TS EAMCET Mathematics (Class XI & XII Syllabus

TS EAMCET Mathematics (Class XI & XII: topic-wise syllabus

1. 1

   Algebra

   ~18 marks

   • Complex Numbers — Argand, Modulus, Argument, Conjugate, De Moivre, Roots of Unity, Euler Form, Geometry (Circles, Lines, Loci), Applications
   • Quadratic Equations — Roots, Nature, Discriminant, Sign, Maxima/Minima, Graphical, Inequalities, Symmetric Functions
   • Matrices — Types, Operations, Transpose, Symmetric, Skew, Determinants, Properties, Adjoint, Inverse, Cramer's, System of Equations, Rank, Cayley-Hamilton, Eigenvalues, Eigenvectors, Diagonalization, Characteristic Equation, Quadratic Forms, Applications
   • Binomial Theorem — General Term, Middle Term, Independent, Approximations, Binomial Coefficients, Pascal's Triangle, Multinomial
   • Sequences & Series — AP, GP, HP, AM, GM, HM, AM-GM-HM, Sum of n terms, Mean, Variance, Σn, Σn², Σn³, Method of Differences, Special Series
   • Permutations & Combinations — Fundamental Principle, Factorial, nPr, nCr, Applications, Derangements, Multinomial Theorem, Multinomial Expansions
   • Partial Fractions — Proper/Improper, Linear/Repeated/Quadratic Factors, Mixed
   • Sets, Relations, Functions — Types, Domain, Range, Composition, Inverse, Binary Operations, Venn Diagrams, De Morgan, Inclusion-Exclusion
   • Mathematical Induction, Logic, Statements, Connectives, Truth Tables, Tautology, Quantifiers, Converse, Contrapositive, Principle of Duality
   • Inequalities, Modulus, Graphical Solutions, Linear Programming Problem (LPP), Bounded/Unbounded, Simplex, Duality, Transportation, Assignment
   • Algebraic Structures — Group, Ring, Field Basics, Boolean Algebra (Operations, Laws, Simplification, Logic Gates, K-Map, Quine-McCluskey)
2. 2

   Trigonometry

   ~10 marks

   • Trigonometric Ratios, Identities, Compound, Multiple, Sub-multiple, Transformation of Products to Sums & Vice Versa
   • Trigonometric Equations — General Solutions, Principal Values, Methods
   • Inverse Trigonometric Functions — Properties, Domain, Range, Graphs, Principal Values, Conversion, Identities
   • Properties of Triangles — Sine, Cosine Rules, Projection, Half-Angle, Napier, Area, Circumradius, Inradius, Heights & Distances, Medians, Angle Bisectors
   • Heights & Distances — Angle of Elevation, Depression, Bearings, Navigation, Surveying, Astronomy
   • Complex Numbers with Trigonometry — Argand, Polar, Demoivre, Roots of Unity, Geometry
3. 3

   Coordinate Geometry

   ~14 marks

   • Straight Lines — Slope, Equation Forms, Parallel, Perpendicular, Angle, Distance, Pair of Lines, Homogeneous, General Equation, Angle Bisectors, Foot of Perpendicular, Image, Family of Lines
   • Circles — Standard, General Form, Centre, Radius, Tangent, Normal, Chord of Contact, Pair of Tangents, Radical Axis, Orthogonal Circles, Family of Circles, Coaxial System, Limiting Points
   • Conic Sections — Parabola, Ellipse, Hyperbola — Standard Equations, Focus, Eccentricity, Directrix, Latus Rectum, Tangent, Normal, Chord, Polar, Parametric, Asymptotes, Rectangular Hyperbola, Director Circle
   • Locus, Transformation of Axes, Shift of Origin, Rotation, Polar Coordinates, Equation of Line/Circle in Polar, General Equation of Conic
   • 3D Geometry — Coordinates, Distance, Section Formula, Direction Cosines, Ratios, Equation of Line, Coplanar, Skew, Plane, Distance, Bisectors, Foot, Image, Tetrahedron, Projection
   • Vectors — Types, Addition, Subtraction, Scalar/Vector Product, Triple Product, Direction Cosines, Vector Equation of Line, Plane, Applications to Geometry, Mechanics, Work, Moment, Centroid, Incenter, Circumcenter, Orthocenter
4. 4

   Calculus (Differentiation, Integration & DE)

   ~22 marks

   • Limits & Continuity — Standard Limits, L'Hopital, Infinite Limits, Continuity, Differentiability, Algebra of Limits, Squeeze Theorem, Important Limits
   • Differentiation — Standard Derivatives, Chain Rule, Implicit, Logarithmic, Parametric, Higher Order, Partial Derivatives, Euler's Theorem, Total Derivatives, Jacobian, Differentials
   • Applications of Derivatives — Tangent, Normal, Maxima/Minima, Rolle's, Lagrange's, Mean Value, Monotonicity, Concavity, Rate of Change, Approximation, Errors, Asymptotes, Curve Sketching, Orthogonal Trajectories
   • Integration — Standard Integrals, Methods (Substitution, Parts, Partial Fractions, by Parts, Reduction Formulae), Definite Integrals, Properties, Beta, Gamma Functions, Improper Integrals, Walli's Formula, Differentiation under Integral Sign
   • Applications of Integration — Area Under Curve, Area Between Curves, Volume of Revolution (Disk, Shell, Washer), Arc Length, Surface Area, Work, Moment, Centre of Mass, Pressure, KE, PE, Probability, Improper Integrals
   • Differential Equations — Order, Degree, Formation, Solution (Variable Separable, Homogeneous, Linear, Bernoulli, Exact, Reducible to Exact, Clairaut, Lagrange), Integrating Factor, First Order, Higher Order (Homogeneous, Non-homogeneous, Euler-Cauchy), Laplace Transform, Applications (Growth, Decay, Newton's Cooling, RL/RC Circuits, Population, Projectile, Brachistochrone), Wronskian, Particular Integral
   • Series — Taylor, Maclaurin, Binomial, Exponential, Logarithmic, Trigonometric, Convergence, Divergence, Tests (Ratio, Root, Comparison, Integral, Raabe's, Logarithmic, Cauchy), Power Series, Range of Validity
5. 5

   Probability & Statistics

   ~10 marks

   • Probability — Classical, Empirical, Axiomatic, Conditional, Bayes, Independent Events, Random Variables, Binomial, Poisson, Normal, Mean, Variance, Moments, Moment Generating Function, Skewness, Kurtosis, Chebyshev's Inequality, Law of Large Numbers, Central Limit Theorem
   • Statistics — Mean, Median, Mode, Quartiles, Deciles, Percentiles, Range, IQR, Mean Deviation, Variance, SD, Skewness, Kurtosis, Moments, Central Tendency, Dispersion, Box Plot, Outliers
   • Correlation, Regression, Rank Correlation, Karl Pearson, Spearman, Lines of Regression, Bivariate Distribution, Multiple Regression
   • Sampling, Sampling Distributions, Estimation, Hypothesis Testing, t-test, z-test, Chi-square, F-test, ANOVA, Confidence Intervals, P-value, Type I/II Errors, Power of Test, Non-parametric Tests
   • Index Numbers, Time Series, Moving Averages, Seasonal Index, Trend Analysis, Forecasting, Decomposition, ARIMA, Exponential Smoothing
   • Linear Programming Problem (LPP) — Graphical Method, Simplex Method, Big M Method, Two-Phase Method, Duality, Dual Simplex, Transportation, Assignment, Hungarian Method, Game Theory, Integer Programming, Branch and Bound
6. 6

   Other Important Topics

   ~6 marks

   • Inequalities, Modulus, Linear Programming Problem (Graphical, Corner Point, Optimal Solution, Duality, Sensitivity Analysis)
   • Locus & Transformation, Conic Sections — Properties, Tangent, Normal, Chord, Pole, Polar
   • Numerical Methods — Bisection, Newton-Raphson, Secant, Trapezoidal, Simpson, Runge-Kutta, Euler, Milne, Picard, Taylor Series
   • Combinatorics, Graph Theory, Trees, Paths, Cycles, BFS, DFS, Shortest Path, MST, Coloring, Planarity, Euler, Hamiltonian, Matching, Covering, Connectivity, Isomorphism
   • Miscellaneous — Mathematical Reasoning, Quantifiers, Implications, Converse, Contrapositive, Tautology, Contradiction, Principles of Counting, Inclusion-Exclusion, Pigeonhole, Recurrence Relations, Generating Functions, Asymptotic Notation, Big O, Theta, Omega
7. 7

   Arithmetic

   ~2 marks

   Number System, HCF-LCM

   • Number System
   • Divisibility Rules
   • HCF and LCM
   • Indices, Exponents
   • Surds
   • Simplification, BODMAS
   • Fractions, Decimals
   • Number Series
   • Unit Conversion
   • Place Value
8. 8

   Arithmetic

   ~2 marks

   Percentages, Profit-Loss, SI, CI

   • Percentages
   • Successive Percentages
   • Profit and Loss
   • Simple Interest
   • Compound Interest
   • CI vs SI
   • Discount
   • Stocks and Shares
   • GST, VAT
   • Growth Rate
9. 9

   Arithmetic

   ~2 marks

   Ratio, Proportion, Mixture, Partnership

   • Ratio and Proportion
   • Variation
   • Mixture and Alligation
   • Partnership
   • Time and Work
   • Wages
   • Pipes and Cisterns
   • Ages
   • Time and Distance
   • Trains, Boats, Races
10. 10

    Algebra

    ~2 marks

    Equations, Polynomials, Inequalities

    • Linear Equations
    • Quadratic Equations
    • Polynomials
    • Algebraic Identities
    • Factorization
    • Algebraic Expressions
    • Inequalities
    • Linear Programming
    • Simultaneous Equations
    • Variation
11. 11

    Geometry, Mensuration, Coordinate Geometry

    ~2 marks

    • Lines and Angles
    • Triangles
    • Quadrilaterals
    • Circles
    • Polygons
    • Coordinate Geometry
    • Area, Perimeter
    • Surface Area, Volume
    • Trigonometry
    • Pythagoras Theorem
12. 12

    Data Interpretation

    ~2 marks

    • Table DI
    • Bar Graph DI
    • Pie Chart DI
    • Line Graph DI
    • Caselet DI
    • Data Sufficiency
    • Comparison DI
    • Missing Data DI
    • Radar/Web/Mixed Chart DI
    • Quant-Based DI
13. 13

    Modern Math

    ~2 marks

    Sets, Probability, Statistics

    • Sets, Relations, Functions
    • Permutation and Combination
    • Probability
    • Statistics (Mean, Median, Mode)
    • Matrices and Determinants
    • Trigonometry
    • Sequences and Series
    • Logarithms
    • Number Series
    • Clock, Calendar