#### Unit 1: Algebra (44)

- Logic and Set: Statements, logical connectives, truth tables, theorems based on set
operations.

Click Here - Real numbers: Geometric representation of real numbers, interval,absolute value
- Function: Domain and range of a function, Inverse function, composite function, introduction of functions; algebraic (linear, quadratic & cubic), Transcendental (trigonometric, exponential, logarithmic)
- Curve sketching: Odd and even functions, periodicity of a function, symmetry (about origin, X-and Y-axis),monotonicity of a function, sketching the graphs of Quadratic, Cubic and rational functions of the form \(\frac{1}{ax+b}\) where \(a \ne 0\), Trigonometric (\(a \sin bx ,a \cos bx\)), exponential (\(e^x\)), logarithmic function (\( \ln x \))
- Sequence and series: Arithmetic, geometric, harmonic sequences and series and their properties A.M, G.M, H.M and their relations, sum of infinite geometric series

Click Here - Matrices and determinants: Transpose of a matrix and its properties, Minors and cofactors, Adjoint, Inverse matrix, Determinant, Properties of determinants (without proof)

Click Here - Quadratic Equation: Nature and roots of a quadratic equation, Relation between roots and coefficient. Formation of a quadratic equation, Symmetric roots, one or both roots common
- Complex number: Imaginary unit, algebra of complex numbers, geometric representation,
absolute (Modulus) value and conjugate of a complex numbers and their properties, square root of a complex
number.

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#### Unit 2: Trigonometry (12)

- Inverse circular functions.
- Trigonometric equations and general values

#### Unit 3: Analytic Geometry (20)

- Straight Line: Length of perpendicular from a given point to a given line, Bisectors of the angles between two straight lines.
- Pair of straight lines: General equation of second degree in x and y, condition for representing a pair of lines, Homogenous second-degree equation in x and y, angle between pair of lines, Bisectors of the angles between pair of lines
- Coordinates in space:Points in space,distance between two points, direction cosines and ratios of a line

#### Unit 4: Vectors (12)

- Collinear and non collinear vectors, coplanar and non-coplanar vectors, linear combination of vectors, Linearly dependent and independent

#### Unit 5:Statistics and Probability (12)

- Measure of Dispersion: Standard deviation, variance, coefficient of variation, Skewness, Karl Pearson's coefficient of skewness
- Probability:Independent cases, mathematical and empirical definition of probability, two basic laws of probability (without proof).

#### Unit 6:Calculus (48)

- Limits and continuity: Limits of a function, indeterminate forms. algebraic properties of limits (without proof), Basic theorems on limits of algebraic, trigonometric, exponential and logarithmic functions, continuity of a function, types of discontinuity, graphs of discontinuous function
- Derivatives: Derivative of a function, derivatives of algebraic, trigonometric, inverse of trigonometric, exponential and logarithmic functions by definition (simple forms), rules of differentiation. derivatives of parametric and implicit functions, higher order derivatives, geometric interpretation of derivative, monotonicity of a function, interval of monotonicity, extreme values of a function, concavity, points of inflection
- Anti-derivatives:Integration using basic integrals,integration by substitution and by parts methods, the definite integral, the definite integral as an area under the given curve, area between two curves

#### Unit 7:Computational Methods (12) or Mechanics

- System of linear equations: Gauss Elimination Method, Gauss Seidel Method
- Linear programming problems (LPP): simplex method (two variables only)

#### Unit 7:Mechanics(12) or Computational Methods

- Statics: Triangle law of forces and Lami's theorem
- Newton's laws of motion and projectile

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