CBSE Class 10 Maths Half Yearly Sample Paper 2025 with Solution, Download PDF

CBSE Class 10 Maths Half Yearly Sample Paper 2025: The CBSE Class 10 Term I Question Paper for the academic year 2025-26 is a crucial tool for students getting ready for their mid-term tests. These sample papers help students check how well they understand the topics and get used to the exam format and the kinds of questions they might see in their final exams.By practicing with these papers, students can find out what they are good at and what they need to work on. This helps them prepare better for the end term exam. The CBSE Class 10 Mid Term Question Paper 2025-26 is an important resource for students preparing for their mid-term exams, typically held in September and October.

These question papers help students understand the exam pattern, identify key topics, and become familiar with the types of questions that might appear in the exams.Students can easily find and download these papers from the below mentioned link, making them a useful way to test themselves and review what they've learned. These sample papers by experts are designed to help the students for their Half Yearly exam. In this article we have covered all the topics and important questions so that students can check and practice to score well. After viewing all the questions students can download the PDF for sample paper and solutions. 

Check: CBSE Class 10 Maths Syllabus 2025-26 (PDF)

CBSE Class 10 Maths Units and Weightage (2025-26)

CBSE Class 10 Maths Half Yearly Sample Paper 2025

General Instructions:

• All Questions are compulsory.
• Draw neat figures wherever required.
• Take π = 22/7 wherever required if not stated.

Section A 

1. The graph of a quadratic polynomial p(x) passes through the points (-6,0), (0, -30), (4,-20) and (6,0). The zeroes of the polynomial are

A) - 6,0 

B) 4, 6 

C) - 30,-20 

D) - 6,6

2. The value of k for which the system of equations 3x-ky= 7 and 6x+ 10y =3 is inconsistent, is

A) -10 

B) -5 

C) 5 

D) 7

3. Which of the following statements is not true?

A) A number of secants can be drawn at any point on the circle.

B) Only one tangent can be drawn at any point on a circle.

C) A chord is a line segment joining two points on the circle

D) From a point inside a circle only two tangents can be drawn.

4. If the system of equations 3x+y =1 and (2k-1)x +(k-1)y =2k+1 is inconsistent, then k = 

(a) -1 (b) 0 (c) 1 (d) 2

5. If the vertices of a parallelogram PQRS taken in order are P(3,4), Q(-2,3) and R(-3,-2), then the coordinates of its fourth vertex S are

(a) (-2,-1) (b) (-2,-3) (c) (2,-1) (d) (1,2)

6. ∆ABC~∆PQR. If AM and PN are altitudes of ∆ABC and ∆PQR respectively and AB2: PQ2 = 4 : 9, then AM: PN =

(a) 3:2 (b) 16:81 (c) 4:9 (d) 2:3

7. If x tan 60° cos 60°= sin60° cot 60° , then x = 

(a) cos30° (b) tan30° (c) sin30° (d) cot30°

8.

9.

10. The roots of the quadratic equation 𝑥 2+x-1 = 0 are 

A) Irrational and distinct B) not real C ) rational and distinct D) real and equal

11. If two tangents inclined at an angle of 60ᵒ are drawn to a circle of radius 3cm, then the length of each tangent is equal to

(a) 3√3 2 cm (b) 3cm (c) 6cm (d) 3√3cm

12. If 𝜃 = 30𝑜 then the value of 3tan𝜃 is

A)1 B) 1 √3 C ) 3 √3 (D) not defined

13. The point on the x- axis nearest to the point (-4,-5) is

A) (0, 0) B) (-4, 0) C ) (-5, 0) D) (√41, 0)

14. The sum of the length, breadth and height of a cuboid is 6√3cm and the length of its diagonal is 2√3cm. The total surface area of the cuboid is

(a) 48 cm2 (b) 72 cm2 (c) 96 cm2 (d) 108 cm2

15. Two dice are rolled simultaneously. What is the probability that 6 will come up at least once?

(a)1/6 (b) 7/36 (c) 11/36 (d) 13/36

16.

17. 

18. 

DIRECTION: In the question number 19 and 20, a statement of Assertion (A) is followed by a statement of Reason (R). Choose the correct option

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.

19. Assertion (A): HCF of any two consecutive even natural numbers is always 2. Reason (R): Even natural numbers are divisible by 2.

20. Assertion (A): If the radius of sector of a circle is reduced to its half and angle is doubled then the perimeter of the sector remains the same.

Section B

21. (A)Find the H.C.F and L.C.M of 480 and 720 using the Prime factorisation method.

OR

(A) The H.C.F of 85 and 238 is expressible in the form 85m -238. Find the value of m.

22. 

23. 

24. Find the point(s) on the x-axis which is at a distance of √41 units from the point (8, -5).

25. Show that the points A(-5,6), B(3, 0) and C( 9, 8) are the vertices of an isosceles triangle.

Section C

26. Given that √3 is irrational, prove that 5 + 2√3 is irrational.

27. The sum of two numbers is 18 and the sum of their reciprocals is 9/40. Find the numbers.

28. If the zeroes of the polynomial x2 +px +q are double in value to the zeroes of the polynomial 2x2 -5x -3, then find the values of p and q.

29. If cosθ + sinθ = 1 , then prove that cosθ - sinθ = ±1

30. Prove that √3 is an irrational number.

31. 

Section D

32. (A) Solve the following system of linear equations graphically: x+2y = 3, 2x-3y+8 = 0

OR

(B) Places A and B are 180 km apart on a highway. One car starts from A and another from B at the same time. If the car travels in the same direction at 5 A P R Q B D C O A B different speeds, they meet in 9 hours. If they travel towards each other with the same speeds as before, they meet in an hour. What are the speeds of the two

33. A boy whose eye level is 1.35 m from the ground, spots a balloon moving with the wind in a horizontal line at some height from the ground. The angle of elevation of the balloon from the eyes of the boy at an instant is 60𝑜 . After 12 seconds, the angle of elevation reduces to 30°. If the speed of the wind is 3m/s then find the height of the balloon from the ground. (Use √3= 1.73)

34. Prove that if a line is drawn parallel to one side of a triangle intersecting the other two sides in distinct points, then the other two sides are divided in the same ratio. Using the above theorem prove that a line through the point of intersection of the diagonals and parallel to the base of the trapezium divides the non parallel sides in the same ratio.

35. The median of the following data is 525. Find the values of x and y, if the total frequency is 100

Section E

36. Ms. Sheela visited a store near her house and found that the glass jars are arranged one above the other in a specific pattern. A B C P R Q On the top layer there are 3 jars. In the next layer there are 6 jars. In the 3rd layer from the top there are 9 jars and so on till the 8th layer. On the basis of the above situation answer the following questions.

i) Write an A.P whose terms represent the number of jars in different layers starting from top . Also, find the common difference.

(ii) Is it possible to arrange 34 jars in a layer if this pattern is continued? Justify your answer.

(iii) (A) If there are ‘n’ number of rows in a layer then find the expression for finding the total number of jars in terms of n. Hence find 𝑆8 .

OR

(iii) (B) The shopkeeper added 3 jars in each layer. How many jars are there in the 5th layer from the top?

37. Metallic silos are used by farmers for storing grains. Farmer Girdhar has decided to build a new metallic silo to store his harvested grains. It is in the shape of a cylinder mounted by a cone. Dimensions of the conical part of a silo is as follows:

Radius of base = 1.5 m

Height = 2 m

Dimensions of the cylindrical part of a silo is as follows:

Radius = 1.5 m

Height = 7 m

On the basis of the above information answer the following questions.

(i) Calculate the slant height of the conical part of one silo.

(ii) Find the curved surface area of the conical part of one silo.

(iii)(A) Find the cost of metal sheet used to make the curved cylindrical part of 1 silo at the rate of ₹2000 per 𝑚2

 OR

(iii) (B) Find the total capacity of one silo to store grains.

38. The school auditorium was to be constructed to accommodate at least 1500 people. The chairs are to be placed in concentric circular arrangement in such a way that each succeeding circular row has 10 seats more than the previous one.

(i) If the first circular row has 30 seats, how many seats will be there in the 10th row?

(ii) For 1500 seats in the auditorium, how many rows need to be there?

OR

If 1500 seats are to be arranged in the auditorium, how many seats are still left to be put after 10th row?

(iii) If there were 17 rows in the auditorium, how many seats will be there in the middle row?

Check CBSE Class 10 Maths Chapter-Wise MCQs

CBSE Class 10 Maths Half Yearly Sample Paper 2025: Answer Key

Section A
1.	D) -6,6 1 2.
2	B) -5 1 3.
3.	D) From a point inside a circle only two tangents can be drawn
4.	(d) 2
5.	(c) (2,-1)
6.	(d) 2:3
7.	(b) tan 30°
8.
9.	C) 140°
10.	A) Irrational and distinct
11.	(d) 3√3cm
12.	C) 3 √3
13.	B) (-4, 0)
14.	(c) 96 cm2
15.	(c) 11/36
16.	(b) 25
17.	B) isosceles and similar
18.	C) 30
19.	B) Both assertion (A) and reason (R) are true and reason (R) is not the correct explanation of assertion (A)
20.	D) Assertion (A) is false but reason (R) is true.
Section B
21.	480 = 2 5 x 3 x 5 720 = 2 4 x 3 2 x 5 LCM (480,720) = 2 5 x 3 2x 5 = 1440 HCF (480, 720) = 2 4 x 3x 5 = 240 OR 85 = 5x17, 238 = 2x7x17 HCF( 85, 238) = 17 17 = 85xm -238 m = 3
22.	In ΔABC, ∠1 = ∠2 ∴ AB = BD ………………………(i) Given, AD/AE = AC/BD Using equation (i), we get AD/AE = AC/AB ……………….(ii) In ΔBAE and ΔCAD, by equation (ii), AC/AB = AD/AE ∠A= ∠A (common) ∴ ΔBAE ~ ΔCAD [By SAS similarity criterion]
23.
24.	Let the required point be (x,0) √(8 − 𝑥) 2 + 25 = √41 => (8 − 𝑥) 2 = 16 => 8 - x =土4 => x = 4 , 12 Two points on the x-axis are (4,0) & (12,0).
25.
Section C
26.	Let us assume 5 + 2√3 is rational, then it must be in the form of p/q where p and q are co-prime integers and q ≠ 0 i.e 5 + 2√3 = p/q So √3 = 𝑝−5𝑞 2𝑞 ……………………(i) Since p, q, 5 and 2 are integers and q ≠ 0, HS of equation (i) is rational. But LHS of (i) is √3 which is irrational. This is not possible. This contradiction has arisen due to our wrong assumption that 5 + 2√3 is rational. So, 5 + 2√3 is irrational.
27.
28.
29.
30.
31.
Section D
32.	x+2y=3, 2x-3y+8=0 Correct graph of each equation Solution x=-1 and y=2 OR Let car I starts from A with speed x km/hr and car Il Starts from B with speed y km/hr (x>y) Case I- when cars are moving in the same direction. Distance covered by car I in 9 hours = 9x. Distance covered by car II in 9 hours = 9y Therefore 9 (x-y) = 180 => x-y= 20 ……………. (i) case II- when cars are moving in opposite directions. Distance covered by Car I in 1 hour = x Distance covered by Car II in 1 hour = y Therefore x + y=180 ………….. (ii) Solving (i) and (ii) we get, x=100 km/hr, y=80 km/hr.
33.
34.
35.
Section- E
36.
37.
38.

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Regular practice with the CBSE Class 10 Maths Half Yearly Sample Paper 2025 with Solutions is essential for achieving excellent scores in the upcoming mid-term examinations. These sample papers provide an invaluable opportunity to familiarize yourself with the syllabus, exam pattern, and question types. By diligently working through these problems and understanding their solutions, students can identify their strengths and weaknesses, allowing for targeted revision and improved performance. Utilize this resource to its fullest potential and approach your exams with confidence.

Also Check:

NCERT Book for Class 10 Maths ( Latest Edition)

NCERT Solutions for Class 10 Maths (Updated)