BHU UET Mathematics (Class XI & XII Syllabus

BHU UET Mathematics (Class XI & XII: topic-wise syllabus

1. 1

   Algebra

   ~12 marks

   • Complex Numbers — Argand, Modulus, Argument, Conjugate, De Moivre, Roots of Unity, Euler, 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, Reduction, 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

   ~7 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, Pedal Triangle, Excentral Triangle
   • Heights & Distances — Angle of Elevation, Depression, Bearings, Navigation, Surveying
   • Complex Numbers with Trigonometry — Argand, Polar, Demoivre, Roots of Unity, Geometry
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, 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 (Symmetric, Unsymmetric, Two Points, Vector), Coplanar, Skew, Plane (Equation, Normal, Intercept, through 3 Points, Parallel, Perpendicular, Angle), Distance, Bisectors, Foot of Perpendicular, 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)

   ~14 marks

   • Limits & Continuity — Standard Limits, L'Hopital, Infinite Limits, Continuity, Differentiability, Algebra of Limits, Squeeze Theorem, Important Limits (sin x / x, (1+1/n)^n, e)
   • 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, Increasing/Decreasing, Asymptotes, Curve Sketching, Tangents, Normals, 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 by PI
   • 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

   ~7 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 (Sign, Wilcoxon, Mann-Whitney, Kruskal-Wallis)
   • 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