AP EAPCET 2026 Syllabus: Engineering (E) Stream

📘 Mathematics Syllabus

1. ALGEBRA

a) Functions:

• Ordered pairs, Types of functions - Definitions - Inverse functions and Theorems - Domain, Range, Inverse of real valued functions.

b) Mathematical Induction:

• Principle of Mathematical Induction & Theorems - Applications of Mathematical Induction - Problems on divisibility.

c) Matrices:

• Types of matrices - Scalar multiple of a matrix and multiplication of matrices - Transpose of a matrix - Determinants - Adjoint and Inverse of a matrix - Consistency and Inconsistency system of Simultaneous equations - Rank of a matrix - Solution of simultaneous linear equations.

d) Complex Numbers:

• Complex number as an ordered pair of real numbers-Fundamental operations - Representation of complex numbers in the form a+ib - Modulus and amplitude of complex numbers - Illustrations - Geometrical and Polar Representation of complex numbers in Argand plane- Argand diagram.

e) De Moivre’s Theorem:

• De Moivre’s theorem- Integral and Rational indices - nth roots of unity- Geometrical Interpretations - Illustrations.

f) Quadratic Expressions:

• Quadratic expressions, equations in one variable - Sign of quadratic expressions - Change in signs - Maximum and minimum values - Quadratic inequations.

g) Theory of Equations:

• The relation between the roots and coefficients in an equation - Solving the equation when two or more of its roots are connected by certain relations - Equations with real coefficients, occurrence of complex roots in conjugate pairs and its consequences - Transformation of equations - Reciprocal Equations.

h) Permutations and Combinations:

• Fundamental Principle of counting - Linear and Circular permutations- Permutations of ‘n’ dissimilar things taken ‘r’ at a time - Permutations when repetitions are allowed - Circular permutations - Permutations with constraint repetitions - Combinations – Definitions and certain theorems.

i) Binomial Theorem:

• Binomial theorem for positive integral index - Binomial theorem for rational Index - Approximations using Binomial theorem.

j) Partial fractions:

• Partial fractions of f(x)/g(x) when g(x) contains non–repeated, repeated, and/or non-repeated irreducible factors.

2. TRIGONOMETRY

• Trigonometric Ratios upto Transformations: Graphs and Periodicity, Compound angles, multiple and sub-multiple angles, Sum and Product transformations.
• Trigonometric Equations: General Solution of Simple Trigonometric Equations.
• Inverse Trigonometric Functions: Bijective functions, Graphs, Properties.
• Hyperbolic Functions: Definitions, Graphs, Inverse Functions, Addition formulae.
• Properties of Triangles: Sine, Cosine, Tangent, Projection rules, Half angle formulae, Areas, Incircle and Excircle.

3. VECTOR ALGEBRA

• Addition of Vectors: Types of vectors, scalar multiplication, angle between vectors, linear combination, component form, vector equations of line and plane.
• Product of Vectors: Scalar (dot) product and its properties, Vector (cross) product and its properties, Vector Areas, Scalar Triple Product, Vector Triple Product.

4. PROBABILITY

• Measures of Dispersion: Range, Mean deviation, Variance and standard deviation, Coefficient of variation.
• Probability: Classical definition, Axiomatic approach, Addition theorem, Conditional probability, Multiplication theorem, Baye’s theorem.
• Random Variables and Probability Distributions: Random Variables, Binomial and Poisson Distributions.

5. COORDINATE GEOMETRY

• Locus: Definition and equations.
• Transformation of Axes: Translation and Rotation of axes.
• The Straight Line: Normal form, Symmetric form, Intersection, Family of lines, Angle between lines, Perpendicular distance.
• Pair of Straight lines: Homogenizing, angle between lines, bisectors.
• Circle & System of circles: Standard equation, Tangent, Polar, Radical axis.
• Conic Sections (Parabola, Ellipse, Hyperbola): Standard equations, Parametric forms, Tangents and Normals.
• Three Dimensional Coordinates: Coordinates, Section formulae, Direction Cosines and Ratios, Cartesian equation of a Plane.

6. CALCULUS

• Limits and Continuity: Standard Limits, Continuity.
• Differentiation: Derivatives of various functions, Methods of Differentiation, Second Order Derivatives.
• Applications of Derivatives: Errors, Geometrical Interpretation, Tangents and Normals, Rate of change, Rolle’s and Lagrange’s Mean Value theorems, Maxima and Minima.
• Integration: Integration as inverse of differentiation, standard forms, integration by substitution, parts, and partial fractions.
• Definite Integrals: Definite Integral as limit of sum, area interpretation, properties, reduction formulae, application to areas.
• Differential Equations: Formation, degree and order, solving by various methods (Variables separable, Homogeneous, Linear).

⚛️ Physics Syllabus

The Physics syllabus covers topics from classical mechanics to modern physics, aligned with the Intermediate curriculum.

🧪 Chemistry Syllabus

The Chemistry syllabus covers Physical, Inorganic, and Organic Chemistry topics as per the BIE TG curriculum.