Class 8 Half Yearly Question Paper 2025-26 Maths

CBSE CLASS 8
Half Yearly Question Paper
Session 2025-26

MATHS

Exam CBSE Class 8
Subject Maths
Session 2025-26
Document Type Half Yearly Question Paper

Notes · Sample Papers · Previous Year Papers · Mock Tests

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Question Paper
Half Yearly Examination
SESSION 2025-2026 ag
CLASS: VIII MAXIMUM MARKS: 80
SUBJECT: Mathematics TIME: 3 HOURS
General Instructions:
i. The question paper contains 38 questions of 5 printed pages. All questions are compulsory.
ii. The question paper consists of five sections: A; B; C; D; E
Section A: Question No. 1 to 20 are of 1 mark each ( 18 MCQ Type and 2 are Assertion- Reasoning type

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questions).

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Section B: Question No. 21 to 25 are Short Answer Type –1 questions of 2 marks each.

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Section C: Question No. 26 to 31 are Short Answer Type –2 questions of 3 marks each.

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Section D: Question No. 32 to 35 are Long Answer Type questions of 5 marks each.
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Section E: Question No. 36 to 38 are of Case Based questions. Each such questions has 3 sub parts, of
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which two are of 1 mark each and third sub part is a SA type (2 marks) having internal choice..
iii. Please write the serial number of the question before attempting it.
iv.In questions of constructions/graph , the drawing should be neat ,clean and exactly as per given
measurement. Use ruler and compass only.
v. All questions are compulsory. However internal choices have been given in some questions.
SECTION-A
1. The number of non-perfect square numbers lie between 2 and 2
? 1
(a ) 171 (b) 85 (c) 86 (d) 170

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2. 1

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If √ = , then value of n is
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(a) 28 (b) 4 (c) 7 (d) 16

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3. The smallest number by which 125 must be divided to make it a perfect square is : 1

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(a ) 7 (b) 5 (c) 8 (d) 2

4. 3
0.027  3 0.008 is equal to 1
(a) 1 (b) 0.1 (c) 0.11 (d) 0.09

5. Cube of 0.1 is equal to : 1
(a ) 1.11 (b) 0.101 (c) 0.001 (d) 0.01
6. The volume of a cube is 729 m³. Length of its side is 1

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(a) 3 m (b) 6 m (c) 9 m (d) 27 m

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7. (x+5) (x-3) = 1

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(a) x2+5x-15 (b) x2-3x-15 (c) x2 +2x-15 (d) x2+2x+15

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8. The value of ( ( ( ( ( ( is : 1

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(a ) (b) (c) (d) 0

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9. Two lines intersected by a transversal will be parallel if : 1
(a) Interior angles on the same side of the transversal are complementary.
(b) Vertically opposite angles are equal.
(c) Alternate interior angles are equal.
(d) Corresponding angles are supplementary.

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10. In the given figure l||m, find the value of x: 1

(a) 50 (b) 60 (c) 75 (d) 90
11. In the given figure m||n and p||q. If ∠1 = 70°, then ∠2 is: 1

(a) 100° (b) 70° (c) 80° (d) 110°
12. If 10 men can complete a work in 6 days, then 30 men can complete the same work in 1
(a) 2 days (b) 3 days (c) 4 days (d) 5 days
13. If x and y vary directly with each other and x = 24, calculate y when constant of variation is 3. 1
1
(a) 21 (b) (c) 8 (d) 27
8
14. Which of the following quantities vary inversely with each other : 1
(a) Speed and Distance (b) Time and Distance
(c) Speed and Time (d) Work done and Time taken
15. If cost price of an article is equal to its selling price then there is : 1
(a ) 100% loss (b) 100% gain (c) loss 50 % (d) no gain or loss
16. Discount is always calculated on: 1
(a) Cost price (b) Marked price (c) Selling price (d) GST
17. The volume of a cube of side 0.01 m in cm3 is 1
(a) 0.001 (b) 1 (C) 0.0001 (D) 0.000001
18. Three cubes whose edges are 3 cm, 4 cm and 5 cm respectively, melted without any loss of 1
metal into a single cube. Then the edge of new cube is :
(a ) 7 cm (b) 5 cm (c) 8 cm (d) 6 cm
Assertion(A): The square of an even number is always odd.
19. Reason(R):An even number can be expressed as 2n,where n is an integer.
(a) Both assertion(A) and Reason(R) are true and Reason(R) is the correct explanation of
Assertion(A)
(b) Both assertion(A) and Reason(R) are true and Reason(R) is not the correct explanation of
Assertion(A) 1
(c) Assertion(A) is true but Reason(R) is false.
(d) Assertion(A) is false but Reason(R) is true.
2 2 2
20. Assertion(A): ( is an algebraic identity. 1
Reason(R): A statement of equality which holds for all values of the variables is called an
identity.
(a) Both assertion(A) and Reason(R) are true and Reason(R) is the correct explanation of
Assertion(A)
(b) Both assertion(A) and Reason(R) are true and Reason(R) is not the correct explanation of
Assertion(A)
(c) Assertion(A) is true but Reason(R) is false.
(d) Assertion(A) is false but Reason(R) is true.
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se 21. By which smallest number must 1944 be multiplied to make it g
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SECTION-B
a perfect cube ? 2

22. Find the cube root of ( 13824) by prime factorization method. 2
OR
704
Find the cube root of
1375

23. In a quadrilateral ABCD all the four angles are equal. Show that 2

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24. In the given figure, , 2

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find the value of ∠

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In the figure AB CD, If ∠EPB=25°

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find ∠APQ and ∠PQD

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25. If the selling price of 5 pens is equal to the cost price of 4 pens, then find the gain or loss 2
percent.
SECTION-C
26. Find the least number which must be added to 7581 to obtain a perfect square. Also find the 3
square root of the number obtained.
OR
Find the greatest four-digit number which is a perfect square.

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27. Prove that if a number is tripled, then its cube is 27 times the cube of the given number. 3

. cFactorise: 25a2 - 4b2 +28bc - 49c2
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28. 3

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OR

las Evaluate x if 6.2 x = 8.1×8.1 – 1.9×1.9
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a 29. In the diagram given below, find the angles ∠x, ∠y and ∠z. 3

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30. How long will a train,120 m long, take to cross a platform, 130 m long ,if the speed is 3
50km/hour?

31. The perimeter of a trapezium is 104 m. If its non-parallel sides are 18 m and 22 m long and its 3
altitude is 16 m, find the area of the trapezium.
SECTION-D
32. 1 17 1 5
If a+ = , find the value of a -
4

33. There is a provision of food for 28 days of 1200 soldiers in a fort. After 4 days, some soldiers 5
were transferred to another fort and thus the food lasted now for 32 days. How many soldiers
left the fort?
34. Ram sold an article to Peter at 20% profit and Peter sold it to Mohan at 5% loss. If Mohan paid 5
₹912 for the article, find how much did Ram pay for it?
OR
A cycle merchant allows 25% discount on the marked price of a cycle and still makes a profit
of 20%. If he gains ₹600 over the sale of one cycle, find the marked price of the cycle?

35. An Iron pipe 56 cm long has exterior diameter equal to 14 cm. If the thickness of the pipe is 1 5
cm, find the whole surface area of the pipe.
OR
A well is dug 20 m deep and it has a diameter 7m. The earth which is so dug out is spread
evenly on a rectangular plot 22 m long and 14 m broad. What is the height of the platform so
formed?
SECTION-E
During the dance practice in school 7581 students of different schools are arranged in rows
36. such that the number of students in each row is equal to the number of rows. In doing so the 4
instructor finds out that few students are left out.

Based on the above information answer the following question:
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se (a) How many students are left out?
(b) What is the number of students forming a square?
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(c) Find the number of children in each row of the square. 2
OR
If the dance conducted in a square room of area 2401 sq. m, then find the side of the room.

37. CASE STUDY -2
Riya owns a stationery shop. She buys items in bulk and sells them to students at reasonable
prices. One day, she bought 50 notebooks at ₹40 each. She planned to sell each notebook at

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a marked price of ₹60. To attract more customers, she offered a 10% discount on the marked

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price. By the end of the week, she sold 40 notebooks.

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Based on the above information answer the following questions:-

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(i) What is the total cost price (C.P.) of 40 note books?

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(ii) Find the selling price (S.P.) of each note book? 1

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(iii) What is the profit or loss for Riya on selling 40 notebooks?
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OR

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If Riya wants to make a 80% profit on the cost price, what should be the new marked price if
she still wants to give a 10% discount?

38. Anup after retirement thought to stay in village's house. After going there he found there was
shortage of water in the village, so he thought of constructing a well. He hired some labours
and guided them that well should be 7 m in diameter and 20 m deep.

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Based on the above information answer the following questions:
(i) Name the 3-dimensional geometric figure representing the well.
(ii) Determine the radius of the well. 1
(iii) (a) Find the volume of the earth dug out. 1
OR 2

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(b) Find the curved surface area of the well.

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