KCET 2025 Mathematics Syllabus - Important Topics, PDF and Weightage

Mathematical Reasoning

Problems, Negation, Quantifiers, Proving a Statement - Using the Method of Contradiction by giving Counter Examples, Compound Propositions, Logical Connectives, Definitions of Problems, and Proposition

• Logical Connectives
• Definition of Problems and Proposition
• Using Method of Contradiction by Giving Counter Example

Introduction to 3-D Geometry

Section Formula and Problems, Distance Between Two Points, Coordinates of a Point, Coordinate Planes and Coordinate Axes in 3-D

• Coordinate Planes and Coordinate Axes in 3-D
• Distance Between Two Points

Principle of Mathematical Induction

Simple Problems Based on Summation, Principle of Mathematical Induction, Process of the Proof of Induction, etc

• Principle of Mathematical Induction
• Simple Problems Based on Summation

Statistics

Analysis of Frequency Distributions with Equal Means (Different Variances), Mean Deviation, Range, Measure of Dispersion, Variance and Standard Deviation of Grouped or Ungrouped Data

• Analysis of Frequency Distributions with Equal Means
• Variance and Standard Deviation of Grouped or Ungrouped Data

Linear Inequalities

Algebraic Solutions of Linear Inequalities, Linear Inequalities, Graphic Solutions of Linear Inequalities, etc

Complex Numbers and Quadratic Equations

Square Root of a Complex Number given in Supplement and Problems, Solution of Quadratic Equations in the Complex Number System, Brief Description of Algebraic Properties of Complex Numbers, Need of Complex Numbers - esp. √

• Square Root of a Complex Number given in Supplement and Problems
• Solution of Quadratic Equations in the Complex Number System

Binomial Theorem

Coefficient of X(r), Middle Term, Term Independent of X, Finding Any Term, Problems Based on Expansion, General and Middle Term in Binomial Expansion, Pascal’s Triangle, History, etc

• Pascal’s Triangle
• Term Independent of X
• Coefficient of X(r)

Permutation and Combination

Combinations - Definition, Examples proving nCr= nPr r!, nCr = nCn-r; nCr +nCr-1 = n+1Cr, Fundamental Principle of Counting, Permutation when all the objects are not distinct, problems, Factorial permutations: Definition, examples, derivation of formulae nPr

• Examples proving nCr= nPr r!, nCr = nCn-r; nCr +nCr-1 = n+1Cr
• derivation of formulae nPr

Sets

Simple Practical Problems on Union and Intersection of Two Sets, Properties of Complement Sets, Complement of a Set, Difference of Sets, Union and Intersection of Sets, Universal Set, Power Set, Subsets of the set of real numbers especially intervals (with notations), Subsets, Equal Sets, Finite and Infinite Sets, Empty Set

• Difference of Sets, Union, and Intersection of Sets
• Subsets of the set of real numbers especially intervals
• Finite and Infinite Sets

Matrices

Concept of Elementary Row and Column Operations, Symmetric and Skew Symmetric Matrices, Transpose of a Matrix, Scalar Multiplication of Matrices, Multiplication, Addition, Equality of Matrices, Scalar and Unit Matrix, Diagonal Matrix, Zero Matrix, Square Matrix, Rectangular Matrix, Row Matrix and Column Matrix

• Square Matrix
• Scalar Multiplication of Matrices
• Symmetric and Skew Symmetric Matrices

Inverse Trigonometric Functions

Conversion of One Trigonometric Function to Another, Principle Value Branches, Domain, Range, Definition, Mentioning domain and range of trigonometric and inverse trigonometric functions

• Mentioning domain and range of trigonometric and inverse trigonometric functions
• Principle Value Branches

Linear Programming

Different Types of L.P.P, Mathematical Formulation of L.P.P, Non-Negativity Restrictions, Constraint Equations, Optimization, Objective Function, Introduction of L.P.P Definition of Constraints

• Mathematical Formulation of L.P.P, Non-Negativity Restrictions
• Introduction of L.P.P Definition of Constraints
• Different Types of L.P.P

Application of Integrals

Problems - Area Bounded by Two Above Curves, Arcs of Ellipses/Parabolas/Circles, Area Under the Curve

• Arcs of Ellipses/Parabolas/Circles
• Area Under the Curve

Mathematical Reasoning

06

Introduction to 3-D Geometry

07

Principle of Mathematical Induction

05

Statistics

07

Linear Inequalities

07

Complex Numbers and Quadratic Equations

09

Binomial Theorem

08

Permutation and Combination

09

Sets

08

Matrices

09

Inverse Trigonometric Functions

08

Linear Programming

07

Application of Integrals

08

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