CBSE Class 12 · Mathematics · board exam 2027 · pre-board season

CBSE Class 12 Maths important questions 2027, chapter-wise

130 original questions across all 13 chapters, in the five question types of the board paper, each with a step-marked worked answer. Below they are grouped by unit and ordered by the CBSE unit weightage, so you revise Calculus (35 marks) and Vectors and Three-Dimensional Geometry (14 marks) first. Then sit a full sample paper written to the same blueprint.

130 questions, 13 chapters
Ordered by the 80-mark weightage
65 worked answers open; the rest with a free account

Start with the heaviest unit Sit a full sample paper Start the free 7-day trial

Important questions, not leaked questions

Nobody outside CBSE knows the 2027 paper. These questions are written by CBSE Math Revision, not taken from NCERT, NCERT Exemplar or CBSE papers, and every answer was re-solved independently. Our prediction is only the weighting: the units that carry the most marks come first. Always sit CBSE's own 2026-27 sample question paper too, linked from our Class 12 question papers page.

Chapter-wise important questions, by unit weightage

Units in order of their marks in the 80-mark theory paper (the other 20 marks are internal assessment). Across the 13 chapters: 26 1-mark MCQ, 13 assertion–reason, 26 2-mark short answer, 26 3-mark short answer, 26 5-mark long answer, 13 4-mark case study questions.

Calculus · 35 of 80 marks

Chapter 5: Continuity and Differentiability 10 questions on Continuity; Differentiability and derivatives; Implicit and parametric differentiation; Logarithmic differentiation; Second-order derivatives.
Chapter 6: Application of Derivatives 10 questions on Increasing and decreasing functions; Rate of change; Maxima and minima; Optimisation problems.
Chapter 7: Integrals 10 questions on Integration by substitution; Definite integrals and their properties; Integration by parts; Partial fractions.
Chapter 8: Application of Integrals 10 questions on Area under lines and parabolas; Area of circles and ellipses; Area with the y-axis.
Chapter 9: Differential Equations 10 questions on Order and degree; Linear differential equations; Variables separable; Homogeneous equations.

Vectors and Three-Dimensional Geometry · 14 of 80 marks

Chapter 10: Vector Algebra 10 questions on Scalar (dot) product; Vectors, magnitude and direction; Vector (cross) product.
Chapter 11: Three Dimensional Geometry 10 questions on Direction cosines and ratios; Angle between two lines; Equation of a line; Shortest distance between lines.

Algebra · 10 of 80 marks

Chapter 3: Matrices 10 questions on Order and types of matrices; Transpose, symmetric and skew-symmetric matrices; Operations on matrices; Invertible matrices.
Chapter 4: Determinants 10 questions on Evaluating determinants; Adjoint and inverse; Area of a triangle; Solving linear systems.

Relations and Functions · 8 of 80 marks

Chapter 1: Relations and Functions 10 questions on Types of relations; One-one and onto functions; Equivalence relations.
Chapter 2: Inverse Trigonometric Functions 10 questions on Principal values; Domain and range; Evaluating expressions.

Probability · 8 of 80 marks

Chapter 13: Probability 10 questions on Independent events and multiplication theorem; Conditional probability; Random variables and their mean; Total probability and Bayes' theorem.

Linear Programming · 5 of 80 marks

Chapter 12: Linear Programming 10 questions on Graphical solution; Feasible region and corner points; Formulating LPPs.

Try one from each unit

One short-answer question from each unit, with its worked answer. Try it first, then open the answer and check every step mark.

Ch 5·3 marks·Short answerContinuity and Differentiability: Implicit and parametric differentiation

If $x = 2 t^{2}$ and $y = t^{3}$ , find $\frac{d y}{d x}$ and $\frac{d^{2} y}{d x^{2}}$ in terms of $t$ , and their values at $t = 2$ .

Show worked answer

Answer:

\frac{3 t}{4}

\frac{3}{16 t}

;

\frac{3}{2}

and

\frac{3}{32}

$\frac{d x}{d t} = 4 t$ , $\frac{d y}{d t} = 3 t^{2}$ , so $\frac{d y}{d x} = \frac{3 t}{4}$ ( $= \frac{3}{2}$ at $t = 2$ ) M1
$\begin{aligned} \frac{d^{2} y}{d x^{2}} & = \frac{d}{d t} (\frac{3 t}{4}) \div \frac{d x}{d t} \\ = \frac{3}{4} \times \frac{1}{4 t} \\ = \frac{3}{16 t} \end{aligned}$ A1
At $t = 2$ : $\frac{3}{32}$ A1

Ch 10·3 marks·Short answerVector Algebra: Scalar (dot) product

Find the projection of $\vec{a} = 3 \hat{i} - \hat{j} + 4 \hat{k}$ on $\vec{b} = \hat{i} + 2 \hat{j} + 2 \hat{k}$ .

Show worked answer

Answer:

3

$\vec{a} \cdot \vec{b} = 3 - 2 + 8 = 9$ M1
$| \vec{b} | = \sqrt{1 + 4 + 4} = 3$ A1
Projection $= \frac{\vec{a} \cdot \vec{b}}{| \vec{b} |} = 3$ A1

Ch 3·3 marks·Short answerMatrices: Transpose, symmetric and skew-symmetric matrices

Write $A = [\begin{matrix} 6 & - 2 \\ 8 & 1 \end{matrix}]$ as $P + Q$ , where $P$ is symmetric and $Q$ is skew-symmetric.

Show worked answer

Answer:

[\begin{matrix} 6 & 3 \\ 3 & 1 \end{matrix}] + [\begin{matrix} 0 & - 5 \\ 5 & 0 \end{matrix}]

$\begin{aligned} P & = \frac{1}{2} (A + A^{'}) \\ = \frac{1}{2} [\begin{array}{c} 12 & 6 \\ 6 & 2 \end{array}] \\ = [\begin{array}{c} 6 & 3 \\ 3 & 1 \end{array}] \end{aligned}$ , and $P^{'} = P$ A1
$\begin{aligned} Q & = \frac{1}{2} (A - A^{'}) \\ = \frac{1}{2} [\begin{array}{c} 0 & - 10 \\ 10 & 0 \end{array}] \\ = [\begin{array}{c} 0 & - 5 \\ 5 & 0 \end{array}] \end{aligned}$ , and $Q^{'} = - Q$ A1
$\begin{aligned} P + Q & = [\begin{array}{c} 6 & - 2 \\ 8 & 1 \end{array}] \\ = A \end{aligned}$ A1

Ch 1·3 marks·Short answerRelations and Functions: Types of relations

On $A = {1, 2, 3, \dots, 10}$ , $R = {(a, b) : a + b = 11}$ . Determine whether $R$ is reflexive, symmetric and transitive.

Show worked answer

Answer: Symmetric only

Not reflexive: $(a, a) \in R$ needs $2 a = 11$ , which no $a \in A$ satisfies (e.g. $(1, 1) \notin R$ ) A1
Symmetric: $a + b = 11 \Rightarrow b + a = 11$ A1
Not transitive: $(1, 10) \in R$ and $(10, 1) \in R$ , but $(1, 1) \notin R$ A1

Ch 13·3 marks·Short answerProbability: Random variables and their mean

A fair coin is tossed twice and $X$ is the number of tails. Find the probability distribution of $X$ and its mean.

Show worked answer

Answer:

\frac{1}{4}, \frac{1}{2}, \frac{1}{4}

; mean

1

$X$ takes the values $0, 1, 2$ M1
$P (X = 0) = \frac{1}{4}$ , $P (X = 1) = \frac{1}{2}$ , $P (X = 2) = \frac{1}{4}$ A1
Mean $= 0 \times \frac{1}{4} + 1 \times \frac{1}{2} + 2 \times \frac{1}{4} = 1$ A1

Ch 12·3 marks·Short answerLinear Programming: Graphical solution

Use the corner-point method to find the maximum of $Z = 5 x + 3 y$ , given $x + 2 y \leq 10$ , $3 x + y \leq 15$ and $x, y \geq 0$ .

Graph of the lines x + 2y = 10 and 3x + y = 15 in the first quadrant, with the feasible region below both lines shaded. — Feasible region for x + 2y ≤ 10, 3x + y ≤ 15

Show worked answer

Answer:

29

(4, 3)

Corner points: $(0, 0)$ , $(5, 0)$ , $(0, 5)$ and the intersection of $x + 2 y = 10$ and $3 x + y = 15$ , which is $(4, 3)$ M1
$Z$ : $0$ , $25$ , $15$ , $20 + 9 = 29$ A1
Maximum $Z = 29$ at $x = 4$ , $y = 3$ A1

Final 6 Weeks: your final prediction set

Dates confirmed when CBSE publishes

A free six-week plan counted back from your first paper, ending with a final set of timed papers. Each paper opens only once it is checked.

Start the free plan

Then sit a full paper

The honest "predicted paper". Our Class 12 sample papers follow the 2026-27 blueprint exactly: 80 marks, 38 questions, sections A to E, each unit at its weightage, with a 3-hour timer and a step-marking scheme.
Pre-boards coming up? The Class 12 pre-board revision plan sets the days out for you, and the free four-week pre-board plan counts back from the day your pre-boards start.
Section A drill. MCQ and case study questions and assertion–reason questions for every chapter.
No formula sheet in the exam. Learn them first from the Class 12 formula sheet (free PDF).

Questions

Are these the questions that will come in the CBSE Class 12 Maths board exam 2027?

No. Nobody outside CBSE knows the 2027 questions, and we do not claim to. These are original questions written by CBSE Math Revision in the board paper's question types. What we can do honestly is weight your revision: the board's unit weightage says where the 80 marks are, so the chapters here are ordered by it.

How were the important questions chosen?

Each chapter has 10 questions covering its main topics in the five question types of the board paper, from 1-mark MCQs and assertion–reason to 5-mark long answers and a 4-mark case study. On this page the chapters are grouped by unit and the units are ordered by their marks out of 80, heaviest first, so you know where to start.

Are they free?

Yes. 65 of the 130 worked answers are open on the chapter pages to everyone. The other 65 open with a free account (no card).

Is there a predicted paper for CBSE Class 12 Maths 2027?

Not a leaked or official one: any site that says it has the real paper is guessing. Our sample papers are the honest version: full 80-mark papers written to the 2026-27 blueprint, with each unit at its exact weightage, a 3-hour timer and a step-marking scheme.

When is the CBSE Class 12 Maths board exam in 2027?

CBSE has not published the 2027 date sheet yet. For reference, in 2026 Class 12 Mathematics was on Monday 9 March 2026. Our exam dates page adds the 2027 date once CBSE publishes it.

How should I use them in pre-board season?

Start with the heaviest units, do a chapter's 10 questions in one sitting, mark them against the worked answers and redo what you dropped two days later. Then sit a full sample paper against the 3-hour timer. If your school's pre-boards are in December or January, the pre-board revision plan sets this out day by day.

Free account, no card: 5 more practice questions on every chapter with instant feedback, full worked answers on free questions, and marking schemes for our sample papers. Join free

Original questions and worked answers written by CBSE Math Revision; not taken from NCERT, NCERT Exemplar or CBSE papers. CBSE Math Revision is independent and not affiliated with CBSE or NCERT.