HTET PGT MATHS  SYLLABUS

Arithmetic, Algebra & Trigonometry

• Real number system and its analysis

• Arithmetic Progressions

• Polynomials

• Linear equations in two variables

• Quadratic Equations

• Introduction to Trigonometry

• Applications of Trigonometry (Heights and Distances)

Geometry & Mensuration

• Euclid's Geometry

• Lines and Angles

• Congruence and Similarity of Triangles

• Quadrilateral

• Circle

• Heron's Formula

• Area related to Circles

• Surface Area and Volumes of Combination of Solids

Statistics & Probability

• Bar graph

• Histogram

• Frequency Polygon

• Measures of Central Tendency: Mean, Median, Mode

• Measures of Dispersion: Range, Mean deviation, Variance, Standard deviation (ungrouped/grouped data)

• Probability – Theoretical Approach

Class 11–12 Level Keywords

Sets, Relations & Functions

• Sets and their Representations

• Types of Sets

• Venn Diagrams

• Operations on Sets: Union, Intersection, Difference

• Complement of a Set

• Ordered Pairs

• Cartesian Product of Sets

• Relation and its Types

• Function and its Types

• Algebra of Functions

• Composition of Functions

• Invertible Functions

• Radian and Degree Measure

• Trigonometric Functions and their Graphs

• Principal Value

• Properties of Inverse Trigonometric Functions

Algebra

• Complex Numbers and Quadratic Equations

• Argand Plane

• Linear Inequalities

• Linear Programming Problem – Mathematical Formation

• Permutations and Combinations

• Binomial Theorem

• Pascal’s Triangle

• Sequences and Series (G.P.)

• Relation between Arithmetic and Geometric Means

• Matrices and its Types

• Operations on Matrices

• Transpose of a Matrix

• Symmetric and Skew Symmetric Matrices

• Invertible Matrices

• Determinants of order 1, 2, 3

• Area of a Triangle using Determinants

• Minors and Cofactors

• Adjoint and Inverse of a Matrix

• Solution of System of Linear Equations using Inverse of a Matrix

Calculus

• Intuitive Idea of Limit

• Limits of functions (Polynomial, Rational, Trigonometric, Exponential, Logarithmic)

• Continuity and Differentiability

• Algebra of Continuous and Differentiable Functions

• Definition of Derivative

• Algebra of Derivatives

• Derivatives of different functions:

  • Polynomial function

  • Trigonometric function

  • Composite functions

  • Chain Rule

  • Implicit functions

  • Inverse Trigonometric functions

  • Exponential and Logarithmic functions

• Logarithmic Differentiation

• Derivatives of Parametric Forms

• Second Order Derivative

• Rate of Change of Quantities

• Applications of Derivatives: Increasing/Decreasing functions, Maxima and Minima

• Integration: Process, Methods, Fundamental Theorem of Calculus

• Definite Integrals by Substitution, Properties of Definite Integrals

• Applications of Integrals: Area under Simple Curves

Vectors & Coordinate Geometry

• Two and Three Dimensional Coordinate Geometry

• Straight Lines

• Conic Sections (circle, ellipse, parabola, hyperbola, degenerate cases)

• Coordinate axes & planes in 3D

• Distance between two points

• Vectors: Definition, Position Vector, Direction Cosines, Types

• Addition of Vectors, Multiplication by Scalar

• Components of a Vector

• Vector joining Two Points

• Section Formula

• Scalar (dot) Product of Two Vectors

• Projection of a Vector on a Line

• Vector (cross) Product of Two Vectors

• Direction Cosines & Ratios of a Line

• Equation of a Line in Space

• Angle between Two Lines

• Shortest Distance between Two Lines

Graduation Level / Higher Concept Keywords

Probability (Advanced)

• Axiomatic Approach

• Conditional Probability

• Multiplication Theorem on Probability

• Independent Events

• Bayes’ Theorem

• Theorem of Total Probability

Linear Algebra (Advanced)

• Matrix Algebra beyond basic types

• Systems of Linear Equations (Advanced solution methods)

Calculus (Advanced Applications)

• Applications of Derivatives and Integrals in optimization and area/volume problems beyond school level