CUET Maths Syllabus 2023, CUET Mathematics Syllabus PDF (2023)

CUET Mathematics Syllabus was released by National Testing Agency for the candidates who are going to appear in the Mathematics Exams. Candidates who are attempting to crack the Mathematics Entrance exams must have a clear understanding of the topics and the CUET syllabus that might be asked in the examination. Candidates will be given a question paper consisting of 45/50 questions out of which at least 35/40 questions must be attempted. Given below is an illustration of the same:

• There will be one Question Paper which will contain Two Sections i.e. Section A and Section B [B1 and B2].
• Section A will have 15 questions covering both i.e. Mathematics/Applied Mathematics which will be compulsory for all candidates
• Section B1 will have 30 questions from Mathematics out of which 20 questions need to be attempted. Section B2 will have 30 questions purely from Applied Mathematics out of which 20 questions will be attempted.
• Candidates can check the CUET paper patternfor understanding the exam patterns.
• Candidates must have an all-around understanding of the following topics.

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CUET Mathematics Syllabus 2023

SECTION A

Algebra

(i) Matrices and types of Matrices

(ii) Equality of Matrices, transpose of a Matrix, Symmetric and Skew Symmetric Matrix

(iii) Algebra of Matrices

(iv) Determinants

(v) Inverse of a Matrix

(vi) Solving of simultaneous equations using Matrix Method

Calculus

(i) Higher order derivatives

(ii) Tangents and Normals

(iii) Increasing and Decreasing Functions

(iv). Maxima and Minima

Integration and its Applications

(i) Indefinite integrals of simple functions

(ii) Evaluation of indefinite integrals

(iii) Definite Integrals

(iv). Application of Integration as area under the curve

Differential Equations

(i) Order and degree of differential equations

(ii) Formulating and solving of differential equations with variable separable

Probability Distributions

(i) Random variables and its probability distribution

(ii) Expected value of a random variable

(iii) Variance and Standard Deviation of a random variable

(iv). Binomial Distribution

Linear Programming

(i) Mathematical formulation of Linear Programming Problem

(ii) Graphical method of solution for problems in two variables

(iii) Feasible and infeasible regions

(iv). 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 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: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 andex. 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 inverse process of differentiation. Integration of a variety of functions by substitution, by partial fractions and by parts, only simple integrals of the type – 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/el-lipses (in standard form only), area between the two above said curves (the region should be cleraly 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 dy + Py = Q , where P and Q are functions of x or constant dy dxdy + Px = Q , where P and Q are functions of y or constant

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UNIT IV: VECTORS AND THREE-DIMENSIONAL GEOMETRY 1. 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, the 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, the shortest distance between two lines. Cartesian and vector equation of a plane. The 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

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

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Section B2: Applied Mathematics

Unit I:Numbers, Quantification, and Numerical Applications

• Allegation andMixture
  • Understand the rule of allegation to produce a mixture at a given price
  • Determine the mean price of a mixture
  • Apply rule of the allegation
• Modulo Arithmetic
  • Define the modulus of an integer
  • Apply arithmetic operations using modular arithmetic rules
• Congruence Modulo
  • Define congruence modulo
  • Apply the definition in various problems
• Numerical Problems
  • Solve real-life problems mathematically

• Boats and Streams
  • Express the problem in the formof an equation
  • Distinguish between upstream and downstream
• 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 to due
  • consideration of the time volume/surface area for solid formed using two or more shapes
• Pipes and cisterns
  • Determine the time taken by two or more pipes to fill or
• Boats and Streams
  • Distinguish between upstream and downstream
  • Express the problem in the form of an equation
• Races and games
  • Compare the performance of two players w.r.t. time,
  • distance taken/distance covered/ Work done from the given data
• 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 a 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 the probability distribution of the discrete random variable
• MathematicalExpectation
  • Apply arithmetic mean of frequency distribution to find the expected value of a random variabl
• Variance
  • Calculate the Variance and S.D.of a random variable

UNIT V:INDEX NUMBERS AND TIME-BASED DATA

• Construct different types of index numbers
  • Construction of index numbers
• Index Numbers
  • Define Index numbers as a special type of average
• Test of Adequacy of Index Numbers
  • Apply time reversal test

UNIT VI: UNIT V:INDEX NUMBERS AND TIME-BASED DATA

Population and Sample

• Define Population and Sample
• Differentiate between population and sample
• Define a representative sample from a population

Parameter and statistics and Statistical Interferences

• Define Parameter with reference to Population
• Define Statistics with reference to Sample
• Explain the relation between parameter and Statistic
• Explain the limitation of Statisticto 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:INDEX NUMBERS AND TIME-BASED DATA

• Distinguish between different components of time series
• Components of Time Series
• Time Series
  • Identify time series as chronological data
• Time Series analysis for univariate data
  • Solve practical problems based on statistical data and Interpret

UNIT VIII:FINANCIAL MATHEMATICS

• Calculation of EMI
  • Explain the concept of EMI
  • Calculate EMI using various methods
• 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 bonds and related terms
  • Calculate the value of the bond using the present value approach
• Linear method of Depreciation
  • Define the concept of linear method of Depreciation
  • Interpret the cost, residual value, and useful life of an asset from the given information
  • Calculate depreciation

UNIT IX:LINEAR PROGRAMMING

• Feasible and InfeasibleRegions
  • Identify feasible, infeasible and bounded regions
• Different types of Linear Programming Problems
  • Identify and formulate different types of LPP
• Introduction and related terminology
  • Familiarize with terms related to Linear Programming Problem
• Mathematical formulation of Linear ProgrammingProblem
  • Formulate Linear ProgrammingProblem
• 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 solutions, optimal feasible solution
  • Understand feasible and infeasible solutions
  • Find the optimal feasible solution

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List of Universities Offering CUET Mathematics Courses in 2023

Here are some of the expected Universities offering Mathematics coursesThese courses are at a Bachelor's as well as a Master's level. The list of universities, their codes and the names of courses offered have been tabulated below.

Find the CUET College List here!

CUET Mathematics Eligibility Criteria 2023

Candidates who are planning to appear for the CUET Exam 2023 are required to meet certain eligibility criteria mentioned by the respective Universities. These eligibility criteria are related to a candidate’s educational qualifications and age. The CUET Eligibility Criteria for the subject of Mathematics are different for every university. However, the expected basic eligibility criteria for every university are explained below.

• Candidates must have passed the 10+2 examination or Equivalent from a recognized Board/ University.
• The criteria for minimum percentage of marks scored in Class 12 differs for every University for all categories of candidates.
• There are certain eligibility criteria related to the subjects studied in Class 12. These criteria also differ based on the course and university you are applying for.
• Some Universities also put age limit restrictions. These eligibility criteria can be checked on the official notification of the university.

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Preparation Tips for CUET Mathematics Exam 2023

Although mathematics is regarded as a high-scoring subject, it can be troublesome and difficult for some candidates. Exam preparations can be confusing. There is so much that goes on in the mind of the candidate that they might start feeling anxious about the exam. Hence, we have curated a list of preparation tips that can help candidates score better marks in Mathematics in the CUET Exam 2023. Read these suggestions carefully and try implementing them.

• Go through the syllabus. Carefully examine all the topics you shall need to study.
• Make a list of all the topics that are your strengths and weaknesses.
• Start preparing a study plan that you can follow on a daily basis. Make sure that you provide some extra time to the list of topics that require more attention and focus.
• Take up one topic each day and practice several questions from that topic.
• Try to answer questions in a timed manner. Competitive exams require candidates to answer fast. They’re all about a candidate’s speed and accuracy of answering questions.
• Have a look at some of the previous year’s question papers. Notice the variety of questions, their difficulty level etc.
• Candidates must attempt mock tests everyday. They can begin practicing these mock tests 3-4 weeks before the exam.

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Study Material CUET Mathematics Exam 2023

Selecting the right sources of information during exam preparation is one of the key factors that can affect your chances of selection. Candidates are recommended to use study materials that are reliable, trustworthy and authentic. Candidates can prepare using the following list of study materials for the CUET Mathematics Exam 2023.

Books

Having books that are reliable and commonly used for exam preparation can improve your chances of getting your desired course in a university of your choice. We have provided a list of books that you can use to prepare for the subject of Mathematics in the CUET Exam 2023.

Check the list of CUET Books for Preparation here!

NCERT Books

Candidates must revise the topics of thesyllabus from the NCERT Books of Class 12 Mathematics. Candidates can download the chapter-wise PDFs provided in the table below to study certain topics from the Class12 NCERT Books.

Mock Tests

Candidates can purchase CUET Mock Testfrom the official website of Testbook at affordable prices to practice Math on a daily basis. These mock tests are highly recommended for all candidates as they help enhance your speed and effectiveness in answering questions. They also make you feel exam-ready and confident. Candidates who face exam anxiety should definitely practice some mock tests.

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