# Crucial topics for CAT

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## Mathematics

Following are the topics available in the NCERT Books. Please refer the NCERT Books section available on the website.

- Basic Building I: NUMBERS, WHOLE NUMBERS, BASIC GEOMETRICAL IDEAS, UNDERSTANDING ELEMENTARY SHAPES, INTEGERS, FRACTIONS, DECIMALS, DATA HANDLING, MENSURATION, ALGEBRA, RATIO AND PROPORTION, SYMMETRY, PRACTICAL GEOMETRY
- Basic Building II: Integers, Fractions and Decimals, Data Handling, Simple Equations, Lines and Angles, The Triangle and its Properties, Congruence of Triangles, Comparing Quantities, Rational Numbers, Practical Geometry, Perimeter and Area, Algebraic Expressions, Exponents and Powers, Symmetry and Visualizing Basic Shapes.
- Basics III: Rational Numbers, Linear Equations in One Variable, Understanding Quadrilaterals, Practical Geometry, Data Handling, Squares and Square Roots, Cubes and Cube Roots, Comparing Quantities, Algebraic Expressions and Identities, Visualising Solid Shapes, Mensuration, Exponents and Powers, Direct and Inverse Proportions, Factorisation, Introduction to Graphs and Playing with Numbers.
- Basics IV: NUMBER SYSTEMS, POLYNOMIALS, COORDINATE GEOMETRY, LINEAR EQUATIONS IN TWO VARIABLES, Introduction TO EUCLID's GEOMETRY, LINES AND ANGLES, TRIANGLES, QUADRILATERALS, AREAS OF PARALLELOGRAMS AND TRIANGLES, CIRCLES, CONSTRUCTIONS, HERON's FORMULA, SURFACE AREAS AND VOLUMES, STATISTICS, PROBABILITY.
- Advanced I: Real Numbers, Polynomials, Pair of Linear Equations in Two Variables, Quadratic Equations, Arithmetic Progressions, Triangles, Coordinate Geometry, Introduction to Trigonometry, Some Applications of Trigonometry, Circles, Constructions, Areas Related to Circles, Surface Areas and Volumes, Statistics, Probability.
- Advanced II: Sets, Relations and Functions, Trigonometric Functions, Principle of Mathematical Induction, Complex Numbers and Quadratic Equations, Linear Inequalities, Permutations and Combinations, Binomial Theorem, Sequences and Series, Straight Lines, Conic Sections, Introduction to Three Dimensional Geometry, Limits and Derivatives, Mathematical Reasoning, Statistics, Probability.
- Advanced III: Relations and Functions, Inverse Trigonometric Functions, Matrices, Determinants Continuity and Differentiability and Application of Derivatives.
- Advanced IV: Integrals, Application of Integrals, Differential Equations, Vector Algebra, Three Dimensional Geometry, Linear Programming and Probability.
- Problems I: NUMBER SYSTEMS, POLYNOMIALS, COORDINATE GEOMETRY, LINEAR EQUATIONS IN TWO VARIABLES, Introduction TO EUCLID's GEOMETRY, LINES AND ANGLES, TRIANGLES, QUADRILATERALS, AREAS OF PARALLELOGRAMS AND TRIANGLES, CIRCLES, CONSTRUCTIONS, HERON's FORMULA, SURFACE AREAS AND VOLUMES, STATISTICS, PROBABILITY.
- Problems II: Real Numbers, Polynomials, Pair of Linear Equations in Two Variables, Quadratic Equations, Arithmetic Progressions, Triangles, Coordinate Geometry, Introduction to Trigonometry, Some Applications of Trigonometry, Circles, Constructions, Areas Related to Circles, Surface Areas and Volumes, Statistics, Probability.
- Problems III: Questions on Sets, Relations and Functions, Trigonometric Functions, Principle of Mathematical Induction, Complex Numbers and Quadratic Equations, Linear Inequalities, Permutations and Combinations, Binomial Theorem, Sequences and Series, Straight Lines, Conic Sections, Introduction to Three Dimensional Geometry, Limits and Derivatives, Mathematical Reasoning, Statistics, Probability.