CUET 2026 Maths Formulas, Chapter-wise Important Formulas for Quick Revision

CUET 2026 Maths Formulas provide a quick revision of important chapters like Relations, Trigonometry, Matrices, Calculus, Vectors, 3D Geometry, and Probability. These formulas are essential for solving direct questions and improving accuracy in the exam.

By focusing on key identities, derivatives, integrals, and properties, students can strengthen conceptual clarity and boost their problem-solving speed, making Maths a high-scoring subject in CUET.

CUET 2026 Maths Formulas 

Mastering essential mathematical formulas is critical for success in the CUET UG 2026 examination. This comprehensive information reviews core formulas and concepts across various crucial chapters. Understanding these fundamental principles and their applications will enable students to tackle direct questions efficiently and improve their problem-solving accuracy, making it a high-scoring aspect of their preparation.

1. Relation and Function

This chapter forms the backbone of set theory and functions, with direct formula-based questions frequently appearing in the exam.

• Set Elements: If a set has n elements.

• Total Number of Relations (A x A):

• Formula: 2^n²

• Types:

• Total Relations: Includes empty relations.

• Non-Empty Relations: 2^n² - 1

• Types of Relations:

• Reflexive Relation: Total number of reflexive relations: 2n-1

• Symmetric Relation: (Formula not explicitly stated in spoken words for total count)

• Transitive Relation: (No exact formula for total count)

• Function: Given Set A with m elements and Set B with n elements.

• Total Number of Functions: n^m

• One-to-One Function (Injective):

• If n >= m: n P m or n! / (n - m)!

• If m > n: 0

• Onto Function (Surjective):

• Formula: Σ r=1 to n^(n-r) * n C r * r^m

• m = elements in A; n = elements in B. r varies from 1 to n.

• Bijective Function (One-to-One and Onto):

• If m = n: m!

• If m != n: 0

2. Inverse Trigonometry Function

This is a concise chapter, guaranteeing 1-2 questions in the CUET exam.

• Domain and Range: It is essential to know and memorize the domain and range for all inverse trigonometric functions.

• Negative Angles in Inverse Trigonometric Functions:

• Important Identities/Formulas:

• sin⁻¹(x) + cos⁻¹(x) = π/2

• tan⁻¹(x) + cot⁻¹(x) = π/2

• sec⁻¹(x) + cosec⁻¹(x) = π/2

• tan⁻¹(x) + tan⁻¹(y): tan⁻¹((x + y) / (1 - xy)) (Valid if xy < 1)

• 2 tan⁻¹(x): (Various forms depending on the range) (Applicable if -1 < x < 1)

3. Matrices and Determinants

This is a highly scoring chapter, with 7 to 8 direct questions expected. Focus on solving many PYQs.

• Properties of Matrix Operations:

• Addition: Commutative (A + B = B + A)

• Subtraction: Not commutative (A - B ≠ B - A)

• Multiplication: Not commutative (AB ≠ BA); Associative (A(BC) = (AB)C)

• Transpose: (Aᵀ)ᵀ = A

• Identity Matrix: AI = IA = A

• Inverse Matrix: If AB = BA = I, then B = A⁻¹

• Product Resulting in Zero Matrix: If AB = 0, A or B is not necessarily a zero matrix.

• Distributive Law: A(B + C) = AB + AC

• Matrix Representation: Any matrix A can be expressed as: (1/2)(A + Aᵀ) (symmetric) + (1/2)(A - Aᵀ) (skew-symmetric).

• Area of a Triangle using Determinants:

• For vertices (x₁, y₁), (x₂, y₂), (x₃, y₃):

• Area = (1/2) * |det(X)|, where $X = \begin{vmatrix} x_1 & y_1 & 1 \ x_2 & y_2 & 1 \ x_3 & y_3 & 1 \end{vmatrix}$

• Inverse of a Matrix: A⁻¹ = (adj A) / |A|

• Properties of Determinants and Adjoint:

• Scalar Multiplication: |kA| = kⁿ |A| (for n order matrix) - very important.

• Relation between A, adj A, and |A|: A * adj(A) = adj(A) * A = |A| * I - highly important.

• Determinant of Adjoint: |adj A| = |A|^(n-1) - frequent direct questions.

• Singular Matrix: |A| = 0

• Determinant of a Product: |AB| = |A| * |B|

• Inverse of a Product: (AB)⁻¹ = B⁻¹ A⁻¹

• Determinant of an Inverse: |A⁻¹| = 1/|A|

• Determinant of a Transpose: |Aᵀ| = |A|

• Inverse and Transpose: (A⁻¹)ᵀ = (Aᵀ)⁻¹ - very important.

4. Continuity and Differentiability

This chapter, along with integration, is very important. Students must memorize all formulas.

• Basic Derivatives:

• d/dx (xⁿ) = nx^(n-1)

• d/dx (eˣ) = eˣ

• d/dx (√x) = 1 / (2√x)

• d/dx (log x) = 1/x (Memory Tip: In this context, "log" refers to the natural logarithm (ln).)

• d/dx (constant) = 0

• d/dx (aˣ) = aˣ log a

• Trigonometric Derivatives: (Must be memorized)

• d/dx (sin x) = cos x

• d/dx (cos x) = -sin x

• d/dx (tan x) = sec² x

• d/dx (cot x) = -cosec² x

• d/dx (sec x) = sec x tan x

• d/dx (cosec x) = -cosec x cot x

• Inverse Trigonometric Derivatives:

• d/dx (sin⁻¹ x) = 1 / √(1 - x²)

• d/dx (cos⁻¹ x) = -1 / √(1 - x²)

• d/dx (tan⁻¹ x) = 1 / (1 + x²)

• Logarithmic Properties (Crucial for Derivatives):

• log(xy) = log x + log y

• log(x/y) = log x - log y

• log(xⁿ) = n log x

• log_b(b) = 1

• log(1) = 0

5. Integrals

This chapter is highly important, potentially accounting for 4-5 questions (30-40 marks). Memorizing formulas is key.

• Basic Integrals:

• ∫ sin x dx = -cos x + C

• ∫ cos x dx = sin x + C

• ∫ tan x dx = log |sec x| + C

• ∫ cot x dx = log |sin x| + C

• ∫ sec x dx = log |sec x + tan x| + C

• ∫ cosec x dx = log |cosec x - cot x| + C

• ∫ xⁿ dx = (x^(n+1))/(n+1) + C (for n ≠ -1)

• ∫ eˣ dx = eˣ + C

• ∫ (1/x) dx = log |x| + C

• ∫ 1 dx = x + C

• Note: The constant of integration + C must be added for indefinite integrals.

• Other Important Integral Forms: Various specific integral forms (e.g., involving √(a² - x²), √(x² - a²), √(x² + a²)) are essential to memorize.

6. Vectors

Vectors and 3D Geometry are both very important and scoring chapters.

• Vector Cross Product (A x B):

• For A = a₁i + a₂j + a₃k and B = b₁i + b₂j + b₃k:

• A x B is calculated as the determinant:
  $\begin{vmatrix} i & j & k \ a_1 & a_2 & a_3 \ b_1 & b_2 & b_3 \end{vmatrix}$

• (Memory Tip: The cross product is also called the vector product because its result is a vector.)

• Area Formulas:

• Parallelogram (adjacent sides A and B): Area = |A x B|

• Parallelogram (diagonals D₁ and D₂): Area = (1/2) |D₁ x D₂|

• Triangle (sides A and B): Area = (1/2) |A x B|

• Direction Cosines (l, m, n) and Direction Ratios (a, b, c):

• If |V| is the magnitude of the vector:

• l = a / |V|, m = b / |V|, n = c / |V|

• Relation: l² + m² + n² = 1 (or cos²α + cos²β + cos²γ = 1)

• Dot Product Properties:

• i . i = j . j = k . k = 1

• Cross Product Properties:

• i x i = j x j = k x k = 0

• Cyclic Cross Products:

• i x j = k, j x k = i, k x i = j

• (Memory Tip: Moving anti-clockwise (i → j → k → i) gives a positive result; clockwise gives negative.)

7. 3D Geometry

This is a very strong and scoring chapter.

• Direction Ratios of a Line (passing through (x₁, y₁, z₁) and (x₂, y₂, z₂)):

• a = x₂ - x₁, b = y₂ - y₁, c = z₂ - z₁

• Direction Cosines from Direction Ratios (a, b, c):

• l = ± a / √(a² + b² + c²)

• m = ± b / √(a² + b² + c²)

• n = ± c / √(a² + b² + c²)

• Equation of a Line:

• Vector Form: (passing through A, parallel to B) r = A + λB

• Cartesian Form: (passing through (x₁, y₁, z₁), direction ratios (a, b, c)) (x - x₁)/a = (y - y₁)/b = (z - z₁)/c

• Angle Between Two Lines (parallel vectors B₁ and B₂):

• cos θ = |(B₁ . B₂) / (|B₁| * |B₂|)|

• Conditions for Lines:

• Perpendicular Lines: B₁ . B₂ = 0 (or a₁a₂ + b₁b₂ + c₁c₂ = 0)

• Parallel Lines: a₁/a₂ = b₁/b₂ = c₁/c₂

• Shortest Distance Between Two Skew Lines:

• d = |(A₂ - A₁) . (B₁ x B₂)| / |B₁ x B₂|

• (Memory Tip: If d = 0, the lines are intersecting.)

• Shortest Distance Between Two Parallel Lines:

• d = |B x (A₂ - A₁)| / |B| (where B is the common parallel vector)

• (Memory Tip: If d = 0, the lines are coincident.)

8. Probability

Probability is a very scoring chapter.

• Conditional Probability:

• P(E|F) = P(E ∩ F) / P(F) (Probability of E given F has occurred)

• Independent Events:

• Definition: Occurrence of one does not affect the other.

• Properties:

• P(E|F) = P(E)

• P(F|E) = P(F)

• P(E ∩ F) = P(E) * P(F)

• Multiplication Theorem of Probability:

• P(E ∩ F) = P(E) * P(F|E)

• Theorem of Total Probability:

• For mutually exclusive and exhaustive events E₁, E₂, …, Eₙ, and any event A:

• P(A) = P(E₁)P(A|E₁) + P(E₂)P(A|E₂) + … + P(Eₙ)P(A|Eₙ)

• Bayes' Theorem:

• Calculates the probability of a specific prior event Eᵢ, given that event A has already occurred.

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