(Grade I (+1, +2 level), Grade II (Graduation level maths (Optional Graduation level maths only for selected universities.
1) Algebra: Indices, Logarithmics, Surds, Expansions, Factorization, Linear, Quadratic and higher degree equations, Arithmetic Progression, Geometric progression, Harmonic Progression, Arithmetico geometric series and some other special series, Binomial and multinomial theorem, Exponential and logarithmic series, Permutations and Combinations, Complex numbers and its geometric applications.
2) Trigonometry: Angle measurement systems, Trigonometric identities, Trigonometric equations, Inverse Trigonometric functions, Solutions and properties of triangles, Heights and distances, Hyperbolic functions etc.
3) Two Dimensional Geometry: Rectangular Cartesian coordinates, Straight lines and family of straight lines, Circles and properties, Conics(Parabola, Ellipse, Hyperbola) and properties, Simple geometric transformations such as translation, Rotation and scaling.
4) Vector I: Position vector of points, addition, Substraction of vectors, Multiplication by scalars, Collinearity, Scalar product of two vectors and applications, Vector product of two vectors and applications, Work, torque, Scalar product of three vectors, Scalar and vector product of four vectors, Reciprocal system.
5) Vector II: Curl, Divergence, Gradient etc (Optional Graduation level maths only for selected universities)
6) Three Dimensional Geometry: Cartesian co-ordinates of points in 3-D and properties, Straight lines in 3D and properties. Planes in 3D and properties, Planes and straight lines, Plane and sphere etc.
7) Three Dimensional Geometry (Advanced) (Optional Graduation level maths only for selected universities): Cones, Cylinders and their properties.
8) Calculus I: Functions and their properties. Limits and continuity, Differentiability, Differentiation, Applications of derivatives, Indefinite integral, Definite integral, Differential equations.
9) Calculus II: (Optional Graduation level maths only for selected universities): Partial differentiation, Beta-Gamma functions in definite integration, Higher order differential equations, Multiple integration, Taylor series, Maclaurin’s series, Polar curves, Curvature, Singular points, Asymptotes, Area and Volume by triple integration, Real analysis (convergence and divergence of sequences and series), Curve tracing.
10) Probability: Mathematical definition of probability, Odds in favour and odds against the event, Theorems of total probability, Conditional probability, Multiplication theorem, expectation, Probability distribution (Binomial distribution and its properties and its mean and median, Normal poisson distribution and its properties)
11) Statics I: Measures of central tendency (mean, median, mode), Quartiles, Dispersion and their types, Measures and properties, Standard deviation, coeff of SD, Correlation and Regression.
12) Statics II: (Optional Graduation level maths only for selected universities). Curve fitting and principles of generating functions, Binomial, Normal and Poisson distribution, Tests of significance based of f-distributions etc.
13) Linear Programming: Graphical methods to solve LPP in two variables, Simplex method, Dual, Convex sets.
14) Numerical Methods: (Only for selected universities) Different methods to approximate roots of algebraic equations, Numerical integration (Trapezoidal Simpson’s one third, Simpson’s three eight, Weiddles formula etc.) Interpolation and different operators and properties.
15) Matrices and Determinants: Definition of matrices & determinants, Types of matrices, Algebra of Matrices. Transpose of a Matrix. Symmetrical and Skew symmetrical, Hermitian & Skew Hermitian matrices and their properties, Minors & Cofactors, Trace of a matrix, Properties of Determinants, Adjoint of square matrix, System of Linear Equations. Cramer’s Rule, Matrix Method for the simultaneous linear equations, Rank of a matrix and properties, Characteristic equation of a matrix, Eigen values etc.
16) Number Theory (Optional Graduation level maths only for selected universities): Congruence, Formats theorem, Euler’s theorem, Wilson’s theorem, Divisibility etc.
17) Linear Algebra (Optional Graduation level maths only for selected universities): Vector spaces, Sup – spaces, Dependence and independence of the vectors, Basis and dimensions of vector spaces, Linear transformations, Ranks and Eigen values etc.
18) Modern Algebra (Optional Graduation level maths only for selected universities): Groups, Sub-groups, Semi-groups, Permutation groups, Cyclic groups, Rings, Sub rings, Ideads, Fields, Sub fields and their properties etc.
19) Mechanics: Statics and Dynamics (Optional Graduation level maths only for selected universities)