For the TG EAPCET 2026 (formerly TG EAMCET), the Mathematics syllabus is extensive, covering 100% of the Telangana Intermediate First and Second-year curriculum.
Mathematics: First Year (Junior Inter)
These topics focus on the basics of Algebra, Trigonometry, and the beginning of Calculus.
Algebra
- Functions: Types of functions, inverse functions, domain and range.
- Mathematical Induction: Principles and applications.
- Matrices: Types of matrices, addition, multiplication, determinants, adjoint, and inverse. Solving linear equations using Cramer’s Rule and Matrix Inversion method.
Trigonometry
- Trigonometric Ratios up to Transformations: Periodicity, compound angles, multiple and sub-multiple angles.
- Trigonometric Equations: General solutions.
- Inverse Trigonometric Functions: Properties and principal values.
- Hyperbolic Functions: Definitions and relations.
- Properties of Triangles: Sine, Cosine, Tangent rules, and solution of triangles.
Vector Algebra
- Addition of Vectors: Classification, linear combination, and vector equations of lines/planes.
- Product of Vectors: Scalar (dot) product and Vector (cross) product; triple products.
Coordinate Geometry (2D)
- Locus & Transformation of Axes.
- The Straight Line: Different forms of line equations, angle between lines.
- Pair of Straight Lines: Homogeneous and non-homogeneous equations.
Calculus (Part 1)
- Limits and Continuity.
- Differentiation: First principles, derivatives of algebraic, trig, and inverse functions.
- Applications of Derivatives: Errors and approximations, Tangents and Normals, Rate of change, and Mean Value Theorems (Rolle's and Lagrange's).
Mathematics: Second Year (Senior Inter)
The second year shifts towards advanced Algebra, Conic Sections, and heavy Integral Calculus.
Algebra
- Complex Numbers: $a + ib$ form, modulus, and amplitude.
- De Moivre’s Theorem: Powers and $n^{th}$ roots of complex numbers.
- Quadratic Expressions: Nature of roots, maximum and minimum values.
- Theory of Equations: Relation between roots and coefficients.
- Permutations and Combinations: Linear and circular permutations.
- Binomial Theorem: General and middle terms, binomial coefficients.
- Partial Fractions.
Probability & Statistics
- Measures of Dispersion: Mean deviation and Variance/Standard deviation.
- Probability: Classical and Axiomatic approaches; Addition and Multiplication theorems; Bayes' Theorem.
- Random Variables: Probability distributions and Mean/Variance of a random variable.
Coordinate Geometry (Conics & 3D)
- Circles: Standard equation, power of a point, tangent/normal.
- System of Circles: Radical axis and orthogonal circles.
- Conic Sections: Parabola, Ellipse, and Hyperbola (standard forms and properties).
- Three Dimensional Coordinates: 3D distance and section formulas.
- Direction Cosines and Direction Ratios.
- Planes.
Calculus (Part 2)
- Integration: Indefinite integrals, standard forms, and substitution methods.
- Definite Integrals: Reduction formulas and calculating Area under curves.
- Differential Equations: Order and degree; solving first-order equations using Variables Separable and Homogeneous methods.