CUET Maths Formulas, List of Chapter Wise Maths Formulas, Solved Examples

CUET Maths Formulas: The Common University Entrance Test (CUET) is a crucial exam that enables students to secure admission to top colleges and universities across India. CUET comprises three main sections: the Language section, the General Test, and Domain-specific subjects. Mathematics is one of the domain-specific subjects that covers topics such as calculus, Algebra, linear programming, and many more.

This Story also Contains

1. Overview of CUET Exam Pattern
2. CUET 2026 Mathematics Chapterwise Distribution
3. CUET Mathematics Formulae
4. CUET Quantitative Aptitude formulae
5. CUET 2026 Formula Memorisation Strategies

This article from Careers360 will discuss the most essential math formulas you need to know for CUET 2026. Overview of CUET Syllabus and Exam Pattern, Chapterwise Distribution, Important Mathematics Formulae, Strategies to memorise Formulae for CUET 2026 exam day. This information will help aspirants approach the Mathematics section with a better strategic plan.

Overview of CUET Exam Pattern

The CUET 2026 has been designed to evaluate the knowledge and skills of candidates in various fields. Before starting with the Mathematics resources, aspirants must understand the CUET Exam pattern well.

As in the sections above, each is again a set of multiple-choice questions; the scoring scheme is +5 for a correct answer and -1 for an incorrect one. The test is taken in CBT Mode for a total duration of 3 hours, and one can choose up to 5 subjects, as well as several languages, if that helps to gain admission into one's desired course.

CUET 2026 Mathematics Chapterwise Distribution

The CUET 2026 exam distributes questions related to various chapters, allowing it to assess candidates' overall understanding of the subject. Each subject has specific topics or chapters from which questions are drawn. From the table below, you can analyse the various questions that come from which chapters for a better preparation strategy of CUET 2026.

CUET Mathematics Formulae

The Mathematics formulae can be used in solving the General test’s Quantitative aptitude section and help those who have mathematics as their domain subject. Below discussed is the importance and the topic-wise weightage:

Relations and Functions

The section “Relations and Functions” focuses on the types of relations, such as reflexive, symmetric, and transitive relations. Below are the essential formulae and properties for this section:

Assuming a function f: A→B and R is the set of real numbers, A, B are two sets.

Relations

Reflexive Relation: (a, a)∈R, ∀a∈A

Symmetric Relation: If (a,b)∈R⇒(b ,a)∈R

Transitive Relation: If (a,b)∈R and (b,c)∈R, then (a,c)∈R.

Learn more about the relation and its types.

Functions

One-one function (Injective): If f(a1)=f(a2), then ⟹a1=a2

Onto function (Surjective): A function f: A→B is onto if for every b∈B, there exists an a∈A such that f(a)=b.

Composite function: (fog)(x)=f(g(x))

Inverse of a Function: f(f−1(x))=x implies f−1(f(x))=x

Learn more about Relations and functions.

A total of 2 questions were asked in CUET 2025 from the chapter on relations and functions.

Inverse Trigonometric Functions

Inverse trigonometric functions contain as many formulae as trigonometry; below are the important ones listed:

Reciprocal Identities

• sin⁡(sin−1⁡x)=x for −1≤x≤1

• cos⁡(cos−1⁡x)=x for −1≤x≤1

• tan⁡(tan−1⁡x)=x for ∀x

• cot⁡(cot−1⁡x)=x for ∀x

• sec⁡(sec−1⁡x)=x for |x|≤1

• csc⁡(csc−1⁡x)=x for |x|≤1

Addition/ Subtraction Identities

• sin−1⁡x+cos−1⁡x=π2for−1≤x≤1

• tan−1⁡x+cot−1⁡x=π2for allx

• sec−1⁡x+csc−1⁡x=π2for|x|≥1

Negative Angle Identities

• sin−1⁡(−x)=−sin−1⁡x

• cos−1⁡(−x)=π−cos−1⁡x

• tan−1⁡(−x)=−tan−1⁡x

• cot−1⁡(−x)=π−cot−1⁡x

• sec−1⁡(−x)=π−sec−1⁡x

• csc−1⁡(−x)=−csc−1⁡x

Product Identities

• 2sin−1⁡x=sin−1⁡(2x1−x2)for−12≤x≤12

• 2cos−1⁡x=cos−1⁡(2x2−1)for0≤x≤1

• 2tan−1⁡x=tan−1⁡(2x1−x2)for−1<x<1

Double and Half-angle identities

• sin−1⁡(1−2x21−x2)=2sin−1⁡x

• cos−1⁡(2x2−1)=2cos−1⁡x

• tan−1⁡(2x1−x2)=2tan−1⁡xfor−1<x<1

Learn more: Inverse trigonometric functions

A total of 2 questions were asked in CUET 2025 from the chapter on inverse trigonometric functions.

Algebra

For the algebra section, there are numerous concepts related to matrices and determinants. Matrices and determinants are a central theme in the CUET 2026 QA exam, focusing on the operations that matrices can undergo, properties of these operations, and the use of determinants in solving systems of linear equations. The questions test your understanding of addition, multiplication, finding the inverses of the matrices, and your ability to compute the determinant of square matrices, mostly up to 3x3. Here are the essential formulae:

Matrices

Order of matrix: For matrix A having m rows and n columns, the order is m×n.

Equal Matrices: If A=[aij] and B=[bij], then A=B if aij=bij for all i,j.

Symmetric Matrix: AT=A (transpose of A is equal to A).

Skew Symmetric Matrix: AT=−A

Transpose of a Matrix: AT=[aji].

Matrix Addition: If A=[aij] and B=[bij], then their sum C=A+B is given by: C=[aij+bij]

Scalar Multiplication: kA=kaij, where k is a scalar.

Matrix Multiplication: Cij=∑k=1naikbkj

Cofactor: Cij=(−1)i+j⋅Minor of aij

Inverse of a matrix: A−1=1det(A)⋅adj(A) provided det(A)≠0.

Learn more about: Matrices, Types of matrices and determinants

A total of 11 questions were asked in CUET 2025 from the chapter matrices.

Determinants

Determinant of 2 order matrix: For a matrix A=[abcd],The determinant is: det(A)=ad−bc

Determinant of 3 order matrix: For a matrix A=[abcdefghi], the determinant is:

det(A)=a(ei−fh)−b(di−fg)+c(dh−eg)

Solution of linear equations: X=A−1B, where A is a square matrix, and A−1 is the inverse of A.

A total of 4 questions were asked in CUET 2025 from the chapter on determinants.

Calculus

There are numerous formulae in the branch of calculus, which include formulae related to continuity, differentiability, integration, etc. Below is the list of important formulae:

Continuity: limx→cf(x)=f(c)

Differentiability: f′(x)=limh→0f(x+h)−f(x)h

Chain Rule: dydx=dydu⋅dudx

A total of 4 questions were asked in CUET 2025 from the chapter on continuity and differentiability.

Derivatives

Derivative of trigonometric functions:

ddxsin−1⁡(x)=11−x2

ddxcos−1⁡(x)=−11−x2

ddxtan−1⁡(x)=11+x2

ddxcot−1⁡(x)=−11+x2

ddxsec−1⁡(x)=1|x|x2−1

ddxcsc−1⁡(x)=−1|x|x2−1

Derivative of implicit functions:

dydx=−FxFy

For Exponential and Logarithmic Functions:

ddxex=ex

ddxlog⁡x=1x

ln⁡y=g(x)ln⁡f(x)

Parametric Form Derivatives:

dydx=dydtdxdt

Second-Order Derivatives:

f″(x)=ddx(df′(x)dx)

Tangent: y−f(a)=f′(a)(x−a)(Equation of Tangent)

Normal: y−f(a)=−1f′(a)(x−a)(Equation of Normal)

Integration

∫f′(x)dx=f(x)+C

∫f(g(x))g′(x)dx=∫f(u)du

Integration by Parts:∫udv=uv−∫vdu

Integration of Simple Functions:

∫xndx=xn+1n+1+C(n≠−1)

∫exdx=ex+C

∫1xdx=ln⁡|x|+C

Definite Integrals:

∫abf(x)dx=F(b)−F(a)

Learn about definite integrals.

Applications of Integrals

Area Under Curves: A=∫abf(x)dx

Area Between Curves: A=∫ab(f(x)−g(x))dx

A total of 6 questions were asked in CUET 2025 from the chapter Integrals.

Differential Equations

dydx=f(x,y)

Solution of Linear Differential Equations:

dydx+P(x)y=Q(x)

y=1μ(x)(∫μ(x)Q(x)dx+C)

μ(x)=e∫P(x)dx

μ= Integration constant

Visit: Differential equations

A total of 4 questions were asked in CUET 2025 from the chapter on differential equations.

Vectors and Three-Dimensional Geometry

Vectors and Three-Dimensional Geometry is crucial for CUET 2026 QA You will find questions on the magnitude and direction of vectors, the scalar and vector products, and the equations of lines and planes in 3D. The key topics are the cross product, dot product, and various geometric interpretations. This branch of mathematics deals with the vector quantities, planes, lines and angles. Below are the formulas listed:

Vectors

Magnitude of a vector: |A|=Ax2+Ay2+Az2

Direction cosines of a vector: cos⁡α=Ax|A|,cos⁡β=Ay|A|,cos⁡γ=Az|A|

Addition of vectors: A+B=(Ax+Bx,Ay+By,Az+Bz)

Multiplication by a scalar: kA=(kAx,kAy,kAz)

Position vector: r=xi^+yj^+zk^

Negative of a vector: −A=(−Ax,−Ay,−Az)

Scalar (dot) product of vectors: A⋅B=AxBx+AyBy+AzBz

Cross product: A×B=|i^j^k^AxAyAzBxByBz|

Scalar triple product: A⋅(B×C)=|AxAyAzBxByBzCxCyCz|

Learn more: Vectors

A total of 4 questions were asked in CUET 2025 from the chapter vector algebra.

3-D Geometry

Direction cosines: cos⁡α=x2−x1(x2−x1)2+(y2−y1)2+(z2−z1)2,cos⁡β=y2−y1(x2−x1)2+(y2−y1)2+(z2−z1)2,cos⁡γ=z2−z1(x2−x1)2+(y2−y1)2+(z2−z1)2

Equation of a line: r=a+λb

Equation of a line (Cartesian form): x−x1a=y−y1b=z−z1c

Angle between two lines: cos⁡θ=A⋅B|A||B|

Angle between two planes: cos⁡θ=n1⋅n2|n1||n2|

Angle between a line and a plane: cos⁡θ=l⋅n|l||n|

Distance of a point from a plane: Distance=|ax1+by1+cz1+d|a2+b2+c2

Learn more about three-dimensional geometry.

You will need to calculate angles between vectors, find projections of vectors, or calculate distances between points and lines. A total of 4 questions were asked in CUET 2025 on three-dimensional geometry.

Linear Programming

A linear programming problem consists of variables, an objective function, and constraints. These are often used to represent equations and inequalities. Below are the formulas listed:

Maximise or Minimise Z=c1x1+c2x2+⋯+cnxnSubject to the constraints:a11x1+a12x2+⋯+a1nxn≤b1a21x1+a22x2+⋯+a2nxn≤b2…am1x1+am2x2+⋯+amnxn≤bmx1,x2,…,xn≥0

A total of 6 questions were asked in CUET 2025 from the chapter linear programming and inequalities.

Probability

Probability helps us calculate the chances of uncertainty and predict information. There are important concepts such as Bayes' theorem, multiplication theorem, etc. Below are the formulae listed:

Multiplication Theorem on Probability: P(A∩B)=P(A|B)P(B)

Conditional Probability: P(A|B)=P(A∩B)P(B)

Independent Events: P(A∩B)=P(A)P(B)

Total Probability Theorem: P(A)=∑i=1nP(A|Bi)P(Bi)

Bayes’ Theorem: P(Bi|A)=P(A|Bi)P(Bi)∑j=1nP(A|Bj)P(Bj)

Random Variable and Probability Distribution: ∑i=1nP(X=xi)=1

Mean and Variance of a Random Variable: E(X)=∑i=1nxiP(X=xi)

Binomial Distribution: P(X=k)=(nk)pk(1−p)n−k

Learn more about Probability.

The CUET 2026 exam might focus on problems involving dice, cards, or real-world probability problems where you have to compute the probability of an event happening under certain conditions. A total of 2 questions were asked in CUET 2025 from the chapter on probability.

CUET Quantitative Aptitude formulae

The Quantitative Aptitude is one of the most essential parts of the CUET 2026 exam, designed to measure a candidate's mathematical and problem-solving skills. Topics like arithmetic, algebra, geometry, mensuration, trigonometry, and number systems are very diversified. Below are the crucial formulae concerning the topics:

Mensuration

Mensuration is a prominent topic in CUET 2026 QA. In solving many problems on the measurement of areas and volumes and surface areas of different geometric figures, you may have to find the area and the perimeter of any 2D shape - triangles, circles, and quadrilaterals; and the surface area and volume of various 3D solids - cubes, spheres, and cylinders. All the key formulae and their applications need to be well understood to solve them efficiently. Key formulae for mensuration that you are supposed to know for CUET 2026 QA are :

Area of a Circle: A=πr2

Circumference of a Circle: C=2πr

Area of a Triangle (Heron’s formula): A=s(s−a)(s−b)(s−c)where s=a+b+c2

Area of a Rectangle: A=l×b

Perimeter of a Rectangle: P=2(l+b)

Surface Area of a Sphere: A=4πr2

Volume of a Sphere: V=43πr3

Surface Area of a Cylinder: A=2πr(h+r)

Volume of a Cylinder: V=πr2h

Lateral Surface Area of a Cylinder: A=2πrh

Surface Area of a Cone: A=πr(l+r)where l=r2+h2

Volume of a Cone: V=13πr2h

Curved Surface Area of a Cone: A=πrlwhere l=r2+h2

Area of a Parallelogram: A=b×h

Area of a Rhombus: A=12×d1×d2

Area of a Trapezium: A=12×(a+b)×h

Surface Area of a Cuboid: A=2(lb+bh+hl)

Volume of a Cuboid: V=l×b×h

Surface Area of a Cube: A=6a2

Volume of a Cube: V=a3

Diagonal of a Cube: d=3a

Diagonal of a Cuboid: d=l2+b2+h2

Length of an Arc of a Circle: L=θ360×2πr

Area of a Sector of a Circle: A=θ360×πr2

Surface Area of a Hemisphere: A=3πr2

Volume of a Hemisphere: V=23πr3

Ratio and Percentage

Both ratio and percentage are quite fundamental concepts in solving several problems that may arise in statistics and real life. The ratios and percentages may form part of the problems in CUET 2026 QA, such as comparing quantities, calculating discounts, profit, and loss, or changes in value over time, each requires considerable use of ratios and percentages. Here are the formulas for ratio and percentage:

Ratio

If the ratio of two quantities is a:b, then their respective values can be written as ax and bx.

The ratio of two quantities is a:b, and their sum is S, then the quantities are: aa+b×S and ba+b×S

If a:b=c:d, then the cross multiplication rule applies: ad=bc.

If a:b=c:d and b:c=e:f, then a:b:c=ae:be:bf.

Learn about ratios.

Percentage

Percentage of a value A relative to B=(AB×100)%.

If a value increases by x%: New value = Original value×(1+x100).

If a value decreases by x%: New value = Original value×(1−x100).

Successive percentage changes of x% and y%: Effective change =x+y+xy100.

To calculate x% of a number N: Result = x100×N.

If a population increases by r% per year, the population after n years is: P×(1+r100)n

If a population decreases by r% per year, the population after n years is: P×(1−r100)n

Percentage change between two values: Difference in valuesOriginal value×100.

Trigonometry

Applications of trigonometry are crucial in CUET 2026 QA, particularly in problems that involve angles, heights, distances, and periodic phenomena. Problems that include the basic trigonometric ratios, such as sine, cosine, tangent, and their reciprocals, can appear in CUET 2026 QA. One should also be familiar with trigonometric identities, formulas involving angles, and their applications. Some of the essential formulas and identities used in trigonometry are as follows :

Basic Trigonometric Ratios

sin⁡θ=oppositehypotenuse

cos⁡θ=adjacenthypotenuse

tan⁡θ=sin⁡θcos⁡θ=oppositeadjacent

cot⁡θ=cos⁡θsin⁡θ=adjacentopposite

sec⁡θ=1cos⁡θ

csc⁡θ=1sin⁡θ

Pythagorean Identities:

sin2⁡θ+cos2⁡θ=1

1+tan2⁡θ=sec2⁡θ

1+cot2⁡θ=csc2⁡θ

Sum and Difference Formulas:

sin⁡(A±B)=sin⁡Acos⁡B±cos⁡Asin⁡B

cos⁡(A±B)=cos⁡Acos⁡B∓sin⁡Asin⁡B

tan⁡(A±B)=tan⁡A±tan⁡B1∓tan⁡Atan⁡B

Double Angle Formulas:

sin⁡(2A)=2sin⁡Acos⁡A

cos⁡(2A)=cos2⁡A−sin2⁡A=2cos2⁡A−1=1−2sin2⁡A

tan⁡(2A)=2tan⁡A1−tan2⁡A

Half-Angle Formulas:

sin⁡(A2)=±1−cos⁡A2

cos⁡(A2)=±1+cos⁡A2

tan⁡(A2)=±1−cos⁡A1+cos⁡A

Triple Angle Formulas:

sin⁡(3A)=3sin⁡A−4sin3⁡A

cos⁡(3A)=4cos3⁡A−3cos⁡A

tan⁡(3A)=3tan⁡A−tan3⁡A1−3tan2⁡A

Product-to-Sum Formulas:

sin⁡Asin⁡B=12[cos⁡(A−B)−cos⁡(A+B)]

cos⁡Acos⁡B=12[cos⁡(A−B)+cos⁡(A+B)]

sin⁡Acos⁡B=12[sin⁡(A+B)+sin⁡(A−B)]

Sum-to-Product Formulas:

sin⁡A+sin⁡B=2sin⁡(A+B2)cos⁡(A−B2)

sin⁡A−sin⁡B=2cos⁡(A+B2)sin⁡(A−B2)

cos⁡A+cos⁡B=2cos⁡(A+B2)cos⁡(A−B2)

cos⁡A−cos⁡B=−2sin⁡(A+B2)sin⁡(A−B2)

Trigonometry will comprise 3-5 questions in CUET QA, which will include problems on trigonometric identities, angles, and functions, along with solving triangles and inverse applications of trigonometric functions.

Arithmetic Calculations

Arithmetic calculations form a good quantitative reasoning base for CUET 2026 QA. This section tests the ability to do quick and accurate calculations, involving percentages, ratios, averages, and other formulas:

Sum of an Arithmetic Series: Sn=n2(2a+(n−1)d)

Nth Term of an Arithmetic Sequence: Tn=a+(n−1)d

Sum of First n Natural Numbers: Sn=n(n+1)2

Sum of Squares of First n Natural Numbers: Sn=n(n+1)(2n+1)6

Sum of Cubes of First n Natural Numbers: Sn=(n(n+1)2)2

Arithmetic calculations will be the primary component of most questions in CUET QA, and you would expect to get 4 or 5 questions in this section.

Speed, Distance and Time

This unit covers the relationship between speed, distance, and time, and is also crucial in solving other practical problems related to motion. You will meet questions where constant speed applies, relative speed applies, and problems where you need to find time or distance when given certain conditions. You should use the formula:

Speed=DistanceTime

Distance=Speed×Time

Time=DistanceSpeed

Problems on speed, distance, and time generally form 2-3 questions in the CUET QA exam.

Average

This topic tests your ability to analyse data sets and use the appropriate formula for calculating averages. Simple problems involving the average of test scores, expenses, or prices are common, and you will need to calculate the mean to find solutions quickly.

Average=Sum of all observations/Number of observations

Weighted Average=∑i=1n(xi⋅wi)∑i=1nwi

In these formulas:

xi represents individual observations,

wi represents the weights corresponding to each observation.

The concept of average will be covered in approximately 2 to 3 questions in the CUET QA exam. This could include finding the average of a set of numbers, calculating weighted averages, determining average speed, average marks, or average income, among other types of questions.

Learn more about average.

Compound Interest

Compound interest questions ask you to calculate interest on the principal and the interest obtained over time by the formula:

Amount (A)=P(1+r100)n

Compound Interest (CI)=A−P=P((1+r100)n−1)

Where:

A is the amount after interest.

P is the principal amount.

r is the rate of interest per year.

n is the number of years.

Visit: Compound Interest

Simple Interest

Understanding the difference between simple interest and compound interest is crucial for CUET 2026 QA, particularly when working with financial calculations. Simple interest problems involve calculating interest on a principal amount over a specified period using the formula:

Simple Interest (SI)=P×R×T100

Where:

P = Principal amount

R = Rate of interest per annum

T = Time in years

You would expect 2-3 questions under the simple and compound interest. There are problems which talk about computing an interest, amounts or the amount of time it will take for a given amount of principal to grow under these conditions.

Learn more about Simple interest.

Median & Mode

Both median and mode being an important measures of the central tendency in data analysis. In CUET 2026 QA, you might be given a set of values, in which you may be asked to find its mean and mode. Below are the formulas for median and mode:

For a grouped frequency distribution:

Mode=L+(f1−f0)(2f1−f0−f2)×h

Where

L = Lower boundary of the modal class

f1 = Frequency of the modal class

f0 = Frequency of the class preceding the modal class

f2 = Frequency of the class succeeding the modal class

h = Class width

Median=L+(N2−F)f×h

L = Lower boundary of the median class

N = Total number of observations

F = Cumulative frequency of the class preceding the median class

f = Frequency of the median class

h = Class width

Learn about mode and median.

CUET 2026 Formula Memorisation Strategies

Memorising mathematical formulas effectively is crucial for scoring well in CUET 2026, as no formula resources are provided during the exam. The motive is to move beyond rote memorisation and develop understanding-based memory hacks that create lasting remembrance of formulas on the actual exam day.

Key Memorisation Tips:

• Create formula cards - Write each formula on one side of a card, with the topic/application on the other side for quick review

• Link formulas to real applications - Connect abstract formulas to practical problems you can visualise

• Practice daily writing - Write out 10-15 essential formulas from memory every morning to strengthen muscle memory

• Teach someone else - Explain formulas to friends or family members to reinforce your understanding

• Practice under time pressure - Set 2-minute timers to write as many formulas as possible from each chapter