. Correct answer: B 
21b - 32 + 7b - 20b  
= 21b + 7b - 20b – 32  
= 8b – 32 
 
 
10. Correct answer: D 
  
 
11. Correct answer: A 
The two triangles can be proved to be congruent by using SAS congruency criterion. 
The corresponding equal parts in triangles ABC and ADE are 
  
 
12. Correct answer: C 
Let the whole number be x. 
Twice of the whole number = 2x 
9 added to twice of the whole number = 9 + 2x 
From the given information, we have: 
9 + 2x = 31 
2x = 31 - 9 
2x = 22 
x = 11 
Thus, the required whole number is 11. 
 
 
 
 
 
  
 
CBSE VII | Mathematics 
Sample Paper 3 - Solution  
 
     
Section B 
 
13. Given that, m||p and t is the transversal 
We know that, if two parallel lines are cut by a transversal, each pair of alternate 
interior angles are equal. 
So, ? a = ? z (pair of alternate interior angles) 
 Thus, ? z = 57
o
. 
  
14. The numbers in ascending order are: 
11, 12, 12, 12, 19, 23, 33, 34, 34, 45, 46, 49, 50, 55, 56, 65, 67, 78, 81, 87, 98 
As the number of observations (21) are odd, 
Median = middle observation = 11
th
 observation = 46 
Mode is the observation that appears most often. 
Here, 12 appears maximum number of times (thrice). So, 12 is the mode. 
 
15. 725 × (-35) + (-725) × 65 
 = 725 × (-35) - 725 × 65 
 = 725 x (-35 - 65)         [Using distributive property] 
 = 725 × (-100) 
 = -72500 
 
16. Sum of 38 and -87 = 38 + (-87) = 38 - 87 = -49 
 
 Subtracting (-134) from -49, we get 
 -49 - (-134) = -49 + 134 = 85 
 
 
17. Average score = mean score 
? ? ? ? ? ? ? ? ? ?
?
?
?
Sum of all observations
Mean=
Total number of observations
12 23 10 77 15 78 90 54 23 10 1
11
393
11
35.7
 
  
 
18. Pie filling made in 1 minute = 9.2 kg 
Pie filling made in 6 minutes = 6 × 9.2 kg = 55.2 kg 
 
  
 
CBSE VII | Mathematics 
Sample Paper 3 - Solution  
 
     
19. Distance travelled with 1 gallon = 
2 32
10 =
33
miles 
Distance travelled with 
1 11
5=
22
gallons. 
11 32
= × miles
23
16
=11× miles
3
176
= miles
3
mile 
Thus, Sam can go 
176
3
miles with 
11
2
gallons. 
 
20.  ASA congruence criterion: 
The Angle Side Angle (ASA) postulate states that if under correspondence, two 
angles and the included side of a triangle is equal to two corresponding angles and 
included side of another triangle, then the two triangles are congruent. 
Consider the triangles ABC and XYZ as shown below. 
 
 
 
Two angles and the included side are congruent. 
? ABC = ? XYZ (equal angle) 
BC = YZ (equal side) 
? ACB = ? XZY (equal angle) 
So, ABC XYZ  
Therefore, by the ASA congruence criterion, the triangles are congruent. 
 
 
 
 
 
 
 
 
Page 5


  
 
CBSE VII | Mathematics 
Sample Paper 3 - Solution  
 
     
CBSE Board 
Class VII Mathematics 
Term I 
Sample Paper 3 - Solution 
Time: 2 ½ hours                          Total Marks: 80 
 
Section A 
 
1. Correct answer: A 
(128 ÷32)÷ (-4) 
 = 4 ÷ (-4) 
 = -1 
 
2. Correct answer: A 
Total cost = 2.40 × 10 
 = Rs. 24 
 
3. Correct answer: B 
The given observations can be arranged in ascending order as 
4, 6, 9, 10, 11, 12 and 18 
Here, number of observations = 7 (odd) 
Median = Middle observation = 10 
 
4. Correct answer: A 
2x + 3 = 7 
If we will transpose 3 to RHS, then the term with variable will remain on one side 
and the constants will be on other side. 
So, the first step is to transpose 3 to RHS. 
i.e. 2x = 7 – 3 
 
5. Correct answer: C 
?BCA = 180° - 150° = 30°                      (linear pair angles) 
Also, ?B = ?BCA = 30°                           (Angles opp. to equal sides are equal) 
? ?A = 180° - 30° - 30° = 120°            (Using angle sum property of triangle) 
 
6. Correct answer: B 
Increased amount =  
12
Rs. ×54=Rs. 6.48
100
  
 
 
 
  
 
CBSE VII | Mathematics 
Sample Paper 3 - Solution  
 
     
7. Correct answer: C 
?
28
2
33
 
So the multiplicative inverse is
3
8
. 
 
8. Correct answer: D 
The triangle ABC is a right angled triangle,  
By Pythagoras theorem, we have: c
2
 = a
2
 + b
2 
 
9. Correct answer: B 
21b - 32 + 7b - 20b  
= 21b + 7b - 20b – 32  
= 8b – 32 
 
 
10. Correct answer: D 
  
 
11. Correct answer: A 
The two triangles can be proved to be congruent by using SAS congruency criterion. 
The corresponding equal parts in triangles ABC and ADE are 
  
 
12. Correct answer: C 
Let the whole number be x. 
Twice of the whole number = 2x 
9 added to twice of the whole number = 9 + 2x 
From the given information, we have: 
9 + 2x = 31 
2x = 31 - 9 
2x = 22 
x = 11 
Thus, the required whole number is 11. 
 
 
 
 
 
  
 
CBSE VII | Mathematics 
Sample Paper 3 - Solution  
 
     
Section B 
 
13. Given that, m||p and t is the transversal 
We know that, if two parallel lines are cut by a transversal, each pair of alternate 
interior angles are equal. 
So, ? a = ? z (pair of alternate interior angles) 
 Thus, ? z = 57
o
. 
  
14. The numbers in ascending order are: 
11, 12, 12, 12, 19, 23, 33, 34, 34, 45, 46, 49, 50, 55, 56, 65, 67, 78, 81, 87, 98 
As the number of observations (21) are odd, 
Median = middle observation = 11
th
 observation = 46 
Mode is the observation that appears most often. 
Here, 12 appears maximum number of times (thrice). So, 12 is the mode. 
 
15. 725 × (-35) + (-725) × 65 
 = 725 × (-35) - 725 × 65 
 = 725 x (-35 - 65)         [Using distributive property] 
 = 725 × (-100) 
 = -72500 
 
16. Sum of 38 and -87 = 38 + (-87) = 38 - 87 = -49 
 
 Subtracting (-134) from -49, we get 
 -49 - (-134) = -49 + 134 = 85 
 
 
17. Average score = mean score 
? ? ? ? ? ? ? ? ? ?
?
?
?
Sum of all observations
Mean=
Total number of observations
12 23 10 77 15 78 90 54 23 10 1
11
393
11
35.7
 
  
 
18. Pie filling made in 1 minute = 9.2 kg 
Pie filling made in 6 minutes = 6 × 9.2 kg = 55.2 kg 
 
  
 
CBSE VII | Mathematics 
Sample Paper 3 - Solution  
 
     
19. Distance travelled with 1 gallon = 
2 32
10 =
33
miles 
Distance travelled with 
1 11
5=
22
gallons. 
11 32
= × miles
23
16
=11× miles
3
176
= miles
3
mile 
Thus, Sam can go 
176
3
miles with 
11
2
gallons. 
 
20.  ASA congruence criterion: 
The Angle Side Angle (ASA) postulate states that if under correspondence, two 
angles and the included side of a triangle is equal to two corresponding angles and 
included side of another triangle, then the two triangles are congruent. 
Consider the triangles ABC and XYZ as shown below. 
 
 
 
Two angles and the included side are congruent. 
? ABC = ? XYZ (equal angle) 
BC = YZ (equal side) 
? ACB = ? XZY (equal angle) 
So, ABC XYZ  
Therefore, by the ASA congruence criterion, the triangles are congruent. 
 
 
 
 
 
 
 
 
  
 
CBSE VII | Mathematics 
Sample Paper 3 - Solution  
 
     
21.  Let A and B be the two numbers such that, 
40% of A = 
2
B
3
 
Then,   
?
??
??
? ? ? ?
??
??
??
40 2
100 3
22
53
2 5 10
3 2 3
: 5:3
AB
AB
A
B
AB
 
 
22. Here, AB = PR (= 3.5 cm), 
BC = PQ (= 7.1 cm) 
And AC = QR (= 5 cm) 
 
This shows that the three sides of one triangle are equal to the three sides 
Of the other triangle. So, by SSS congruence rule, the two triangles are 
congruent. From the above three equality relations, it can be easily seen 
that A ? R, B ? P and C ? Q. 
So, we have ?ABC ? ?RPQ