CUET 2026 Maths Formula Sheet: Chapter-wise Quick Revision Guide for Last-Minute Prep

CUET 2026 Mathematics formulas help you quickly revise key chapters. These include Relations, Trigonometry, Matrices, Calculus, Vectors, Three-Dimensional Geometry, and Probability. You will need these formulas to solve direct questions in the exam and to improve your accuracy.

When you focus on key identities, derivatives, integrals, and properties, your conceptual understanding becomes stronger. You also become able to solve problems more quickly. This is why Mathematics is one of the highest-scoring subjects in CUET.

CUET 2026 Mathematics Formulas

If you wish to clear the CUET UG 2026 examination, you must master the fundamental formulas of Mathematics. This guide covers all the key formulas and concepts from the most important chapters.

Once you grasp these basics and learn how to apply them, you will be able to easily answer direct questions and enhance your accuracy. In this way, you can make Mathematics a high-scoring subject in your preparation.

👉 Download CUET 2026 Maths Formulas PDF

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: You can write any matrix A as the sum of (1/2)(A + Aᵀ), which is symmetric, and (1/2)(A - Aᵀ), which is skew-symmetric.

Area of a Triangle Using Determinants:

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

Area = (1/2) × |det(X)|, where X is the determinant formed by these coordinates with 1 in the third column.

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

Properties of Determinants and Adjoint:

• Scalar Multiplication: |kA| = kⁿ |A| for an n-order matrix. This one's really important.
• Relation Between A, adj A, and |A|: A × adj(A) = adj(A) × A = |A| × I. Don't skip this one.
• Determinant of Adjoint: |adj A| = |A|^(n-1). Direct questions show up often.
• Singular Matrix: |A| = 0
• Determinant of a Product: |AB| = |A| × |B|
• Inverse of a Product: (AB)⁻¹ = B⁻¹A⁻¹
• Determinant of an Inverse: |A⁻¹| = 1/|A|
• Determinant of a Transpose: |Aᵀ| = |A|
• Inverse and Transpose: (A⁻¹)ᵀ = (Aᵀ)⁻¹. This one's super important too.

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

Integrals can fetch you 4-5 questions, which works out to 30-40 marks. Memorising the formulas is half the battle.

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, where n ≠ -1
• ∫ eˣ dx = eˣ + C
• ∫ (1/x) dx = log |x| + C
• ∫ 1 dx = x + C

Note: Always add the constant of integration (+ C) when you're solving indefinite integrals.

Other Important Integral Forms: Make sure you memorise the special integral forms, especially the ones that involve √(a² - x²), √(x² - a²), and √(x² + a²).

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 one of those chapters that can really push your score up.

Conditional Probability:

• P(E|F) = P(E ∩ F) / P(F), which is the probability of E given that F has already happened.

Independent Events:

• Definition: When one event happens, it doesn't 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:

This one helps you find the probability of a specific prior event Eᵢ, given that event A has already occurred.

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