Sample Solution Paper 2 - Term- 1 Math, Class 8 Class 8 Notes | EduRev

Mathematics (Maths) Class 8

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Class 8 : Sample Solution Paper 2 - Term- 1 Math, Class 8 Class 8 Notes | EduRev

 Page 1


  
 
CBSE VIII | Mathematics 
Sample Paper 2 -  Solution 
 
     
CBSE Board 
Class VIII Mathematics 
Term I 
Sample Paper 2 - Solution 
Time: 2 ½ hours                          Total Marks: 80 
 
Section A 
 
1. Correct answer: B 
  
 
2. Correct answer: A 
 Indefinitely on both sides of 0 
 
3. Correct answer: A 
An octagon is made up of 8 sides. 
 
4. Correct answer: B 
Original Price = Rs. 50 
Increased Price = 55 - 50 = 5 
Thus, 
Increased price
Percentage increase = 100 %
Original price
??
?
??
??
 
  
 
5. Correct answer: C 
We know that the sum of first n odd natural numbers is n
2
. 
Therefore, 
 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 = 9
2 
 
6. Correct answer: A 
2 3
(4) 1000 = 4 × 4 × 10 = 2 × 2 × 2 × 2 × 2 × 5 = (2 × 2 × 2) × 2 × 2 × 5 
 So, the given number must be divided by 2 × 2 × 5 = 20 to make it a perfect cube. 
Page 2


  
 
CBSE VIII | Mathematics 
Sample Paper 2 -  Solution 
 
     
CBSE Board 
Class VIII Mathematics 
Term I 
Sample Paper 2 - Solution 
Time: 2 ½ hours                          Total Marks: 80 
 
Section A 
 
1. Correct answer: B 
  
 
2. Correct answer: A 
 Indefinitely on both sides of 0 
 
3. Correct answer: A 
An octagon is made up of 8 sides. 
 
4. Correct answer: B 
Original Price = Rs. 50 
Increased Price = 55 - 50 = 5 
Thus, 
Increased price
Percentage increase = 100 %
Original price
??
?
??
??
 
  
 
5. Correct answer: C 
We know that the sum of first n odd natural numbers is n
2
. 
Therefore, 
 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 = 9
2 
 
6. Correct answer: A 
2 3
(4) 1000 = 4 × 4 × 10 = 2 × 2 × 2 × 2 × 2 × 5 = (2 × 2 × 2) × 2 × 2 × 5 
 So, the given number must be divided by 2 × 2 × 5 = 20 to make it a perfect cube. 
  
 
CBSE VIII | Mathematics 
Sample Paper 2 -  Solution 
 
     
7. Correct answer: B 
 Trapezium is not a parallelogram as it has only one pair of parallel sides. 
 
8. Correct answer: A 
 Number of Red Rome apple = 4 × 10 = 40 
 
9. Correct answer: A 
It is known that the adjacent angles of a parallelogram are supplementary. 
 Therefore, measure of required angle = 180
o
 - 50
o
 = 130
o 
 
10. Correct answer: B 
The probability of an event always lies between 0 and 1. 
 
11. Correct answer: B 
Using the given pattern, 
 2000
2
 = 4000000 
 
12. Correct answer: C 
The discount 50% + 50% is equal to a single discount of 75%. 
The S.P. is 25% of C.P. 
 So, S.P. = 
25
1200 300
100
??  
 
Section B 
 
13.   
(i) Let x be the multiplicative inverse of  
 
(ii) Let x be the multiplicative inverse of  
 
Or, x = 
5
2
 
 
 
 
 
 
Page 3


  
 
CBSE VIII | Mathematics 
Sample Paper 2 -  Solution 
 
     
CBSE Board 
Class VIII Mathematics 
Term I 
Sample Paper 2 - Solution 
Time: 2 ½ hours                          Total Marks: 80 
 
Section A 
 
1. Correct answer: B 
  
 
2. Correct answer: A 
 Indefinitely on both sides of 0 
 
3. Correct answer: A 
An octagon is made up of 8 sides. 
 
4. Correct answer: B 
Original Price = Rs. 50 
Increased Price = 55 - 50 = 5 
Thus, 
Increased price
Percentage increase = 100 %
Original price
??
?
??
??
 
  
 
5. Correct answer: C 
We know that the sum of first n odd natural numbers is n
2
. 
Therefore, 
 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 = 9
2 
 
6. Correct answer: A 
2 3
(4) 1000 = 4 × 4 × 10 = 2 × 2 × 2 × 2 × 2 × 5 = (2 × 2 × 2) × 2 × 2 × 5 
 So, the given number must be divided by 2 × 2 × 5 = 20 to make it a perfect cube. 
  
 
CBSE VIII | Mathematics 
Sample Paper 2 -  Solution 
 
     
7. Correct answer: B 
 Trapezium is not a parallelogram as it has only one pair of parallel sides. 
 
8. Correct answer: A 
 Number of Red Rome apple = 4 × 10 = 40 
 
9. Correct answer: A 
It is known that the adjacent angles of a parallelogram are supplementary. 
 Therefore, measure of required angle = 180
o
 - 50
o
 = 130
o 
 
10. Correct answer: B 
The probability of an event always lies between 0 and 1. 
 
11. Correct answer: B 
Using the given pattern, 
 2000
2
 = 4000000 
 
12. Correct answer: C 
The discount 50% + 50% is equal to a single discount of 75%. 
The S.P. is 25% of C.P. 
 So, S.P. = 
25
1200 300
100
??  
 
Section B 
 
13.   
(i) Let x be the multiplicative inverse of  
 
(ii) Let x be the multiplicative inverse of  
 
Or, x = 
5
2
 
 
 
 
 
 
  
 
CBSE VIII | Mathematics 
Sample Paper 2 -  Solution 
 
     
14. 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, 
 
4x + 14 = 11x + 7  
4x - 11x = 7 - 14  
-7x = -7  
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. 
 
15. y = ? EHP (Alternate interior angles as OP||HE) 
y = 40°  
70° = ? EHO = z + 40 ? (Corresponding angles as OP||HE) 
70° - 40° = z 
z = 30° 
? HEP = ? EHO (Adjacent pair of angles as HO||EP) 
x + (z + 40 ?) = 180°  
x + 70 ? = 180° 
 x = 110° 
 
16. Total number of students = 35 
i) Number of boys = 20 
20 4
Required probability
35 7
? ? ? 
ii) Number of girls = 15 
15 3
Required probability
35 7
? ? ?
 
 
17. 82
2
 = (80 + 2)
2
 
In the property (a + b)
2
 = a
2 
+ b
2
 + 2ab 
Substituting a = 80 and b = 2, we get 
(80 + 2)
2
 = 80
2
 + 2
2 
+ 2 × 80 × 2 
                  = 6400 + 4 + 320  
                      = 6724 
 
 
 
Page 4


  
 
CBSE VIII | Mathematics 
Sample Paper 2 -  Solution 
 
     
CBSE Board 
Class VIII Mathematics 
Term I 
Sample Paper 2 - Solution 
Time: 2 ½ hours                          Total Marks: 80 
 
Section A 
 
1. Correct answer: B 
  
 
2. Correct answer: A 
 Indefinitely on both sides of 0 
 
3. Correct answer: A 
An octagon is made up of 8 sides. 
 
4. Correct answer: B 
Original Price = Rs. 50 
Increased Price = 55 - 50 = 5 
Thus, 
Increased price
Percentage increase = 100 %
Original price
??
?
??
??
 
  
 
5. Correct answer: C 
We know that the sum of first n odd natural numbers is n
2
. 
Therefore, 
 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 = 9
2 
 
6. Correct answer: A 
2 3
(4) 1000 = 4 × 4 × 10 = 2 × 2 × 2 × 2 × 2 × 5 = (2 × 2 × 2) × 2 × 2 × 5 
 So, the given number must be divided by 2 × 2 × 5 = 20 to make it a perfect cube. 
  
 
CBSE VIII | Mathematics 
Sample Paper 2 -  Solution 
 
     
7. Correct answer: B 
 Trapezium is not a parallelogram as it has only one pair of parallel sides. 
 
8. Correct answer: A 
 Number of Red Rome apple = 4 × 10 = 40 
 
9. Correct answer: A 
It is known that the adjacent angles of a parallelogram are supplementary. 
 Therefore, measure of required angle = 180
o
 - 50
o
 = 130
o 
 
10. Correct answer: B 
The probability of an event always lies between 0 and 1. 
 
11. Correct answer: B 
Using the given pattern, 
 2000
2
 = 4000000 
 
12. Correct answer: C 
The discount 50% + 50% is equal to a single discount of 75%. 
The S.P. is 25% of C.P. 
 So, S.P. = 
25
1200 300
100
??  
 
Section B 
 
13.   
(i) Let x be the multiplicative inverse of  
 
(ii) Let x be the multiplicative inverse of  
 
Or, x = 
5
2
 
 
 
 
 
 
  
 
CBSE VIII | Mathematics 
Sample Paper 2 -  Solution 
 
     
14. 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, 
 
4x + 14 = 11x + 7  
4x - 11x = 7 - 14  
-7x = -7  
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. 
 
15. y = ? EHP (Alternate interior angles as OP||HE) 
y = 40°  
70° = ? EHO = z + 40 ? (Corresponding angles as OP||HE) 
70° - 40° = z 
z = 30° 
? HEP = ? EHO (Adjacent pair of angles as HO||EP) 
x + (z + 40 ?) = 180°  
x + 70 ? = 180° 
 x = 110° 
 
16. Total number of students = 35 
i) Number of boys = 20 
20 4
Required probability
35 7
? ? ? 
ii) Number of girls = 15 
15 3
Required probability
35 7
? ? ?
 
 
17. 82
2
 = (80 + 2)
2
 
In the property (a + b)
2
 = a
2 
+ b
2
 + 2ab 
Substituting a = 80 and b = 2, we get 
(80 + 2)
2
 = 80
2
 + 2
2 
+ 2 × 80 × 2 
                  = 6400 + 4 + 320  
                      = 6724 
 
 
 
  
 
CBSE VIII | Mathematics 
Sample Paper 2 -  Solution 
 
     
18. From the graph, it is clear that: 
5 students favoured orange and 1 student favoured green colour.  
Now, 5 - 1 = 4  
Therefore, 4 more students favoured orange colour than green. 
 
19. Cost of TV set = Rs. 36500. 
Sales tax = 8% of Rs. 36500 
 
 Therefore, Bill amount = Rs. (36500 + 2920) = Rs. 39420 
 
20. First four triangular numbers are: 1, 3, 6 and 10. 
Now, 1 + 3 = 4 = 2
2
 
3 + 6 = 9 = 3
2
 
6 + 10 = 16 = 4
2
 
Here, 4, 9 and 16 all are square numbers. 
 
21. 3(2x - 1) = 2(x + 4) + 1 
6x - 3 = 2x + 8 + 1  
6x – 3 - 2x = 8 + 1 (Transposing 2x to LHS )  
6x - 2x = 8 + 1 + 3 (Transposing -3 to RHS)  
4x = 12  
Dividing both sides by 4, 
x = 
12
4
= 3 
 x = 3 
 
22.  
 
 
 
 
 
 
Page 5


  
 
CBSE VIII | Mathematics 
Sample Paper 2 -  Solution 
 
     
CBSE Board 
Class VIII Mathematics 
Term I 
Sample Paper 2 - Solution 
Time: 2 ½ hours                          Total Marks: 80 
 
Section A 
 
1. Correct answer: B 
  
 
2. Correct answer: A 
 Indefinitely on both sides of 0 
 
3. Correct answer: A 
An octagon is made up of 8 sides. 
 
4. Correct answer: B 
Original Price = Rs. 50 
Increased Price = 55 - 50 = 5 
Thus, 
Increased price
Percentage increase = 100 %
Original price
??
?
??
??
 
  
 
5. Correct answer: C 
We know that the sum of first n odd natural numbers is n
2
. 
Therefore, 
 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 = 9
2 
 
6. Correct answer: A 
2 3
(4) 1000 = 4 × 4 × 10 = 2 × 2 × 2 × 2 × 2 × 5 = (2 × 2 × 2) × 2 × 2 × 5 
 So, the given number must be divided by 2 × 2 × 5 = 20 to make it a perfect cube. 
  
 
CBSE VIII | Mathematics 
Sample Paper 2 -  Solution 
 
     
7. Correct answer: B 
 Trapezium is not a parallelogram as it has only one pair of parallel sides. 
 
8. Correct answer: A 
 Number of Red Rome apple = 4 × 10 = 40 
 
9. Correct answer: A 
It is known that the adjacent angles of a parallelogram are supplementary. 
 Therefore, measure of required angle = 180
o
 - 50
o
 = 130
o 
 
10. Correct answer: B 
The probability of an event always lies between 0 and 1. 
 
11. Correct answer: B 
Using the given pattern, 
 2000
2
 = 4000000 
 
12. Correct answer: C 
The discount 50% + 50% is equal to a single discount of 75%. 
The S.P. is 25% of C.P. 
 So, S.P. = 
25
1200 300
100
??  
 
Section B 
 
13.   
(i) Let x be the multiplicative inverse of  
 
(ii) Let x be the multiplicative inverse of  
 
Or, x = 
5
2
 
 
 
 
 
 
  
 
CBSE VIII | Mathematics 
Sample Paper 2 -  Solution 
 
     
14. 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, 
 
4x + 14 = 11x + 7  
4x - 11x = 7 - 14  
-7x = -7  
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. 
 
15. y = ? EHP (Alternate interior angles as OP||HE) 
y = 40°  
70° = ? EHO = z + 40 ? (Corresponding angles as OP||HE) 
70° - 40° = z 
z = 30° 
? HEP = ? EHO (Adjacent pair of angles as HO||EP) 
x + (z + 40 ?) = 180°  
x + 70 ? = 180° 
 x = 110° 
 
16. Total number of students = 35 
i) Number of boys = 20 
20 4
Required probability
35 7
? ? ? 
ii) Number of girls = 15 
15 3
Required probability
35 7
? ? ?
 
 
17. 82
2
 = (80 + 2)
2
 
In the property (a + b)
2
 = a
2 
+ b
2
 + 2ab 
Substituting a = 80 and b = 2, we get 
(80 + 2)
2
 = 80
2
 + 2
2 
+ 2 × 80 × 2 
                  = 6400 + 4 + 320  
                      = 6724 
 
 
 
  
 
CBSE VIII | Mathematics 
Sample Paper 2 -  Solution 
 
     
18. From the graph, it is clear that: 
5 students favoured orange and 1 student favoured green colour.  
Now, 5 - 1 = 4  
Therefore, 4 more students favoured orange colour than green. 
 
19. Cost of TV set = Rs. 36500. 
Sales tax = 8% of Rs. 36500 
 
 Therefore, Bill amount = Rs. (36500 + 2920) = Rs. 39420 
 
20. First four triangular numbers are: 1, 3, 6 and 10. 
Now, 1 + 3 = 4 = 2
2
 
3 + 6 = 9 = 3
2
 
6 + 10 = 16 = 4
2
 
Here, 4, 9 and 16 all are square numbers. 
 
21. 3(2x - 1) = 2(x + 4) + 1 
6x - 3 = 2x + 8 + 1  
6x – 3 - 2x = 8 + 1 (Transposing 2x to LHS )  
6x - 2x = 8 + 1 + 3 (Transposing -3 to RHS)  
4x = 12  
Dividing both sides by 4, 
x = 
12
4
= 3 
 x = 3 
 
22.  
 
 
 
 
 
 
  
 
CBSE VIII | Mathematics 
Sample Paper 2 -  Solution 
 
     
23. Original number = 4000 
Increased % = 35% 
Thus, Number of students now = Original number + 35% of 4000 
 
 
24. Here, n(S) = 10 + 25 = 35 
Let E be the event of getting a prize. 
n(E) = 10 
? ? ? ?
n(E) 10 2
P(E)
n(S) 35 7
 
  Probability of getting a prize = 
2
7
 
 
Section C 
 
25.  
a) If we choose a scale of 1:50 for the frequency then the vertical bar chart will be 
as  shown. 
 
b) Percentage increase in the visitors in March as compared to January is  
  
c) Percentage of visitors who came in February as compared to the total number of 
visitors is  
 
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