Sample Solution Paper 3 - Term- 1 Math, Class 8 Class 8 Notes | EduRev

Mathematics (Maths) Class 8

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Class 8 : Sample Solution Paper 3 - Term- 1 Math, Class 8 Class 8 Notes | EduRev

 Page 1


  
 
CBSE VIII | Mathematics 
Sample Paper – 3 Solutions 
 
     
CBSE  
Class VIII Mathematics 
Sample Paper – 3 Solution 
Time: 3 hours                     Total Marks: 80 
 
Section A 
1. Correct answer: D 
A rational number is a number of the form  
p
q
 where q? 0. So, in case of reciprocal of 0, 
denominator will be 0. 
 
2. Correct answer: B 
20
20% of x= 
100 5
x
x ? 
 
3. Correct answer: A  
Five vertices. 
 
4. Correct option : A 
?
196 2
484
?
1
7
2
?
?
1
7
11
11
 
 
5. Correct answer: B 
0 and 1 
 
6. Correct answer: A 
 1
3
 = 1 
Thus, the natural number 1 is equal to its cube. 
 
7. Correct answer: D 
A rational number is a number of the form  
p
q
 where q? 0. So, in case of reciprocal of 0, 
denominator will be 0. 
 
8. Correct option: A 
6 17 29
2
12 34 29
17 34
2
k
k
kk
k
k
?
?
? ? ?
??
??
 
Page 2


  
 
CBSE VIII | Mathematics 
Sample Paper – 3 Solutions 
 
     
CBSE  
Class VIII Mathematics 
Sample Paper – 3 Solution 
Time: 3 hours                     Total Marks: 80 
 
Section A 
1. Correct answer: D 
A rational number is a number of the form  
p
q
 where q? 0. So, in case of reciprocal of 0, 
denominator will be 0. 
 
2. Correct answer: B 
20
20% of x= 
100 5
x
x ? 
 
3. Correct answer: A  
Five vertices. 
 
4. Correct option : A 
?
196 2
484
?
1
7
2
?
?
1
7
11
11
 
 
5. Correct answer: B 
0 and 1 
 
6. Correct answer: A 
 1
3
 = 1 
Thus, the natural number 1 is equal to its cube. 
 
7. Correct answer: D 
A rational number is a number of the form  
p
q
 where q? 0. So, in case of reciprocal of 0, 
denominator will be 0. 
 
8. Correct option: A 
6 17 29
2
12 34 29
17 34
2
k
k
kk
k
k
?
?
? ? ?
??
??
 
  
 
CBSE VIII | Mathematics 
Sample Paper – 3 Solutions 
 
     
 
9. Correct answer: C 
The given shape has 12 edges. 
 
10. Correct answer: D 
Sales tax = 
4
380 15.20
100
?? 
 
11. Correct option: C 
? ? ? ? ? ? ? ? ?
22
484 2 2 11 11 2 11 2 11 22 
 
12. Correct option: B 
?
?
? ? ?
14 441
22
22 441
.693
14
x
x Rs
 
 
Section B 
(Questions 8 to 11 carry 2 marks each) 
 
13. The number 
2
5
lies between 0 and 1.  
Draw a number line. Mark points O and A to represent 0 and 1, respectively.  
Divide OA into 5 equal parts (equal to the denominator of 
2
5
).The second point, Q, 
represents the rational number 
2
5
. 
 
14. Steps of construction: 
a) Draw AC = 8 cm. 
b) Draw perpendicular bisector XY of AC meeting AC at O. 
c) From O cut off OD = 
1
2
× 6 cm = 3 cm along OX and OB = 
1
2
× 6 cm =3 cm along OY. 
d) Join AB, BC, CD and DA. 
Page 3


  
 
CBSE VIII | Mathematics 
Sample Paper – 3 Solutions 
 
     
CBSE  
Class VIII Mathematics 
Sample Paper – 3 Solution 
Time: 3 hours                     Total Marks: 80 
 
Section A 
1. Correct answer: D 
A rational number is a number of the form  
p
q
 where q? 0. So, in case of reciprocal of 0, 
denominator will be 0. 
 
2. Correct answer: B 
20
20% of x= 
100 5
x
x ? 
 
3. Correct answer: A  
Five vertices. 
 
4. Correct option : A 
?
196 2
484
?
1
7
2
?
?
1
7
11
11
 
 
5. Correct answer: B 
0 and 1 
 
6. Correct answer: A 
 1
3
 = 1 
Thus, the natural number 1 is equal to its cube. 
 
7. Correct answer: D 
A rational number is a number of the form  
p
q
 where q? 0. So, in case of reciprocal of 0, 
denominator will be 0. 
 
8. Correct option: A 
6 17 29
2
12 34 29
17 34
2
k
k
kk
k
k
?
?
? ? ?
??
??
 
  
 
CBSE VIII | Mathematics 
Sample Paper – 3 Solutions 
 
     
 
9. Correct answer: C 
The given shape has 12 edges. 
 
10. Correct answer: D 
Sales tax = 
4
380 15.20
100
?? 
 
11. Correct option: C 
? ? ? ? ? ? ? ? ?
22
484 2 2 11 11 2 11 2 11 22 
 
12. Correct option: B 
?
?
? ? ?
14 441
22
22 441
.693
14
x
x Rs
 
 
Section B 
(Questions 8 to 11 carry 2 marks each) 
 
13. The number 
2
5
lies between 0 and 1.  
Draw a number line. Mark points O and A to represent 0 and 1, respectively.  
Divide OA into 5 equal parts (equal to the denominator of 
2
5
).The second point, Q, 
represents the rational number 
2
5
. 
 
14. Steps of construction: 
a) Draw AC = 8 cm. 
b) Draw perpendicular bisector XY of AC meeting AC at O. 
c) From O cut off OD = 
1
2
× 6 cm = 3 cm along OX and OB = 
1
2
× 6 cm =3 cm along OY. 
d) Join AB, BC, CD and DA. 
  
 
CBSE VIII | Mathematics 
Sample Paper – 3 Solutions 
 
     
ABCD is the required rhombus. 
 
15. We have, 
Number of vertices (V) = 8 
Number of edges (E) = 12 
Let, number of faces = F 
Since every polyhedron satisfy Euler's formula, therefore 
F + V = E + 2 
Or, F + 8 = 12 + 2 
Or, F = 14 - 8 = 6 
Hence, the number of faces are 6. 
16. We have: 
(a + b)
2
 = a
2 
+ b
2
 + 2abTaking, a = -20 and b = -5, we get 
(-25)
2
 = {-20 + (-5)}
2
  
= (-20)
2
 + (-5)
2
 + 2(-20)(-5)  
= 400 + 25 + 200 = 625 
17. From the graph, it is clear that 5 students favoured orange and 1 student favoured 
green.  
Now, 5 – 1 = 4  
Therefore, 4 more students favoured orange colour than green. 
 
18. Since ABCD is an isosceles trapezoidal, we have AD = BC 
Therefore, AD = BC = 4 cm. 
Now the perimeter of given trapezium  
= AB + BC + CD + DA 
= 12 + 4 + 8 + 4 
= 28 
Page 4


  
 
CBSE VIII | Mathematics 
Sample Paper – 3 Solutions 
 
     
CBSE  
Class VIII Mathematics 
Sample Paper – 3 Solution 
Time: 3 hours                     Total Marks: 80 
 
Section A 
1. Correct answer: D 
A rational number is a number of the form  
p
q
 where q? 0. So, in case of reciprocal of 0, 
denominator will be 0. 
 
2. Correct answer: B 
20
20% of x= 
100 5
x
x ? 
 
3. Correct answer: A  
Five vertices. 
 
4. Correct option : A 
?
196 2
484
?
1
7
2
?
?
1
7
11
11
 
 
5. Correct answer: B 
0 and 1 
 
6. Correct answer: A 
 1
3
 = 1 
Thus, the natural number 1 is equal to its cube. 
 
7. Correct answer: D 
A rational number is a number of the form  
p
q
 where q? 0. So, in case of reciprocal of 0, 
denominator will be 0. 
 
8. Correct option: A 
6 17 29
2
12 34 29
17 34
2
k
k
kk
k
k
?
?
? ? ?
??
??
 
  
 
CBSE VIII | Mathematics 
Sample Paper – 3 Solutions 
 
     
 
9. Correct answer: C 
The given shape has 12 edges. 
 
10. Correct answer: D 
Sales tax = 
4
380 15.20
100
?? 
 
11. Correct option: C 
? ? ? ? ? ? ? ? ?
22
484 2 2 11 11 2 11 2 11 22 
 
12. Correct option: B 
?
?
? ? ?
14 441
22
22 441
.693
14
x
x Rs
 
 
Section B 
(Questions 8 to 11 carry 2 marks each) 
 
13. The number 
2
5
lies between 0 and 1.  
Draw a number line. Mark points O and A to represent 0 and 1, respectively.  
Divide OA into 5 equal parts (equal to the denominator of 
2
5
).The second point, Q, 
represents the rational number 
2
5
. 
 
14. Steps of construction: 
a) Draw AC = 8 cm. 
b) Draw perpendicular bisector XY of AC meeting AC at O. 
c) From O cut off OD = 
1
2
× 6 cm = 3 cm along OX and OB = 
1
2
× 6 cm =3 cm along OY. 
d) Join AB, BC, CD and DA. 
  
 
CBSE VIII | Mathematics 
Sample Paper – 3 Solutions 
 
     
ABCD is the required rhombus. 
 
15. We have, 
Number of vertices (V) = 8 
Number of edges (E) = 12 
Let, number of faces = F 
Since every polyhedron satisfy Euler's formula, therefore 
F + V = E + 2 
Or, F + 8 = 12 + 2 
Or, F = 14 - 8 = 6 
Hence, the number of faces are 6. 
16. We have: 
(a + b)
2
 = a
2 
+ b
2
 + 2abTaking, a = -20 and b = -5, we get 
(-25)
2
 = {-20 + (-5)}
2
  
= (-20)
2
 + (-5)
2
 + 2(-20)(-5)  
= 400 + 25 + 200 = 625 
17. From the graph, it is clear that 5 students favoured orange and 1 student favoured 
green.  
Now, 5 – 1 = 4  
Therefore, 4 more students favoured orange colour than green. 
 
18. Since ABCD is an isosceles trapezoidal, we have AD = BC 
Therefore, AD = BC = 4 cm. 
Now the perimeter of given trapezium  
= AB + BC + CD + DA 
= 12 + 4 + 8 + 4 
= 28 
  
 
CBSE VIII | Mathematics 
Sample Paper – 3 Solutions 
 
     
 Hence, the perimeter of the given trapezium is 28 cm. 
19. Original price of the book = Rs. 50 
Increased % = 6% 
Thus, New Price = Original Price + 6% of Original price 
New price = Rs. 
6
50 50 .(50 3) .53
100
Rs Rs ? ? ? ? ? 
20. Area of square = (5a – 2b)
2
 
 We use the identity (x – y )
2
 = x
2
 – 2xy + y
2 
 Taking, x = 5a and y = 2b  
 We get, (5a – 2b)
2
 = (5a)
2
 – 2(5a)(2b ) + (2b)=25a
2
 – 20ab + 4b
2
  
21. 82
2
 = (80 + 2)
2
 
 In the property (a + b)
2
 = a
2 
+ b
2
 + 2ab, putting a = 80 and b = 2, we get: 
 (80 + 2)
2
 = 80
2
 + 2
2 
+ 2 × 80 × 2 
                 = 6400 + 4 + 320  
                  = 6724 
22. Let x be the ten’s digit of the two-digit number.  
Then its unit's digit = x + 7.  
Number = unit’s digit + 10(ten’s digit) = (x + 7) + 10(x) = 11x + 7.  
Sum of the digits = (x + 7) + (x) = 2x + 7.  
Given, sum of the digits is half of the whole number.  
Therefore, 
1
(2 7) (11 7)
2
xx ? ? ? 
4x + 14 = 11x + 7  
? ? ?
? ? ?
4 11 7 14
77
xx
x
  
i.e. x = 1  
Ten’s digit of the two-digit number is x = 1.  
Unit’s digit of the two-digit number = x + 7 = 1 + 7 = 8  
 Thus, the required number is 18. 
23.  Let the required number be x. Then, 
 26% of x = 65 
Page 5


  
 
CBSE VIII | Mathematics 
Sample Paper – 3 Solutions 
 
     
CBSE  
Class VIII Mathematics 
Sample Paper – 3 Solution 
Time: 3 hours                     Total Marks: 80 
 
Section A 
1. Correct answer: D 
A rational number is a number of the form  
p
q
 where q? 0. So, in case of reciprocal of 0, 
denominator will be 0. 
 
2. Correct answer: B 
20
20% of x= 
100 5
x
x ? 
 
3. Correct answer: A  
Five vertices. 
 
4. Correct option : A 
?
196 2
484
?
1
7
2
?
?
1
7
11
11
 
 
5. Correct answer: B 
0 and 1 
 
6. Correct answer: A 
 1
3
 = 1 
Thus, the natural number 1 is equal to its cube. 
 
7. Correct answer: D 
A rational number is a number of the form  
p
q
 where q? 0. So, in case of reciprocal of 0, 
denominator will be 0. 
 
8. Correct option: A 
6 17 29
2
12 34 29
17 34
2
k
k
kk
k
k
?
?
? ? ?
??
??
 
  
 
CBSE VIII | Mathematics 
Sample Paper – 3 Solutions 
 
     
 
9. Correct answer: C 
The given shape has 12 edges. 
 
10. Correct answer: D 
Sales tax = 
4
380 15.20
100
?? 
 
11. Correct option: C 
? ? ? ? ? ? ? ? ?
22
484 2 2 11 11 2 11 2 11 22 
 
12. Correct option: B 
?
?
? ? ?
14 441
22
22 441
.693
14
x
x Rs
 
 
Section B 
(Questions 8 to 11 carry 2 marks each) 
 
13. The number 
2
5
lies between 0 and 1.  
Draw a number line. Mark points O and A to represent 0 and 1, respectively.  
Divide OA into 5 equal parts (equal to the denominator of 
2
5
).The second point, Q, 
represents the rational number 
2
5
. 
 
14. Steps of construction: 
a) Draw AC = 8 cm. 
b) Draw perpendicular bisector XY of AC meeting AC at O. 
c) From O cut off OD = 
1
2
× 6 cm = 3 cm along OX and OB = 
1
2
× 6 cm =3 cm along OY. 
d) Join AB, BC, CD and DA. 
  
 
CBSE VIII | Mathematics 
Sample Paper – 3 Solutions 
 
     
ABCD is the required rhombus. 
 
15. We have, 
Number of vertices (V) = 8 
Number of edges (E) = 12 
Let, number of faces = F 
Since every polyhedron satisfy Euler's formula, therefore 
F + V = E + 2 
Or, F + 8 = 12 + 2 
Or, F = 14 - 8 = 6 
Hence, the number of faces are 6. 
16. We have: 
(a + b)
2
 = a
2 
+ b
2
 + 2abTaking, a = -20 and b = -5, we get 
(-25)
2
 = {-20 + (-5)}
2
  
= (-20)
2
 + (-5)
2
 + 2(-20)(-5)  
= 400 + 25 + 200 = 625 
17. From the graph, it is clear that 5 students favoured orange and 1 student favoured 
green.  
Now, 5 – 1 = 4  
Therefore, 4 more students favoured orange colour than green. 
 
18. Since ABCD is an isosceles trapezoidal, we have AD = BC 
Therefore, AD = BC = 4 cm. 
Now the perimeter of given trapezium  
= AB + BC + CD + DA 
= 12 + 4 + 8 + 4 
= 28 
  
 
CBSE VIII | Mathematics 
Sample Paper – 3 Solutions 
 
     
 Hence, the perimeter of the given trapezium is 28 cm. 
19. Original price of the book = Rs. 50 
Increased % = 6% 
Thus, New Price = Original Price + 6% of Original price 
New price = Rs. 
6
50 50 .(50 3) .53
100
Rs Rs ? ? ? ? ? 
20. Area of square = (5a – 2b)
2
 
 We use the identity (x – y )
2
 = x
2
 – 2xy + y
2 
 Taking, x = 5a and y = 2b  
 We get, (5a – 2b)
2
 = (5a)
2
 – 2(5a)(2b ) + (2b)=25a
2
 – 20ab + 4b
2
  
21. 82
2
 = (80 + 2)
2
 
 In the property (a + b)
2
 = a
2 
+ b
2
 + 2ab, putting a = 80 and b = 2, we get: 
 (80 + 2)
2
 = 80
2
 + 2
2 
+ 2 × 80 × 2 
                 = 6400 + 4 + 320  
                  = 6724 
22. Let x be the ten’s digit of the two-digit number.  
Then its unit's digit = x + 7.  
Number = unit’s digit + 10(ten’s digit) = (x + 7) + 10(x) = 11x + 7.  
Sum of the digits = (x + 7) + (x) = 2x + 7.  
Given, sum of the digits is half of the whole number.  
Therefore, 
1
(2 7) (11 7)
2
xx ? ? ? 
4x + 14 = 11x + 7  
? ? ?
? ? ?
4 11 7 14
77
xx
x
  
i.e. x = 1  
Ten’s digit of the two-digit number is x = 1.  
Unit’s digit of the two-digit number = x + 7 = 1 + 7 = 8  
 Thus, the required number is 18. 
23.  Let the required number be x. Then, 
 26% of x = 65 
  
 
CBSE VIII | Mathematics 
Sample Paper – 3 Solutions 
 
     
 
26
65
100
100
65
26
250
x
x
x
??
??
? ? ?
??
??
??
 
 Hence, the required number is 250. 
 
24.  
(by commutativity) 
 
 
(by distributivity) 
 
 
Section C 
25. Here, at unit's place A × 5 = A 
That is we need to search for a number, which when multiplied to 5 gives the same unit 
place. 
Such a number is 5 or 0, as 5 × 5 = 25 or 0 × 5 = 0 
Case (1) Taking 5 in place of A, we get 
2
B   A
    5
C B 5
?
 
Here, B can take the value 2, which satisfy the condition, taking, B = 2, we get 
2
2   5
    5
1 2 5
?
 
Thus, A = 5, B = 2 and C = 1 
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