CBSE Class 12 Maths Half Yearly Sample Paper 2025 with Solutions

The CBSE Half-yearly exams are around the corner, and all the students are now starting their preparation with great focus. In the Intermediate, class 12 Maths is considered one of the most challenging due to its vast syllabus. To help students, we have shared the CBSE Class 12th Maths Half Yearly Sample Question Paper 2025 with Solutions on this page.

CBSE Class 12 Maths Half Yearly Sample Paper 2025

The Half Yearly Exam in Class 12 Mathematics serves as a checkpoint to help you prepare for the Final Board Exam. The CBSE Class 12 Maths Half Yearly Sample Question Paper is an important resource in this preparation.

The Sample paper is based on the most recent CBSE exam pattern and marking scheme, which helps students learn how Very Short, Short, and Long Answer Questions are distributed throughout different sections.

Apart from these, students may refer to the CBSE Class 12th Maths official Sample paper and previous year questions as a practice resource to polish their concepts.

Class 12 Maths Half yearly Sample Paper Pattern

Despite the fact that the class 12th half-yearly math paper does not cover the whole 12th maths syllabus, the pattern of the paper will be the same as the official one. Before moving to the mathematics question paper, let’s take a look at the Class 12th Maths Sample paper pattern given below.

1. This Maths 12th Mid Term paper contains 38 questions. All questions are compulsory.
2. This Question paper is divided into five Sections – A, B, C, D and E.
3. In Section A, Questions no. 1 to 18 are multiple choice questions (MCQs) with only one correct option and Questions no. 19 and 20 are Assertion-Reason based questions of 1 mark each.
4. In Section B, Questions no. 21 to 25 are Very Short Answer (VSA)-type questions, carrying 2 marks each.
5. In Section C, Questions no. 26 to 31 are Short Answer (SA)-type questions, carrying 3 marks each.
6. In Section D, Questions no. 32 to 35 are Long Answer (LA)-type questions, carrying 5 marks each.
7. In Section E, Questions no. 36 to 38 are Case study-based questions, carrying 4 marks each.
8. There is no overall choice. However, an internal choice has been provided in 2 questions in Section B, 3 questions in Section C, 2 questions in Section D and one subpart each in 2 questions of Section E.

Class 12 Maths Half yearly Sample Paper 2025-26

Check some of the sample questions for the CBSE class 12 mathematics subject below.

Q) If |𝑎⃗| = 3, |𝑏⃗⃗| = 4 and |𝑎⃗ + 𝑏⃗⃗| =5, then |𝑎⃗ − 𝑏⃗⃗| =

(A) 3      (B) 4      (C) 5      (D) 8

Q) The value of 𝛼 if the angle between 𝑝⃗ = 2𝛼²𝑖̂− 3𝛼𝑗̂+ 𝑘̂ and 𝑞⃗ = 𝑖̂+ 𝑗̂+ 𝛼𝑘̂ is obtuse, is

(A) 𝑅 − [0, 1]     (B) (0, 1)     (C) [0, ∞)      (D) [1, ∞)

Q) A student observes an open-air Honeybee nest on the branch of a tree, whose plane figure is parabolic
shape given by x² = 4y. Then the area (in sq units) of the region bounded by parabola x² = 4y and the line y = 4 is
(A) 32/3     (B) 64/3     (C) 128/3     (D) 256/3

Q) If vectors 𝑎⃗ = 2ı̂+ 2ȷ̂+ 3k̂, 𝑏⃗⃗ = − ı̂+ 2ȷ̂+ k̂ and 𝑐⃗ = 3ı̂+ ȷ̂are such that 𝑏⃗⃗ + λ𝑐⃗ is perpendicular to 𝑎⃗ , then find the value of λ.

Q) A person standing at O (0, 0, 0) is watching an aeroplane which is at the coordinate point A (4, 0, 3). At the same time he saw a bird at the coordinate point B (0, 0, 1). Find the angles which 𝐵𝐴⃗ makes with the x, y and z axes.

Q) The two co-initial adjacent sides of a parallelogram are 2ı̂− 4ȷ̂− 5k̂ and 2ı̂+ 2ȷ̂+ 3k̂. Find its diagonals and use them to find the area of the parallelogram.

Q) A kite is flying at a height of 3 metres and 5 metres of string is out. If the kite is moving away horizontally at the rate of 200 cm/s, find the rate at which the string is being released

Q) Consider the following Linear Programming Problem:

Minimise Z = x + 2y
Subject to 2x + y ≥ 3, x + 2y ≥ 6, x, y ≥ 0
Show graphically that the minimum of Z occurs at more than two points

Q) The probability that it rains today is 0.4. If it rains today, the probability that it will rain tomorrow is 0.8. If it does not rain today, the probability that it will rain tomorrow is 0.7. If
𝑃1: denotes the probability that it does not rain today.
𝑃2: denotes the probability that it will not rain tomorrow, if it rains today.
𝑃3: denotes the probability that it will rain tomorrow, if it does not rain today.
𝑃4: denotes the probability that it will not rain tomorrow, if it does not rain today.

(i) Find the value of 𝑃1 x 𝑃4 – 𝑃2 x 𝑃3

(ii) Calculate the probability of raining tomorrow.

Q) . Ramesh, the owner of a sweet selling shop, purchased some rectangular card board sheets of dimension 25 by 40 cm to make container packets without top. Let x cm be the length of the side of the square to be cut out from each corner to give that sheet the shape of the container by folding up the flaps.
Based on the above information answer the following questions

(i) Express the volume (V) of each container as function of x only.

(ii) Find dv/dx

(iii) For what value of x, the volume of each container is maximum?

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