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

Overview of CUET 2027 Exam Pattern

The CUET 2027 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.

CUET 2027 Mathematics Chapterwise Distribution

The CUET 2027 exam hands out questions that come from different chapter areas, so it can judge a candidate’s overall grasp of the subject. For each subject, there are specific themes, topics, or chapters where the questions are taken. From the table below, you can sort of analyse the kinds of questions and figure out which chapters they mostly originate from, so you can build a stronger preparation strategy for CUET 2027.

CUET 2027 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 is discussed 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: $(a,a)\in R,\ \forall a\in A$

Symmetric Relation: If $(a,b)\in R\Rightarrow(b,a)\in R$

Transitive Relation: If $(a,b)\in R$ and $(b,c)\in R$, then $(a,c)\in R$

Learn more about the relation and its types.

Functions

One-one function (Injective): If $f(a_1)=f(a_2)$, then $\Rightarrow a_1=a_2$
Onto function (Surjective): A function $f:A\to B$ is onto if for every $b\in B$, there exists an $a\in A$ such that $f(a)=b$.
Composite function: $(f\circ g)(x)=f(g(x))$
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 $-1\le x\le1$

$\cos(\cos^{-1}x)=x$ for $-1\le x\le1$

$\tan(\tan^{-1}x)=x$ for all $x$

$\cot(\cot^{-1}x)=x$ for all $x$

$\sec(\sec^{-1}x)=x$ for $|x|\ge1$

$\csc(\csc^{-1}x)=x$ for $|x|\ge1$

Addition/Subtraction Identities

$\sin^{-1}x+\cos^{-1}x=\frac{\pi}{2}$ for $-1\le x\le1$

$\tan^{-1}x+\cot^{-1}x=\frac{\pi}{2}$ for all $x$

$\sec^{-1}x+\csc^{-1}x=\frac{\pi}{2}$ for $|x|\ge1$

Negative Angle Identities

$\sin^{-1}(-x)=-\sin^{-1}x$

$\cos^{-1}(-x)=\pi-\cos^{-1}x$

$\tan^{-1}(-x)=-\tan^{-1}x$

$\cot^{-1}(-x)=\pi-\cot^{-1}x$

$\sec^{-1}(-x)=\pi-\sec^{-1}x$

$\csc^{-1}(-x)=-\csc^{-1}x$

Product Identities

$2\sin^{-1}x=\sin^{-1}\left(2x\sqrt{1-x^2}\right)$ for $-\frac{1}{2}\le x\le\frac{1}{2}$

$2\cos^{-1}x=\cos^{-1}(2x^2-1)$ for $0\le x\le1$

$2\tan^{-1}x=\tan^{-1}\left(\frac{2x}{1-x^2}\right)$ for $-1<x<1$

Double and Half-angle Identities

$\sin^{-1}x=\frac12\cos^{-1}(1-2x^2),\qquad 0\le x\le1$

$\cos^{-1}(2x^2-1)=2\sin^{-1}x,\qquad 0\le x\le1$

$\tan^{-1}\left(\frac{2x}{1-x^2}\right)=2\tan^{-1}x$ for $-1<x<1$

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 2027 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 $m\times n$.

• Equal Matrices: If $A=[a_{ij}]$ and $B=[b_{ij}]$, then $A=B$ if $a_{ij}=b_{ij}$ for all $i,j$.

• Symmetric Matrix: $A^T=A$ (transpose of $A$ is equal to $A$).

• Skew Symmetric Matrix: $A^T=-A$

• Transpose of a Matrix: $A^T=[a_{ji}]$

• Matrix Addition: If $A=[a_{ij}]$ and $B=[b_{ij}]$, then their sum $C=A+B$ is given by $C=[a_{ij}+b_{ij}]$

• Scalar Multiplication: $kA=[ka_{ij}]$, where $k$ is a scalar.

• Matrix Multiplication: $C_{ij}=\sum_{k=1}^{n}a_{ik}b_{kj}$

• Cofactor: $C_{ij}=(-1)^{i+j}\times(\text{Minor of }a_{ij})$

• Inverse of a matrix: $A^{-1}=\frac{1}{\det(A)}\cdot\operatorname{adj}(A)$ provided $\det(A)\ne0$

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 $A=\begin{bmatrix}a & b \\ c & d\end{bmatrix}$, the determinant is: $\det(A)=ad-bc$

Determinant of 3 order matrix: For a matrix $A=\begin{bmatrix}a & b & c \\ d & e & f \\ g & h & i\end{bmatrix}$, the determinant is: $\det(A)=a(ei-fh)-b(di-fg)+c(dh-eg)$

Solution of linear equations: $X=A^{-1}B$, 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: $\lim_{x\to c}f(x)=f(c)$

Differentiability: $f'(x)=\lim_{h\to0}\dfrac{f(x+h)-f(x)}{h}$

Chain Rule: $\dfrac{dy}{dx}=\dfrac{dy}{du}\cdot\dfrac{du}{dx}$

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

Derivatives

Derivative of trigonometric functions:

$\dfrac{d}{dx}\sin^{-1}(x)=\dfrac{1}{\sqrt{1-x^2}}$

$\dfrac{d}{dx}\cos^{-1}(x)=\dfrac{-1}{\sqrt{1-x^2}}$

$\dfrac{d}{dx}\tan^{-1}(x)=\dfrac{1}{1+x^2}$

$\dfrac{d}{dx}\cot^{-1}(x)=\dfrac{-1}{1+x^2}$

$\dfrac{d}{dx}\sec^{-1}(x)=\dfrac{1}{|x|\sqrt{x^2-1}}$

$\dfrac{d}{dx}\csc^{-1}(x)=\dfrac{-1}{|x|\sqrt{x^2-1}}$

Derivative of implicit functions:
$\dfrac{dy}{dx}=-\dfrac{F_x}{F_y}$

Exponential and Logarithmic Functions:

$\dfrac{d}{dx}e^x=e^x$

$\dfrac{d}{dx}\log x=\dfrac{1}{x}$

$\ln y=g(x)\ln f(x)$

Parametric Form Derivatives:
$\dfrac{dy}{dx}=\dfrac{dy/dt}{dx/dt}$

Second-Order Derivatives:
$f''(x)=\dfrac{d}{dx}\left(\dfrac{df'(x)}{dx}\right)$

Tangent:
$y-f(a)=f'(a)(x-a)$ (Equation of Tangent)

Normal:
$y-f(a)=-\dfrac{1}{f'(a)}(x-a)$ (Equation of Normal)

Integration

$\int f'(x)\,dx=f(x)+C$

$\int f(g(x))g'(x)\,dx=\int f(u)\,du$

Integration by Parts:
$\int u\,dv=uv-\int v\,du$

Integration of Simple Functions:
$\int x^n\,dx=\dfrac{x^{n+1}}{n+1}+C,\; n\neq-1$

$\int e^x\,dx=e^x+C$

$\int \dfrac{1}{x}\,dx=\ln|x|+C$

Definite Integrals:
$\int_a^b f(x)\,dx=F(b)-F(a)$

Learn about definite integrals.

Area Under Curves:
$A=\int_a^b f(x)\,dx$

Area Between Curves:
$A=\int_a^b\left(f(x)-g(x)\right)\,dx$

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

Differential Equations

Differential Equations:
$\dfrac{dy}{dx}=f(x,y)$

Solution of Linear Differential Equations:

$\dfrac{dy}{dx}+P(x)y=Q(x)$

$y=\dfrac{1}{\mu(x)}\left(\int\mu(x)Q(x)\,dx+C\right)$

$\mu(x)=e^{\int P(x)\,dx}$

$C=$ Integration constant

Learn more about: 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 2027 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 vector quantities, planes, lines and angles. Below are the formulas listed:

Vectors

• Magnitude of a vector: $|A|=\sqrt{A_x^2+A_y^2+A_z^2}$

• Direction cosines of a vector: $\cos\alpha=\frac{A_x}{|A|},\ \cos\beta=\frac{A_y}{|A|},\ \cos\gamma=\frac{A_z}{|A|}$

• Addition of vectors: $A+B=(A_x+B_x,\ A_y+B_y,\ A_z+B_z)$

• Multiplication by a scalar: $kA=(kA_x,\ kA_y,\ kA_z)$

• Position vector: $r=x\hat{i}+y\hat{j}+z\hat{k}$

• Negative of a vector: $-A=(-A_x,\ -A_y,\ -A_z)$

• Scalar (dot) product of vectors: $A\cdot B=A_xB_x+A_yB_y+A_zB_z$

• Cross product: $A\times B=\begin{vmatrix}\hat{i}&\hat{j}&\hat{k}\\A_x&A_y&A_z\\B_x&B_y&B_z\end{vmatrix}$

• Scalar triple product: $A\cdot(B\times C)=\begin{vmatrix}A_x&A_y&A_z\\B_x&B_y&B_z\\C_x&C_y&C_z\end{vmatrix}$

Learn more: Vectors

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

3-D Geometry

• Direction cosines: $\cos\alpha=\frac{x_2-x_1}{\sqrt{(x_2-x_1)^2+(y_2-y_1)^2+(z_2-z_1)^2}},\ \cos\beta=\frac{y_2-y_1}{\sqrt{(x_2-x_1)^2+(y_2-y_1)^2+(z_2-z_1)^2}},\ \cos\gamma=\frac{z_2-z_1}{\sqrt{(x_2-x_1)^2+(y_2-y_1)^2+(z_2-z_1)^2}}$

• Equation of a line: $\mathbf{r}=\mathbf{a}+\lambda\mathbf{b}$

• Equation of a line (Cartesian form): $\frac{x-x_1}{a}=\frac{y-y_1}{b}=\frac{z-z_1}{c}$

• Angle between two lines: $\cos\theta=\frac{A\cdot B}{|A||B|}$

• Angle between two planes: $\cos\theta=\frac{n_1\cdot n_2}{|n_1||n_2|}$

• Angle between a line and a plane: $\cos\theta=\frac{l\cdot n}{|l||n|}$

• Distance of a point from a plane: $\mathrm{Distance}=\frac{|ax_1+by_1+cz_1+d|}{\sqrt{a^2+b^2+c^2}}$

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:

Linear Programming Problem (LPP):

Maximise or Minimise $Z=c_1x_1+c_2x_2+\cdots+c_nx_n$

Subject to the constraints:

$a_{11}x_1+a_{12}x_2+\cdots+a_{1n}x_n\le b_1$ $a_{21}x_1+a_{22}x_2+\cdots+a_{2n}x_n\le b_2$
$\vdots$
$a_{m1}x_1+a_{m2}x_2+\cdots+a_{mn}x_n\le b_m$

Non-negativity constraints:
$x_1,x_2,\ldots,x_n\ge0$

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: $P(A\cap B)=P(A\mid B)P(B)$

• Conditional Probability: $P(A\mid B)=\frac{P(A\cap B)}{P(B)}$

• Independent Events: $P(A\cap B)=P(A)P(B)$

• Total Probability Theorem: $P(A)=\sum_{i=1}^{n}P(A\mid B_i)P(B_i)$

• Bayes' Theorem: $P(B_i\mid A)=\frac{P(A\mid B_i)P(B_i)}{\sum_{j=1}^{n}P(A\mid B_j)P(B_j)}$

• Random Variable and Probability Distribution: $\sum_{i=1}^{n}P(X=x_i)=1$

• Mean and Variance of a Random Variable: $E(X)=\sum_{i=1}^{n}x_iP(X=x_i)$

• Binomial Distribution: $P(X=k)=\binom{n}{k}p^k(1-p)^{n-k}$

Learn more about Probability.

The CUET 2027 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

Quantitative Aptitude is one of the most essential parts of the CUET 2027 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 2027 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 2027 QA are :

• Area of a Circle: $A=\pi r^2$

• Circumference of a Circle: $C=2\pi r$

• Area of a Triangle (Heron's formula): $A=\sqrt{s(s-a)(s-b)(s-c)}$ where $s=\frac{a+b+c}{2}$

• Area of a Rectangle: $A=l\times b$

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

• Surface Area of a Sphere: $A=4\pi r^2$

• Volume of a Sphere: $V=\frac{4}{3}\pi r^3$

• Surface Area of a Cylinder: $A=2\pi r(h+r)$

• Volume of a Cylinder: $V=\pi r^2h$

• Lateral Surface Area of a Cylinder: $A=2\pi rh$

• Surface Area of a Cone: $A=\pi r(l+r)$ where $l=\sqrt{r^2+h^2}$

• Volume of a Cone: $V=\frac{1}{3}\pi r^2h$

• Curved Surface Area of a Cone: $A=\pi rl$ where $l=\sqrt{r^2+h^2}$

• Area of a Parallelogram: $A=b\times h$

• Area of a Rhombus: $A=\frac{1}{2}\times d_1\times d_2$

• Area of a Trapezium: $A=\frac{1}{2}\times(a+b)\times h$

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

• Volume of a Cuboid: $V=l\times b\times h$

• Surface Area of a Cube: $A=6a^2$

• Volume of a Cube: $V=a^3$

• Diagonal of a Cube: $d=\sqrt{3}a$

• Diagonal of a Cuboid: $d=\sqrt{l^2+b^2+h^2}$

• Length of an Arc of a Circle: $L=\frac{\theta}{360}\times2\pi r$

• Area of a Sector of a Circle: $A=\frac{\theta}{360}\times\pi r^2$

• Surface Area of a Hemisphere: $A=3\pi r^2$

• Volume of a Hemisphere: $V=\frac{2}{3}\pi r^3$

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 2027 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

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

Two quantities with given ratio and sum: If the ratio of two quantities is $a:b$, and their sum is $S$, then the quantities are: $\frac{a}{a+b}\times S$ and $\frac{b}{a+b}\times S$.

Cross multiplication rule: If $a:b=c:d$, then $ad=bc$.

Extending ratio to three quantities: 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: $\mathrm{Percentage\ of\ }A\mathrm{\ relative\ to\ }B=\frac{A}{B}\times100$

Increase by $x\%$: $\mathrm{New\ value}=\mathrm{Original\ value}\times\left(1+\frac{x}{100}\right)$

Decrease by $x\%$: $\mathrm{New\ value}=\mathrm{Original\ value}\times\left(1-\frac{x}{100}\right)$

Successive percentage changes of $x\%$ and $y\%$: $\mathrm{Effective\ change}=x+y+\frac{xy}{100}$

To calculate $x\%$ of a number $N$: $\mathrm{Result}=\frac{x}{100}\times N$

Population increase by $r\%$ per year: $\mathrm{Population\ after\ }n\mathrm{\ years}=P\left(1+\frac{r}{100}\right)^n$

Population decrease by $r\%$ per year: $\mathrm{Population\ after\ }n\mathrm{\ years}=P\left(1-\frac{r}{100}\right)^n$

Percentage change between two values: $\mathrm{Percentage\ change}=\frac{\mathrm{Difference\ in\ values}}{\mathrm{Original\ value}}\times100$

Trigonometry

Applications of Trigonometry in CUET 2027 QA are vital for solving questions on heights, distances, and angles. CUET often features problems using sine, cosine, tangent, and their reciprocals. A strong grasp of trigonometric identities, angle formulas, and key applications is essential for scoring well. Here are the most important trigonometry formulas and identities for CUET 2027 QA:

Basic Trigonometric Ratios:

• $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$

• $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$

• $\tan\theta=\frac{\sin\theta}{\cos\theta}=\frac{\text{opposite}}{\text{adjacent}}$

• $\cot\theta=\frac{\cos\theta}{\sin\theta}=\frac{\text{adjacent}}{\text{opposite}}$

• $\sec\theta=\frac{1}{\cos\theta}$

• $\csc\theta=\frac{1}{\sin\theta}$

Pythagorean Identities:

• $\sin^2\theta+\cos^2\theta=1$

• $1+\tan^2\theta=\sec^2\theta$

• $1+\cot^2\theta=\csc^2\theta$

Sum and Difference Formulas:

• $\sin(A\pm B)=\sin A\cos B\pm\cos A\sin B$

• $\cos(A\pm B)=\cos A\cos B\mp\sin A\sin B$

• $\tan(A\pm B)=\frac{\tan A\pm\tan B}{1\mp\tan A\tan B}$

Double Angle Formulas:

• $\sin(2A)=2\sin A\cos A$

• $\cos(2A)=\cos^2A-\sin^2A=2\cos^2A-1=1-2\sin^2A$

• $\tan(2A)=\frac{2\tan A}{1-\tan^2A}$

Half-Angle Formulas:

• $\sin\left(\frac{A}{2}\right)=\pm\sqrt{\frac{1-\cos A}{2}}$

• $\cos\left(\frac{A}{2}\right)=\pm\sqrt{\frac{1+\cos A}{2}}$

• $\tan\left(\frac{A}{2}\right)=\pm\sqrt{\frac{1-\cos A}{1+\cos A}}$

Triple Angle Formulas:

• $\sin(3A)=3\sin A-4\sin^3A$

• $\cos(3A)=4\cos^3A-3\cos A$

• $\tan(3A)=\frac{3\tan A-\tan^3A}{1-3\tan^2A}$

Product-to-Sum Formulas:

• $\sin A\sin B=\frac{1}{2}\left[\cos(A-B)-\cos(A+B)\right]$

• $\cos A\cos B=\frac{1}{2}\left[\cos(A-B)+\cos(A+B)\right]$

• $\sin A\cos B=\frac{1}{2}\left[\sin(A+B)+\sin(A-B)\right]$

Sum-to-Product Formulas:

• $\sin A+\sin B=2\sin\left(\frac{A+B}{2}\right)\cos\left(\frac{A-B}{2}\right)$

• $\sin A-\sin B=2\cos\left(\frac{A+B}{2}\right)\sin\left(\frac{A-B}{2}\right)$

• $\cos A+\cos B=2\cos\left(\frac{A+B}{2}\right)\cos\left(\frac{A-B}{2}\right)$

• $\cos A-\cos B=-2\sin\left(\frac{A+B}{2}\right)\sin\left(\frac{A-B}{2}\right)$

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 in CUET 2027 QA tests your speed and accuracy with calculations involving percentages, ratios, averages, and basic formulas - forming the core of quantitative reasoning preparation.

• Sum of an Arithmetic Series: $S_n=\frac{n}{2}\left[2a+(n-1)d\right]$

• Nth Term of an Arithmetic Sequence: $T_n=a+(n-1)d$

• Sum of First $n$ Natural Numbers: $S_n=\frac{n(n+1)}{2}$

• Sum of Squares of First $n$ Natural Numbers: $S_n=\frac{n(n+1)(2n+1)}{6}$

• Sum of Cubes of First $n$ Natural Numbers: $S_n=\left(\frac{n(n+1)}{2}\right)^2$

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: $\mathrm{Speed}=\frac{\mathrm{Distance}}{\mathrm{Time}}$

Distance: $\mathrm{Distance}=\mathrm{Speed}\times\mathrm{Time}$

Time: $\mathrm{Time}=\frac{\mathrm{Distance}}{\mathrm{Speed}}$

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: $\mathrm{Average}=\frac{\mathrm{Sum\ of\ all\ observations}}{\mathrm{Number\ of\ observations}}$

Weighted Average: $\mathrm{Weighted\ Average}=\frac{\sum_{i=1}^{n}(x_i\cdot w_i)}{\sum_{i=1}^{n}w_i}$

Note: In these formulas, $x_i$ represents the individual observations and $w_i$ represents the corresponding weights.

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 the 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): $A=P\left(1+\frac{r}{100}\right)^n$

• Compound Interest (CI): $CI=A-P=P\left[\left(1+\frac{r}{100}\right)^n-1\right]$

Where:
A is the amount after interest, P is the principal amount, r is the rate of interest per year, and n is the number of years.

Learn more about: Compound Interest

Simple Interest

Understanding the difference between simple interest and compound interest is crucial for CUET 2027 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): $SI=\frac{PRT}{100}$

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 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 the median and the mode are important measures of the central tendency in data analysis. In CUET 2027 QA, you might be given a set of values, in which you may be asked to find the mean and mode. Below are the formulas for median and mode:

Mode (for grouped data): $\mathrm{Mode}=L+\frac{f_1-f_0}{2f_1-f_0-f_2}\times h$

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 (for grouped data): $\mathrm{Median}=L+\frac{\frac{N}{2}-F}{f}\times h$

Where:
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 2027 Formula Memorisation Strategies

Memorising mathematical formulas properly is important if you want good marks in CUET 2027 because during the exam, no formula resources are given. The idea is to get out of simple rote memorisation and build understanding-based memory tricks that stick, like real remembrance, when you’re sitting on the actual exam day.

Key Memorisation Tips:

• Create formula cards - Write each formula on one side of a card, then on the other side add the topic or use-case, so it becomes easy for quick revision.

• Link formulas to real applications - Instead of keeping them abstract, connect each expression with practical problems you can actually imagine.

• Practice daily writing - Every morning, write 10-15 important formulas from memory. This builds muscle memory and reduces last-minute panic.

• Teach someone else - Explain the formulas to a friend or family member. When you talk it out, the logic becomes sharper.

• Practice under time pressure - Use a 2-minute timer and try to write as many formulas as possible from one chapter, without looking.

Benefits of Using CUET 2027 Maths Formulas

• Having a complete CUET 2027 maths formula sheet can give several advantages to aspirants. First, it helps you do a quick revision before the exam, so recalling formulas under pressure becomes easier.

• Also, doing regular formula revision improves problem-solving speed, so you can handle tough questions more efficiently. It can also show you which chapters matter most and which high-weight topics repeat often, so your studying stays focused and strategic.

• Finally, if you rely on a structured formula list, it improves accuracy and confidence, which naturally lowers silly mistakes and exam anxiety.

How to Use CUET 2027 Maths Formulas Effectively

Learning CUET 2027 maths formulas isn’t only about mugging them; it’s about applying them the right way in questions, previous year sets, and mock tests. Below are strategies to push speed, accuracy, and conceptual clarity together.

Step-by-Step Approach to Memorisation and Practice

Group formulas by chapters and revise them daily. Use flashcards, formula sheets, and handwritten notes so the recall becomes automatic. Start with easier examples first, then move to harder CUET-level questions, so you understand where and why a formula works, not just when to use it.

Combining Formulas with Previous Year Questions

Mix CUET previous-year questions with your formula practice. This makes it easier to spot repeated patterns, high-frequency question types, and overall exam trends, so your preparation matches the CUET 2027 exam style more closely.

Using Solved Examples to Strengthen Conceptual Clarity

While learning each chapter, use solved examples alongside the formulas. This improves problem-solving speed and accuracy, and it links the theory behind the formula to practical use. If you keep revisiting solved examples regularly, retention becomes better, and your confidence improves for CUET 2027.