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

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

``` Page 1

CBSE VIII | Mathematics
Sample Paper 1 -  Solution

CBSE Board
Class VIII Mathematics
Term I
Sample Paper 1 - Solution
Time: 2 ½ hours                          Total Marks: 80

Section A

2.5 is greater than 2.4 and less than 2.6 and 2.7.
Hence, on a number line, 2.5 will lie between 2.4 and 2.7.

= 5 + 5 + 3 = 13

1 is a square as well as a triangular number.

Cube root of (-8) x (-343) x (125) = (-2) x (-7) x 5 = 70

On cross multiplying, we get 4x + 28 = 3x - 3
4x - 3x = - 3 - 28
x = -31
x + 31 = 0
Page 2

CBSE VIII | Mathematics
Sample Paper 1 -  Solution

CBSE Board
Class VIII Mathematics
Term I
Sample Paper 1 - Solution
Time: 2 ½ hours                          Total Marks: 80

Section A

2.5 is greater than 2.4 and less than 2.6 and 2.7.
Hence, on a number line, 2.5 will lie between 2.4 and 2.7.

= 5 + 5 + 3 = 13

1 is a square as well as a triangular number.

Cube root of (-8) x (-343) x (125) = (-2) x (-7) x 5 = 70

On cross multiplying, we get 4x + 28 = 3x - 3
4x - 3x = - 3 - 28
x = -31
x + 31 = 0

CBSE VIII | Mathematics
Sample Paper 1 -  Solution

In a rhombus, if one angle is 70
o
, then its opposite angle will be 70
o
.
(Since, opposite angles of a rhombus are equal)

o o o
Value of component 1
360 360 90
Total va
Central
lue 4
angle ? ? ? ? ?

Square root = 2 × 3 × 3 × 5 = 90

Actual C.P. = C.P. + Overhead expenses = Rs. (900 + 200) = Rs. 1100
Profit = S.P. – C.P. = Rs. 1200 – Rs. 1100 = Rs. 100
100 1
Profit percent= 100 9 %
1100 11
??

Section B

13.
(by commutativity)

(by distributivity)

14. Let x be the greater part.
Then, 64 - x is the smaller part.
Then 3x = 5(64 - x)
3x = 320 - 5x
3x + 5x = 320
8x = 320
x = 40
So, the two parts are 40 and 24.

Page 3

CBSE VIII | Mathematics
Sample Paper 1 -  Solution

CBSE Board
Class VIII Mathematics
Term I
Sample Paper 1 - Solution
Time: 2 ½ hours                          Total Marks: 80

Section A

2.5 is greater than 2.4 and less than 2.6 and 2.7.
Hence, on a number line, 2.5 will lie between 2.4 and 2.7.

= 5 + 5 + 3 = 13

1 is a square as well as a triangular number.

Cube root of (-8) x (-343) x (125) = (-2) x (-7) x 5 = 70

On cross multiplying, we get 4x + 28 = 3x - 3
4x - 3x = - 3 - 28
x = -31
x + 31 = 0

CBSE VIII | Mathematics
Sample Paper 1 -  Solution

In a rhombus, if one angle is 70
o
, then its opposite angle will be 70
o
.
(Since, opposite angles of a rhombus are equal)

o o o
Value of component 1
360 360 90
Total va
Central
lue 4
angle ? ? ? ? ?

Square root = 2 × 3 × 3 × 5 = 90

Actual C.P. = C.P. + Overhead expenses = Rs. (900 + 200) = Rs. 1100
Profit = S.P. – C.P. = Rs. 1200 – Rs. 1100 = Rs. 100
100 1
Profit percent= 100 9 %
1100 11
??

Section B

13.
(by commutativity)

(by distributivity)

14. Let x be the greater part.
Then, 64 - x is the smaller part.
Then 3x = 5(64 - x)
3x = 320 - 5x
3x + 5x = 320
8x = 320
x = 40
So, the two parts are 40 and 24.

CBSE VIII | Mathematics
Sample Paper 1 -  Solution

15. Opposite sides are equal in a parallelogram
Therefore, 3y + 1 = 19
Or, 3y = 19 - 1
Or, 3y = 18
Or, y = 6
Also, 4x+3 = 23
Or, 4x = 23-3
Or, 4x = 20
Or, x = 5
Hence x = 5 and y = 6.

16. Let the number of chairs in each row be x.
Then, the number of rows = x.
Total number of chairs in the auditorium
? ?
2
x x x ? ? ?
But the number of chairs that the auditorium can accommodate = 1764 (given)

? ?
??
? ? ? ? ? ?
? ? ? ?
?
2
x 1764
2 2 3 3 7 7
x 2 3 7
42

Hence, the number of chairs in each row is 42.

17. Here,
Total number of outcomes = 10 + 25 = 35
Let E be the event of getting a prize.
Number of outcomes favourable to event E = 10
? ?
Number of favourable outcomes 10 2
Total number of outcome
P E
s7

35
? ? ?
2
Probability of getting a prize
7
?

Page 4

CBSE VIII | Mathematics
Sample Paper 1 -  Solution

CBSE Board
Class VIII Mathematics
Term I
Sample Paper 1 - Solution
Time: 2 ½ hours                          Total Marks: 80

Section A

2.5 is greater than 2.4 and less than 2.6 and 2.7.
Hence, on a number line, 2.5 will lie between 2.4 and 2.7.

= 5 + 5 + 3 = 13

1 is a square as well as a triangular number.

Cube root of (-8) x (-343) x (125) = (-2) x (-7) x 5 = 70

On cross multiplying, we get 4x + 28 = 3x - 3
4x - 3x = - 3 - 28
x = -31
x + 31 = 0

CBSE VIII | Mathematics
Sample Paper 1 -  Solution

In a rhombus, if one angle is 70
o
, then its opposite angle will be 70
o
.
(Since, opposite angles of a rhombus are equal)

o o o
Value of component 1
360 360 90
Total va
Central
lue 4
angle ? ? ? ? ?

Square root = 2 × 3 × 3 × 5 = 90

Actual C.P. = C.P. + Overhead expenses = Rs. (900 + 200) = Rs. 1100
Profit = S.P. – C.P. = Rs. 1200 – Rs. 1100 = Rs. 100
100 1
Profit percent= 100 9 %
1100 11
??

Section B

13.
(by commutativity)

(by distributivity)

14. Let x be the greater part.
Then, 64 - x is the smaller part.
Then 3x = 5(64 - x)
3x = 320 - 5x
3x + 5x = 320
8x = 320
x = 40
So, the two parts are 40 and 24.

CBSE VIII | Mathematics
Sample Paper 1 -  Solution

15. Opposite sides are equal in a parallelogram
Therefore, 3y + 1 = 19
Or, 3y = 19 - 1
Or, 3y = 18
Or, y = 6
Also, 4x+3 = 23
Or, 4x = 23-3
Or, 4x = 20
Or, x = 5
Hence x = 5 and y = 6.

16. Let the number of chairs in each row be x.
Then, the number of rows = x.
Total number of chairs in the auditorium
? ?
2
x x x ? ? ?
But the number of chairs that the auditorium can accommodate = 1764 (given)

? ?
??
? ? ? ? ? ?
? ? ? ?
?
2
x 1764
2 2 3 3 7 7
x 2 3 7
42

Hence, the number of chairs in each row is 42.

17. Here,
Total number of outcomes = 10 + 25 = 35
Let E be the event of getting a prize.
Number of outcomes favourable to event E = 10
? ?
Number of favourable outcomes 10 2
Total number of outcome
P E
s7

35
? ? ?
2
Probability of getting a prize
7
?

CBSE VIII | Mathematics
Sample Paper 1 -  Solution

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
Hence, the perimeter of the given trapezium is 28 cm.

19. Total number of votes = (1136 + 7636 + 11628) = 20400.
11628
Therefore, required percentage 100 % 57%
20400
??
? ? ?
??
??

20. Since, the measure of each angle of rectangle is 90
o
.
Therefore, ?ADC = y = 90
o

o

This gives, x + 45
o
= 90
o

x = 90
o
- 45
o
= 45
o

Hence, x = 45
o
and y = 90
o
.

21. It can be observed that the squares of the given numbers can be found by first
writing the counting number up to the number of 1's and then writing  the reverse
counting till 1.
Thus, 1111
2
= 1234321
11111
2
= 123454321

22. By cross multiplication, we get,
3(3x-1) = 4(2x+5)
9x-3 = 8x +20
9x-8x-3 = 20 (transposing 8x to LHS)
9x-8x = 20+3 (transposing -3 to RHS)
x = 23

23.

Page 5

CBSE VIII | Mathematics
Sample Paper 1 -  Solution

CBSE Board
Class VIII Mathematics
Term I
Sample Paper 1 - Solution
Time: 2 ½ hours                          Total Marks: 80

Section A

2.5 is greater than 2.4 and less than 2.6 and 2.7.
Hence, on a number line, 2.5 will lie between 2.4 and 2.7.

= 5 + 5 + 3 = 13

1 is a square as well as a triangular number.

Cube root of (-8) x (-343) x (125) = (-2) x (-7) x 5 = 70

On cross multiplying, we get 4x + 28 = 3x - 3
4x - 3x = - 3 - 28
x = -31
x + 31 = 0

CBSE VIII | Mathematics
Sample Paper 1 -  Solution

In a rhombus, if one angle is 70
o
, then its opposite angle will be 70
o
.
(Since, opposite angles of a rhombus are equal)

o o o
Value of component 1
360 360 90
Total va
Central
lue 4
angle ? ? ? ? ?

Square root = 2 × 3 × 3 × 5 = 90

Actual C.P. = C.P. + Overhead expenses = Rs. (900 + 200) = Rs. 1100
Profit = S.P. – C.P. = Rs. 1200 – Rs. 1100 = Rs. 100
100 1
Profit percent= 100 9 %
1100 11
??

Section B

13.
(by commutativity)

(by distributivity)

14. Let x be the greater part.
Then, 64 - x is the smaller part.
Then 3x = 5(64 - x)
3x = 320 - 5x
3x + 5x = 320
8x = 320
x = 40
So, the two parts are 40 and 24.

CBSE VIII | Mathematics
Sample Paper 1 -  Solution

15. Opposite sides are equal in a parallelogram
Therefore, 3y + 1 = 19
Or, 3y = 19 - 1
Or, 3y = 18
Or, y = 6
Also, 4x+3 = 23
Or, 4x = 23-3
Or, 4x = 20
Or, x = 5
Hence x = 5 and y = 6.

16. Let the number of chairs in each row be x.
Then, the number of rows = x.
Total number of chairs in the auditorium
? ?
2
x x x ? ? ?
But the number of chairs that the auditorium can accommodate = 1764 (given)

? ?
??
? ? ? ? ? ?
? ? ? ?
?
2
x 1764
2 2 3 3 7 7
x 2 3 7
42

Hence, the number of chairs in each row is 42.

17. Here,
Total number of outcomes = 10 + 25 = 35
Let E be the event of getting a prize.
Number of outcomes favourable to event E = 10
? ?
Number of favourable outcomes 10 2
Total number of outcome
P E
s7

35
? ? ?
2
Probability of getting a prize
7
?

CBSE VIII | Mathematics
Sample Paper 1 -  Solution

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
Hence, the perimeter of the given trapezium is 28 cm.

19. Total number of votes = (1136 + 7636 + 11628) = 20400.
11628
Therefore, required percentage 100 % 57%
20400
??
? ? ?
??
??

20. Since, the measure of each angle of rectangle is 90
o
.
Therefore, ?ADC = y = 90
o

o

This gives, x + 45
o
= 90
o

x = 90
o
- 45
o
= 45
o

Hence, x = 45
o
and y = 90
o
.

21. It can be observed that the squares of the given numbers can be found by first
writing the counting number up to the number of 1's and then writing  the reverse
counting till 1.
Thus, 1111
2
= 1234321
11111
2
= 123454321

22. By cross multiplication, we get,
3(3x-1) = 4(2x+5)
9x-3 = 8x +20
9x-8x-3 = 20 (transposing 8x to LHS)
9x-8x = 20+3 (transposing -3 to RHS)
x = 23

23.

CBSE VIII | Mathematics
Sample Paper 1 -  Solution

24.

Section C

25. Represent the months on the x-axis and the number of visitors on the y-axis.
The double bar graph is as follows:

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