CBSE Class 12th Maths Important Formulas & Questions -

The Central Board of Secondary Education has announced to conduct the CBSE Class 12th Exam 2026 between February 17, 2026 and April 09, 2026. All the students of the commerce and science stream who are to appear for the Mathematics exam will be looking forward to completing their exam preparations using the detailed CBSE Class 12 Maths Syllabus 2026.

To assist students with their preparation phase, we have shared the list of CBSE Class 12th Maths Important Formulas & Questions in the article below. Scroll down in the article and check the list of important formulas.

CBSE Class 12th Maths Important Formulas

Mathematics is one of the most important and scoring subjects in CBSE Class 12. For students aiming to secure 95+ marks in their board exams, having a clear command over formulas, theorems, and solving techniques is crucial. Since a majority of the questions in CBSE Class 12 Maths are based directly on standard formulas and their applications, memorizing and practicing them is the key to success.

In this article, we have compiled a list of chapter-wise important formulas along with some important questions that will help students revise effectively before the exams.

1. Relations and Functions

Reflexive, Symmetric, Transitive properties
Inverse of a function:
$f^{-1}(f(x)) = x$
$f^{-1} (f (x)) = x$
Composition of functions:
$(f \circ g)(x) = f(g(x))$
$(f \circ g) (x) = f (g (x))$

2. Inverse Trigonometric Functions

$\sin^{-1}x + \cos^{-1}x = \dfrac{\pi}{2}$
$sin^{-1} x + cos^{-1} x = 2 π$
$\tan^{-1}x + \cot^{-1}x = \dfrac{\pi}{2}$
$tan^{-1} x + cot^{-1} x = 2 π$
$\sin^{-1}x = \tan^{-1}\left(\dfrac{x}{\sqrt{1-x^2}}\right)$
$sin^{-1} x = tan^{-1} (1 - x ^{2} x)$

3. Matrices

$(AB)^T = B^T A^T$
$(A B)^{T} = B^{T} A^{T}$
$(AB)^{-1} = B^{-1} A^{-1}$
$(A B)^{-1} = B^{-1} A^{-1}$
Determinant properties:
- $\det(AB) = \det(A) \cdot \det(B)$
  $det (A B) = det (A) \cdot det (B)$
- If two rows/columns are identical → Determinant = 0

4. Determinants

Area of triangle:
$\dfrac{1}{2}\begin{vmatrix} x_1 & y_1 & 1 \\ x_2 & y_2 & 1 \\ x_3 & y_3 & 1 \end{vmatrix}$
$21 x^{1} x^{2} x^{3} y^{1} y^{2} y^{3} 111$
Cramer’s Rule for system of equations.

5. Continuity and Differentiability

Derivative of inverse function:
$\dfrac{dy}{dx} = \dfrac{1}{\dfrac{dx}{dy}}$
$d x d y = d y d x 1$
Chain Rule:
$\dfrac{dy}{dx} = \dfrac{dy}{du} \cdot \dfrac{du}{dx}$
$d x d y = d u d y \cdot d x d u$
Derivatives of trigonometric, logarithmic, exponential, and inverse functions.

6. Application of Derivatives

Increasing/Decreasing function test:
$f'(x) > 0$
$f^{'} (x) > 0$ → increasing
Maxima and Minima conditions using 1st & 2nd derivative test.
Rate of change formula:
$\dfrac{dy}{dt} = \dfrac{dy}{dx} \cdot \dfrac{dx}{dt}$
$d t d y = d x d y \cdot d t d x$

7. Integrals

Standard integrals:
- $\int \dfrac{1}{x} dx = \ln|x| + C$
  $\int x 1 d x = ln ∣ x ∣ + C$
- $\int e^x dx = e^x + C$
  $\int e^{x} d x = e^{x} + C$
- $\int \cos x dx = \sin x + C$
  $\int cos x d x = sin x + C$
Integration by parts:
$\int (uv) dx = u \int v dx – \int \left( \dfrac{du}{dx} \int v dx \right) dx$
$\int (uv) d x = u \int v d x - \int (d x d u \int v d x) d x$
Substitution method:
$\int f(g(x))g'(x) dx = \int f(u) du$
$\int f (g (x)) g^{'} (x) d x = \int f (u) d u$

8. Application of Integrals

Area under curve:
$\text{Area} = \int_a^b [f(x) – g(x)] dx$
$Area = \int_{a b} [f (x) - g (x)] d x$

9. Differential Equations

General solution = Particular + Arbitrary constant
Linear differential equation:
$\dfrac{dy}{dx} + Py = Q$
$d x d y + P y = Q$
Solution:
$y \cdot e^{\int P dx} = \int Q e^{\int P dx} dx + C$
$y \cdot e^{\int P d x} = \int Q e^{\int P d x} d x + C$

10. Vector Algebra

Dot product:
$\vec{a} \cdot \vec{b} = |\vec{a}||\vec{b}|\cos\theta$
$a \cdot b = ∣ a ∣∣ b ∣ cos θ$
Cross product:
$\vec{a} \times \vec{b} = |\vec{a}||\vec{b}|\sin\theta \hat{n}$
$a \times b = ∣ a ∣∣ b ∣ sin θ n^$
Scalar triple product:
$[\vec{a} \ \vec{b} \ \vec{c}] = \vec{a} \cdot (\vec{b} \times \vec{c})$
$[a b c] = a \cdot (b \times c)$

11. Three Dimensional Geometry

Distance between two points:
$\sqrt{(x_2-x_1)^2 + (y_2-y_1)^2 + (z_2-z_1)^2}$
$(x^{2} - x^{1})^{2} + (y^{2} - y^{1})^{2} + (z^{2} - z^{1})^{2}$
Equation of line:
$\dfrac{x-x_1}{l} = \dfrac{y-y_1}{m} = \dfrac{z-z_1}{n}$
$l x - x ^{1} = m y - y ^{1} = n z - z ^{1}$
Angle between two lines:
$\cos \theta = \dfrac{l_1l_2 + m_1m_2 + n_1n_2}{\sqrt{l_1^2+m_1^2+n_1^2}\sqrt{l_2^2+m_2^2+n_2^2}}$
$cos θ = l ^{12} + m ^{12} + n ^{12} l ^{22} + m ^{22} + n ^{22} l ^{1} l ^{2} + m ^{1} m ^{2} + n ^{1} n ^{2}$

12. Probability

Bayes’ theorem:
$P(A|B) = \dfrac{P(B|A) \cdot P(A)}{P(B)}$
$P (A ∣ B) = P ( B ) P ( B ∣ A ) \cdot P ( A )$
Conditional probability:
$P(A|B) = \dfrac{P(A \cap B)}{P(B)}$
$P (A ∣ B) = P ( B ) P ( A \cap B )$

Vector Formulas

A + B = B + A (Commutative Law)
A + (B + C) = (A + B) + C (Associative Law)
(A • B )= |P| |Q| cos θ ( Dot Product )
(A × B )= |P| |Q| sin θ (Cross Product)
k (A + B )= kA + kB
A + 0 = 0 + A (Additive Identity)

Trigonometry Formulas

sin-1(-x) = – sin-1x
tan-1x + cot-1x = π / 2
sin-1x + cos-1 x = π / 2
cos-1(-x) = π – cos-1x
cot-1(-x) = π – cot-1x

Calculus Formulas

∫ f(x) dx = F(x) + C
Power Rule: ∫ xn dx = (xn+1) / (n+1) + C. (Where n ≠ -1)
Exponential Rules: ∫ ex dx = ex + C
∫ ax dx = ax / ln(a) + C
∫ ln(x) dx = x ln(x) – x + C
Constant Multiplication Rule: ∫ a dx = ax + C, where a is the constant.
Reciprocal Rule: ∫ (1/x) dx = ln(x)+ C
Sum Rules: ∫ [f(x) + g(x)] dx = ∫f(x) dx + ∫g(x) dx
Difference Rules: ∫ [f(x) – g(x)] dx = ∫f(x) dx – ∫g(x) dx
∫k f(x) dx = k ∫f(x) dx, , where k is any real number.
Integration by parts: ∫ f(x) g(x) dx = f(x) ∫ g(x) dx – ∫[d/dx f(x) × ∫ g(x) dx]dx
∫cos x dx = sin x + C
∫ sin x dx = -cos x + C
∫ sec2x dx = tan x + C
∫ cosec2x dx = -cot x + C
∫ sec x tan x dx = sec x + C
∫ cosec x cot x dx = – cosec x + C

Geometry Formulas

Cartesian equation of a plane: lx + my + nz = d
Distance between two points P(x1, y1, z1) and Q(x2, y2, z2): PQ = √ ((x1 – x2)2 + (y1 – y2)2 + (z1 – z2)2)

Importance of Learning CBSE Class 12th Maths Important Formulas

Below we have listed some pointers that explain the importance of learning CBSE Class 12th Maths Important Formulas. Read the pointers and read the formulas:

Foundation for Problem-Solving – Maths questions in CBSE Class 12 heavily depend on formulas. A strong grasp of formulas ensures that students can quickly identify the right approach to solve problems.
Saves Time in Exams – During board exams, time management is crucial. Knowing formulas by heart helps students solve questions faster without wasting time on derivations.
Boosts Accuracy – Correct application of formulas minimizes silly mistakes and improves the chances of scoring full marks, especially in calculation-heavy questions.
Essential for Higher Studies – Class 12 Maths formulas form the base for competitive exams like JEE, CUET, NDA, and further studies in engineering, commerce, and science streams.
Helps in Understanding Concepts – Learning formulas isn’t about rote memorization; it deepens understanding of concepts like calculus, probability, and vectors, making problem-solving more logical.
Improves Confidence – Memorizing and practicing formulas regularly reduces exam fear, builds confidence, and enables students to attempt all types of questions with ease.
Supports Step-Wise Presentation – CBSE marking scheme awards marks step by step. Using correct formulas in the first step ensures students secure marks even if they make calculation errors later.