Class VIII Session 2024-25

Subject - Mathematics
Sample Question Paper - 1

Time Allowed: 3 hours Maximum Marks: 80

General Instructions:

1. This Question Paper has 4 Sections A-D.

2. Section A has 20 MCQs carrying 1 mark each.

3. Section B has 6 questions carrying 02 marks each.

4. Section C has 8 questions carrying 03 marks each.

5. Section D has 6 questions carrying 04 marks each.

6. All Questions are compulsory.

7. Draw neat figures wherever required. Take π =22/7 wherever required if not stated.

1. Which of the following properties of rational numbers is shown below? [1]

3 7 −4 3 7 −4
× ( × ) = ( × ) ×
4 3 5 4 3 5

a) Distributivity of addition over multiplication b) Commutativity of addition

c) Distributivity of multiplication over addition d) Associativity of multiplication

2. The property represented by a × (b + c) = a × b + a × c is [1]

a) closure property b) distributive property

c) associative property d) commutative property

3. If , then the numerical value of 2x - 7 is [1]
5x 2x
− 4 =
3 5

a) b)
19 13

13 19

c) − 13

19
d) 0
4. Solve: 5t − 3 = 3t − 5 [1]

a) 0 b) 2

c) 1 d) -1
5. For which of the following figures, diagonals are perpendicular to each other? [1]

a) Trapezium b) Kite

c) Parallelogram d) Rectangle
6. State the name of a regular polygon of 9 sides. [1]

a) heptagon b) octagon

c) nonagon d) Hexagon
7. The length and breadth of a rectangle are in the ratio 4 : 3. If the diagonal measures 25 cm then the perimeter of [1]

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 the rectangle is

a) 70 cm b) 60 cm

c) 80 cm d) 56 cm
8. 7396 students are sitting in an auditorium in such a manner that there are as many students in a row as there are [1]
rows in the auditorium. How many rows are there in the auditorium?

a) 76 b) 86

c) 80 d) 75
9. The smallest number by which 3087 may be multiplied so that the product is a perfect cube, is [1]

a) 4 b) 6

c) 5 d) 3
10. Find the cubes of x, 4x and 5x. [1]

a) 4x3, 9x3, 16x3 b) x3, 64x3, 125x3

c) 8x2, 27x2, 64x2 d) 4x2, 9x2, 16x2

11. Find C.I. on Rs 25,000 for 2 years at 20% per annum compounded annually. [1]

a) Rs 12,000 b) Rs 13,000

c) Rs 11,000 d) Rs 10,000

12. Factorised form of r2 - 10r + 21 is [1]

a) (r + 7) (r + 3) b) (r - 7)(r - 3)

c) (r - 7) (r + 3) d) (r -1) (r - 4)
13. The three-dimensional figure formed by rotating a circle is: [1]

a) Sphere b) Cone

c) Hemisphere d) Cylinder
14. The following figure represents a: [1]

a) Convex polyhedron b) Cylinder

c) Concave polyhedron d) Polygon

15. A room is 15 metres long, 4 metres broad and 3 metres high. Find the cost of whitewashing its four walls at 50 P. [1]

per m2.

a) ₹ 55 b) ₹ 60

c) ₹ 57 d) ₹ 52

16. If the volume of a cube is 1728 cm3, then its surface area is: [1]

a) 144 cm2 b) 912 cm2

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 c) 864 cm2 d) 288 cm2
−2

17. The value of ( 2

) is [1]
5

a) b)
4 5

25 2

c) 4

5
d) 25

18. If 3x+8 = 272x+1 then the value of x will be: [1]

a) 1 b) -2

c) 7 d) 3
2

19. Simplify: (−3)

2
× (
5
)
[1]
3

a) 4 b) 27

c) 25 d) 8

20. 9m2 + 12mn + 4n2 is same as [1]

a) (3m + 2n)2 b) (3m - 2n)2

c) (3m - 2n) d) (3m + 2n)

21. Using suitable rearrangement find the sum: −5 + [2]
7 3 5 −4
+ + (−3) + +
10 7 14 5

22. Solve the equation and check your result: 5x + 9 = 5 + 3x [2]

23. A bag has 4 red balls and 2 yellow balls. (The balls are identical in all respects other than colour). A ball is [2]
drawn from the bag without looking into the bag. What is probability of getting a red ball? Is it more or less than
getting a yellow ball?
OR
A survey was carried out to find the favourite beverage preferred by a certain group of young people. The following
pie chart shows the findings of this survey.

From this pie chart, answer the following:

i. Which type of beverage is liked by the maximum number of people?
ii. If 45 people like tea, how many people were surveyed?
24. The dimensions of a rectangular field are 80 m and 18 m. Find the length of its diagonal. [2]
25. For the given solid draw the side view and front view? [2]

26. Find the value of x, so that (-2)3 × (- 2)-6 = (- 2)2x - 1 [2]

OR

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 Simplify and write in exponential form :(– 2)–3 × (– 2)–4
27. Solve: 5x + [3]
7 2
= x − 14
2 2

28. In the following figure of a ship, ABDH and CEFG are two parallelograms. Find the value of x. [3]

OR
ABCD is a parallelogram. The bisector of angle A intersects CD at X and bisector of angle C intersects AB at Y. Is
AXCY a parallelogram? Give reason.
29. 2025 plants are to be planted in a garden in such a way that each row contains as many plants as the number of [3]
rows. Find the number of rows and the number of plants in each row.
30. Is 1188 a perfect cube? If not, by which smallest natural number should 1188 be divided so that the quotient is a [3]
perfect cube?
31. The price of a TV is ₹13000. The sales tax charged on it is at the rate of 12%. Find the amount that Vinod will [3]
have to pay if he buys it.
OR
The marked price of a DVD is ₹4500. A shopkeeper allows two successive discounts of 10% and 5% by the force of
a customer. Find the selling price of the customer after two discounts are given.
32. Add p3 – 1 , p3 + p + 2 and p2 – 2p + 1. [3]

33. Rukhsar painted the outside of the cabinet of measure 1 m × 2 m × 1.5 m. How much surface area did she [3]
cover if she painted all except the bottom of the cabinet.

34. Factorise: (l + m)2 – (l – m)2 [3]

35. Draw a pie chart showing the following information. The table shows the colours preferred by a group of people. [4]

Colours Number of people

Blue 18

Green 9

Red 6

Yellow 3

Total 36

Find the proportion of each sector. For example, Blue is Green is and so on.Use thisto find the
18 1 9 1
= ; =
36 2 36 4

corresponding angle.
36. A sum of money becomes ₹ 17,640 in 2 years and ₹ 18,522 in 3 years at the same rate of interest compounded [4]
annually. Find the rate of interest.

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37. Find the product of ( 1 3 6
p q )(
−2 4 2
p q) (pq ) [4]
2 3

38. Find the area of the following fields. All dimensions are in metres. [4]

OR
The dimensions of a cuboid are in the ratio of 2:3:4 and its total surface area is 208m2. Find its dimensions.

39. Factorize 6x2 – 13x + 6 [4]

OR

Factorise the expression and divide them as directed: (5p2 – 25p + 20) ÷ (p – 1)
40. Consider the relation between the area and the side of a square given by A = x2. [4]

a. Draw a graph to show this relation.

b. From the graph, find the value of A when x = 4.
c. Is this graph a linear graph?

Side of square (x) 0 1 2 3 4 5

Area of square (A) 0 1 4 9 16 25

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