CUET Maths Important Topics & Chapter Wise Weightage

Number of questions

50 (compulsory)

Type of questions

Multiple Choice Question (MCQ)

CUET Maths exam duration

60 minutes

CUET marking scheme

+5 for each correct answer

-1 for each incorrect answer

Section A

Unit I: 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 of simultaneous equations using Matrix Method

Unit II: Calculus

• Higher Order Derivatives (upto second order)
• Increasing and Decreasing Functions
• Maxima and Minima

Unit III: Integration and its Applications

• Indefinite integrals of simple functions
• Evaluation of indefinite integrals
• Definite Integrals
• Application of Integration as area under the curve

Unit IV: Differential Equations

• Order and Degree of Differential Equations
• Solving of Differential Equations with Variable Separable

Unit V: Probability Distributions

• Simple Probability

Unit VI: Linear Programming

• Graphical Method of Solution for Problems in Two Variables
• Feasible and Infeasible Regions
• Optimal Feasible Solution

Section B (1)

Unit I: Relations And Functions

• Types of relations: Reflexive, symmetric, transitive and equivalence relations. One to one and onto functions.
• Inverse Trigonometric Functions: Definition, range, domain, principal value branches. Graphs 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.
  • Operations on matrices: Addition, multiplication and multiplication with a scalar. Simple properties of addition, multiplication and scalar multiplication.
  • Non-commutativity of multiplication of matrices and existence of non-zero matrices whose product isthe zero matrix (restrict to square matrices of order 2).
  • 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 (upto 3×3 matrices), minors, co-factors and applications of determinants in finding the area of a triangle.
  • Adjoint and 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
• Applications of Derivatives
• Integrals
• Applications of the Integrals
• Differential Equations

Unit IV: Vectors and Three Dimensional Geometry

• Vectors
• Three-dimensional Geometry

Unit V: Linear Programming

Introduction, related terminology such as constraints, objective function, optimization, graphical method of solution for problems in two variables, feasible and infeasible regions (bounded or unbounded), feasible and infeasible solutions, optimal feasible solutions (up to three non-trivial constraints).

Unit VI: Probability

• Conditional probability, Multiplications theorem on probability, independent events, total probability, Baye’s theorem.
• Random variable

Section B (2)

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 empty the tank
• Races and Games - Compare the performance of two players w.r.t. time, distance
• Numerical Inequalities
  • Describe the basic concepts of numerical inequalities
  • Understand and write numerical inequalities

UNIT II: Algebra

• Matrices and types 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
• Algebra of Matrices
  • Perform operations like addition & subtraction on matrices of same order
  • Perform multiplication of two matrices of appropriate order
  • Perform the multiplication of a scalar with matrix

• Determinant of Matrices

  • Determinant of a square matrix
  • Use elementary properties of determinants
  • Singular matrix, Non-singular matrix
  • |AB|=|A||B|
  • Simple problems to find determinant value
• Inverse of a Matrix
  • Define the inverse of a square matrix
  • Apply properties of inverse of matrices
  • Inverse of a matrix using cofactors

UNIT III: Calculus

• Higher Order Derivatives

• Application of Derivatives

• Marginal Cost and Marginal Revenue using derivatives

• Increasing/Decreasing Functions

• Maxima and Minima

• Integration

• Indefinite integrals as family of curves

• Definite Integral as area under the curve

• Application of Integration

• Differential Equations

UNIT IV: Probability And Distributions

• Probability Distribution
• Mathematical Expectation
• Variance

• Binomial Distribution

• Poisson Distribution

• Normal Distribution

UNIT V: Time Based Data

• Time Series

• Components of Time Series

• Time Series Analysis for Univariate Data

• Secular Trend

• Methods of Measuring trend

UNIT VI: Inefrential Statistics

• Population and Sample
• Parameter and Statistics and Statistical Interferences

• t-Test (one sample t-test for a small group sample)

UNIT VII: Financial Mathematics

• Perpetuity, Sinking Funds
• Calculation of EMI

• Calculation of Returns, Nominal Rate of Return

• CAGR
• Linear method of Depreciation
• Valuation of bonds

UNIT VIII: Linear Programming

• Introduction and related terminology
• Mathematical formulation of Linear Programming Problem
• Different types of Linear Programming Problems
• Graphical Method of Solution for problems in two Variables

• Feasible and Infeasible Regions

• Feasible and infeasible solutions, optimal feasible solution

Algebra

• Matrices and types of Matrices
• Determinants
• Inverse of a Matrix

2 - 3

Integration and its Applications

• Indefinite integrals of simple functions
• Definite Integrals

3 - 4

Calculus

• Higher-order derivatives
• Tangents and Normals
• Maxima and Minima
• Continuity and Differentiability
• Applications of Derivatives

3 - 4

Probability Distributions

• Random variables and its probability distribution, 
• Variance and Standard Deviation of a random variable
• Binomial Distribution

2 - 3

Differential Equations

• Order and degree of differential equations
• Formulating and solving of differential equations with variable separable

2 - 3

Relations and Functions

• Types of relations
• Inverse Trigonometric Functions

4 - 5

Linear Programming

• Mathematical formulation of LPP
• Graphical method of solution for problems in two variables
• Feasible and infeasible regions

2 - 3

Vectors

• Vectors and scalars
• components of a vector
• Vector(cross) product of vectors
• Scalar triple product

3 - 4

Integrals

• Integration as inverse process of differentiation
• Definite integrals as a limit of a sum
• Fundamental Theorem of Calculus
• Applications of Integrals
• Differential Equations

3 - 4

Probability

• Multiplications theorem on probability
• Conditional probability
• Baye’s theorem

2 - 3

3D Geometry

• Direction cosines/ratios of a line joining two points
• Cartesian and vector equation of a line

3 - 4

Numbers, Quantification and Numerical Applications

• Modulo Arithmetic
• Congruence Modulo
• Allegation and Mixture
• Numerical Problems
• Boats and Streams
• Pipes and Cisterns
• Races and Games

3 - 4

English

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Biology

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