Algebra | - Complex numbers, addition, multiplication, conjugation, etc.
- Quadratic equations theory, quadratic equations in real and complex number systems and their solutions.
- Arithmetic and geometric progressions, etc.
- Logarithms and their properties.
- Exponential series.
- Permutations and combinations, Permutations as an arrangement and combination as selection, etc.
- Matrices and determinants of order two or three, etc.
- Sets, Relations and Functions, algebra of sets applications, equivalence relations, mappings, etc.
- Maths reasoning and methods of proofs, acceptable statements.
- Linear Inequalities, ways to solve linear inequalities in one variable
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Trigonometry | - Measurement of angles in radians and degrees, positive and negative angles, etc.
- Solution of trigonometric equations.
- Inverse trigonometric functions
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Two-dimensional Coordinate Geometry | - Cartesian coordinates, the distance between two points, etc.
- Straight lines and pairs of straight lines: Equation of straight lines in various forms, etc.
- Circles: Equation of a circle in standard form, parametric equations of a circle.
- Conic sections: parabola, ellipse, and hyperbola, their eccentricity, etc.
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Three-dimensional Coordinate Geometry | - Coordinate axes and coordinate planes, the distance between two points, section formula, etc.
- The angle between two lines whose direction ratios are given, the shortest distance between two lines.
- Equation of a plane, distance of a point from a plane, etc.
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Differential calculus | - Domain and range of a real-valued function, Limits and Continuity of the sum, etc.
- Derivative of different types of functions, etc.
- Geometric interpretation of the derivative, Tangents, and Normal.
- Increasing and decreasing functions, Maxima, and minima of a function.
- Rolle’s Theorem, Mean Value Theorem, and Intermediate Value Theorem
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Integral calculus | - Integration, indefinite integrals of standard functions.
- Methods of integration: Integration by substitution, Integration by parts, etc.
- Integrals and their properties, Fundamental Theorem of Integral Calculus, applications in finding areas under simple curves.
- Application of definite integrals to the determination of areas of regions bounded by a simple curve
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Ordinary Differential Equations | - Order and degree of a differential equation, variables separable method.
- Solution of homogeneous differential equations of first order and first degree
- Linear first order differential equations
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Probability | - Various terminology in probability, axiomatic, and other approaches of probability, addition, and multiplication rules of probability.
- Conditional probability, total probability, and Bayes theorem
- Independent events
- Discrete random variables and distributions with mean and variance.
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Vectors | - Direction ratio/cosines of vectors, addition of vectors, scalar multiplication, position vector of a point dividing a line segment in a given ratio.
- Dot and cross products of two vectors, projection of a vector on a line.
- Scalar triple products and their geometrical interpretations
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Stats | - Measures of dispersion
- Analysis of frequency distributions with equal means but different variances
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Linear Programming | - Various terminology and formulations of linear Programming
- Linear Programming and its solution, feasible and infeasible regions, feasible and infeasible solutions, optimal feasible solutions.
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Maths modelling | Formulation of a simple real-life problem, and solution using matrices, calculus, and linear programming. |
