CBSE Class 12 students preparing for the 2025–26 board exams can now strengthen their Mathematics revision with the CBSE Class 12 Maths Pre Board Sample Paper 2025–26, available here for free PDF download. This specially curated sample paper has been designed to help students understand the latest exam pattern, marking scheme, and question trends expected in the upcoming pre-board and board examinations. The Maths pre board sample paper is provided along with detailed solutions, enabling students to analyse their performance and improve problem-solving accuracy. Prepared by experienced subject matter experts, the questions are carefully selected from previous year important questions, frequently repeated questions, and high-weightage topics, making it an ideal practice resource for effective exam preparation and last-minute revision.
CBSE Class 12 Maths: Chapter-Wise Exam Pattern & Marking Scheme
The CBSE Class 12 Mathematics exam is divided into an 80-mark theory paper and a 20-mark internal assessment. The chapter-wise exam pattern and marking scheme for Mathematics are detailed below.
| No. | Units | Marks |
| 1. | Relations & Functions | 08 |
| 2. | Algebra | 10 |
| 3. | Calculus | 35 |
| 4. | Vectors and Three - Dimensional Geometry | 14 |
| 5. | Linear Programming | 05 |
| 6. | Probability | 08 |
| Total |
| 80 |
|
| Internal Assessment
| 20 10 10 |
| Grand Total |
| 100 |
CBSE Class 12 Maths Syllabus 2025-26 |
CBSE Class 12 Maths Pre-Board Sample Paper 2026
General Instructions: -
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This Question Paper contains five sections - A, B, C, D and E. Each section is compulsory. However, there are internal choices in some questions.
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Section A has 18 MCQs and 2 Assertion –Reason based questions of 1 mark each.
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Section B has 5 Very Short Answer (VSA) type questions of 2 marks each.
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Section C has 6 Short Answer type questions of 3 marks each.
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Section D has 4 Long Answer type questions of 5 marks each.
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Section E has 3 source based /case based/passage based/integrated units of assessment (4 marks each) with sub parts.
SECTION A: Multiple Choice Questions, Each question carries 1 mark
4. If y=cos x -sin x /cos x +sin x , then dy/dx is :
A. -sec24-x
B. sec24-x
C. ln sec 4-x
D. -ln sec 4-x
7. If PA∩B=1/8 and PA'=3/4, then P(B/A) is equal to :
A. 12
B. 13
C. 16
D. 23
8. If α, β and γ are the angles which a line makes with positive directions of x, y and z axes respectively, then which of the following is not true?
A. cos2α+cos2β+cos2γ=1
B. sin2α+sin2β+sin2γ=2
C. cos 2α +cos 2β +cos 2γ =-1
D. cos +cos +cos =1
9. If A and B are independent events, then which of the following is not true?
A. A' and B are independent events.
B. A and B'are independent events.
C. A' and B'are independent events.
D. None of these
10. The restrictions imposed on decision variables involved in an objective function of a linear programming problem are called :
A. Feasible solutions
B. Constraints
C. Optimal solutions
D. Infeasible solutions
11. Consider the non-empty set consisting of members in a family and a relation R defined as aRb if a is wife of b. Then R is:
(a) Symmetric but not transitive
(b) transitive but not symmetric
(c) Neither symmetric nor transitive
(d) both symmetric and transitive
12. If A and B are non-singular matrices of same order with 𝒅𝒆𝒕(𝑨)=𝟓, then 𝒅𝒆𝒕(𝑩−𝟏𝑨𝑩)𝟐is equal to
(a)5
(b) 25
(c) 125
(d) 625
13. If 𝑓(𝑥)=𝑥tan−1𝑥, then 𝑓′ (1) is equal to
(a) 𝜋/ 4 – 1/ 2
(b) 𝜋/ 4 + 1/ 2
(c)− 𝜋/ 4 – 1/ 2
(d) −𝜋 /4 + 1/ 2
14. Assume that in a family, each child is equally likely to be a boy or a girl. A family with two children is chosen at random. The probability that the eldest child is a girl given that the family has at least one girl is
(a) 12
(b) 13
(c) 23
(d) 47
15. What is the domain of the function fx=2x-3
(a) -1,1
(b) (1,2)
(c) (-1,1)
(d) 1,2
16. The value of c in Rolle’s theorem for the function, f(x) = sin 2x in [0, π/2] is
A. π/4
B. π/6
C. π/2
D. π/3
17. If x sin(a+y) = sin y, then dy/dx is equal to
A. [sin2(a+y)]/sin a
B. sin a /[sin2(a+y)]
C. [sin(a+y)]/sin a
D. sin a /[sin(a+y)]
18. The solution of the differential equation 𝑥𝑑𝑥+𝑦𝑑𝑦=0 represents a family of
(a) straight lines
(b) parabolas
(c) Circles
(d) Ellipses
Question number 19 and 20 are Assertion and Reason based questions. Two statements are given, one labelled Assertion (A) and the other labelled Reason (R). Select the correct answers from the codes A, B C and D as given below.
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Both A and R are true and R is the correct explanation of A.
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Both A and R are true but R is not the correct explanation of A.
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A is true and R is false.
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A is false and R is true.
19. Assertion (A): Consider the function defined as (𝑥)= |𝑥|+ |𝑥−1|, 𝑥∈𝑅. Then f (x ) is not differentiable at 0 and 1 .
Reason (R): Suppose f be defined and continuous on (a, b) ,and c∈ (a, b) ,then f(x ) is not differentiable at 𝑥=𝑐 if [f(c+h)-f(c)]/ h ≠[f(c+h)-f(c)]/ h
20. Assertion(A): Given two non-zero vectors a and b. If 𝑟⃗ is another non-zero vector in the plane in which a and b lie such that 𝑟⃗. (𝑎⃗ 𝑏 ⃗) = 0. Then 𝑟⃗ is perpendicular to 𝑎⃗ × 𝑏 ⃗.
Reason (R): The vector (𝑎⃗ 𝑏 ⃗) is perpendicular to the plane of 𝑎⃗ and 𝑏 ⃗.
SECTION B: This section comprises very short answer type questions of 2 marks each.
23. There are two coins. One of them is a biased coin such that P (head): P (tail) is 1:3 and the other coin is a fair coin. A coin is selected at random and tossed once. find the probability of getting ahead.
OR
If x=a tan3θ and y=a sec3, then find dy/dx .
25. The two vectors 𝑖̂+𝑗̂+𝑘 ̂ and 3𝑖̂−𝑗̂+3𝑘 ̂ represent the two sides 𝑂𝐴 and 𝑂𝐵, respectively of a ∆𝑂𝐴𝐵, where 𝑂 is the origin. The point 𝑃 lies on 𝐴𝐵 such that O𝑃 is a median. Find the area of the parallelogram formed by the two adjacent sides as 𝑂𝐴 and 𝑂𝑃.
CBSE 12th Maths Sample Papers Solutions
SECTION A
| Sl.No. | Answers |
| 1. | D |
| 2. | C |
| 3. | B |
| 4. | A |
| 5. | D |
| 6. | C |
| 7. | A |
| 8. | D |
| 9. | D |
| 10. | B |
| 11. | B |
| 12. | B |
| 13. | B |
| 14. | C |
| 15. | D |
| 16. | A |
| 17. | A |
| 18. | C |
| 19. | A |
| 20. | B |
CBSE Class 12 Maths Pre-Board 2025-26 Sample Paper with Solutions: Download PDF |
CBSE Class 12 Mathematics 2025-26: QUESTION PAPER DESIGN
Check the below to get an idea of how the CBSE Class 12 Mathematics Question Paper will be designed for the academic year 2025-26
| Sl. No | Typology of Questions | Total Marks | Percentage Weightage |
| 1. | Remembering: Exhibit memory of previously learned material by recalling facts, terms, basic concepts, and answers. Understanding: Demonstrate understanding of facts and ideas by organizing, comparing, translating, interpreting, giving descriptions, and stating main ideas | 44 | 55 |
| 2. | Applying: Solve problems to new situations by applying acquired knowledge, facts, techniques and rules in a different way. | 20 | 25 |
| 3. | Analysing: Examine and break information into parts by identifying motives or causes. Make inferences and find evidence to support generalizations Evaluating: Present and defend opinions by making judgments about information, validity of ideas, or quality of work based on a set of criteria. Creating: Compile information together in a different way by combining elements in a new pattern or proposing alternative solutions | 16 | 20 |
| Total |
| 80 | 100 |
Mastering CBSE Class 12 Maths requires consistent practice and understanding the exam format. This Pre-Board Sample Paper (2025-26) with solutions offers a realistic simulation to identify weak areas, refine time management, and build confidence for the board exam. Treat the provided PDF as your final rehearsal. Meticulously analyze the solutions to understand concept application. Consistent practice with authentic material like this is the most effective path to an exceptional Class 12 Board score. Download the PDF to solidify your success preparation.
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