SATHEE CUET: Course 1

Prepare for CUET UG Mathematics

Welcome to the comprehensive Mathematics preparation hub for CUET UG. This page organizes all available study materials, video lectures, practice questions, exams, and resources in one place.

📘 Preparation Guides

Expert-curated preparation guides for specific Mathematics topics in CUET UG:

📹 Video Lectures

Unit 1: Relations and Functions

Unit 2: Algebra

Unit 3: Calculus

Unit 4: Vectors and Three-Dimensional Geometry

Unit 5: Linear Programming

Unit 6: Three Dimensional Geometry

Unit 7: Statistical Inferences

📝 Study Notes

Unit-01 Sets and Functions

Unit-02 Algebra

Unit-03 Coordinate Geometry

Unit-04 Calculus

Chapter 12 Limits And Derivaties

Unit-05 Statistics and Probability

💡 Study Tips

Start with the Syllabus: Understand the complete syllabus before diving into topics
Follow the Video Lectures: Watch lectures organized by units for structured learning
Make Notes: Review study notes and create your own summaries
Practice Regularly: Solve practice questions to test your understanding
Take Mock Tests: Attempt exams to assess your preparation level

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📋 Important Prerequisites

Master these foundational topics for better understanding:

Algebra
Calculus
Trigonometry

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Total Resources: 13 Preparation Guides | 180 Video Lectures | 165 Notes | 0 Practice Questions | 0 Exams

Unit 2: Relations and Functions

Unit 3: Algebra

Unit 4: Calculus

Unit 5: Vectors and Three-Dimensional Geometry

Unit 8: Inferential Statistics

Unit 10: Linear Programming

Unit 2: Relations and Functions

Unit 3: Algebra

Unit 4: Calculus

Unit 5: Vectors and Three-Dimensional Geometry

SETS

RELATIONS AND FUNCTIONS

INVERSE TRIGONOMETRIC FUNCTIONS

MATRICES

DETERMINANTS

CONTINUITY, DIFFERENTIABILITY AND APPLICATION OF DERIVATIVES

INTEGRALS

APPLICATION OF INTEGRALS

DIFFERENTIAL EQUATIONS

VECTORS AND THREE-DIMENSIONAL GEOMETRY

LINEAR PROGRAMMING

PROBABILITY

NCERT Books

Mathematics Formula

Notes

Section A

Algebra
- Matrices and Types of Matrices
- Equality of Matrices
- Transpose of a Matrix
- Symmetric and Skew Symmetric Matrix
- Algebra of Matrices
- Determinants
- Inverse of a Matrix
- Solving Simultaneous Equations using Matrix Method
Calculus
- Higher Order Derivatives
- Tangents and Normals
- Increasing and Decreasing Functions
- Maxima and Minima
Integration and its Applications
- Indefinite Integrals of Simple Functions
- Evaluation of Indefinite Integrals
- Definite Integrals
Differential Equations
- Order and Degree of Differential Equations
- Formulating and Solving Differential Equations
- Variable Separable
Probability Distributions
- Random Variables and its Probability Distribution
- Expected Value of a Random Variable
- Variance and Standard Deviation of a Random Variable
- Binomial Distribution
Linear Programming
- Mathematical Formulation of Linear Programming Problem
- Graphical Method of Solution for Problems in Two Variables
- Feasible and Infeasible Regions
- Optimal Feasible Solution

Section B1: Mathematics

UNIT I: RELATIONS AND FUNCTIONS

Relations and Functions
- Types of relations: Reflexive, symmetric, transitive and equivalence relations.
- One to one and onto functions, composite functions,
- inverse of a function.
- Binary operations.
Inverse Trigonometric Functions
- Definition, range, domain, principal value branches.
- Graphs of inverse trigonometric functions.
- Elementary properties of inverse trigonometric functions.

UNIT II: ALGEBRA

Matrices
- Concept, notation, order, equality
- types of matrices
- zero matrix
- transpose of a matrix, symmetric and skew symmetric matrices.
- Addition, multiplication and scalar multiplication of matrices, simple properties of addition, multiplication and scalar multiplication.
- Non-commutativity of multiplication of matrices and existence of non-zero matrices whose product is the zero matrix (restrict to square matrices of order 2).
- Concept of elementary row and column operations.
- Invertible matrices and proof of the uniqueness of inverse, if it exists; (Here all matrices will have real entries).
Determinants
- Determinant of a square matrix (up to 3 × 3 matrices)
- properties of determinants
- minors, cofactors and applications of determinants in finding the area of a triangle.
- Adjoint
- inverse of a square matrix.
- Consistency, inconsistency and number of solutions of system of linear equations by examples, solving system of linear equations in two or three variables (having unique solution) using inverse of a matrix.

UNIT III: CALCULUS

Continuity and Differentiability
- Continuity and differentiability
- derivative of composite functions, chain rule
- derivatives of inverse trigonometric functions
- derivative of implicit function.
- Concepts of exponential, logarithmic functions.
- Derivatives of log x and e^x.
- Logarithmic differentiation.
- Derivative of functions expressed in parametric forms.
- Second-order derivatives.
- Rolle’s and Lagrange’s Mean Value Theorems (without proof) and their geometric interpretations.
Applications of Derivatives
- Applications of derivatives:
- Rate of change,
- increasing/decreasing functions
- tangents and normals
- approximation
- maxima and minima (first derivative test motivated geometrically and second derivative test given as a provable tool)
- Simple problems (that illustrate basic principles and understanding of the subject as well as real-life situations).
- Tangent and Normal.
Integrals
- Integration as inverseprocess of differentiation.
- Integration of avarietyof functions bysubstitution, bypartial fractions andbyparts, only simple integrals ofthetype –
- $$\int \frac{dx}{x^2 \pm a^2}, \quad \int \frac{dx}{\sqrt{x^2 \pm a^2}}, \quad \int \frac{dx}{\sqrt{a^2 - x^2}}, \quad \int \frac{dx}{ax^2 + bx + c}, \quad \int \frac{dx}{\sqrt{ax^2 + bx + c}},$$
- $$\int \frac{(px + q)}{ax^2 + bx + c} , dx, \quad \int \frac{(px + q)}{\sqrt{ax^2 + bx + c}} , dx, \quad \int \sqrt{a^2 \pm x^2} , dx \quad \text{and} \quad \int \sqrt{x^2 - a^2} , dx,$$
- $$\int \sqrt{ax^2 + bx + c} , dx \quad \text{and} \quad \int (px + q) \sqrt{ax^2 + bx + c} , dx $$ to be evaluated.
- Definite integrals as a limit of a sum.
- Fundamental Theorem of Calculus (without proof)
- Basic properties of definite integrals and evaluation of definite integrals.
Applications of the Integrals
- Applications in finding the area under simple curves,
- especially lines,
- arcs of circles/parabolas/ellipses (in standard form only),
- area between the two above said curves (the region should be clearly identifiable).
Differential Equations
- Definition, order and degree, general and particular solutions of a differential equation.
- Formation of differential equation whose general solution is given.
- Solution of differential equations by method of separation of variables
- homogeneous differential equations of first order and first degree.
- Solutions of linear differential equation of the type –
- $$\frac{dy}{dx} + Py = Q, \text {where P and Q are functions of x or constant}$$
- $$\frac{dx}{dy} + Px = Q, \text{where P and Q are functions of y or constant.} $$

UNIT IV: VECTORS AND THREE-DIMENSIONAL GEOMETRY

Vectors
- Vectors and scalars, magnitude and direction of a vector.
- Direction cosines/ratios of vectors.
- Types of vectors (equal, unit, zero, parallel and collinear vectors),
- position vector of a point,
- negative of a vector,
- components of a vector,
- addition of vectors,
- multiplication of a vector by a scalar,
- position vector of a point dividing a line segment in a given ratio.
- Scalar (dot) product of vectors, projection of a vector on a line.
- Vector (cross) product of vectors,
- scalar triple product.
Three-dimensional Geometry
- Direction cosines/ratios of a line joining two points.
- Cartesian and vector equation of a line,
- coplanar and skew lines,
- shortest distance between two lines.
- Cartesian and vector equation of a plane.
- Angle between (i) two lines, (ii) two planes, (iii) a line and a plane.
- Distance of a point from a plane.

Unit V: Linear Programming

Introduction, related terminology such as constraints, objective function, optimization,
different types of linear programming (L.P.) problems,
mathematical formulation of L.P. problems,
graphical method of solution for problems in two variables,
feasible and infeasible regions,
feasible and infeasible solutions,
optimal feasible solutions (up to three non-trivial constraints).

Unit VI: Probability

Multiplication theorem on probability.
Conditional probability, independent events, total probability, Baye’s theorem.
Random variable and its probability distribution, mean and variance of a random variable.
Repeated independent (Bernoulli) trials and Binomial distribution.

Section B2: Applied Mathematics

Unit I: Numbers, Quantification and Numerical Applications

Modulo Arithmetic
- Define modulus of an integer
- Apply arithmetic operations using modular arithmetic rules
Congruence Modulo
- Define congruence modulo
- Apply the definition in various problems
Allegation and Mixture
- Understand the rule of allegation to produce a mixture at a given price
- Determine the mean price of a mixture
- Apply rule of allegation
Numerical Problems
- Solve real life problems mathematically
Boats and Streams
- Distinguish between upstream and downstream
- Express the problem in the form of an equation
Pipes and Cisterns
- Determine the time taken by two or more pipes to fill or drain
Races and Games
- Compare the performance of two players w.r.t. time, distance taken/distance covered/ work done from the given data
Partnership
- Differentiate between active partner and sleeping partner
- Determine the gain or loss to be divided among the partners in the ratio of their investment with due consideration of the time
Numerical Inequalities
- Describe the basic concepts of numerical inequalities
- Understand and write numerical inequalities

UNIT II: ALGEBRA

Matrices and Types of Matrices
- Define matrix
- Identify different kinds of matrices
Equality of Matrices, Transpose of a Matrix, Symmetric and Skew Symmetric Matrix
- Determine equality of two matrices
- Write transpose of given matrix
- Define symmetric and skew symmetric matrix

UNIT III: CALCULUS

Higher Order Derivatives
- Determine second and higher order derivatives
- Understand differentiation of parametric functions and implicit functions
- Identify dependent and independent variables
Marginal Cost and Marginal Revenue Using Derivatives
- Define marginal cost and marginal revenue
- Find marginal cost and marginal revenue
Maxima and Minima
- Determine critical points of the function
- Find the point(s) of local maxima and local minima and corresponding local maximum and local minimum values
- Find the absolute maximum and absolute minimum value of a function

UNIT IV: PROBABILITY DISTRIBUTIONS

Probability Distribution
- Understand the concept of Random Variables and its Probability Distributions
- Find probability distribution of discrete random variable
Mathematical Expectation
- Apply arithmetic mean of frequency distribution to find the expected value of a random variable
Variance
- Calculate the Variance and S.D. of a random variable

UNIT V: INDEX NUMBERS AND TIME BASED DATA

Index Numbers
- Define Index numbers as a special type of average
Construction of Index Numbers
- Construct different types of index numbers
Test of Adequacy of Index Numbers
- Apply time reversal test
Time Series
- Identify time series as chronological data
Components of Time Series
- Distinguish between different components of time series
Time Series Analysis for Univariate Data
- Solve practical problems based on statistical data and interpret

UNIT VI: INFERENTIAL STATISTICS

Population and Sample
- Define Population and Sample
- Differentiate between population and sample
- Define a representative sample from a population
Parameter and Statistics and Statistical Inferences
- Define Parameter with reference to Population
- Define Statistics with reference to Sample
- Explain the relation between Parameter and Statistic
- Explain the limitation of Statistic to generalize the estimation for population
- Interpret the concept of Statistical Significance and Statistical Inferences
- State Central Limit Theorem
- Explain the relation between Population-Sampling Distribution-Sample

UNIT VII: FINANCIAL MATHEMATICS

Perpetuity, Sinking Funds
- Explain the concept of perpetuity and sinking fund
- Calculate perpetuity
- Differentiate between sinking fund and saving account
Valuation of Bonds
- Define the concept of valuation of bond and related terms
- Calculation of Bond Using Present Value Approach
Calculation of EMI
- Explain the concept of EMI
- Calculate EMI using various methods
Linear Method of Depreciation
- Define the concept of linear method of Depreciation
- Interpret cost, residual value and useful life of an asset from the given information
- Calculate depreciation

UNIT VIII: LINEAR PROGRAMMING

Introduction and Related Terminology
- Familiarize with terms related to Linear Programming Problem
Mathematical Formulation of Linear Programming Problem
- Formulate Linear Programming Problem
Different Types of Linear Programming Problems
- Identify and formulate different types of LPP
Graphical Method of Solution for Problems in Two Variables
- Draw the Graph for a system of linear inequalities involving two variables and to find its solution graphically
Feasible and Infeasible Regions
- Identify feasible, infeasible and bounded regions
Feasible and Infeasible Solutions, Optimal Feasible Solution
- Understand feasible and infeasible solutions
- Find optimal feasible solution

Mathematics

Prepare for CUET UG Mathematics

📘 Preparation Guides

📹 Video Lectures

Unit 1: Relations and Functions

Unit 2: Algebra

Unit 3: Calculus

Unit 4: Vectors and Three-Dimensional Geometry

Unit 5: Linear Programming

Unit 6: Three Dimensional Geometry

Unit 7: Statistical Inferences

📝 Study Notes

Unit-01 Sets and Functions

Unit-02 Algebra

Unit-03 Coordinate Geometry

Unit-04 Calculus

Unit-05 Statistics and Probability

💡 Study Tips

🔗 Related Subjects

📋 Important Prerequisites

🎯 Career Opportunities

🧭 Quick Navigation

Unit 2: Relations and Functions

Unit 3: Algebra

Unit 4: Calculus

Unit 5: Vectors and Three-Dimensional Geometry

Unit 8: Inferential Statistics

Unit 10: Linear Programming

Unit 2: Relations and Functions

Unit 3: Algebra

Unit 4: Calculus

Unit 5: Vectors and Three-Dimensional Geometry

SETS

RELATIONS AND FUNCTIONS

INVERSE TRIGONOMETRIC FUNCTIONS

MATRICES

DETERMINANTS

CONTINUITY, DIFFERENTIABILITY AND APPLICATION OF DERIVATIVES

INTEGRALS

APPLICATION OF INTEGRALS

DIFFERENTIAL EQUATIONS

VECTORS AND THREE-DIMENSIONAL GEOMETRY

LINEAR PROGRAMMING

PROBABILITY

Section A

Section B1: Mathematics

UNIT I: RELATIONS AND FUNCTIONS

UNIT II: ALGEBRA

UNIT III: CALCULUS

UNIT IV: VECTORS AND THREE-DIMENSIONAL GEOMETRY

Unit V: Linear Programming

Unit VI: Probability

Section B2: Applied Mathematics

Unit I: Numbers, Quantification and Numerical Applications

UNIT II: ALGEBRA

UNIT III: CALCULUS

UNIT IV: PROBABILITY DISTRIBUTIONS

UNIT V: INDEX NUMBERS AND TIME BASED DATA

UNIT VI: INFERENTIAL STATISTICS

UNIT VII: FINANCIAL MATHEMATICS

UNIT VIII: LINEAR PROGRAMMING

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NCERT Books

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