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

In Class 10 Half yearly Exams, most of the students are quite tense about their Mathematics exam, due to its complexity and vast syllabus. Most of the students are not able to complete the maths syllabus just before the mid-term exams. So we at Adda Education have provided CBSE Class 10 Maths Half Yearly Sample Paper 2025 with Solutions on this page. This Maths half question paper is designed on the basis of the latest exam pattern and includes all the frequently asked question types of the last five years. By practising these CBSE 10th Maths Mid-term Half-yearly Sample papers, you can familiarise yourself with the real exam pattern and understand the format, marking scheme, and several sorts of questions. Practice Class 10 Maths Half Yearly Sample Paper 2025 as much you can to get a decent score in the upcoming exam.

Class 10 Maths Half Yearly Sample Paper 2025

The CBSE Class 10 Maths Half Yearly Sample Paper 2025 serves as a revision guide, ensuring that students focus on important areas while honing their problem-solving skills. Practising these Sample question papers helps students understand the types of questions to expect, the weightage of different chapters, and how to manage their time successfully on the actual test. The CBSE Class 10 Maths Half Yearly Exam 2025-26 Question Paper with Detailed Solutions PDF is available here.

Get CBSE Class 10 Maths Half Yearly Question Paper with Solutions PDF

Class 10 Maths Half Yearly Question Paper 2025 Pattern

Before moving towards solving the question paper, let’s take a quick look at the general instructions that each and every students need to minutely follow.

• The Total marks of the CBSE Class 10 Maths Sample Paper is 80 Marks
• Candidates have prvided three houres or 180 minutes to write the exam.
• This question paper contains 38 questions. All Questions are compulsory.
• This Question Paper is divided into 5 Sections: A, B, C, D and E.
• In Section A, Question numbers 1-18 are multiple choice questions (MCQs) and questions no. 19 and 20 are Assertion-Reason based questions of 1 mark each.
• In Section B, Question numbers 21-25 are very short answer (VSA) type questions, carrying 02 marks each.
•  In Section C, Question numbers 26-31 are short answer (SA) type questions, carrying 03 marks each.
• In Section D, Question numbers 32-35 are long answer (LA) type questions, carrying 05 marks each.
• In Section E, Question numbers 36-38 are case study-based questions carrying 4 marks each with sub parts of the values of 1, 1 and 2 marks each respectively.
• There is no overall choice. However, an internal choice in 2 questions of Section B, 2 questions of Section C and 2 questions of Section D has been provided. An internal choice has been provided in all the 2 marks questions of Section E.
• Draw neat and clean figures wherever required. Take 𝜋 = 22/7 wherever required if not stated.
• Use of calculators is not allowed.

CBSE Class 10 Maths Half Yearly Sample Paper 2025 with Solutions

Q.1 Find the value of k for which the system of equations x + (k + 1)y = 5 and (k + 1)x + 9y = 8k − 1 has
infinitely many solutions (1 Mark)
(a) 2 (b) 3 (c) 4 (d) 5

Ans. (a) 2

Q.2 The quadratic equation x² + 5x − 2 = 0 has                       (1 Mark)

(a) two distinct real roots
(b) two equal real roots
(c) no real roots
(d) more than 2 real roots
Ans. (a) two distinct real roots

Q.3 ΔABC~ΔPQR. If AM and PN are altitudes of ΔABC and ΔPQR, respectively, and AB² : PQ² = 25: 36, then
AM: PN =  (1 Mark)
(a) 2:5 (b) 5:6 (c) 25:36 (d) 2:3

Ans. (b) 5:6

Q.4 The quadratic polynomial, the sum of whose zeroes is -5 and product is 6, is, (1 Mark)
(a) x² + 5x + 6
(b) x² − 5x + 6
(c) x²− 5x − 6
(d) −x² + 5x + 6

Ans. (a) x² + 5x + 6

Q.5 ΔPQR is shown below. ST is drawn such that ∠PRQ = ∠STQ (1 Mark)

If ST is divided QR in a ratio of 2: 3, then what is the length of ST?
(a) 10/3cm
(b) 8 cm
(c) 12 cm
(d) 40

Ans. (b) 8 cm

Q.6 P, (5,1), Q (1,4) and R (8,5) are the coordinates of the vertices of a triangle. Which of the following types of triangles will ΔPQR be (1 Mark)

(a) equilateral triangle (b) Scalene (c) Isosceles (d) None
Ans. (c) Isosceles

Q.7 If – 2 and 3 are the zeroes of the quadratic polynomial x

2 + (p + 1)x + q, then p and q are… respectively
(a) -7,3 (b) -6, -2 (c) 2,6 (d) -2,-6 (1 Mark)
Ans. (d) -2,-6

Q.8 A point (x y) is at a distance of 7 units from the origin. How many such points lie in the third quadrant?
(a) 0 (b) 1 (c) 2 (d) Infinitely many (1 Mark)
Ans. (d) Infinitely many

Q.9 The value of k for which the system of equation x + y − 4 = 0 and 2x + ky = 3 has no. solution is
(a) -2 (b) ≠2 (c) 3 (d) 2 (1 Mark)
Ans   (d) 2

Q.10 The 11th term of an AP ; −5, −5, … .. (1 Mark)
(a) -20 (b) 30 (c) 20 (d) -30
Ans  (c) 20

Q.11 If g − 1, g + 3 and 3g − 1 are in A.P, then find the value of g. (1 Mark)
(a) 3 (b) 4 (c) 5 (d) 7
Ans. (b) 4

Q.12 Which of the following is equal to the given expression? (1 Mark)
(cotθ sec2 θ) / cosec θ =?
(a) sec θ
(b) cosec θ
(c) cot2 θ sec θ
(d) cot2 θ cosec θ
Ans. (a) sec θ

Q.13 If the n th term of an AP is given by an = 5n − 3, then the sum of the first 10 term is (1 Mark)
(a) 225
(b) 245
(c) 255
(d) 270
Ans.  (b) 245
Q.14 Find the 11th term from the end of the given progression 10 , 7, 4….. -62. (1 Mark)
(a) -32 (b) -16 (c) -25 (d) 0
Ans.  (a) -32

Q.15 Shown below is a solved trigonometric problem. (1 Mark)

In which step is there an error in solving?
(a) Step 1 (b) Step 2 (c) Step 3 (d) There is no error
Ans. (a) Step 1

Q.16 In triangles ABC and DEF, ∠B, ∠E, ∠F = ∠C, and AB = 3DE. Then the two triangles are. (1 Mark)
(a) congruent but not similar. (b) similar but not congruent
(c) neither congruent nor similar (d) congruent as well as similar
Ans. (b) similar but not congruent

Q.17 What is the HCF of the least prime number and the least composite number (1 Mark)
(a) 1 (b) 2 (c) 3 (d) 4
Ans. (b) 2

Q.18 √n is a natural number such that n > 1. Which of these can definitely be expressed as a product of
primes? (1 Mark)
(i) √n (ii) n (iii) √n

(a) only (i) (b) only (i) and (ii) (c) all (i), (ii) and (iii) (d) None of these
Ans.  (c) all (i), (ii) and (iii)

DIRECTIONS: 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
(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.

Q.19 Statement A (Assertion): HCF of 26 and 91 is 13 and the LCM is 182. (1 Mark)
Statement R (Reasons) As HCF (a, b) X (a x b) = LCM (a, b)
Ans. (C) Assertion (A) is true, but reason (R) is false.

Q.20 Assertion (A): The mid-point of a line segment divides it in ratio 1: 1. (1 Mark)
Reason (R): Three points are collinear if they lie on the same straight line.
Ans. (B) Both assertion (A) and reason (R) are true and reason (R) is not the correct explanation of assertion (A)

Q.21 Solve for x and y 71𝑥 + 37𝑦 = 253 (2 Marks)
37𝑥 + 71𝑦 = 287

Ans.

Q.22 A line intersects the y-axis and x-axis at the points P and Q respectively. If (2, -5) is the mid-point of PQ then find the coordinates of P and Q. (2 Marks)
Ans.

Q.23 Using the fundamental theorem of Arithmetic, final HCF and LCM of 6, 72 and 120. (2 Marks)
Ans.

Q.24 Find the ratio in which the point (-3, p) divides the line segment joining the point (-5, -4) and (-2, -3).
Also find the value of p. (2 Marks)
Ans.24

Q.25 Find a quadratic polynomial whose zeros are (3 + √3) and (3 − √3) (2 Marks)

Last-Minute Tips for Class 10 Maths Half Yearly Exam

As the Class 10 Maths Half Yearly Exam approaches, smart revision is the key to success. Start by revising all important formulas and theorems, as they form the base of most questions. Make a separate sheet for quick formula reference and go through it regularly. Next, practice sample papers and previous year papers, as they help you understand the question pattern, marking scheme, and improve your problem-solving speed. This will also make you more confident during the actual exam. Pay attention to time management while solving these papers—set a timer and try to finish within the allotted time. Identify weak areas and revise them quickly instead of picking new topics at the last moment. Also, focus on chapters carrying higher weightage and ensure your steps are clearly written, as marks are awarded for proper working. Lastly, keep your mind calm, avoid stress, and sleep well before the exam day. A clear mind combined with smart revision and practice can help you score well and perform with confidence.

The key to success as the Class 10 Maths Half Yearly Exam approaches is effective revision. Below, we have shared some last-minute Tips for the Class 10 Maths Half-Yearly Exam

• Begin by reviewing all of the essential formulas and theorems, as most questions are based on them. Create a separate document for simple formula reference and review it on a regular basis.
• Next, review previous years’ papers and practice sample papers to improve your problem-solving abilities and obtain a better understanding of the grading scheme and question format. This will also enhance your confidence in the actual test.
• When working on these assignments, be conscious of time management; set a timer and try to complete them within the allotted time.
• Instead of choosing new topics from the syllabus at the last minute, evaluate your weaknesses and make immediate changes.
• Focus on chapters with a larger weightage and ensure your steps are properly defined, as scores are rewarded for proper work. Finally, relax your thoughts, prevent stress, and get plenty of sleep before the exam.
• A clear mind, paired with effective revision and practice, can help you score high and perform confidently.

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