## CBSE Solved Sample Papers for Class 8 for Maths – Second Term

CBSE Solved Sample Papers for Class 8 for Maths Subject (Term 2) is given below. The solved sample papers are created as per the latest CBSE syllabus and curriculum keeping in mind the latest marking scheme.

**SECTION – A**

Q 1 The value of (5˚ + 7^{-1})^{ *} 7 are:

(a) 35

(b) 36

(c) 8

(d) 84

Ans (c)

Q 2 Factories x^{2 +} 5x + 6:

(a) (x+3) (x+2)

(b) (x-3) (x+2)

(c) (x+3) (x- 2)

(d) All of above

Ans (a)

Q 3 A train is moving at a uniform speed of 80 km/hr. How for it will travel in 15 minutes.

(a) 85 km

(b) 120km

(c) 20km

(d) 30km

Ans (c)

Q 4 (1.02)^{2} – (0.98)^{2} are equal to:

(a) 0.04

(b) 0.08

(c) 0.8

(d) 2

Ans (b)

Q 5 what is the coordinate of point P on the graph:

(a) 7

(b) (7,0)

(c) (1,5)

(d) (0,7)

Ans (d)

Q 6 the cost of 5 pens is Rs. 25.50. What is the cost of 8 pens?

(a) 40.80

(b) 40

(c) 50

(d) 45.20

Ans (a)

Q 7 Which one of the following pair forms like terms:

(a) 7x – 5y

(b) 2x – 3x^{2}

(c) 2/3x – 5/7x

(d) 2/5x – 3xy

Ans (c)

Q 8 The relation between F,V and E are represented by Euler’s formula as follows:

(a) F – V + E = 0

(b) F + E + V = 1

(c) F – V + E = 2

(d) F + V – E = 2

Ans (d)

Q 9 which one is binomial:

(a) 4l + 5m

(b) 3x^{2}– 5x + 2

(c) 4 + 3/x

(d) X + 1/y

Ans (a)

Q 10 if the longer side of a trapezium is 10 cm and the distance between the parallel sides is 8 cm. The area is 50 cm^{2. }What is the smaller parallel side?

(a) 10 cm

(b) 2 cm

(c) 2.5 cm

(d) 3.5 cm

Ans (c)

**SECTION – B**

Q 11 How many sides of the following have?

(a) Nonagon

(b) Octagon

Ans

(a) Nonagon: Nonagon has 9 sides.

(b) Octagon: octagon has 8 sides.

Q 12 What is the volume of a cube with side 6 cm?

Ans side of cube = 6 cm

Volume of cube= side * side * side

= (6 * 6 * 6) cm

= 216 cm^{3 }

Q 13 Simplify (-5)^{-2}

Ans (-5)^{-2} = 1 / (-5)^{-2} = 1/-5 * -5

=1 / 25

Q 14 Find the value of: (2^{-1} + 4^{-1}) / 2)^{-2}

Ans (2^{-1} + 4^{-1}) / 2)^{-2}

= [1/2+ ¼] / 1/2^{2}

= (2 + 1 / 4) / (1/4)

= (¾) / (1/4)

= ¾ * 4 = 3

Q 15 Write 2 – dimensional or 3 – dimensional for the following shapes:

Square, cone, circle, cylinder

AnsSquare, circle = 2 – dimensional

Cone, cylinder = 3 – dimensional

Q 16 What formula would you use to calculate the area of a rectangle?

AnsArea of a rectangle = length * breadth

Q 17 what is range of the data?

Ans The difference between the highest and the lowest values of the observation in a data is called the range of the data.

Q 18 Evaluate (2/3)^{-3}

Ans(2/3)^{-3 =} (3/2)^{3}

= 3/2 * 3/2 * 3/2

= 27/8

SECTION – C

Q 19 The lateral surface area of a hollow cylinder is 4224 cm^{2. }It is cut along its height and formed a rectangle sheet of width 33 cm. Find the perimeter of the rectangle sheet.

Ans lateral surface area of cylinder = 4224 cm^{2}

Width of sheet (b) = 33 cm

Length of sheet (l) = area/width

L = 4224/33 = 128 cm

Perimeter of sheet = 2(l + b)

= 2 (128 + 33)

= 2(161)

= 322 cm

Q 20 Factories 16x^{5} – 121x^{3}

Ans 16x^{5} – 121x^{3}

= x^{3}(16x^{2}– 121)

= x^{3}[(4x)^{ 2}– (11)^{2}]

= [(a^{ 2}– b^{ 2)} = (a +b) (a – b)]

= x^{3}[(4x + 11)– (4x – 11)]

Q 21 Find the value of 9^{-1} * 5^{-3 }/ 3^{-4}

Ans 9^{-1} * 5^{-3 }/ 3^{-4}= 3^{4} * 5^{3} / 9

= 3^{4} * 5^{3} / 3^{2}

= 3^{4 – 2 }* 5^{3}

^{ }= 3^{2} * 5^{3}

^{ }= (3 * 3) (5 * 5 * 5)

= 9 * 125

= 1125

Q 22 A loaded truck travels 14 km in 25 minute. If the speed remains the same. How far can it ravel in 5 hours?

AnsDistance covered in 25 minute = 14 km

Distance covered in 1 minute = 14 / 25 km

Distance covered in 5 hours = (5 hours = 5 * 60 = 300 minute)

= 14 / 25 * 300

= 14 * 12 = 168 km

He can travel 168 km in 5 hours.

Q 23 In a model of a ship, the mast is 9 cm high, while the mast of the actual ship is 12 m high. If the length of the ship is 28 m. How long is the mast on the ship?

Ans The height of the mast and the length of the model ship are indirect proportion.

Let x =length of model

Y= length of ship

X = 9 cm , y =12 cm

X =? , y = 28 cm

X_{1}/y_{1 } = x_{2}/y_{2}

9 / 12 = x_{2}/28

_{X2} = 9 * 28 /12

_{ X2}= 3 * 7s

_{X2} = 21 cm

Thus Model ship is 21 cm long.

Q 24 Find the height of a cuboid whose base area is 180 cm^{2} and volume is 900 cm^{3}.

Ans Base area of a cuboid = 180 cm^{2}

Volume of a cuboid = 900 cm^{3}

Height of a cuboid = volume/base area

= 900 / 180

Thus height of a cuboid = 5 cm.

Q 25 Using suitable identity, evaluate:

(a) 1.05 * 0.95

(b) 9.7 * 9.8

Ans

(a) 1.05 * 0.95

= (1 + 0.05)(1-0.05)

= 1 – 0.0025 = .9975

(b) 9.7 * 9.8

= (9 + .7) (9 + .8)

= (9)^{2} + (.7 + .8) * 9 + (.7 * .8)

=81 + (1.5) * 9 + (.56)

= 95.06

Q 26 multiply (2 / 3 xy) * (-9 / 10 x^{2}y^{2})

Ans (2 / 3 xy) * (-9 / 10 x^{2}y^{2})

= (2 / 3 * -9 / 10) xy * x^{2}y^{2}

= -3 / 5 x^{3}y^{3}

Q 27 Using identity solve 99^{2}

Ans 99^{2} = (100 – 1)^{2}

(a – b)^{ 2} = a^{2} +b^{2} -2ab

= (100)^{ 2} + (1)^{ 2} – 2(100) (1)

= 10000 + 1 -200

= 10001 – 200

= 9801

Q 28 Subtract 3xy – 5yz- 7zx from 5xy – 2yz -2zx + 10xyz

Ans (5xy – 2yz -2zx + 10xyz) – (3xy – 5yz- 7zx)

= 5xy – 2yz -2zx + 10xyz – 3xy + 5yz + 7zx

= 5xy – 3xy – 2yz + 5yz -2zx + 7zx + 10xyz

= 2xy +3yz + 5zx +10xyz

Q 29 A field is 60 m long and 24 m broad. In one corner of the filed, a pit which is 8 m long 6.5m broad and 4 m deep has been dug out. The earth taken out of it is evenly spread over the remaining part of the field. Find the rise in the level of the filed.

Ans area of the filed = (60 * 24) m

= 1440 m^{2}

Area of th pit = (8 * 6.5) m

= 52m^{2}

Area over the remaining part of the filed = (1440 – 52) m^{2}

= 1388 m^{2}

Volume of earth dug out = 8 * 6.5 * 4

= 208 m^{2}

Rise in level = Volume of earth dug out/area over the remaining part of filed

=208/1388 m

= 208 * 100/1388 cm

= 10.4 cm

Q 30 If x – 1/x = 6 find (x^{2} + 1 / x^{2}) and x^{4} + 1 / x^{4}

Ans x – 1 / x = 6 = (x – 1 / x)^{ 2} = (6)2

= x^{2} + 1 / x^{2}– 2 = 36

= x^{2} + 1 / x^{2}= 38

=(x2 + 1 / x^{2)2}= (38)^{2}

= x^{4} + 1 / x^{4}+ 2 = 1444

= x^{4} + 1 / x^{4}= 1444

Q 31 A square park has been each side of 100 m. At each corner there is a flower bed in the form of a quadrant of radius 14m as shown in fig. Find the area of the remaining part of the park. (Takeπ =22 / 7)

AnsArea of each quadrant of radius = 14 cm

= 1 / 4 (πr^{2})

=1 / 4 π * 14^{2}

= 1 / 4 * 22 / 7 * 14 *14

= 154 m^{2}

Area of 4 quadrants = (4 * 154) m^{2} = 616 m^{2}

Side of square = 100 m

Area of square = (100 * 100) m^{2}

= 10000 m^{2}

Area of the remaining part of the park

= (1000 – 616) m^{2}

= 9384 m^{2}

Q 32 Factories:

(a) 8x^{3} – 18 xy^{2}

(b) 3x^{2} + 12x – 36

(c) X^{2} + 4xy +4y^{2} – 9z^{2}

Ans

(a) 8x^{3} – 18 xy^{2}

= 2x (4x^{2} – 9y^{2})

= 2x (2x + 3y) (2x – 3y) [By using a^{2} – b^{2} = (a + b) (a – b)]

= 2x (2x + 3y) (2x – 3y)

(b) 3x^{2} + 12x – 36

= 3 (x^{2} + 4x – 12)

= 3 (x^{2} + 6x -2x – 12)

= 3 [x (x + 6) – 2 (x + 6)]

= 3 [(x – 2) (x +6)]

(c) X^{2} + 4xy +4y^{2} – 9z^{2}

= (x^{2} + 4xy + 4y^{2}) – 9z^{2}

= (x + 2y)^{ 2} – (9z^{2})

=(x +2y + 3z) (x + 2y -3z)

= (x + 2y + 3z) (x + 2y – 3z)

Q 33 Subtract: 3a (a + b + c) -2b (a – b + c) from 4c (- a + b + c)

Ans 3a (a + b + c) -2b (a – b + c) from 4c (- a + b + c)

= 4c (- a + b + c) – [3a (a + b + c) -2b (a – b + c)]

= – 4ca + 4bc +4c^{2} – [(3a^{2} + 3ab + 3ac) – 2ba +2b^{2} – 2bc)]

= – 4ca + 4bc +4c^{2} – [3a^{2} + 3ab + 3ac – 2ba +2b^{2} – 2bc]

= – 4ca +4bc +4c^{2} – [+ 3ac -2bc + 3a^{2} + 2b^{2} + 3ab]

= – 4ca +4bc +4c^{2} – 3ac +2bc – 3a^{2} – 2b^{2} – 3ab

= – 7ac + 6bc – 3a^{2} – 2b^{2} +4c^{2} – 3ab

= – 7ac + 6bc – 3ab – 3a^{2} – 2b^{2} +4c^{2}

Q 34 Plot the graph from the following table. Is the graph linear?

Side of square (in cm) | 2 | 3 | 3.5 | 5 | 6 |

Perimeter (in cm) | 8 | 12 | 14 | 20 | 24 |

Ans

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