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

## 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

Indefinitely on both sides of 0

An octagon is made up of 8 sides.

Original Price = Rs. 50
Increased Price = 55 - 50 = 5
Thus,
Increased price
Percentage increase = 100 %
Original price
??
?
??
??

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

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

Indefinitely on both sides of 0

An octagon is made up of 8 sides.

Original Price = Rs. 50
Increased Price = 55 - 50 = 5
Thus,
Increased price
Percentage increase = 100 %
Original price
??
?
??
??

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

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

Trapezium is not a parallelogram as it has only one pair of parallel sides.

Number of Red Rome apple = 4 × 10 = 40

It is known that the adjacent angles of a parallelogram are supplementary.
Therefore, measure of required angle = 180
o
- 50
o
= 130
o

The probability of an event always lies between 0 and 1.

Using the given pattern,
2000
2
= 4000000

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

Indefinitely on both sides of 0

An octagon is made up of 8 sides.

Original Price = Rs. 50
Increased Price = 55 - 50 = 5
Thus,
Increased price
Percentage increase = 100 %
Original price
??
?
??
??

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

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

Trapezium is not a parallelogram as it has only one pair of parallel sides.

Number of Red Rome apple = 4 × 10 = 40

It is known that the adjacent angles of a parallelogram are supplementary.
Therefore, measure of required angle = 180
o
- 50
o
= 130
o

The probability of an event always lies between 0 and 1.

Using the given pattern,
2000
2
= 4000000

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

Indefinitely on both sides of 0

An octagon is made up of 8 sides.

Original Price = Rs. 50
Increased Price = 55 - 50 = 5
Thus,
Increased price
Percentage increase = 100 %
Original price
??
?
??
??

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

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

Trapezium is not a parallelogram as it has only one pair of parallel sides.

Number of Red Rome apple = 4 × 10 = 40

It is known that the adjacent angles of a parallelogram are supplementary.
Therefore, measure of required angle = 180
o
- 50
o
= 130
o

The probability of an event always lies between 0 and 1.

Using the given pattern,
2000
2
= 4000000

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

Indefinitely on both sides of 0

An octagon is made up of 8 sides.

Original Price = Rs. 50
Increased Price = 55 - 50 = 5
Thus,
Increased price
Percentage increase = 100 %
Original price
??
?
??
??

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

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

Trapezium is not a parallelogram as it has only one pair of parallel sides.

Number of Red Rome apple = 4 × 10 = 40

It is known that the adjacent angles of a parallelogram are supplementary.
Therefore, measure of required angle = 180
o
- 50
o
= 130
o

The probability of an event always lies between 0 and 1.

Using the given pattern,
2000
2
= 4000000

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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## Mathematics (Maths) Class 8

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