AMU ENTRANCE Mathematics (Class XI & XII Syllabus

AMU ENTRANCE Mathematics (Class XI & XII: topic-wise syllabus

1. 1

   Algebra

   ~12 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
   • Matrices — Types, Operations, Transpose, Symmetric, Skew, Determinants, Properties, Adjoint, Inverse, Cramer's, System of Equations, Rank, Cayley-Hamilton
   • Binomial Theorem — General Term, Middle Term, Independent, Approximations, Binomial Coefficients, Pascal's Triangle
   • Sequences & Series — AP, GP, HP, AM, GM, HM, AM-GM-HM, Sum of n terms, Mean, Variance, Sum of Special Series (n², n³, Σn, Σn², Σn³)
   • Permutations & Combinations — Fundamental Principle, Factorial, nPr, nCr, Applications, Derangements, Multinomial Theorem
   • Partial Fractions — Proper/Improper, Linear/Repeated/Quadratic Factors
   • Sets, Relations, Functions — Types, Domain, Range, Composition, Inverse, Binary Operations, Venn Diagrams, De Morgan
   • Mathematical Induction, Logic, Statements, Connectives, Truth Tables, Tautology, Quantifiers
   • Inequalities, Modulus, Graphical Solutions, Linear Programming Problem (LPP) — Graphical Method, Corner Point, Optimal Solution, Duality, Bounded/Unbounded
   • Algebraic Structures — Group, Ring, Field Basics, Boolean Algebra (Operations, Laws, Simplification, Logic Gates)
   • Exponential & Logarithmic Series, Applications
2. 2

   Trigonometry

   ~7 marks

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

   Coordinate Geometry

   ~10 marks

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

   Calculus (Differentiation, Integration & DE)

   ~14 marks

   • Limits & Continuity — Standard Limits, L'Hopital, Infinite Limits, Continuity, Differentiability, Algebra of Limits, Squeeze Theorem
   • Differentiation — Standard Derivatives, Chain Rule, Implicit, Logarithmic, Parametric, Higher Order, Partial Derivatives, Euler's Theorem, Total Derivatives, Jacobian
   • Applications of Derivatives — Tangent, Normal, Maxima/Minima, Rolle's, Lagrange's, Mean Value, Monotonicity, Concavity, Rate of Change, Approximation, Errors, Increasing/Decreasing, Asymptotes, Curve Sketching
   • Integration — Standard Integrals, Methods (Substitution, Parts, Partial Fractions, by Parts, Reduction Formulae), Definite Integrals, Properties, Beta, Gamma Functions, Improper Integrals
   • 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
   • Differential Equations — Order, Degree, Formation, Solution (Variable Separable, Homogeneous, Linear, Bernoulli, Exact, Reducible to Exact), Integrating Factor, First Order, Higher Order (Homogeneous, Non-homogeneous), Euler-Cauchy, Laplace Transform, Applications (Growth, Decay, Newton's Cooling, RL/RC Circuits, Population)
   • Series — Taylor, Maclaurin, Binomial, Exponential, Logarithmic, Convergence, Divergence, Tests (Ratio, Root, Comparison, Integral)
5. 5

   Probability & Statistics

   ~7 marks

   • Probability — Classical, Empirical, Axiomatic, Conditional, Bayes, Independent Events, Random Variables, Binomial, Poisson, Normal, Mean, Variance, Moments, Moment Generating Function
   • Statistics — Mean, Median, Mode, Quartiles, Deciles, Percentiles, Range, IQR, Mean Deviation, Variance, SD, Skewness, Kurtosis, Moments, Central Tendency, Dispersion
   • Correlation, Regression, Rank Correlation, Karl Pearson, Spearman, Lines of Regression, Bivariate Distribution
   • Sampling, Sampling Distributions, Estimation, Hypothesis Testing, t-test, z-test, Chi-square, F-test, ANOVA, Confidence Intervals, P-value, Type I/II Errors
   • Index Numbers, Time Series, Moving Averages, Seasonal Index, Trend Analysis, Forecasting, Stationary, Autocorrelation
   • Linear Programming Problem (LPP) — Graphical Method, Simplex Method, Duality, Transportation, Assignment, Game Theory, Integer Programming