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

CUET Maths Formulas: The Common University Entrance Test has a variety of subjects and topics. CUET is one of the competitive exams which works as a gateway for admissions in top colleges and universities across the nation. CUET UG has three sections i.e. Language section, general test and domain specific subject. One of its domain specific subjects include Mathematics, which covers the has matopics like Calculus, Algebra, Linear programming, etc.

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This Story also Contains

1. Overview of Syllabus and Exam Pattern
2. Chapterwise Distribution
3. Mathematics Formulae
4. Inverse Trigonometric Functions
5. ALGEBRA
6. CALCULUS
7. Quantitative Aptitude formulae

This article mainly discusses about the main and important formulae of the topics in mathematics. By going through this article, you will be able to strengthen your mathematics preparation for CUET syllabus 2025. A total weightage of questions was 85 in the year 2024 CUET .

Overview of Syllabus and Exam Pattern

The CUET 2025 has been designed to evaluate the knowledge and skills of candidates in various fields. The test can be divided into three separate sections, which are Section I-Language, Section II-Domain Specific Subjects, and Section III-General Test. In the first section, the comprehension of language is tested from English and other languages, according to the choice of the candidate.

Section II deals with the domain-specific topic opted by a student, either Mathematics or Physics or Chemistry or Biology, as the case may be, depending upon the stream chosen by the candidate. Section III will therefore test general knowledge, reasoning ability, and problem-solving skills.

As in 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 through the internet for a total duration of 3 hours, and one can choose more than one subject, and in several languages if that helps to gain admission into one's desired course.

Chapterwise Distribution

The CUET exam distributes questions related to different chapters such that it shall assess the candidates' overall understanding of the subject. Each subject has certain topics or chapters from which questions are drawn. Below is the no. of questions distribution based on the mathematics chapters in the CUET exam:

Mathematics Formulae

The mathematics formulae can be used in solving the General test’s Quantitative aptitude section and helps those who have mathematics as their domain subject. Below discussed is the importance and the topicwise 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 important formulae and properties for this section:

Assuming a function $f:A\to B$ and $\mathbb{R}$ is the set of real numbers, $A,B$ are two sets.

Relations

Reflexive Relation: $(a,a)\in \mathbb{R},$ $\mathrm{\forall }a\in A$

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

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

Learn more about the relation and its types.

Functions

One-one function (Injective): If $f(a_1)=f(a_2)$, then $⟹a_1=a_2$

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: $(fog)(x)=f(g(x))$

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 2024 from the chapter relations and functions.

Learn more about 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 $-1\le x\le 1$

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

• $\tan ({\tan }^{-1}x)=x$ for $\mathrm{\forall }x$

• $\cot ({\cot }^{-1}x)=x$ for $\mathrm{\forall }x$

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

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

Addition/ Subtraction Identities

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

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

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

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

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

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

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

Double and Half angle identities

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

• ${\cos }^{-1}(2x^2-1)=2{\cos }^{-1}x$

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

Learn more: Inverse trigonometric functions

A total of 2 questions were asked in CUET 2024 from the chapter inverse trigonometric functions.

ALGEBRA

For the algebra section, there are a lot of concepts of matrices and determinants, Matrices and determinants are a very central theme in the CUET QA exam, focusing on the operations matrices can go under, properties of these operations, and the use of determinants in solving a system 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 important 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: $kA=k{a}_{ij}$, where $k$ is a scalar.

Matrix Multiplication: $C_{ij}=\sum _{k=1}^n{a}_{ik}{b}_{kj}$

Cofactor: $C_{ij}=(-1{)}^{i+j}\cdot \text{Minor of}{a}_{ij}$

Inverse of a matrix: $A^{-1}=\frac{1}{\text{det}(A)}\cdot \text{adj}(A)$ provided $\text{det}(A)\ne 0$.

You may visit: Matrices, Types of matrices and determinants

A total of 11 questions were asked in CUET 2024 from the chapter matrices.

Determinants

Determinant of 2 order matrix: For a matrix $A=\left[\begin{array}{cc}a& b\\ c& d\end{array}\right]$,The determinant is: $det(A)=ad-bc$

Determinant of 3 order matrix: For a matrix $A=\left[\begin{array}{ccc}a& b& c\\ d& e& f\\ g& h& i\end{array}\right]$, 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 square matrix, and $A^{-1}$ is the inverse of $A$.

A total of 4 questions were asked in CUET 2024 from the chapter determinants.

CALCULUS

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

Continuity: $\underset{x\to c}{lim}f(x)=f(c)$

Differentiability: $f^{\prime }(x)=\underset{h\to 0}{lim}\frac{f(x+h)-f(x)}{h}$

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

A total of 4 questions were asked in CUET 2024 from the chapter continuity and differentiability.

Derivatives

Derivative of trigonometric functions:

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

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

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

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

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

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

Derivative of implicit functions:

$\frac{dy}{dx}=\frac{-F_x}{F_y}$

For Exponential and Logarithmic Functions:

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

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

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

Parametric Form Derivatives:

$\frac{dy}{dx}=\frac{\frac{dy}{dt}}{\frac{dx}{dt}}$

Second-Order Derivatives:

$f^{″}(x)=\frac{d}{dx}\left(\frac{d{f}^{\prime }(x)}{dx}\right)$

Tangent: $y-f(a)=f^{\prime }(a)(x-a)\text{(Equation of Tangent)}$

Normal: $y-f(a)=-\frac{1}{f^{\prime }(a)}(x-a)\text{(Equation of Normal)}$

Integration

$\int f^{\prime }(x)dx=f(x)+C$

$\int f(g(x))g^{\prime }(x)dx=\int f(u)du$

Integration by Parts:

$\int udv=uv-\int vdu$

Integration of Simple Functions:

$\int x^{n}dx=\frac{x^{n+1}}{n+1}+C(n\ne -1)$

$\int e^{x}dx=e^x+C$

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

Definite Integrals:

${\int }_a^{b}f(x)dx=F(b)-F(a)$

Learn about definite integrals.

Applications of Integrals

Area Under Curves: $A={\int }_a^{b}f(x)dx$

Area Between Curves: $A={\int }_a^b(f(x)-g(x))dx$

A total of 6 questions were asked in CUET 2024 from the chapter Integrals.

Differential Equations

$\frac{dy}{dx}=f(x,y)$

Solution of Linear Differential Equations:

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

$y=\frac{1}{\mu (x)}(\int \mu (x)Q(x)dx+C)$

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

$\mu =$ Integration constant

Visit: Differential equations

A total of 4 questions were asked in CUET 2024 from the chapter differential equations.

VECTORS AND THREE-DIMENSIONAL GEOMETRY

Vectors and Three-Dimensional Geometry is crucial for CUET 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 formula listed:

Vectors

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

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

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

Multiplication by a scalar: $k\mathbf{A}=(k{A}_x,k{A}_y,k{A}_z)$

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

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

Scalar (dot) product of vectors: $\mathbf{A}\cdot \mathbf{B}=A_x{B}_x+A_y{B}_y+A_z{B}_z$

Cross product: $\mathbf{A}\times \mathbf{B}=\left|\begin{array}{ccc}\hat{i}& \hat{j}& \hat{k}\\ A_x& A_y& A_z\\ B_x& B_y& B_z\end{array}\right|$

Scalar triple product: $\mathbf{A}\cdot (\mathbf{B}\times \mathbf{C})=\left|\begin{array}{ccc}{A}_x& A_y& A_z\\ B_x& B_y& B_z\\ C_x& C_y& C_z\end{array}\right|$

Learn more: Vectors

A total of 4 questions were asked in CUET 2024 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: $\cos \theta =\frac{\mathbf{A}\cdot \mathbf{B}}{|\mathbf{A}||\mathbf{B}|}$

Angle between two planes: $\cos \theta =\frac{{\mathbf{n}}_{\mathbf{1}}\cdot {\mathbf{n}}_{\mathbf{2}}}{|{\mathbf{n}}_{\mathbf{1}}||{\mathbf{n}}_{\mathbf{2}}|}$

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

Distance of a point from a plane: $\text{Distance}=\frac{|a{x}_1+b{y}_1+c{z}_1+d|}{\sqrt{a^2+b^2+c^2}}$

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 2024 from the three dimensional geometry.

LINEAR PROGRAMMING

Linear programming problem has variables, objective function and constraints. These are often used to represent equation and inequalities. Below are the formula listed:

Maximize or Minimize $Z=c_1{x}_1+c_2{x}_2+\cdots +c_n{x}_n$$\text{Subject to the constraints:}$$a_{11}{x}_1+a_{12}{x}_2+\cdots +a_{1n}{x}_n\le b_1$$a_{21}{x}_1+a_{22}{x}_2+\cdots +a_{2n}{x}_n\le b_2$$\dots$$a_{m1}{x}_1+a_{m2}{x}_2+\cdots +a_{mn}{x}_n\le b_m$$x_1,x_2,\dots ,x_n\ge 0$

A total of 6 questions were asked in CUET 2024 from the chapter linear programming and inequalties.

PROBABILITY

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

Multiplication Theorem on Probability: $P(A\cap B)=P(A|B)P(B)$

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

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

Total Probability Theorem: $P(A)=\sum _{i=1}^{n}P(A|B_i)P(B_i)$

Bayes’ Theorem: $P(B_i|A)=\frac{P(A|B_i)P(B_i)}{\sum _{j=1}^{n}P(A|B_j)P(B_j)}$

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

Mean and Variance of a Random Variable: $E(X)=\sum _{i=1}^n{x}_{i}P(X=x_i)$

Binomial Distribution: $P(X=k)=(\genfrac{}{}{0ex}{}{n}{k})p^k(1-p{)}^{n-k}$

Learn more about Probability.

The CUET 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 2024 from the chapter probability.

Quantitative Aptitude formulae

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

Mensuration

Mensuration is one of the prominent topics in CUET 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 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): $A=\sqrt{s(s-a)(s-b)(s-c)}\text{where}s=\frac{a+b+c}{2}$

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: $V=\pi r^{2}h$

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

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

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

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

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: $L=\frac{\theta }{360}\times 2\pi r$

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

Ratio

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

$\text{The ratio of two quantities is}a:b,\text{and their sum is}S,\text{then the quantities are:}\frac{a}{a+b}\times S\text{and}\frac{b}{a+b}\times S$

$\text{If}a:b=c:d,\text{then the cross multiplication rule applies:}ad=bc.$

$\text{If}a:b=c:d\text{and}b:c=e:f,\text{then}a:b:c=ae:be:bf.$

Learn about ratios.

Percentage

$\text{Percentage of a value}A\text{relative to}B=(\frac{A}{B}\times 100)\mathrm{\%}.$

$\text{If a value increases by}x\mathrm{\%}:\text{New value = Original value}\times (1+\frac{x}{100}).$

$\text{If a value decreases by}x\mathrm{\%}:\text{New value = Original value}\times (1-\frac{x}{100}).$

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

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

$\text{If a population increases by}r\mathrm{\%}\text{per year, the population after}n\text{years is:}P\times {(1+\frac{r}{100})}^n$

$\text{If a population decreases by}r\mathrm{\%}\text{per year, the population after}n\text{years is:}P\times {(1-\frac{r}{100})}^n$

$\text{Percentage change between two values:}\frac{\text{Difference in values}}{\text{Original value}}\times 100.$

Trigonometry

Applications of trigonometry are very important in CUET QA, including 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 QA. One should also be familiar with trigonometric identities, formulas involving angles, and their applications. Some of the important formulas and identities used in trigonometry are as follows :

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:

$\sin (2A)=2\sin A\cos A$

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

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

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:

$\sin (3A)=3\sin A-4{\sin }^{3}A$

$\cos (3A)=4{\cos }^{3}A-3\cos A$

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

Product-to-Sum Formulas:

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

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

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

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 calculations form a good quantitative reasoning base for CUET QA. This section tests the ability of doing quick and accurate calculations, involving percentages, ratios, averages, and other formula:

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

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 of key importance in solving other practical problems in connection with motion. You will meet questions where constant speed applies, relative speed apply, and problems where you need to find time or distance when given certain conditions. You should use the formula:

$\text{Speed}=\frac{\text{Distance}}{\text{Time}}$

$\text{Distance}=\text{Speed}\times \text{Time}$

$\text{Time}=\frac{\text{Distance}}{\text{Speed}}$

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

Average

This topic tests your ability to analyze 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 quickly calculate the mean to find solutions.

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

$\text{Weighted Average}=\frac{\sum _{i=1}^n(x_i\cdot w_i)}{\sum _{i=1}^n{w}_i}$

In these formulas:

$x_i$ represents individual observations,

$w_i$ represents the weights corresponding to each observation.

The concept of average will constitute around 2 to 3 questions in CUET QA exam. This could include finding the average of a set of numbers, weighted averages, or average speed, average marks, or average income type 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:

$\text{Amount (A)}=P{(1+\frac{r}{100})}^n$

$\text{Compound Interest (CI)}=A-P=P({(1+\frac{r}{100})}^n-1)$

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 vital for CUET QA, especially when dealing with financial calculations. Simple interest problems involve calculating interest on a principal amount over a specified time period using the formula:

$\text{Simple Interest (SI)}=\frac{P\times R\times T}{100}$

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 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 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:

$\text{Mode}=\text{L}+\frac{(f_1-f_0)}{(2f_1-f_0-f_2)}\times h$

Where

$L$ = Lower boundary of the modal class

$f_1$ = Frequency of the modal class

$f_0$ = Frequency of the class preceding the modal class

$f_2$ = Frequency of the class succeeding the modal class

$h$ = Class width

$\text{Median}=L+\frac{(\frac{N}{2}-F)}{f}\times h$

$L$ = 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.