Which chapters are most important for Class 12 Maths?

Calculus: 35 of the 80 marks in CBSE's 2026-27 course structure. It covers Continuity and Differentiability, Applications of Derivatives, Integrals, Applications of Integrals and Differential Equations. Then come Vectors and 3D Geometry (14 marks), Algebra, meaning matrices and determinants (10), Relations and Functions (8), Probability (8) and Linear Programming (5).

How do I score full marks in Class 12 Maths?

Three habits: (1) show every step, because CBSE's marking schemes award marks for correct steps; (2) solve every NCERT example and exercise, including the miscellaneous exercises; (3) solve sample papers under timed conditions. Linear Programming and Probability are the most predictable chapters, so don't drop marks there.

Is NCERT enough for Class 12 Maths boards?

For most students, yes. Board questions closely follow the NCERT examples and exercises. Finish NCERT fully, then use NCERT Exemplar and CBSE's sample papers for extra practice. Reference books are optional.

How many marks are from Calculus?

35 of the 80 marks. CBSE gives marks only by unit and says there is no chapter-wise weightage within a unit, so prepare every Calculus chapter rather than betting on one.

Class 12 Maths Important Questions 2027

CBSE Class 12 Maths is 80 marks of theory and 20 of internal assessment. Calculus alone is 35 of the 80 marks. Below are important questions from every chapter, all within the CBSE 2026-27 syllabus; topics CBSE has dropped are listed at the end so you don't waste time on them.

Relations and Functions; Inverse Trigonometric Functions (8 marks)

Question	Type
Show that the relation R on A = {1, 2, 3, 4, 5} given by R = {(a, b) : \|a − b\| is even} is an equivalence relation.	Long answer
Show that f: ℝ → ℝ, f(x) = 3 − 4x, is one-one and onto.	Short answer
Check whether the relation R on ℝ given by R = {(a, b) : a ≤ b²} is reflexive, symmetric or transitive.	Short answer
Find the principal value of cos⁻¹(cos 7π/6).	Very short
Find the domain of sin⁻¹(2x − 1) and draw the graph of y = sin⁻¹x on its principal branch.	Short answer

Matrices and Determinants (10 marks)

Question	Type
Using matrices, solve 2x + 3y + 3z = 5, x − 2y + z = −4, 3x − y − 2z = 3.	Long answer
Find the inverse of a given 3 × 3 matrix using the adjoint, and verify that AA⁻¹ = I.	Long answer
If A is a square matrix with A² = A, show that (I + A)³ = 7A + I.	Short answer
Express a given square matrix as the sum of a symmetric and a skew-symmetric matrix.	Short answer
Find k if the area of the triangle with vertices (2, −6), (5, 4) and (k, 4) is 35 square units.	Short answer

Continuity and Differentiability

Question	Type
Find a and b so that f is continuous: f(x) = 5 for x ≤ 2, ax + b for 2 < x < 10, 21 for x ≥ 10.	Short answer
If y = (sin⁻¹x)², prove that (1 − x²)y₂ − xy₁ − 2 = 0.	Long answer
Differentiate xˣ + (sin x)^(log x) with respect to x.	Short answer
If x = a(cos t + t sin t) and y = a(sin t − t cos t), find d²y/dx².	Long answer

Applications of Derivatives

Question	Type
Find the intervals in which f(x) = 2x³ − 3x² − 36x + 7 is strictly increasing and strictly decreasing.	Short answer
Find the maximum and minimum values of f(x) = sin x + cos x on [0, π].	Short answer
Show that the semi-vertical angle of a cone of maximum volume and given slant height is tan⁻¹√2.	Long answer
A 5 m ladder leans against a wall. Its foot slides away at 2 cm/s. How fast is the top sliding down when the foot is 4 m from the wall?	Short answer

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Integrals

Question	Type
Evaluate ∫ dx / (x² + 4x + 13).	Short answer
Evaluate ∫ x² / [(x² + 1)(x² + 4)] dx using partial fractions.	Long answer
Evaluate ∫ eˣ (sin x + cos x) dx.	Short answer
Evaluate ∫₀^π x sin x / (1 + cos²x) dx using properties of definite integrals.	Long answer
Evaluate ∫ x tan⁻¹x dx using integration by parts.	Short answer
Evaluate ∫ (2x + 3) / √(x² + 4x + 1) dx.	Short answer

Applications of Integrals

Question	Type
Find the area of the region bounded by y = x², the x-axis and the lines x = 1 and x = 2.	Short answer
Find the area of the region bounded by the parabola y² = 4x and the line x = 3.	Long answer
Find the area of the circle x² + y² = a² by integration.	Long answer
Find the area enclosed by the ellipse x²/a² + y²/b² = 1.	Long answer

Differential Equations

Question	Type
Solve dy/dx + y/x = x².	Short answer
Solve (1 + x²) dy/dx + 2xy = 1/(1 + x²).	Long answer
Find the particular solution of dy/dx = y tan x, given y = 1 when x = 0.	Short answer
Solve the homogeneous equation x dy − y dx = √(x² + y²) dx.	Long answer
Find the order and degree of a given differential equation.	Very short

Vectors and 3D Geometry (14 marks)

Question	Type
Find the shortest distance between the lines r⃗ = (1+λ)î + (2−λ)ĵ + (λ+1)k̂ and r⃗ = (2+μ)î − (1−μ)ĵ + (−1+2μ)k̂.	Long answer
If a⃗ × b⃗ = c⃗ × d⃗ and a⃗ × c⃗ = b⃗ × d⃗, show that a⃗ − d⃗ is parallel to b⃗ − c⃗.	Short answer
Find the vector and Cartesian equations of the line through (1, 2, −4) perpendicular to the lines (x−8)/3 = (y+19)/(−16) = (z−10)/7 and (x−15)/3 = (y−29)/8 = (z−5)/(−5).	Long answer
Find the angle between the lines with direction ratios (a, b, c) and (b − c, c − a, a − b).	Short answer
Find the projection of a⃗ = 2î + 3ĵ + 2k̂ on b⃗ = î + 2ĵ + k̂, and the area of the parallelogram with a⃗ and b⃗ as adjacent sides.	Short answer

Linear Programming (5 marks)

Question	Type
Maximise Z = 3x + 2y subject to x + 2y ≤ 10, 3x + y ≤ 15, x, y ≥ 0, graphically.	Long answer
A toy maker makes toys A and B. A needs 5 min cutting and 10 min assembling; B needs 8 min cutting and 8 min assembling. There are 3 h 20 min of cutting and 4 h of assembling time. Profit is ₹50 on A and ₹60 on B. How many of each maximise profit?	Long answer

LP tip: (1) define the variables, (2) write the objective function, (3) write the constraints, (4) draw the graph and shade the feasible region, (5) find the corner points, (6) evaluate Z at each. The graph is part of the answer, so draw it neatly.

Probability (8 marks)

Question	Type
Bag I has 3 red and 4 black balls; Bag II has 5 red and 6 black. A bag is chosen at random and a ball drawn. Find the probability it is red. If it is red, find the probability it came from Bag I.	Long answer
Two cards are drawn from a pack of 52 without replacement. Find the probability of (a) two aces, (b) one ace and one king.	Short answer
A and B are independent events with P(A) = 0.3 and P(B) = 0.4. Find P(A ∩ B), P(A ∪ B) and P(A \| B).	Short answer
A factory has two machines making 60% and 40% of its bolts, with 2% and 3% defective respectively. Find the probability that a bolt picked at random is defective.	Short answer

Not in the CBSE 2026-27 Board Exam

Older question banks still include these, but CBSE no longer assesses them: properties of inverse trigonometric functions, composition and invertible functions, properties of determinants and Cramer's rule, Rolle's and mean value theorems, tangents and normals, area between two curves, forming differential equations, the equation of a plane and angles between planes, and the binomial distribution. ISC and some state boards still include some of these.

Unit marks and topic coverage follow CBSE's Class 12 Mathematics syllabus for 2026-27. Solve every NCERT exercise before practising these.

CBSE Class 12 Maths Important Questions 2027 — Chapter-Wise