Here’s the syllabus for Class 10 Mathematics for both Board of Secondary Education, Andhra Pradesh (AP) and the Board of Secondary Education, Telangana (TS) / SSC. The two states largely follow the same topics for this class.
🎯 AP / TS SSC Maths (Class 10) – Major Chapters
Based on the latest available syllabus for AP/TS
- Real Numbers
- Sets
- Polynomials
- Pair of Linear Equations in Two Variables
- Quadratic Equations
- Progressions (Arithmetic/Geometric)
- Coordinate Geometry
- Similar Triangles
- Tangents and Secants to a Circle
- Mensuration
- Trigonometry
- Applications of Trigonometry
Here’s an overview of the Mathematics syllabus for the two-year Intermediate (Class 11 & 12) programmes for both Board of Intermediate Education, Andhra Pradesh (AP) and Telangana State Board of Intermediate Education (TS).
📘 AP – Intermediate Mathematics
1st Year (Class 11)
- Paper IA (Algebra, Vector Algebra, Trigonometry) — topics include functions, inverse functions, vectors (addition, products), trigonometric ratios, and transformations.
- Paper IB (Coordinate Geometry & Calculus basics) — loci, transformation of axes, straight line, pair of straight lines, 3-D coordinates, limits & continuity, derivatives.
- Syllabus effective 2025-26: sets, relations & functions; trigonometric functions; complex numbers & quadratic equations; linear inequalities; permutations & combinations; binomial theorem; sequences & series; straight lines; conics; 3-D geometry; limits and derivatives; statistics; probability.
2nd Year (Class 12)
- Paper II(A) / II(B) as per Science/Other Groups: includes units such as Complex Numbers, De Moivre’s Theorem; Algebra (partial fractions, permutations, combinations, binomial theorem); Calculus (differentiation, integration, differential equations); Coordinate Geometry (circles, conics); Trigonometry; Vector Algebra; 3-D geometry; Probability and Statistics.
📘 TS – Intermediate Mathematics
1st Year (Class 11)
- Mathematics IA: Functions; Mathematical Induction; Matrices; Addition of Vectors; Product of Vectors; Trigonometric Ratios & Transformations; Trigonometric Equations; Inverse Trigonometric Functions; Hyperbolic Functions; Properties of Triangles.
- Mathematics IB: Locus; Transformation of Axes; Straight Line; Pair of Straight Lines; Three-Dimensional Coordinates; Direction cosines & direction ratios; The Plane; Limits & Continuity; Differentiation & Applications.
2nd Year (Class 12)
- Mathematics II-A: Complex Numbers; De Moivre’s Theorem; Quadratic Expressions; Theory of Equations; Permutations & Combinations; Binomial Theorem; Partial Fractions; Measures of Dispersion; Probability.
- Mathematics II-B: Circles; System of Circles; Parabola; Ellipse; Hyperbola; Integration & Definite Integrals; Differential Equations.
Here’s a detailed syllabus for Mathematics for the JEE Main (and as a broad guide for JEE Advanced) for engineering-entrance preparation in India. The topics broadly cover both Class 11 & 12 levels.
✅ JEE Main – Mathematics Syllabus
Here are major units with representative sub-topics:
- Sets, Relations and Functions
- Sets and their representation; union, intersection, complement; powerset.
- Relations: types of relations, equivalence relations.
- Functions: one-one, onto, into; composition of functions.
- Complex Numbers and Quadratic Equations
- Complex numbers as ordered pairs, representation on Argand plane; modulus and argument. BYJU’S
- Quadratic equations in real & complex number systems; relation between roots and coefficients; nature of roots.
- Matrices and Determinants
- Algebra of matrices, types of matrices (order two/three). BYJU’S
- Determinants: properties, evaluation, area of triangles using determinants.
- Adjoint, inverse of a matrix; test of consistency and solution of linear equations in 2/3 variables.
- Permutations and Combinations
- Fundamental principle of counting; P(n, r) and C(n, r); applications.
- Binomial Theorem and its Simple Applications
- Binomial theorem for positive integral index; general term, middle term; properties of binomial coefficients.
- Sequences and Series
- Arithmetic progression (AP), geometric progression (GP); insertion of arithmetic/geometric means; relation between A.M. and G.M. eSaral
- Limit, Continuity and Differentiability
- Real-valued functions: algebra of functions, polynomials, rational, trigonometric, logarithmic, exponential, inverse functions. BYJU’S+1
- Graphs of simple functions.
- Limit, continuity, differentiability. Differentiation of sum, product, quotient; functions including trigonometric, inverse trigonometric, logarithmic, exponential, composite and implicit functions.
- Derivatives of order up to two; Rolle’s and Lagrange’s Mean Value Theorems; applications: rate of change, monotonic increasing/decreasing functions, maxima/minima of functions of one variable, tangents and normals.
- Integral Calculus
- Integral as an antiderivative. Fundamental integrals involving algebraic, trigonometric, exponential and logarithmic functions. BYJU’S
- Techniques of integration: substitution, parts, partial fractions. Integration using trigonometric identities.
- Integral as limit of sum; properties of definite integrals; evaluation of definite integrals; determining areas of regions bounded by curves in standard form.
- Differential Equations
- Ordinary differential equations: order and degree; formation of differential equations.
- Solution of differential equations by method of separation of variables; solution of homogeneous and certain linear differential equations.
- Coordinate Geometry
- Cartesian system of rectangular coordinates in a plane; distance formula; section formula; locus and its equation; translation of axes; slope of a line; parallel and perpendicular lines; intercepts of a line on axes. BYJU’S
- Straight lines: various forms of equations of a line; intersection of lines; angles between two lines; conditions for concurrence of three lines.
- Three‐Dimensional Geometry (3D-Geometry)
- Coordinates of a point in space; distance between two points; section formula in 3D; direction ratios and direction cosines.
- Angle between two lines; equation of line and plane; skew lines and shortest distance between them.
- Vector Algebra
- Scalars and vectors; addition and subtraction of vectors; components of a vector in 2D and 3D.
- Scalar (dot) product; vector (cross) product; applications in geometry.
- Statistics and Probability
- Statistics: measures of dispersion: mean, median, mode; standard deviation, variance, mean deviation (grouped and ungrouped data).
- Probability: basic probability rules; addition and multiplication theorems; Bayes’ theorem; probability distribution of random variables.
- Trigonometry
- Trigonometric identities and equations; trigonometric functions and graphs; inverse trigonometric functions; properties and transformations.
